Media-Based Modulation for Next-Generation Wireless: Latest Progress and New Applications

Media-based modulation (MBM) is a novel technique for embedding information in the channel states via intentional perturbations of the transmission media. This article provides an overview of MBM and its benefits while highlighting relevant challenges and future research directions. We explain how MBM differs from source-based modulation and how it addresses issues in legacy multiple-input multiple-output (MIMO) systems, such as deep fades and MIMO diversity-multiplexing trade-off. We demonstrate how MBM works in harmony with other index modulations and improves upon them by providing similar advantages with a more compact transmitter. Numerical results (simulation and analytical) support these claims and include outage comparison with legacy MIMO systems, comparisons with other state-of-the-art modulation schemes, and a performance example showcasing transmitting 32 bits of information in a single channel use with an excellent symbol error rate of $\mathsf {SER} \simeq 10^{-5}$ at “energy per bit to noise power spectral density ratio” of $\mathsf {E_{b}/N_{0}} \simeq -3.5$ dB. The article continues with methods to address the issues of receiver training and decoding for large constellation sets. A number of other research questions, such as pulse shaping to limit bandwidth expansion due to the time-varying nature of MBM and the effect of forward error correcting codes on MBM diversity order are discussed. We present an RF transceiver structure that generates independent propagation paths for embedding information. Fabrication and testing of the transceiver structure show close agreement between simulation and measurement. There are inherent connections between MBM and Intelligent Reflecting Surface (IRS). These connections, including the application of MBM in beamforming, are discussed. We present a solution that involves the integration of a filtering radiating patch within the MBM walls to restrict bandwidth expansion. Lastly, we delve into several specific application domains for MBM.

Media-Based Modulation for Next-Generation Wireless: Latest Progress and New Applications Ehsan Seifi , Amir K. Khandani , Fellow, IEEE, and Mehran Atamanesh (Invited Paper) Abstract-Media-based modulation (MBM) is a novel technique for embedding information in the channel states via intentional perturbations of the transmission media.This article provides an overview of MBM and its benefits while highlighting relevant challenges and future research directions.We explain how MBM differs from source-based modulation and how it addresses issues in legacy multiple-input multiple-output (MIMO) systems, such as deep fades and MIMO diversitymultiplexing trade-off.We demonstrate how MBM works in harmony with other index modulations and improves upon them by providing similar advantages with a more compact transmitter.Numerical results (simulation and analytical) support these claims and include outage comparison with legacy MIMO systems, comparisons with other state-of-the-art modulation schemes, and a performance example showcasing transmitting 32 bits of information in a single channel use with an excellent symbol error rate of SER ≃ 10 −5 at "energy per bit to noise power spectral density ratio" of Eb/N0 ≃ −3.5 dB.The article continues with methods to address the issues of receiver training and decoding for large constellation sets.A number of other research questions, such as pulse shaping to limit bandwidth expansion due to the time-varying nature of MBM and the effect of forward error correcting codes on MBM diversity order are discussed.We present an RF transceiver structure that generates independent propagation paths for embedding information.Fabrication and testing of the transceiver structure show close agreement between simulation and measurement.There are inherent connections between MBM and Intelligent Reflecting Surface (IRS).These connections, including the application of MBM in beamforming, are discussed.We present a solution that involves the integration of a filtering radiating patch within the MBM walls to restrict bandwidth expansion.Lastly, we delve into several specific application domains for MBM.

I. INTRODUCTION
A. Motivation spectrum, multiplied by a logarithmic function of the transmit energy.Wireless communication relies on two key attributes, traditionally considered its inherent bottlenecks.First, the spectrum is shared, causing interference among wireless links operating over the same spectrum.Second, the transmission channel includes a multitude of propagation paths, resulting in multi-path fading.Multi-path fading creates deep fades when signals received through different transmission paths add destructively.In many scenarios of practical interest, the transmission paths change slowly with time (slow fading), potentially resulting in a long-lasting degradation of the received signal-to-noise ratio (SNR), referred to as deep fades.
Multiple-input multiple-output (MIMO) antenna systems embrace the above attributes towards improving the spectrum/power efficiency [3], [4], [5], as well as dealing with deep fades [6].The first attribute means signals sent from different transmit antennas add up at each receive antenna.Consequently, the input-output relationship is captured in the form of matrix multiplication.Due to the second attribute, such a channel matrix is, with a high probability, non-singular, resulting in a linear scaling of rate with min(A T , A R ), where A T is the number of transmit antennas and A R is the number of receive antennas.The term min(A T , A R ) is the improvement in spectrum efficiency due to MIMO and is referred to as the multiplexing gain (MG).In the expression for the achievable rate at large values of SNR, MG appears as the scaling factor multiplied by the log(SNR) term.MIMO also helps to combat deep fades by introducing redundancy among data transmitted/received through separate propagation paths.It is well-known that tackling slow-fading by creating diversity in MIMO systems comes at the cost of a reduction in degrees of freedom (i.e., MG) [7].
Although MIMO systems provide an elegant way to tailor wireless communications to embrace the two fundamental attributes mentioned earlier, three issues limit their achievable rate vs. energy.First, the problem of deep fades can be only (partially) alleviated at the cost of a reduction in the achievable rate (i.e., MG) [7].Second, MG increases only with the smaller of the number of transmit and receive antennas.Third, the MIMO channel matrix is typically non-orthogonal, reducing the achievable rate compared to an orthogonal channel matrix of the same dimension.
Media-based modulation (MBM) [1] addresses these three issues.The idea is to randomize the wireless channel by perturbing the propagation environment in the vicinity of the transmit antenna(s), which will change the overall transmission path.Perturbing the medium creates a multitude of channel states, each with a different set of transmission paths.The transmitter uses the incoming data (to be transmitted) as an index to select a particular channel state for each transmission.By contrast, in a traditional source-based wireless system, data is embedded in the variations (e.g., amplitude, phase or frequency) of the radio-frequency (RF) source prior to the transmit antenna, and the wave propagates via random but unaltered paths (media) to the destination.
Fig. 1 shows an MBM transceiver diagram (reproduced based on [8]).A single transmit antenna is placed within a closure surrounded by walls.Each wall can be switched to operate in one of two states: a transparent state, and a reflecting state.The transmit antenna emits a single pulseshaped tone.A transparent wall would pass the incident wave to the outside, and a reflecting wall would send it back to the interior of the RF closure.As a result, the transmitted wave bounces back and forth within the RF closure and, in the process, propagates outside from transparent walls.An RF closure with log 2 M switchable walls creates a set of M states for the end-to-end channel.MBM transmitter selects one of these states in each transmission according to incoming data and thereby embeds R m = log 2 M information bits in selecting the channel state.Additional R s information bits can be transmitted by modulating the RF signal using a traditional source-based modulator (Fig. 1).
In the absence of noise, the received signals (or equivalently the complex fading gains) act as unique signatures for each selected channel state.Let H := {h 0 , h 1 , . . ., h M −1 } denote the set of fading gains corresponding to different channel states.Careful design and placement of reflecting walls warrants totally different transmit RF patterns in different states, which, upon propagation in the multi-path (rich scattering) environment, result in the random vectors in the set H to be mutually independent.
A fundamental property of MBM, which makes it distinct from MIMO systems, is that in a system with K receive antennas, MBM signals formed over the receive spatial dimensions span the entire K-dimensional vector space.That is to say, with high probability, span(H) = K.This property holds true even when using just one transmit RF chain and one antenna, allowing MBM to achieve full multiplexing gain with a single transmit antenna (c.f.appendix C).In a conventional MIMO system, however, the effective number of dimensions is governed by the minimum of the number of transmit and receive antennas.In particular, source-based single-input multiple-output (SIMO) spans a single complex dimension.From an information theoretic standpoint, this property of MBM is analogous to "additivity of information over multiple receive antennas".Reference [2] (also see [9]) shows that a 1×K MBM over a static Rayleigh fading channel asymptotically achieves the capacity of K parallel complex AWGN channels, where for each unit of transmit energy, the effective energy for each of the K AWGN channels is the statistical average of channel fading.Alternative proof for this feature is presented in [9].
The second key property of MBM is that multiple channel states collectively contribute to enlarging the mutual distance among constellation points.In other words, the constellation signal set is constructed by both good channel states (high channel gains) as well as bad channel states (low channel gains).As a result, the deep-fade bottleneck in the case of legacy source-based modulation (SBM) is avoided.In other words, deep fades result in constellation points closer to the origin.Points closer to the origin are as useful as points further away from the origin (higher fading gains) in filling the constellation signal space uniformly.In a Rayleigh fading channel, constellation points along each spatial complex coordinate follow a Gaussian distribution, which agrees with Shannon's random code-book construction.
Article [9] shows that the outage probability due to deep fades is (asymptotically) alleviated as M (number of switchable RF reflectors) increases.Specifically, in a static Rayleigh fading channel with AWGN at receive antennas, the mutual information I in a 1 × K MBM is normally concentrated around K log(1 + SNR), that is, where SNR denotes the signal-to-noise ratio at each receive antenna.As M increases, the variance, and consequently the outage probability, goes to zero according to ( Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.A similar result is derived in [2], using a different approach in which the loss in rate (vs. a set of parallel AWGN channels) is captured in terms of an additive noise with a vanishing variance.Note that, unlike traditional MIMO systems, diversity in MBM does not come at the cost of a reduction in rate (MG).
Another property of an MBM system with multiple receive antennas is the "K times energy harvesting".This means, assuming a single transmit and K receive antennas and fading with an average statistical gain of one, the average received signal energy will be K times the transmit energy.Legacy K × K MIMO enjoys a similar property.However, when the channel matrix is non-orthogonal, MIMO can not fully realize the capacity of a set of K parallel channels with independent noise components.Receiver processing techniques, such as channel inversion, can create a set of parallel channels.However, the non-orthogonality of the channel matrix results in statistical dependencies among resulting noise components.Transmitter processing techniques such as eigen beam forming also diagonalize the channel matrix.However, the underlying issue will surface in another form; it results in different channel gains along different eigen-dimensions.Consequently, in contrast to MBM, which achieves the capacity of a set of parallel channels with equal gains and independent noise components (of equal power), MIMO does not achieve such an upper limit on the achievable rate if the channel matrix is non-orthogonal.Next, we provide a numerical example to elaborate on the above MBM properties.Readers are referred to [10] for additional information on MBM.
Example: Consider a wireless system with a single transmit and a single receive antenna operating over a static multi-path (static Rayleigh fading) channel with AWGN.The channel has 256 states, each resulting in a constellation point with independent, identically distributed (i.i.d.) Gaussian components over the single complex receive dimension.Each realization of such 256 points achieves a rate equal to the mutual information across the AWGN channel.Fig. 2 shows achievable rate values for 10000 realizations of a random constellation and the achievable rate of a 256QAM (quadrature amplitude modulation) constellation.We assume AWGN and uniform probability for constellation points in all cases.The distribution of achievable rate values deviates only slightly from the 256QAM rate.Hence, the outage probability for the random constellation becomes negligible at the cost of a small SNR margin.For example, the required margin is ∼1dB to guarantee (with a negligible outage probability in the rang of 10 −4 ) an SNR of 20 dB at the receiver (see Fig. 3 for realized SNR and rates of random constellation).This significantly outperforms the outage behavior of a 256QAM over a static Fig. 2.
Achievable rate (mutual information) of 256QAM vs. random constellation set with 256 points (2-dimensional points).Components of random constellation points follow Gaussian distribution.At each SNR, the cloud of points show values of mutual information for 10000 realizations of the random constellation.Fig. 3.
Achievable rate (mutual information) for 10000 realizations of random 2-dimensional constellation with 256 points.Transmit energy is equal to 20 dB.
Raleigh fading channel.For instance, Table I shows that 256QAM in a Rayleigh fading channel requires a transmit energy margin of 10, 20, and 30 dB to obtain an SNR of 20 dB at the receiver, with outage probabilities equal to 0.1, 0.01, and 0.001, respectively.Furthermore, as the constellation set size increases, the random constellation realizes the shaping gain (due to the Gaussian distribution of points), which contrasts a QAM constellation with points occurring with uniform probabilities.■

B. Literature Survey
The idea of embedding information in the state of a communications channel is not new.Mach-Zehnder modulators, widely used for signaling over fiber, modify the light beam after leaving the laser.However, due to the lack of multi-path Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
transmission in single-mode fibers, the advantages realized in the context of wireless do not apply.
Reference [1] coined the term media-based modulation for embedding data in the intentional variations of the transmission media (end-to-end channel) and showed that MBM offers considerable improvement vs. traditional single-input single-output (SISO), single-input multiple-output (SIMO), and multiple-input multiple-output (MIMO) wireless systems.In distinction to MBM, traditional modulation schemes, where data is embedded in the variations of an RF source (for example, in amplitude, phase, or frequency) and propagates via a conventional wireless channel to the destination, are called source-based modulation.
Following [1], [2] and (also see [9]) proves that a 1 × K MBM over a static multi-path channel asymptotically achieves the capacity of K (complex) AWGN channels, where for each unit of energy over the single transmit antenna, the effective energy for each of the K AWGN channels is the statistical average of the channel fading.It is shown that significant gains can be realized even in a SISO-MBM setup.An example of the practical realization of the system using RF mirrors, accompanied by realistic RF and ray tracing simulations, is presented in [2], [11], and [12].References [10] and [8] provide a rich body of knowledge about features of MBM (also see [13]).
References [14] and [15] present a method for establishing an unconditionally secure encryption key between two wireless nodes relying on a media-based antenna structure.Different states of the media-based antenna are exploited to measure a set of reciprocal phase values, called masking phase values, between the two nodes.Since each masking phase is uniformly distributed in [0, 2π], it allows hiding b bits of information within a 2 b -PSK (phase shift-keying) constellation (by the addition of phase values modulo 2π).A sequence of bits, upon applying forward error correction (FEC), are mapped to a sequence of such rotated PSK constellations (each constellation is masked by the addition of an independent, uniformly distributed phase).Then, the sequence of hidden bits are securely and reliably transmitted over the channel.These hidden bits can be the message itself, or form a key to be subsequently used in conjunction with a conventional encryption algorithm, e.g., advanced encryption standard (AES).
Authors in [16] and [17] study embedding data in antenna beam patterns, where data is embedded in two orthogonal beam patterns to transmit a binary signal set.Although the use of an orthogonal basis is common in various formulations involving communications systems, it usually does not bring any explicit performance benefits; it merely simplifies the problem formulation, particularly constellation design and detection by keeping the noise projections uncorrelated (independent in signaling over AWGN).The motivation discussed in [16] and [17] has been to reduce the number of transmit chains.
The use of tunable parasitic elements external to the antenna(s) for RF beam forming is also well established.However, the objective in traditional RF beam forming is "to focus/steer" the energy beam, which does not realize the advantages of MBM (where data is modulated by modifying the RF characteristics of the external parasitic elements).Bains [18] discusses using parasitic elements for data modulation and shows energy saving due to the effect of classical RF beamforming.
Spatial modulation (SM) [19], [20], [21] uses multiple transmit antennas with a single RF chain, where a single transmit antenna is selected according to the input data (the rest of the data modulates the signal transmitted through the selected antenna).SM is, in essence, a diagonal space-time code, where the trade-off between diversity and multiplexing gain has favored the latter (MG equal to one).As a result, by relying on a single transmit chain, the hardware complexity of SM reduces, but its rate due to the spatial portion increases with log 2 of the number of antennas.A primary difference between MBM and SM is that, in MBM, the rate is scaled linearly with the number of on/off RF mirrors (parasitic RF elements with two states, acting as reflector or as transparent, respectively) vs. logarithmic scaling in the case of SM.The reason is, while MBM relies on a single RF chain too, due to the interaction among RF mirrors, each on/off configuration results in a different transmit antenna pattern.Due to this exponential growth, the number of data bits embedded in the channel state equals the number of on/off mirrors.
Quadrature spatial modulation (QSM) is proposed in [31] to enhance the throughput of SM by creating a new spatial dimension.The input data select two indices corresponding to two transmit antennas.One of the selected antennas transmits the in-phase part of the modulated RF carrier, and the quadrature component of the RF carrier is transmitted from the other selected antenna.QSM allows the transmission of an additional base two logarithms of the number of transmit antennas with respect to ordinary SM.This comes at the expense of synchronizing the transmit antennas.
References [32] and [33] discuss techniques for bit to index combination mapping in spatial modulation.However, a comparison with these schemes is not meaningful in the context of this article, as MBM constellation mapping directly operates on symbols, rather than on the bits used in the labeling of constellation symbols.
More recently, a promising research direction, based on using an "intelligent reflecting surface (IRS)" to aid in transmitting a wireless signal, has been introduced in [34] (also see [35], [36]).IRS, similar to media-based modulation and spatial modulation, is based on modifying characteristics of a radio frequency signal after it leaves its respective transmit antenna.Indeed, RIS and MBM can be combined, enhancing one another, as discussed in [37].In addition, [38], [39], [40], and [41] discuss methods to combine RIS with IM (index modulation).Since MBM belongs to the family of IM techniques, methods presented in [38], [39], [40], and [41] can be used to combine RIS with MBM.

C. Article Arrangement
The rest of the article is organized as follows.First, the system model for SIMO-MBM is described in Section II.In Section II-B, we discuss the practical issues raised using MBM with a single transmit unit, i.e., single-input multiple-output MBM (SIMO-MBM).Subsequently, we put forward layered MBM (LMBM) architecture and provide the details on how this configuration addresses the complexities in SIMO-MBM setup with minimal performance degradation.Section III provides several numerical results, including coded performance and comparisons with legacy and other index modulation techniques.A desirable property of MBM is that one can obtain an increase in the diversity order by applying FEC; Section IV shows by applying a FEC with error correction capability t, the slope of the diversity order increases by a factor of t + 1. Section V looks into the bandwidth expansion issue in MBM due to its time-varying nature and discusses a time-limited pulse design that mitigates bandwidth expansion.Finally, Section VI studies the practical design for the RF structure of MBM.A new design is presented where the transmit antenna efficiency is improved by adding top and bottom caps to the antenna cylindrical closure.Furthermore, the RF structure is equipped with multiple receive antennas.Section VI-H incorporates filtering operation within MBM walls to combat frequency expansion.Section VI-I is dedicated to providing links between MBM and IRS, including their respective challenges and potential for integration of the two techniques.Along this line, Section VI-J discusses the application of MBM for antenna beamforming.Finally, Section VII presents some specialized applications for MBM, focusing on emerging 6G wireless.

II. SYSTEM MODEL A. Single-Input Multiple-Output MBM (SIMO-MBM)
Fig. 1 shows the diagram of a 1 × K SIMO-MBM system with log 2 M RF mirrors.The transmitter selects a different on/off pattern for the RF mirrors according to message index m ∈ {0, . . ., M − 1}.As a result, a unique fading gain h m will be realized at the receiver.Coordinates of complex vector h m are the fading projections over individual receive antennas.The set of fading gains H = {h 0 , h 1 , . . ., h M −1 } due to all possible on/off combinations of RF mirrors constitute "MBM constellation points".In a Rayleigh fading channel, fading gains h m are modeled as i.i.d.complex Gaussian random vectors.In the absence of FEC codes, the transmission rate due to MBM is equal to R m = log 2 M bits per channel use.
The transmitter does not know the set of fading values (i.e., no channel state information at the transmitter is assumed).The receiver, however, knows fading gains H and also the one-to-one correspondence between the set of message indices and the fading gains.Receiver training is achieved by selecting each possible RF mirror on/off pattern at the transmitter and sending a signal (unmodulated carrier with possible pulse shaping) for the receiver to measure the associated MBM constellation point.For example, the channel state indexed by data m is selected during the mth training period to covey h m to the receiver.
Additional information corresponding to the SBM message may be transmitted by directly modulating the RF signal.Using a linear modulation (for example, amplitude shift keying), the SBM message is communicated as a complex number s multiplying the RF carrier before the transmit antenna.The projected signal at the receiver (ignoring AWGN) will be equal to sh m .Here, both complex number s and index m carry information.For brevity, in what follows, we do not consider transmitting additional SBM messages.

B. Layered MBM
Due to the random nature of the constellation points used in MBM, the constellation structure lacks regularity, which is in contrast to conventional constellations such as 256QAM.Consequently, practical complexities, such as receiver training and decoding, arise that are specific to MBM and its aim to target high data rates.In the following section, we outline these complexities and introduce the Layered MBM (LMBM) structure, which utilizes multiple transmit units to significantly mitigate these complexities.In particular, training overhead as well as decoding complexities are significantly reduced using the proposed layered structure.Additionally, several alternative MIMO detection techniques, as discussed in [42], [43], [44], [45], [46], [47], [48], [49], and [50]   its respective channel state according to its associated data.The generated signals are intended for a common receiver.The set H 0 := {h 0 0 , . . ., h 0 M −1 } denotes the fading gains from the first transmit unit to the receiver, likewise H1 := {h 1 0 , . . ., h 1 M −1 } are the gains from the second unit to the receiver, and so on.Media-based modulator units are arranged such that there is a negligible coupling among them.As a result, the fading gains from each unit to the receiver (also called "constituent vectors") will be independent of each other.The overall projected signal at the receiver will be the superposition of the constituent vectors due to individual units.More specifically, consider the message sequence (m[0], . . ., m[N − 1]), 1 where m[n] ∈ {0, . . ., M − 1} corresponds to the random message sent over the nth transmit unit, i.e., the nth transmit unit selects its own on/off RF mirror configuration according to m[n].Subsequently, a complex K dimensional fading gain h n m[n] is realized between the nth transmit unit and the receiver.The received constellation point c is then formed as Since the constituent vectors are random and independent of each other, the cardinality of the set of received constellation set will be equal to the product of the number of constituent vectors corresponding to different units.As a result, using R m /N RF mirrors at each of the N MBM units creates 2 Rm distinct vectors at the receiver, capable of transmitting R m bits of information per channel use.Like SIMO-MBM, each unit can send additional SBM data by modulating its RF signal.A total of R s additional bits due to source-based modulation is achieved by transmitting R s /N bits per unit.
The following summarizes how the layered structure addresses the shortcomings of SIMO-MBM when transmitting high data rates.B1: For the same transmission rate, the number of RF mirrors used at individual media-based modulator units reduces by a factor of N .B2: Symbol recovery can be performed using a low-complexity successive cancellation decoder.At each step, the decoder searches for the constituent vector contributed by a single modulator unit and cancels its effect before proceeding to the next modulator unit.A list decoder can further improve the successive cancellation decoder.B3: Training is simplified as it is composed of N separate training tasks, each over a smaller set of an alphabet size 2 Rm/N , as compared to training over a set with 2 Rm alphabets.B4: Tracking is simplified as it is composed of N separate tracking tasks, each over a smaller set of an alphabet size 2 Rm/N , as compared to tracking the entire set of 2 Rm alphabets.For example, to send 32 bits of data per channel, one can use 4 media-based modulator units, each modulating 8 bits, meaning only 8 on/off RF mirrors are required in each unit.Training/tracking comprises 4 separate tasks, each involving a much smaller alphabet size of 2 8 = 256 elements.
Remark: Unlike SIMO-MBM, LMBM no longer fulfills the independence requirement of Gaussian random coding over AWGN channels.In particular, in a Rayleigh fading channel, the constituent vectors h n m[n] follow an i.i.d.complex Gaussian distribution.However, the received constellation points c are no longer statistically independent.As such, the performance of LMBM may be inferior to SIMO-MBM.However, numerical results show that the degradation in SNR performance is modest.For example, Fig. 5 shows an example of the gap in performance of MBM vs. LMBM, which is less than 0.5 dB when transmitting 16 bits per complex channel use.
1) Low-Complexity Decoder for Layered MBM Scheme: The layered structure of LMBM enables implementing a low-complexity successive cancellation list decoder that recovers individual constituent vectors ), leading to the elements of the message (m[0], . . ., m[N − 1]).At each step, the successive cancellation decoder makes a decision about the transmitted symbol corresponding to a single modulator unit, say i.The estimate of the constituent vector h i is then used to subtract the contribution of message m[i] from the received signal and use the remainder to recover the rest of messages.This process is continued until an estimate for all the elements of the message sequence The successive decoding algorithm details are explained in appendix A. Using this decoder and Monte-Carlo simulation, we can numerically measure the symbol error probability of LMBM for rates as high as 32 bits per channel use (see Fig. 6).

III. NUMERICAL PERFORMANCE
For numerical performance, we assume a static Rayleigh fading channel where the constituent vectors (fading gains) from each modulator unit to each receive antenna are generated as complex i.i.d.Gaussian random vectors.The performance is averaged over many independent runs of fading gains and AWGN noise.Energy per bit, E b , is defined as the sum of total signal energies of all transmit units divided by the total number of bits per channel use, and N 0 denotes the AWGN spectral Fig. 6.
Analytical upper-bound on the symbol error probability for SIMO-MBM (see appendix C) with 32 RF mirrors in a single transmit unit vs. simulated LMBM performance (8 RF mirrors in each of the 4 transmit units).Both schemes transmit 32 bits in a single complex channel use (without any FEC) using 16 receive antennas.SIMO-MBM upper-bound is tight at high SNR regime, suggesting that the LMBM performance penalty vs. SIMO-MBM is negligible.density at individual receive antennas.MBM performance reported in the following does not consider transmitting any additional source-based data, i.e., R s = 0 (the total data rate is R = R m ).
Note that in this article, MBM relies on directly mapping symbols (rather than bits) to constellation points for data transmission.Consequently, numerical results are presented in terms of symbol error rate.Additionally, forward error-correcting codes also operate on symbols, not bits.In this context, a computation of the bit error rate (BER) would not be useful, since numerical results demonstrate a very low symbol error rate with a sharp and increasing downward slope (without any error floor).Overall, symbol error rates are negligible, which represents a stronger outcome compared to achieving low BER values.

A. Uncoded Performance
Fig. 5 demonstrates the performances of SIMO-MBM and LMBM, transmitting 16 bits per channel use.Fig. 6 shows the performance of 4×16 LMBM system, transmitting 32 bits per channel use.Since maximum likelihood decoding becomes prohibitive for 2 32 points in the constellation, the performance is obtained using the successive cancellation list decoder explained in appendix A. These performances are achieved via a single transmission without FEC.

B. Performance Including FEC
The application of FEC to MBM can be materialized using simple code structures operating on symbols (rather than bits).For MBM with log 2 M RF mirrors, the class of Group codes with alphabet size M would be a natural choice.Reference [51] proves that in searching for good group codes, one can limit the search to those formed over elementary Abelian Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.An RS code of block size N c and dimension K c with minimum distance D, using a hard-decision decoder, can correct up to t = ⌊(D − 1)/2⌋ symbols in errors.Fig. 7 shows the simulated performance of the hard-decision decoder where each symbol of the RS code (i.e., Galois field elements) are mapped to LMBM constituent vectors.
Fig. 8 shows the block error probability performance of coded LMBM.Note the increase in the slope of error Fig. 9. Improvement due to the selection of the subset of points with the highest fading gains employing one and two additional RF mirrors.The error probabilities correspond to 1 × 8 SIMO-MBM attaining 16 bits per complex channel use.probability as the minimum distance D (or equivalently error correction capability t) is increased.
Lastly, note that MBM inherently operates over symbols.Therefore, non-binary variants of LDPC and Polar codes (see [52], [53] for examples) can also be directly applied to MBM symbols.However, it should be noted that LDPC decoding, when utilizing message-passing algorithms, may suffer from an error floor issue.Similarly, the successive decoding process of Polar codes may result in large delays.Owing to its very low uncoded symbol-error rates, the MBM constellation becomes virtually error-free when using simpler codes that operate over symbols, such as RS codes with a small minimum distance.Consequently, the application of simpler codes to MBM achieves ultra-high reliability and ultra-low latency, while providing efficient low-power decoding.

C. Selection Gain
By identifying a subset of points within the constellation set that optimizes a relevant performance metric (e.g., mutual information) and communicating the indices of those points to the transmitter, MBM can achieve a pre-coding gain.Subsequently, the transmitter exclusively selects the on/off RF mirror configurations corresponding to those indices for data transmission.Additionally, to maintain the same transmission rate, subset selection necessitates the integration of additional RF mirrors.A straightforward optimization involves providing the transmitter with the indices of the constellation points exhibiting the highest fading gains.As a numerical example, Fig. 9 depicts the pre-coding gains achieved through subset selection while targeting 16 information bits per complex channel use by implementing one and two extra RF mirrors.
All numerical results in this article could be further improved using additional RF mirrors.In the context of coded MBM, which relies on a symbol-based encoder, these additional RF mirrors enable an increase in FEC redundancy without compromising spectral efficiency.Regarding selection Fig. 10.
Symbol error probability comparison for schemes achieving transmission rate equal to 8 bits per complex channel use using 8 receive antennas.10 gain, the extra RF mirrors allow a choice of more suitable subset of constellation points, thereby improving selection gain.

D. Comparison With Spatial Modulation and Its Variants
Fig. 10 and 11 provide a comparison between MBM and other emerging modulation techniques (see also [54]).Particularly, the symbol error probability of MBM averaged over independent realizations of a static Rayleigh fading channel is compared to spatial modulation (SM), generalized spatial modulation (GSM), quadrature space shift keying (QSSK), and quadrature space modulation (QSM).Comparison is provided for rates of 8 bits per complex channel use and 12 bits per complex channel use.The number of transmit and receive antennas, and quadrature amplitude modulation order for each scheme in Fig. 10 and 11 are provided in Table II and III, respectively.While other techniques rely on multiple antennas/RF chains at the transmitter as well as high modulation orders to achieve specified transmission rates, MBM performance is for a single transmit unit and in the absence of RF source modulation.

E. Outage Probability Comparison With Legacy SISO/SIMO/MIMO
In this section, we compare MBM with traditional MIMO systems from the standpoint of information theory by Symbol error probability comparison for schemes achieving transmission rate equal to 12 bits per complex channel use using 12 receive antennas.

TABLE III
SYSTEM SPECIFICATIONS FOR FIG.11 comparing outage probabilities.First, we review how the outage probability is computed in the MBM setup, and next, we present the numerical results.
MBM constellation points are selected with an equal probability of 1/M .The empirical probability mass function over the constellation set is where δ(h i ) is the Dirac delta measure at point h i .Let h denote the random variable drawn from distribution PH .The outage is defined as the event that the mutual information of a fading realization does not support a target rate R, i.e., Mutual information I(h; h + z) is a random variable whose value depends on the particular realization of MBM constellation set H. In the presence of AWGN, the distribution of output signal at the receive antennas is given by the convolution of the mass function over the constellation set with Gaussian density, indicated by PH * φ.Accordingly, empirical mutual information is Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Function h denotes the differential entropy.The output distribution PH * φ is a Gaussian mixture, where the mixture components are the realized constellation points.It is shown as the cardinality of the constellation set grows, MBM asymptotically achieves the capacity of K parallel AWGN channels [2], [9] and is highly concentrated around K log(1 + SNR).Fig. 12 compares outage capacity curves in SISO setup for rates 3, 5, and 7 bits per complex channel use.The outage probabilities for SISO-MBM are calculated using mutual information corresponding to different realizations of an MBM constellation.The number of points in the constellations used to calculate MBM outage probabilities are 64 (corresponding to 6 RF mirrors), 256 (corresponding to 8 RF mirrors), and 512 (corresponding to 9 RF mirrors) for rates 3, 5, and 7 bits per complex channel use, respectively.This means rates 3, 5, and 7 are achieved by relying on the redundancy of 3, 3, and 2 bits, respectively.It is observed that performance gains are particularly pronounced in SISO setups due to the inherent diversity of MBM.Please note that the simulated performance confirms that the lower-complexity LMBM achieves mutual information performance comparable to that of MBM.Fig. 13 and 14 compare the outage probabilities in MIMO setup when 2 and 4 receive antennas are used, and target transmission rates are 6 bits per complex channel use and 8 bits per complex channel use, respectively.Note that MBM only uses a single RF chain at the transmit side.Moreover, no additional RF source modulation is used for MBM in any of the scenarios considered.
Increasing the number of RF mirrors would lower the required energy for a given outage probability.In this article, we confine to outage measurements for up to 4 receive antennas and 9 RF mirrors merely due to the difficulty of computing mixture entropy in higher dimensions.

IV. INCREASED DIVERSITY ORDER THROUGH
APPLICATION OF FEC Fig. 7 and 8 demonstrate another distinctive property of MBM: the slope of the error probability curve in the MBM  scheme increases by a multiplicative factor when applying MDS error correction codes.This property is reminiscent of transmit diversity in the MIMO setup.However, MBM relies on a single transmit unit while achieving the additional diversity gain.In this section, we quantify the realized gain in the diversity order when applying MDS codes to MBM.
Formally, a scheme is said to achieve diversity gain d and spatial multiplexing order r (see [7]), if it supports the data rate with the average error probability Appendix C shows an uncoded MBM achieves diversity order d = K − r without any special processing other than the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.usual maximum likelihood detection.Furthermore, applying a FEC with minimum distance D increases the diversity order by a multiplicative factor of D for a small reduction in the multiplexing gain.More precisely, an MDS code using a maximum likelihood decoder achieves diversity order d = D × K − r/τ , where τ is the code dimensionless rate (c.f.[55]).Moreover, using a simple hard-decision decoder with t error correction capability, MBM achieves a diversity order of (t + 1) × K. Appendix D provides the analytical analysis for the increase in the diversity order using a hard-decision decoder.
Remark: Unlike legacy MIMO, in MBM, the increase in diversity order is realized using a single transmit unit, i.e., a single RF chain and a single transmit antenna surrounded by RF walls.Therefore, a higher diversity order, resulting in a better error performance, is possible merely through algorithmic complexity.Furthermore, unlike random-like codes such as turbo codes and low-density parity check (LDPC) codes which typically suffer from error floor, the slope of the error curve in coded MBM will not change as SNR increases.

V. MITIGATING BANDWIDTH EXPANSION VIA TIME-LIMITED PULSE DESIGN
MBM and other techniques in the context of "index modulation", including spatial modulation and its variations, inherently correspond to linear time-variant (LTV) systems.Unlike linear time-invariant (LTI) systems that maintain the spectrum occupancy of the signal, an LTV system typically increases the occupied bandwidth beyond the spectrum of the pulse used for transmission.The issue of an increase in the bandwidth can be tackled by careful design of the pulse shaping filter at the transmitter.
The transmit pulse is designed such that it is contained within successive reconfigurations of RF mirrors.Since each pulse reaches zero value by the time RF mirrors change the configuration, bandwidth expansion beyond the spectrum of the shaped pulse will be avoided.More specifically, the MBM signal in the time domain is obtained by convolving a sequence of impulses, where the magnitude of impulses is modulated by i.i.d.Gaussian random values (fading realizations), with the time-domain representation of the pulse shaping filter.Since: 1) the sequence of impulses has a flat power spectrum; 2) convolution translates to multiplication in the frequency (power spectral) domain; and 3) the pulse value will be zero at the time of starting the subsequent transmission, the power spectrum of MBM will be proportional to the power spectrum of the pulse shaping filter.
Let p(t) denote the MBM pulse limited to the interval [−T /2, T /2]: The spectrum of the pulse is The an optimum pulse maximizes the ratio which is the fraction of total power maintained in the allocated band.Reference [56] studies the solution for this optimization problem.Appendix B includes the mathematical formulation for the optimum pulse shape.
The ratio η for the optimum pulse depends only upon T ×B, i.e., the product of pulse length and allocated bandwidth.The shape of optimum pulses as well as power spectral densities (PSD) corresponding to different time-bandwidth products, T × B, are depicted in Fig. 15, and 16, respectively.The quantity 1 − η in Fig. 16 denotes the fraction of the pulse energy outside the given frequency band.Note that T × B = 1/2 corresponds to the traditional Nyquist signaling rate.It is observed that, for a T × B as low as two, the (total) out-ofband energy is about 42.4 dB lower than the pulse's energy.Fig. 17 shows how the total out-of-band leaked power changes for a wide range of T × B values.

VI. RADIO FREQUENCY IMPLEMENTATION
Reference [11] (also see [12]) reports an MBM antenna unit operating at 5.8 GHz.Fig. 18 shows an LMBM structure relying on the corresponding antenna.The RF structure in [11] enjoys low hardware complexity, as it incorporates a single transmit chain, where an RF divider is used to feed multiple transmit antennas.The RF phase shifters in Fig. 18 allow sending additional SBM data.For example, one can select 0 • , 90 • , 180 • , and 270 • phase shifts according to two additional bits of SBM data (per transmit unit).Reference [11] discusses techniques, including the use of RF phase shifters in Fig. 18, to facilitate receiver training.The same techniques apply to the new antenna structure presented in the current article.Readers are referred to [57] for examples of antenna patterns and realizations of MBM constellations corresponding to indoor and outdoor propagation environments (also see [2] for the latter).Simulations are performed using ANSYS high-frequency structural simulator (ANSYS HFSS2 ) to obtain antenna patterns, which are then imported to the ray tracing software (Remcom Wireless Insite3 ) to obtain the constellation points.
Antenna structure reported in [57], although tested for functionality (see [14], [15]), suffers from the following shortcomings: 1   Due to the symmetry of the antenna walls along the spherical angle ϕ (i.e., in the X-Y plane), it is desirable to have a transmit pattern with a similar spherical symmetry.Such symmetry guarantees that each of the 12 RF walls is exposed to (approximately) the same amount of RF energy.Consequently, when switched on and off, each RF wall has (approximately) the same impact on the outgoing RF signal.Accordingly, the transmitter can provide coverage for any receiver located at an angle of ϕ ∈ [0, 360 • ] (with respect to the transmit unit).The two metallic reflectors/closures, called metallic caps hereafter, are responsible for constraining the radiation in the horizontal directions -compare the TX pattern in Fig. 21(a) vs. the one in Fig. 21(b).
In the new design, each wall includes three building-block columns, one large metallic rectangular patch on the interior, and a single RX antenna on the exterior.Each building-block column comprises thirteen small RF patches.The thirteen small patches in each building-block column are connected using RF switches (PIN diodes).RF switches corresponding to each column can be independently controlled (turned on/off).When the switches on a given building-block column are on (low impedance connection), the corresponding patches form a connected metallic strip that reflects the incident wave to the interior of the antenna structure.If the switches are off, the incident wave results in an RF signal propagating outside the antenna structure (i.e., the corresponding building block column acts as if it were transparent to the incident wave).
To optimize the geometry of each wall, one needs to devise a computational method to find an initial approximate solution (with acceptable performance) in a reasonable time.Then, one can include the initial solution obtained in this manner within the entire antenna structure and rely on HFSS to tune (optimize) the underlying dimensions.The basic building block structure is repeated periodically to achieve this goal, forming a plane extending to infinity.Fig. 22(a) and 22(b) show a single building block column in off and on states, respectively, and Fig. 22(c) shows the periodic extension of a single building block column in the on state.The periodic extension in Fig. 22 provides a good starting point for subsequent HFSS optimization.This is because, in the actual antenna structure, columns are placed around a circle mimicking an infinite extension along the X axis in Fig. 22(c), while reflections in the top and bottom metallic caps mimic an infinite extension along the Y axis.Relying on HFSS, a plane wave (with a vertical polarization), propagating along the −z axis, is incident on the periodically extended structure in Fig. 22(c), then the energy of the wave propagating to the opposite side is measured and used to compute S 12 and S 11 (indices 1 and 2 refer to the two sides of the periodically extended surface).In the RF domain, this is achieved by relying on the concept of Floquet ports. 4Upon including the resulting initial design within the rest of the antenna structure, the dimensions of the basic patch element are further optimized (using HFSS) to achieve the curves shown in Fig. 23(a) and (b) for S 12 and S 11 , respectively.The large patch on each wall acts as the RX antenna ground plane.

A. Top and Bottom Caps: Detailed Derivations
In a preliminary design, we used two flat metallic caps to close the antenna structure's top and bottom (see Fig. 24).It was observed that the impedance matching of the TX antenna could not be improved beyond -10 dB.Fig. 25 shows the corresponding S 11 graphs.A new cap structure is designed to improve the impedance matching by guiding the incident  RF wave (see Fig. 19, 20 and 21).Furthermore, the new caps provide other benefits, including higher efficiency (see Table IV) and a pattern concentrated around the horizontal plane (see Fig. 21).Fig. 28, obtained through measurement, confirms that using the curved caps, the S 11 parameter is rather insensitive to the switching pattern, and values for different switching patterns remain at an acceptable level.
The top and bottom caps are designed to reflect a ray initiating from the origin such that it propagates parallel to the horizontal axis.Fig. 26 shows the curvature of a cut in the interior surface of the proposed cap.Let us assume a radiating source point is located at the origin, i.e., (0, 0).The cap surface, which is obtained by rotating the function of y = f (x) around the y-axis, should reflect a ray originating from such source point parallel to the x-axis.Referring to Fig. 26, this means We also have By eliminating θ in ( 12) and ( 13), we obtain The dashed line in Fig. 26 intersecting with the x axis is tangent to the curve y = f (x).Therefore, By substituting ( 14) in ( 15), and noting tan (α) = y/x, it follows that Taking tan of the two sides of ( 16) and using the identity tan(2a) = 2 tan(a)/(1 − tan 2 (a)), we obtain y x = tan 2tan −1 (y ′ ) (17) Equation ( 18) is a quadratic equation of the form in y ′ .Referring to Fig. 26, since y > 0 and y ′ > 0, the quadratic equation ( 19) has a single valid solution of the form To solve the above differential equation, we perform some manipulations as follows: Since y > 0, we have Let us define U := −x + x 2 + y 2 and U ′ := dU/dx.Then, (22) simplifies to Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where c is a constant.After some simplifications, we obtain where S is a parameter to be optimized (through HFSS simulations) to attain the best S 11 for the entire structure.The caps are fabricated using aluminum with a thickness of 5 mm.We have simulated two different scenarios to study the relative merits of optimized (curved) caps.Both scenarios Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.targeted a center frequency of 5.8545 GHz.The objective was to improve TX antenna matching, i.e., reduce the S 11 of the TX antenna over the desired bandwidth centered at 5.8545 GHz.In the first scenario, two flat metallic caps were used to close the antenna structure's top and bottom.Tuning was performed on two parameters: 1) structure diameter; and 2) TX antenna length.These parameters were optimized (using HFSS simulations) while keeping all other parameters at their optimized values obtained beforehand.In the second scenario, caps with optimized curvature were used.Details of tuning are explained in Section VI-F.The conclusion was that to have a reasonable TX impedance matching, the diameter of the structure in the first scenario (flat caps) should be at least 7% larger than the case of the second scenario.Nevertheless, for flat caps, the TX S 11 was rarely (for a small number of switching patterns) below -10 dB (see Fig. 25).On the other hand, in the second scenario, it reaches -20 dB for almost all switching patterns (see Fig. 27, supported by measurement results shown in Fig. 28).Table IV compares the radiation efficiency and maximum gain for the structure with flat caps (case 1) vs. the structure with curved caps (case 2).We observe that the overall efficiency increases from 82% (for flat caps) to 90% (for curved caps).More importantly, the use of curved caps has guided the outgoing RF wave to concentrate around the horizontal plane -see improvement in maximum gain for case 2 vs. case 1 in Table IV, and the focused TX pattern in Fig. 21(c).Finally, measurement results (see Fig. 28) confirm that using the curved caps, the S 11 parameter is acceptable for different switching patterns.

B. Details of Surrounding Walls
The 12 side walls are made of RO4003C material with a thickness of 32 mil.On the outer face of each wall, the RX antenna and the PIN diodes control command signal traces are located.Part of the inside face of the wall is a large copper patch that acts as the RX patch antenna ground.The rest consists of three building block columns of small patches connected using SMP1320-040LF RF PIN diodes.
To optimize the patch dimensions, we defined two Floquet ports at the two sides of a boundary box.Then, the reflection and the transmission coefficients, S 11 and S 21 , respectively, are computed for different patch dimensions and also for the two states of on and off.Dimensions of the basic patch are optimized such that by turning the PIN diodes on and off, the value of the reflection coefficient (or the transmission coefficient) changes significantly.Relying on this initial solution, we subsequently fine-tune the patch dimensions by simulating the entire antenna structure using HFSS.
We randomly selected seven different wall states to optimize the overall structure.Table V shows these selected states.Fig. 27 shows the TX antenna impedance matching, i.e., the S 11 values corresponding to these seven states obtained through simulation.The final patch size at 5.8545 GHz is 5.6 mm by 6 mm wide.Furthermore, the width of the ground patch is around 37.5 mm.There is a 1.6 mm gap along the vertical axis between two adjacent patches in a building block column and a 1.5 mm gap between two adjacent building block columns.The radius of the structure where the PCBs are located is around 119 mm from the center axis (z-axis).The equivalent circuit for the PIN diode is composed of an inductance L s in series with a diode die equivalent circuit, where L s models the effect of the diode packaging.For SMP1320-040LF, we have 5

C. Details of the RX Antenna
The RX antenna is a planar patch element that is fed through a microstrip trace.On each wall, we have one RX antenna and a plane that acts as the patch antenna ground, i.e., the body of the antenna connector will be soldered to it.To have a higher bandwidth, the corners of the patch have been chamfered.Also, the inset feeding technique has been used for matching purposes (similar to the TX antenna).Several parameters in the RX antenna were tuned at the desired center frequency of 5.8545 GHz.These parameters include patch width, patch length, chamfer dimensions, inset length, and trace width.Fig. 29 shows the RX antenna, and Table VI shows final dimensions after fine-tuning in the presence of the entire antenna structure.Parameter S 11 for the RX antenna is shown in Fig. 30(a) (HFSS simulation) and in Fig. 30(b) (measurement).It is observed that the frequency of the point with minimum S 11 in Fig. 30(a) is slightly different from that of Fig. 30(b).Despite this slight disagreement between simulation and measurement, the measured S 11 at the target frequency of 5.8545 GHz is at an acceptable level (about -10 dB).In RF, such a small mismatch between simulation and measurement is quite common and can be corrected.The mismatch can be due to fabrication error or the difference between the parameters of materials used in fabrication vs. what is modeled in HFSS.Computational inaccuracies can be corrected by targeting a (proportionally) higher frequency in simulation.Fig. 31 shows the pattern of the receive antenna.

D. Details of the TX Antenna
Noting the circular symmetry of the structure, an omnidirectional TX antenna is needed to operate at the center of the cylindrical structure.A good candidate for this purpose is a planar monopole antenna.Fig. 32 shows the designed antenna.The antenna is printed on a 60-mil RO4003C Rogers substrate.The top and the bottom ground patches are connected using vias and soldered to the connector's body.To improve TX matching, the inset feeding technique has been used.The following parameters are tuned in optimizing TX matching: the length of ground patches, the notch dimensions in the bottom ground patch, the length and width of the narrow trace of the monopole, dimensions of the wider part of the monopole, and finally, the inset feed length.TX antenna tuning has been performed in the presence of caps and PCB walls for a center frequency of 5.8545 GHz.Fig. 32 shows the TX  antenna and Table VII shows final dimensions after fine-tuning in the presence of the rest of the antenna structure (refer to Section VI-F).

E. Control Board
For driving the PIN diodes, we have designed a control board that is attached to the upper cap from outside of the structure (see Fig. 19).We have used an AD828 dual, lowpower Op-Amp to drive the PIN diodes.This Op-Amp has 130 MHz 3-dB bandwidth at a gain equal to 2 dB and 450 V/µs slew rate.Since we have thirteen PIN diodes in each building block column, considering the forward voltage of 0.85 V for each PIN diode, one needs around 11 V to turn on all the diodes.The selected Op-Amp is able to perform this task since it operates using a ±15 V power supply.

F. Iterative Optimization of Design Components
RX antenna is initially designed as a standalone element and then tuned in the presence of the rest of the structure to optimize the corresponding S 11 parameter.Similarly, the TX antenna is initially designed as a standalone element by optimizing the corresponding S 11 parameter while achieving an omni-directional pattern.The patch dimensions are initially designed using Floquet ports, where the reflection coefficient, S 11 , and the transmission coefficient, S 12 , of the building block, are monitored to approach a reflecting surface in the on state and a transparent surface in the off state.Next, the above initial designs are integrated into the larger structure and the underlying four design decisions, namely geometries of: 1) RX antenna; 2) TX antenna; 3) surrounding walls; and 4) caps, including curvature, i.e., the parameter S in ( 25) and the two radii in Fig. 21(c)) are tuned iteratively.Objectives have been to realize good S 11 for antennas, a TX radiation pattern concentrated around the horizontal plane, and realize desirable S 11 and S 12 for the walls focusing on the seven different test states mentioned in Table V.

G. Simulation Vs. Measurement Results
Fig. 28 shows some measurement results, which closely match the simulation results in Fig. 27.Due to space limitations, only four cases of measurement results are shown.Several other cases have been tested, including some that were not considered in the initial design optimization.Measurement results show that, in all cases, the achieved value of S 11 remains at an acceptable level and is rather insensitive to the switches' state.

H. Incorporating Filtering Operation Within MBM Walls to Combat Frequency Expansion
In earlier sections of this article, we outlined key challenges associated with the practical implementation of MBM.Several of these challenges, such as: 1) receiver-side constellation learning; 2) constellation tracking; and 3) decoding, have been addressed (to a certain degree) in this paper.However, the issue of bandwidth expansion necessitates further investigation.In traditional systems, filters for limiting transmit bandwidth are incorporated within the RF front-end prior to the TX antenna(s), a solution that is not applicable to MBM.One possible solution involves replacing each patch on MBM walls with a so-called filtering-radiating patch (FRP) [58].The filtering process does not depend on discrete components; it is realized using a rectangular patch etched with slots [58].To investigate such filtering operation, a periodic structure of patch elements with slots is assembled.The dimensions adhere to those specified in [58], except for a reduced substrate size, which allows the patch elements to be positioned closer together.The S 11 value, with each patch terminated to a matched load, is presented in Fig. 33.The general shape of S 11 resembles the one reported in Fig. 4 of [58], albeit with a center frequency shift which is adjusted to match the frequency range considered in this article.Further research is necessary to: 1) optimize the patch size for more accurate center frequency adjustment; and 2) explore more advanced filter structures to improve the filtering performance in the rejection band.For instance, one can rely on patch structures etched with a larger number of slots, each optimized in terms of size and position, to create multiple nulls in the frequency domain.More generally, the area of incorporating filters within antennas is an active research area presenting a number of solutions (see [58] for references).

I. Relevance to Intelligent Reflecting Surface (IRS)
Recently, intelligent reflecting surface (IRS), as introduced in [34], has attracted considerable interest (see [59], [60], [61], [62] and references therein).While IRS and MBM share some similarity in objectives and design criteria, these two techniques fundamentally differ in the way they improve MBM and IRS both enhance communication by increasing spectral and energy efficiency, yet they do so through distinct mechanisms.IRS panels are strategically placed outside the transmitter to effectively redirect signals around obstacles.This enhances signal quality at the receiver by carefully optimizing the phase of the reflected signals, thereby combating fading and interference.However, such optimization in IRS requires knowledge of the channel gains to and from the IRS panel.In contrast, MBM combats fading and improve spectral and energy efficiency by embadding information in channel states with different random channel gains through random reflections and refractions at the transmitter.This process generates a random constellation set at the receiver without requiring knowledge of channel gains at the transmitter or engaging in phase optimization.Additionally, it does not require any external elements to be added to the transmitter, thereby reducing both cost and complexity.Since the benefits realized from these mechanisms do not necessarily overlap, both can be simultaneously employed to synergistically improve communication.In fact, several studies have explored methods to integrate IM/MBM with IRS, capitalizing on their respective advantages within a unified system [37], [38], [39], [40], [41], [63].
To elaborate in greater details, Fig. 23 illustrates how the walls in an MBM structure can be configured to either refract (act as transparent) or reflect the incident waves, with high efficiency in both scenarios.This allows an outgoing signal to bounce back and forth within the MBM RF walls before leaving the transmitter.
On the other hand, IRS functions by steering an incident wave toward a desired direction, through reflection or refraction, and by controlling the RF properties of a metasurface panel.The core principle of anomalous reflection, which serves as the foundation for IRS, has also been investigated in the fields of optics and RF [64], [65], [66], [67].
The primary model for the application of IRS is that an incoming plane wave, with any given angle of incidence, can be reflected in any desired direction with 100% efficiency, and without adding any noise.These assumptions form the pillars behind some very promising results, for example, it is concluded that, through beam forming, an IRS with N reflectors can realize an array gain scaling with N 2 (rather than N which is the limit in conventional antenna array structures).To better understand the potentials in combining IRS with MBM, some of the challenges associated with IRS are discussed next.
Perfect (100%) Reflection Efficiency: Reference [62] shows that: (1) For any given incident wave, there exists a trade-off between the power of the reflected and refracted waves (refracted wave refers to what passes through the IRS panel).
(2) Energy in the reflected wave is unavoidably less than 100%.In [62], the relative fraction of incident power divided between the reflected and refracted waves is expressed in terms of certain circuit parameters.Since same parameters govern the two (reflected and refracted) parts, increasing one is associated with decreasing the other one.
Additive Noise: It is assumed that, since IRS is a passive system, any incident wave can be reflected without any noise being added to it.Definition of passive circuit and its relevance to noise needs careful consideration.Readers are referred to [68] (page 506) for a discussion on noise figure of a passive network.In addition, several proposed IRS structures rely on using PIN diodes to change the reflection angle for a given angle of incidence.However, PIN diodes are known to generate noise [69].In addition, noise observed by any receiving element includes terms generated external to the receiver (see [68], pages 697-699).Indeed, noise external to a receiving antenna is exploited in radiometers for RF imaging (see [68] page 696).To study the impact of such an externally added noise component, let us consider an IRS panel programmed to reflect an incoming plane wave, with an incidence angle α, towards an outgoing direction of interest.To realize this goal, each reflecting element is responsible to realize a phase shift that depends on α as well as on the outgoing direction of interest.However, in addition to the desired signal, there is an external noise component that is absorbed by each metasurface atom.As a result, the true (noisy) incidence angle at each atom will be slightly different from α. Indeed, both direction and phase of the incoming plane wave are prone to random fluctuations that are somewhat different from atom to atom.In this case, since the phase shift produced by each atom is designed assuming that the incident angle across all atoms is α, it follows that the passive beam forming, in addition to the (main) outgoing beam 6 produces random side-beams that, unlike the main beam, are not consistent with the receive beam forming direction at the final destination.The net outcome is a noise term at the destination with a power that scales with the power of the signal incident on the IRS.Presence of such noise terms contradicts many of the results established in the area of IRS.In particular, it is not possible to achieve an array gain that scales with N 2 (indeed, since the noise power scales with the power of the incident signal, the resulting array gain scales with N ).
RF Matching: Input matching parameter specifies the fraction of power absorbed by a reflecting surface, with the objective of redirecting (reflecting and/or refracting) the absorbed energy towards desired angle(s).In a tunable reflecting surface, the state of each meta-surface atom needs to change (controlled) depending on the incident angle as well as the desired reflecting and/or the refracting angle(s).Significant work is needed to design IRS structures that provide good input matching is all such states.In the presence of an imperfect matching, part of the absorbed energy is: (1) wasted due to various losses wherein any Ohmic loss results in an additive noise term, or (2) passed to the outgoing signal through parasitic RF paths which means it acts as an extra noise with a power scaling with the power of the incident signal.These effects need further investigation.
The presence of similarities between the structures of IRS and MBM suggests at the possibility of augmenting MBM to facilitate control over the phases of reflected (and/or refracted) signals.Next, to establish connections between functionalities of IRS and MBM, the feasibility of realizing beam forming gain using MBM will be discussed.

J. Antenna Beam Forming Using Parasitic Elements
The use of parasitic elements for the purpose of increasing antenna gain in a direction of interest (and/or reducing it in the direction of an interfering signal) has been extensively studied in the literature (see [70] and references therein).In this section, the MBM antenna structure is modified, as shown in Fig. 34, where by turning the walls on and off, one can adjust the direction of antenna beam.Figure 35(a) shows the antenna beam when half of the walls are OFF (letting the incident wave to pass through) and the rest are ON (reflecting the incident wave).The pattern for the center antenna in the presence of metallic caps are shown in 35(b).Simulations using HFSS shows: (1) radiation efficiency is about 97%, and (2) case 35(a) offers about 2.65dB increase in the antenna effective area with respect to 35(b).Brief discussion presented here is far from adequate in covering the topic of beam forming relying on MBM-like structures.It is provided as an example to show that MBM structures can be used for beam forming as well, an operation that is at the hearth of IRS.Further research is required to study the possibility of changing the direction of an incoming wave, which is incident on MBM at a certain angle, to bounces off the MBM structure towards a direction of interest.This can be realized by turning a first subset of MBM walls off, and turning a second subset, which are at a proper angle with respect to the first subset, on.This would result in an effect similar to anomalous reflection in IRS.The circular structure of MBM closure provides more Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.flexibility, as compared to typically flat panel used in IRS, in anomalously reflecting an incident wave.

VII. SPECIALIZED APPLICATION DOMAINS FOR MEDIA-BASED MODULATION
In prior sections of this article, we examined the merits of MBM, emphasizing its capacity to attain high data rates and mitigate slow fading while preserving spectral efficiency.Within the wireless field, achieving high data rates remains a primary goal.Nonetheless, a single approach cannot be deemed ideal for every application.Beyond bandwidth and power efficiencies, the distinct attributes of MBM render it an appropriate option for particular application domains, which we will elucidate further.In a broader context, [71] and [72] investigate the advantages of employing IM (and consequently MBM) in future wireless systems, i.e., 6G and beyond.

A. Ultra-Low Latency Transmission
In a range of emerging wireless applications, achieving ultra-low latency is paramount [73], [74], [75].For these applications, it's essential to use short block lengths to maintain ultra-low latency while ensuring high reliability.
MBM stands out as an optimal solution in these applications.In MBM, the expected value of the Euclidean distance, |a − b| 2 = N i=1 (a i − b i ) 2 , between two constellation points a = a 1 , . . ., a N and b = b 1 , . . ., b N , scales linearly with the number of receiver antennas N since the components (a i − b i ) 2 are independent for i = 1, . . ., N .This produces a large typical distance value, allowing MBM to deliver coding-like error performance without channel coding (also see III).Furthermore, MBM benefits from a diversity-like advantage through a simple, low-latency hard-decision codes with a small minimum distance, as detailed in this article.Unlike capacity-approaching FEC structures such as Turbocodes, which typically exhibit an error floor, the error curve for MBM sharpens with increasing SNR.

B. MBM Deployment in Gateways for Single Antenna Client Nodes
In certain applications, such as wireless sensor networks (WSN) and the internet of things (IoT), constraints on complexity or size necessitate using a single antenna at each receiver node.Employing MBM at the gateway in these cases allows for (asymptotically) reaching ergodic capacity in the downlink connection, resolving deep fade issues.Using MBM at the gatways, where constraints are less stringent, shifts the complexity away from the end-user nodes which continue to use a single antenna.
Uplink error performance can be improved by adjusting the trade-off between power and spectral efficiencies, which is justifiable when the bulk of the traffic is in the downlink.Scenarios requiring low downlink latency, like dispatching time-sensitive control signals for emergencies, also benefit from this approach based on MBM.Additionally, in many WSN/IoT applications with stationary gateway and client nodes, MBM is ideal due to its ability to address deep fades and ease of constellation tracking in a static channel.

C. Application of MBM for Enhanced Physical Layer Security
Physical layer security (PLS) has been developed to address challenges associated with traditional cryptography techniques [76].Except for [15], known PLS techniques rely on two categories of information-theoretic existence results, as presented in [77] and [78], respectively.For instance, [79], [80], [81], and [82] explore the application of IRS in physical layer security, where [79], [80], and [81] rely on [77] and [82] on [78].A critical, yet often overlooked, point is the challenge associated with realizing the information theoretical bounds (reported in [77] or [78]) that underpin most PLS techniques.
In the context of error-free communication, Turbo-like codes are known to approach capacity upper bounds within a fraction of a dB.However, in PLS, quantifying the implications of the gap to the theoretical bound corresponding to secure capacity (for methods based on [77]) or the leakage of information (for methods based on [78]) is not straightforward.The crucial distinction between reliable and secure communication is that in error-free communication, a gap to capacity bounds merely indicates slightly sub-optimal power efficiency compared to best theoretically achievable value, which does not undermine the goal of reliable communication.However, a gap to information theoretical bounds reported in [77] and [78] implies that perfect secrecy is not achieved.Unlike the case with the reliable communication, the implication of such a compromise in secure communication is not yet well understood.
A category of PLS schemes leverages reciprocity in wireless channels to establish two sets of dependent random variables, denoted as S 1 and S 2 (referred to as common randomness), at the two ends of a wireless link.The existence results presented in [78] indicate that it is possible to extract two identical strings of bits at the link's endpoints.These identical bit strings are then employed as an encryption key in a symmetrical encryption scheme, such as the advanced encryption standard (AES).In addition to the uncertainty associated with relying on information-theoretic existence results, another challenge arises when dealing with slow-fading channels.The limited amount of common randomness available over such channels restrics the rate of encryption key generation.These problems are all resolved in [15], relying on an MBM structure.Note that, in the case of using IRS as a PLS tool, the gain arises from reflecting (beam-forming) the fraction of the transmitted signal that is incident on the IRS panel.However, in the case of using MBM as a PLS tool, an unconditionally secure (quantum-safe) random key is established without relying on any information theoretical existence results [15].This is the only reported approach among PLS techniques as it provides unconditionally secure keys using simple, and widely used transmission techniques for handling issues such as error correction, carrier recovery, synchronization, etc. Alternative PLS techniques rely on information theoretical existence results, yet often overlook the important aspect of how these theoretical results can be practically implemented.
Reference [15] introduces a practical PLS method using an MBM structure for the exchange of information-theoretically secure encryption keys between two legitimate nodes.Initially, several reciprocal phase values are measured at both nodes.Each shared phase value then masks points of a PSK constellation by rotating each PSK constellation with the respective shared phase value.This rotation, which is equivalent to adding phases modulo-2π, ensures confidentiality since the channel phase is uniformly distributed in [0, 2π) and the summation divulges no information about the individual summands.Techniques known for reliable data transmission, such as forward error correction, timing/frequency synchronization, I/Q imbalance correction, etc., can be effectively integrated with the method of [15] to counteract noise and other imperfections.Consequently, two identical bit strings are derived from the noisy shared phase values.To increase the key size over a static or slow fading channel, the RF propagation path is perturbed using an MBM structure.These perturbations generate multiple independent realizations of multi-path fading, with each MBM configuration sharing a new phase value.
To intercept a phase value shared in this manner, the Eavesdropper (Eve) encounters an under-determined system of linear equations, which does not reveal any useful information about its actual solution value.The information-theoretical (unconditional) security of this method is mathematically proved, and measurement results are provided to demonstrate the efficacy of the proposed key-sharing system [15].
Reference [82] employs IRS to augment randomness within the wireless link, leading to an increased key rate over a static channel.However, this technique not only depends on the existence results of [78] but is also challenged since a considerable portion of the transmitted RF energy reaches the destination unaffected by the deployed IRS.This is in contrast to the PLS method leveraging MBM [15], where the energy is contained within the MBM closure and encounters multiple reflections prior to exiting the transmitter.The randomness resulting from these reflections is intensified as the outgoing signal propagates through the multi-path environment toward the second node.An additional benefit of the method outlined in [15] is that, due to the implementation of MBM, the key generation rate is determined by the ergodic capacity of the underlying channel, which is markedly higher than the outage capacity, as previously discussed in this article.
In summary, the use of the MBM structure serves dual purpose: it not only improves reliable communication but also to provides a practical framework for securely generating and sharing encryption keys of an arbitrarily large size.Importantly, employing MBM for secure communication does not require extensive training using a large number of pilots. References [83], [84], [85], and [86] feature a number of elegant approaches to leverage MBM for PLS.

D. Application of MBM in Federated Learning
In conventional frameworks for implementing federated learning (FL) over wireless channels, a portion of edge devices inevitably encounter deep fade, and consequently should be excluded from the FL algorithm.Reference [87] adopts MBM to manipulate the wireless channel in the context of FL.This is accomplished by conducting over-the-air computation (OAC) in multiple phases, during which a distinct MBM channel state is chosen for each phase.Given that the channel gains for each edge device vary across subsequent phases, the likelihood of an edge device encountering deep fade in all phases is significantly reduced.The findings demonstrate that this method of channel randomization allows for increased participation of edge devices in the FL process, subsequently resulting in enhanced computational accuracy.

E. Application of MBM in Randomized Beam Forming
It is well-established that by introducing random variations in the channel gain, slow fading can be mitigated [88].Assuming that each transmission in a coded block undergoes a new and independent fading value, it follows that a rate equal to ergodic capacity can be achieved, with a zero outage probability.The MBM structure serves as an ideal solution for inducing such channel randomization.As the RF energy is confined within the MBM enclosure, the wireless signal repeatedly reflects off different walls before exiting the MBM transmitter.This characteristic diminishes the statistical Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
dependency among various channels realized by distinct MBM configurations.
It is worth noting that in such applications, the MBM enclosure can be effectively combined with conventional modulation schemes, such as orthogonal frequency-division multiplexing (OFDM) or orthogonal frequency-division multiple access (OFDMA).Reference [15] presents a method for altering the MBM configuration during the cyclic prefix in a way that does not impact channel measurements used for equalization.Subsequently, one can rely on successive bursts of OFDM symbols, where each burst is equipped with its dedicated OFDM training preamble, and apply a channel code that spans multiple OFDM bursts (each burst experiencing a different channel realization/gain).Since, due to using MBM, channel gains in successive transmissions will be independent, such a system achieves a diversity order equal to the number of OFDM bursts.It is important to note that by employing conventional OFDM signaling, challenges associated with MBM signaling, such as channel learning, tracking, decoding, and bandwidth expansion, can be effectively addressed (as is common practice in OFDM signaling).

VIII. CONCLUDING REMARKS
Recently, several innovative ideas have emerged that demonstrate benefits when a radio frequency signal is selectively modified after being transmitted.Among the most notable examples are "index modulation," with media-based modulation as a particular case, and "intelligent reflecting surfaces."Media-based modulation provides unparalleled power/bandwidth efficiency improvements while employing a simple transmitter that emits a carrier.The random placement of constellation points across receiving dimensions helps to cope with deep fades and can achieve negligible error rates using simple forward error-correcting codes.
Despite these advantages, media-based modulation faces challenges and limitations that warrant further research.These challenges include: 1) spectral growth resulting from the time-varying nature of the transmit unit, which necessitates the development of new filter design techniques that can be integrated within the media-based transceiver; 2) training for large-size constellation sets is a complex task.Parametric channel models, with a minimal number of parameters, should be used to capture channel variations over time.
is at minimum Euclidean distance to y.The successive cancellation decoder makes a decision about the transmitted symbol over a single modulator unit, subtracts this estimate from the received signal, and continues the process recursively until all messages (corresponding to all transmit units) are recovered.
Denote the code-book comprised of all the constituent vectors for all transmit units by U := ∪ N −1 i=0 H i .Initially, at decoding step t = 0, the decoder search through all the fading gains in the set U to find Let n[0] denote the transmit unit corresponding to the estimate g[0] recovered at step t = 0, i.e., g[0] ∈ H n [0] .Therefore, we set For decoding step t = 1, the received signal is updated according to y[1] ← y − g[0], and since the message corresponding to unit n[0] is already recovered, the search space for the next constituent vector is limited to the smaller set U \ H n[0] , i.e, ← g [1].
The general update rules for step t are h The decoding is concluded at step t = N − 1, where estimates ) for the constituent vectors corresponding to all transmit units, and consequently, ( m[0], . . ., m[N − 1]) are recovered.

B. Improved List Decoder
Successive cancellation decoding may suffer from error propagation due to decision errors in intermediate steps.As a remedy to error propagation, we maintain a list of L unique candidates.A larger list size improves the error performance at the cost of higher complexity.
Consider a list of candidates, where each candidate comprises sequences of the form ( m[0], . . ., m[N −1]) of tentative solutions for symbols transmitted over the N transmit units.At each step t, exactly one constituent vector for each candidate is recovered.The constituent vector recovered for the jth candidate at step t = 0 satisfies g[0, j] ← arg jth min Here, n[t, j] denotes the index of the transmit unit associated with the estimate g[t, j], i.e., g[t, j] ∈ H n[t,j] .At a general step, t ̸ = 0, each candidate uses the same successive cancellation decoder independently of other candidates to obtain an estimate for a new constituent vector: h Once the list decoder concludes the last step t = N − 1, the candidate in the list which is closest to the received signal y (in terms of the Euclidean distance) is chosen as the final decoded message.

APPENDIX B TIME-LIMITED PULSE DESIGN
The solution maximizing the ratio η is given by the characteristic function corresponding to the smallest characteristic value λ of the following Fredholm integral equation: Particularly, p(t) is the first characteristic function corresponding to the smallest characteristic value λ for the Sinc kernel.
The series expansion of the solution is according to where J n+1/2 (t) is Bessel function of order n + 1/2, and coefficients a n are determined from set of linear equations of the form

APPENDIX C ANALYTICAL BOUNDS ON AVERAGE SYMBOL ERROR PROBABILITY
This section provides tight analytical bounds on MBM symbol error probability averaged over the sample space of channel gains and AWGN.

A. Upper Bound
Using maximum likelihood decoding, given that message m = 0 is transmitted, (i.e.fading vector h 0 is projected at the receiver), a decoding error occurs if ∥y − h i ∥ 2 ≤ ∥y − h 0 ∥ 2 for some i ̸ = 0. Let ϕ(h 0 , h i ) denote the pairwise error probability between h 0 and h i , given h 0 is sent.Since h 0 and h i are distributed normally, the squared Euclidean norm of their difference follows a chi-squared distribution with n = 2K degrees of freedom.Therefore, the exact pairwise error probability averaged over the ensemble of MBM realizations is computed as Here, E indicates averaging over the ensemble of MBM constellation (channel realizations), f (z; n) is the probability density function for chi-squared distribution with n degrees of freedom, and Q is the tail distribution function of the standard normal distribution.Note that E[ϕ(h 0 , h i )] is independent of h 0 and h i .Therefore, we use simplified notation E[ϕ] := E[ϕ(h 0 , h i )].
Reference [89] provides a closed form bound on pair-wise error probability E[ϕ], which is given by c/π Γ n+1 Applying the bound given in [90] for Gauss hyper-geometric function, we get Using the union-bound, the average probability of error over the ensemble of media-based constellations is bounded by Equation (45) demonstrates that an uncoded MBM achieves diversity gain d = K − r, while maintaining multiplexing gain equal to r with data rate R = log M = r log SNR.

B. Lower Bound
Given h 0 is transmitted, the pairwise error probability between h 0 and its closest neighbor in the constellation set, h ′ , provides a lower bound on the symbol error probability.The probability density function for Euclidean distance ||h ′ − h 0 ||, of closest neighbour to the transmitted point, is obtained using ordered statistics.Therefore, the lower bound on the expected probability of symbol error averaged over MBM channel realizations is given by where F (z; n) denotes the cumulative density function for chi-squared distribution with n = 2K degrees of freedom.

A. MDS Codes and Information Sets
Let ∆ denote an (N c , K c , D) code over alphabet A. Here, N c , K c , and D, respectively, denote the code block length, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Reference [51] defines the concept of "information set".Let J(N c ) := {1, 2, . . ., N c }.A subset of coordinates I ⊆ J(N c ) is an information set if, in the projection 7 of the codewords over I, every possible |I|-tuple of elements (i.e., |I|-fold Cartesian product of alphabet A) occurs exactly once.Reference [51] proves that for any MDS code of dimension K c , any subset of coordinates with size less than or equal K c is an information set.In other words, an MDS code ∆ has the property that for any K c -tuple of elements of A on any given K c coordinates, there is a unique codeword of ∆ which agrees with these K c -tuple on the given K c coordinates.We refer to this property as the "maximum information property" (MIP).
A consequence of codes satisfying MIP is that the coded symbols in each coordinate I with |I| ≤ K c are independent of each other.Each coordinate reveals the same amount of log 2 q bits of information about the coded message.This in turn means that each of the q constellation points occurs with probability 1/q.Noting that the assignment of constellation points to q code alphabets is one-to-one and random, we can conclude that the constellation points in the ∆ positions (selected by various codewords in a code satisfying MIP) are independent of each other.This property is used in the decoder analysis section to show that using simple MDS codes in MBM increases the diversity order.An example of MDS codes satisfying MIP is Reed-Solomon codes.

B. Encoder Mapping
Given an MDS code over Galois field GF (q), the sequence of symbols forming a codeword in ∆ are mapped into sequences of MBM constellation points.We take the cardinality of MBM constellation set, equal to the Galois field size, i.e., M = q.This requires a transmitter equipped with log 2 q 7 See [51] for definition and further details.RF mirrors.Then, for every u ∈ ∆, the projected sequence of points at the receiver are of the form (h u [1] , . . ., h u[Nc] ), (47) where for all 0 ≤ i ≤ N c −1, 0 ≤ u[i] ≤ q−1, h u[i] ∈ H.In a nutshell, encoder operations include: 1) mapping a message from the set 1, 2, .., M Kc into an MDS codeword u ∈ ∆; and 2) mapping the MDS codeword u into a sequence of MBM constellation points, (h u [1] , . . ., h u[Nc] ).

C. Error Probability Analysis: Hard-Decision Decoder
This section studies the word error probability of MDScoded MBM over the sample space of the ensemble of media-based constellation sets and AWGN.We use the method developed in [91] for bounding the tail probability of weakly dependent random variables.The decoder is assumed to use hard-decision error correction.A code with minimum distance D is capable of correcting t errors up to t = ⌊(D − 1)/2⌋.
For the codeword u ∈ ∆, the noisy projected received sequence at the receiver is of the form Initially, for each coordinate i, 1 ≤ i ≤ N c of the received vector, the decoder finds the closest point in the constellation set to the received signal y[i].This results in the estimate sequence ( h[1], . . ., h[N c ]) for channel gains and an associated message sequence u := ( u[1], . . ., u[N c ]) which is not necessarily a valid codeword in the set ∆. Subsequently, a hard-decision MDS decoder (e.g.Reed-Solomon) corrects for the errors in u.
Let (e[1], . . ., e[N c ]) be the error indicator vector, where Note that the events {e ≥ t+1} and {S t+1 (e[1], . . ., e[N c ]) ≥ 1} are identical.The reason is, if the number of coordinates in error is less than or equal to t, the value of the polynomial S t+1 is zero; Conversely, if the number of errors is greater than t, S t+1 will take a value equal or greater than one.By Markov's inequality Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
The above expectation is over AWGN noise and the ensemble of MBM constellation sets.Next, we use the property of MDS codes where symbols in any set of coordinates of size less than code dimension, K c , are independent of each other.Taking t + 1 ≤ K c , we can write Equation ( 55) follows because: 1) MDS code property that symbols in any t+1 ≤ K c coordinates are independent of each other; and 2) AWGN noise is independent across coordinates.Equation ( 56) follows, noting that AWGN, message symbols, and fading gains have identical distribution across all the coordinates of a codeword.The exponent in (58) shows that applying an MDS code with an error correction capability of t to MBM achieves a diversity order equal to (t + 1) × K (using a single transmit unit).

Fig. 4
shows a N × K layered MBM system.The incoming data is demultiplexed into N streams transmitted over separate media-based transmit units.Each unit independently modifies Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

Fig. 5 .
Fig. 5. 2 × 8 and 2 × 12 LMBM schemes rely on 8 RF mirrors in each of the 2 modulator units.4 × 8 and 4 × 12 LMBM schemes rely on 4 RF mirrors in each of the 4 modulator units.SIMO-MBM uses 16 RF mirrors in a single MBM modulator unit.All schemes transmit 16 bits per channel use in a single transmission without any FEC.

Fig. 7 .
Fig.7.Performance of 4×16 LMBM, uncoded vs. coded using a single parity check SPC(Nc, Kc) code, and Reed-Solomon code RS(Nc, Kc, D).These channel coding schemes act upon MBM symbols.R indicates the effective transmission rate in bits per channel use.Error probability corresponds to block error probability and symbol error probability for the coded and uncoded schemes, respectively.

Fig. 8 .
Fig. 8. Block error probabilities for 4×16 LMBM coded with Reed-Solomon codes acting on LMBM symbols.R indicates the effective transmission rate in bits per channel use.

Fig. 11 .
Fig. 11.Symbol error probability comparison for schemes achieving transmission rate equal to 12 bits per complex channel use using 12 receive antennas.

Fig. 13 .
Fig. 13.Outage probability of 2 × 2 MBM compared with 2 × 2 SBM (legacy) MIMO, targeting a transmission rate equal to 6 bits per complex channel use.The number of RF mirrors used in MBM is 8.

Fig. 14 .
Fig. 14.Outage probability of 1 × 4 MBM compared to 2 × 4 and 4 × 4 SBM (legacy) MIMO, targeting a transmission rate equal to 8 bits per complex channel use.The number of RF mirrors used in MBM is 9.
optimum time-limited pulse minimizes the energy outside of the allocated frequency band [−B, B].In other words, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
) The top and bottom of the antenna's cylindrical shape are left open.Consequently, part of the energy of the radio frequency wave leaves the transmitter through the top/bottom openings.This, in turn, reduces the antenna gain in the horizontal plane.2) It lacks any receive (RX) antenna.Fig. 19 and 20 show the new antenna structure designed to address the above shortcomings.The new structure includes: 1) metallic reflectors closing the top and the bottom; and 2) each wall includes a receive (RX) antenna.

Fig. 18 .
Fig. 18.Overall structure of a transmitter with multiple transmit antennas.

Fig. 21
Fig. 21(c) shows the transmit (TX) antenna placed at the center of the new structure and fixed to the bottom cap.TX antenna is designed to generate an Omni-directional pattern (see Fig. 21(a)) in the absence of the other parts.Next, we explain the reason for choosing Omni-directional pattern.Due to the symmetry of the antenna walls along the spherical angle ϕ (i.e., in the X-Y plane), it is desirable to have a transmit pattern with a similar spherical symmetry.Such symmetry guarantees that each of the 12 RF walls is exposed to (approximately) the same amount of RF energy.Consequently, when switched on and off, each RF wall has (approximately) the same impact on the outgoing RF signal.Accordingly, the transmitter can provide coverage for any receiver located at an angle of ϕ ∈ [0, 360 • ] (with respect to the transmit unit).The two metallic reflectors/closures, called metallic caps hereafter, are responsible for constraining the radiation in the horizontal directions -compare the TX pattern in Fig.21(a) vs. the one in Fig.21(b).In the new design, each wall includes three building-block columns, one large metallic rectangular patch on the interior, and a single RX antenna on the exterior.Each building-block column comprises thirteen small RF patches.The thirteen small patches in each building-block column are connected using RF switches (PIN diodes).RF switches corresponding to each column can be independently controlled (turned on/off).When the switches on a given building-block column are on (low impedance connection), the corresponding patches form a connected metallic strip that reflects the incident wave to the interior of the antenna structure.If the switches are off, the incident wave results in an RF signal propagating outside the antenna structure (i.e., the corresponding building block column acts as if it were transparent to the incident wave).To optimize the geometry of each wall, one needs to devise a computational method to find an initial approximate solution (with acceptable performance) in a reasonable time.Then, one

Fig. 19 .
Fig. 19.Antenna structure: (a) some components, plus a partially assembled antenna structure, (b) fully assembled antenna structure.There are twelve walls, each with three building block columns of switchable parasitic elements and one receive antenna in each wall.Building block columns, in total 36, are controlled independently.

Fig. 20 .
Fig. 20.Antenna structure: (a) view from the top, (b) view from the bottom, (c) view from the inside -including indexing of walls used in TableV.

Fig. 21 .
Fig. 21.Pattern of the transmit antenna: (a) in the absence of the top and bottom metallic closures, (b) in the presence of the top and bottom metallic closures shown in (c).

Fig. 22 .
Fig. 22.(a) An RF building block with RF switches being open (approximated as "open circuit").(b) An RF building block with RF switches being closed (approximated as "short circuit").(c) Periodic repetition of the RF building block in (b), i.e., with switches being closed.

Fig. 23 .Fig. 24 .
Fig. 23.Simulation results for the rectangular patch in two states of on and off: (a) transmission and (b) reflection.In these simulations, dimensions of the basic patch (optimized relying on periodic extension) is 4 mm by 5 mm.Upon integrating this initial patch geometry within the rest of the antenna structure, and further tuning, the final patch dimensions are set at 5.6 mm by 6 mm.

Fig. 27 .
Fig. 27.S 11 of the TX antenna, with optimized caps, for 7 different walls' states mentioned in Table V (HFSS simulation).

Fig. 28 .
Fig. 28.S 11 of the TX antenna (with optimized caps) for some configurations of on/off switches (measurement results).

Fig. 29 .
Fig. 29.RX antenna (refer to Table VI for values of optimized dimensions).
L s = 0.45 nH.The diode die itself is modeled by a parallel RC circuit in which values of the capacitor, C d , and the resistor, R d , depend on the diode state.Since R d in the on state (forward bias) is very small, i.e., ≃ 0, and in the off state (reverse bias) is very large, i.e., ≃ ∞, it turns out that only the value of C d in the off state affects the simulation outcome.Referring to MP1320-040LF application note 5 , the value of C d in the off state (reverse bias capacitance) is set at 0.23 pF.Exact values for R d ≃ 0 in the on (forward bias) and R d ≃ ∞ in the off (reverse bias) states do not affect the simulation outcomes.However, in the HFSS simulations, we have used R d (forward bias) =1 Ohm and R d (reverse bias) =10 MOhm.

Fig. 31 .
Fig. 31.Pattern of a receive antenna in the presence of the entire antenna structure.

Fig. 33 .
Fig. 33.S 11 of a periodic structure composed of patch elements with slots added for the purpose of filtering.

Fig. 35 .
Fig. 35.(a) Antenna pattern when half of the walls are ON and half are off.(b) Antenna pattern without the surrounding walls (top and bottom caps are in place).
Such channel models could assist in tracking the coordinates of MBM constellation points over time.Novel training signals must be designed to efficiently and accurately update the underlying model parameters while minimizing training overhead.APPENDIX A LMIMO-MBM SUCCESSIVE CANCELLATION LIST DECODER A. Successive Cancellation Decoder In the presence of AWGN z, for a received signal y = N −1 n=0 h n m[n] +z, an optimum decoder aims to find a message sequence ( m[0], . . ., m[N − 1]) such that the point c where c := SNR/2 and 2 F 1 (., .; .; ) indicates Gauss hypergeometric function.

Fig. 36 .
Fig.36.Upper and lower bounds on the probability of error for 1 × 8 SIMO-MBM at rate R = 16 bits per complex channel-use.

TABLE I REQUIRED
TRANSMIT ENERGY TO ACHIEVE SNR EQUAL TO 20 DB AT THE RECEIVER FOR THE GIVEN OUTAGE PROBABILITY WITH 256QAM OVER A RAYLEIGH FADING CHANNEL

TABLE II SYSTEM
SPECIFICATIONS FOR FIG.

TABLE IV ANTENNA
RADIATION PARAMETERS AT 5.8545 GHZ FOR FLAT CAPS (CASE 1) AND FOR CAPS WITH OPTIMIZED CURVATURES (CASE 2).MAXIMUM GAIN VALUES ARE COMPUTED OVER A PARTIAL SPHERICAL FAR-FIELD SURFACE WITH θ DEVIATING ±20 • FROM THE HORIZONTAL PLANE.ACCEPTED POWER ACCOUNTS ONLY FOR THE IMPACT OF S 11 .RADIATED POWER ACCOUNTS FOR THE IMPACT OF S 11 AND THE WASTE OF ENERGY IN THE ANTENNA STRUCTURE.RADIATED POWER IS COMPUTED BY INTEGRATING THE ENERGY FLUX DENSITY, I.E., THE POYNTING VECTOR, OVER A SPHERE (AT FAR-FIELD) SURROUNDING THE ENTIRE ANTENNA STRUCTURE.EFFICIENCY IS DEFINED AS THE RATIO: RADIATED POWER/INCIDENT POWER TABLE V DIFFERENT WALLS' STATES SELECTED FOR SIMULATION OF S 11 IN FIG. 25 AND 27.EVEN THOUGH EACH OF THE THREE RF BUILDING BLOCKS FORMING A WALL CAN BE SWITCHED IN FIGS.25, 27 AND 28, ALL SWITCHES ON ANY OF THE WALLS (1 TO 12) HAVE THE SAME STATE (I.E., ALL THREE BUILDING BLOCK COLUMNS ON A GIVEN WALL ARE ON FOR VALUE 1, OR ALL THREE ARE OFF FOR VALUE 0) Fig. 26.The curvature of the proposed cap.

TABLE VI RX
ANTENNA DIMENSIONS REPORTED IN MILLIMETERS

TABLE VII TX
ANTENNA DIMENSIONS (IN mm)