Performance of Full-Duplex Cooperative NOMA With Mode Switching and an EH Near User

This letter investigates a cooperative non-orthogonal multiple access network where a near user (NU) harvests energy using time-switching (TS) or power-splitting (PS) protocol to assist information transmission to far user (FU). Considering nonlinear energy harvesting and opportunistic cooperative mode (CM) to non-cooperative mode (NCM) switching, expressions are derived for FU and NU outage probabilities and throughput. We demonstrate that CM/NCM switching can guarantee NU’s performance similar to OMA without any degradation in FU throughput. Also, the choice of optimum PS/TS parameter is essential to maximize FU throughput while ensuring desired NU throughput. CM/NCM switching ensures higher energy efficiency.


I. INTRODUCTION
T HE EXPEDITIOUS growth in the Internet of Things (IoT) devices and high-speed mobile applications in modern generation wireless networks has escalated the demand for high data rates, increased spectral efficiency (SE), and low energy consumption [1].Non-orthogonal multiple access (NOMA) and full-duplex (FD) signaling have shown tremendous potential to meet these requirements.NOMA allows multiple users to share the same time and frequency resource.On the other hand, FD ensures higher SE by enabling simultaneous reception and transmission in same frequency band [2].
For wider coverage and enhanced reliability, the use of cooperative-NOMA (C-NOMA) has been studied where the near user (NU) assists in information transmission (IT) to the far user (FU) [3] using its own energy.However, this can be an issue when the NU is an IoT node with limited battery energy.To ensure a long battery lifetime at NU, energy harvesting (EH) can be used.To overcome the energy constraint, time-switching (TS) and power-splitting protocols were developed.Simultaneous wireless information and power transfer (SWIPT) in C-NOMA was investigated in [4].In [5], the data rate of the NU was maximized by optimizing the PS ratio and the beamforming vector in a cooperative multipleinput single-output SWIPT network.In [6] and [7], the ergodic rate of a C-NOMA system was derived with a FD NU using TS and PS protocols for EH respectively.However, they assume a simple linear EH (L-EH) model.
In practice, the energy conversion efficiency (ECE) of EH circuits is limited due to the use of nonlinear (NL) devices like diodes and transistors.Therefore, the harvested energy is always constrained to a saturation threshold [8].Further, in C-NOMA (where NU assists FU), the performance of the FU depends a lot on the decoding status at NU. Sometimes, both NU and FU may lose out on their performance due to unsuccessful decoding of FU's symbols at NU [9].In case of SWIPT based C-NOMA, NU decodes the FU symbol first then performs successive interference cancellation (SIC) to decode its own symbol.In case of unsuccessful decoding of NU's symbol, NU cooperates with FU by relaying its symbol, which leads to performance loss for NU in terms of SE and energy efficiency (EE) (NU uses the harvested energy to relay the FU's symbol) [6], [7], [10], [11].However, using cooperative mode/non-cooperative mode (CM/NCM) switching1 at NU may help both users attain a good QoS.This CM/NCM switching at NU can allow more power to be allocated to FU while ensuring a good QoS at NU.A C-NOMA network in which a FD NU with EH capabilities assists IT to an FU with CM/NCM switching2 has never been studied with a practical NL-EH model.Therefore its performance needs to be analyzed.This is due to its potential applications in wireless sensor networks where a node uses its own battery to assist the information transmission to distant nodes.The major contributions are listed as follows: • Considering CM/NCM switching and both TS and PS protocols with NL-EH at NU, we derive the expressions for outage probability (OP) and throughput of both NU and FU in closed-form.We then show that with CM/NCM switching, NU performance does not degrade because of the cooperation.• We also derive expressions for outage probabilities at NU and FU for the L-EH case (as a special case of NL-EH) and demonstrate that NL-EH causes a diversity loss at FU. CM/NCM switching ensures that performance at NU remains the same as in a network (similar to OMA) in which FU is absent.• Further, we demonstrate that an optimum value of TS/PS parameter exists, which maximizes FU throughput while simultaneously guaranteeing the desired NU throughput.• We then demonstrate that the use of CM/NCM switching ensures better RSI immunity with higher EE.
II. SYSTEM MODEL We consider a C-NOMA network consisting of a base station (S), a full-duplex NU (U n ), and a FU (U f ).S shares a direct link to communicate with U n , while U n harvests the energy to assist the IT to U f .The S −U f link is not considered due to severe shadowing [6].S and U f are equipped with a single transmit antenna and a single receive antenna, respectively.To allow FD capabilities, U n is equipped with two separate antennas, one for transmission and the other for the reception.Either the TS or PS protocol is used for harvesting energy at U n3 .
Let h ab ∼ CN (0, 1/λ ab ) denotes the channel coefficient between any two nodes a and b with a ∈ {s, n}, b ∈ {n, f}.
Here, λ ab = d θ ab , with θ denoting the path-loss exponent and d ab is the distance between node a and b.The self-interference (SI) channel at U n is denoted by h nn ∼ CN (0, 1/λ nn ).With recent advancements in analog and digital cancellation, SI suppression up to 110 dB has been achieved [12].For this reason, the residual SI (RSI) E[|h nn | 2 ] is very small, and as in [13], |h nn | 2 is replaced by its mean λ nn .
Denote the TS parameter, PS parameter, and the signaling frame interval by α, ρ and T, respectively.In the PS protocol, the received signal power at U n is partitioned according to the power ratio ρ : 1 − ρ for EH and IT, respectively.In the TS protocol, each signaling frame interval T is divided in the time ratio of α : 1− α for EH and IT, respectively.Note that 0 < ρ, α < 1. S is assumed to have knowledge of the average channel gains.Also, energy requirement for information decoding and threshold activation at R is negligible compared to the energy needed for IT [13].The EH circuit exhibits NL characteristics.With these considerations, this letter analyzes the performance of TS/PS EH protocols in a C-NOMA network.

A. PS SWIPT
A linear combination of unit-energy symbols s n (k ) and s f (k ) is transmitted to U n and U f , with symbol energy Q s and symbol rate R s .The superposed signal is s , where the transmit power of S, i.e., P s = Q s R s is apportioned into U n and U f in the ratio a n :a f , with a f = 1 − a n .
The FD NU decodes s f (k ) and s n (k ).After decoding, it transmits the symbol s f (k − δ) to U f , where δ ≥ 1 denotes the processing delay.The signal received at , where Q n,PS is the transmit energy available at U n , and w n,a ∼ CN (0, σ 2 n,a ) is the additive antenna noise.
Due to the use of PS protocol, a part k ) is available for decoding information.With this, the sampled matched filter output at U f is given by (1)

B. TS SWIPT
In the duration αT , S transmits symbols to U n for EH.The signal received at where w n,a ∼ CN (0, σ 2 n,a ) is the additive antenna noise.In the IT phase, S and U n transmit at the same time.For IT, the received signal at U n is given by y IT n,TS = h sn s(k ) + Q n,TS h nn s f (k − δ) + w n , where δ ≥ 1 denotes the delay in processing, and w n ∼ CN (0, σ 2 ) represents the additive noise at U n .The sampled matched filter output at U f is given by is the additive noise at U f .

C. Energy Harvesting Model
A practical NL-EH model is considered capturing the saturation characteristics of the EH circuit [14].Having overlooked the insignificant antenna noise [13], the available energy per symbol interval for EH in case of PS and TS is and Q h = ηQ th otherwise, where η is the ECE, and Q th denotes the saturation threshold.Additionally, we present unified expressions for harvested energy and SNRs for both the EH protocols (TS and PS).
where C 1 , C 2 , and C 3 are as defined in Table I.Note that L-EH is a special case that follows when where γ th = Q th /σ 2 and γ s = Q s /σ 2 .The SINR to decode s n (k ) (after performing SIC) is given by The received signal at where w f ∼ CN (0, σ 2 ) represents the additive noise at U f .
The signal-to-noise ratio (SNR) at U f can be expressed as Non-Cooperative Mode: If in the initial training phase U n is not able to successfully decode the symbols s n and s f intended for U n and U f respectively, it sends a one-bit feedback to S, which then switches to NCM and transmits the U n symbol with energy Q s (Table II presents the decoding based switching strategy).The received symbol at

III. OUTAGE PROBABILITY (OP) AND THROUGHPUT
In this section expressions are derived for OPs p switch n and p CM n with and without switching (respectively) of U n and similarly p f of U f .This will allow the comparison of performance with and without switching.The threshold SNR at NU is Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE II DECODING BASED SWITCHING STRATEGY
denoting target rates of NU and FU symbols, respectively.For ease of exposition, we use |h sn | 2 = X , and The OP at U n in the case of CM/NCM switching at NU for the considered FD C-NOMA network with NL-EH is given by 4 where I 1 , I 2 , I 3 ,I 4 ,I 5 and I 6 are expressed as follows where μ 1 = max( Proof: The detailed derivations for I 1 , I 2 , I 5 , I 6 , I 7 and I 8 are provided in the Appendix. Remark 1: It is evident from (7) that the OP at U n for the FD C-NOMA network without using CM/NCM switching is given by (14) Remark 2: The closed-form expression for the OP of NU in the L-EH case can be obtained by substituting Q th = ∞ into (7), and is given by p CM n = 1 − exp( −λsnΘ 1 C 1 γs μ 1 ).Remark 3: The OP of U n using NCM technique can be expressed as 4 Superscript CM, NCM and switch represent the case of cooperative mode, non-cooperative mode and switching between them, respectively.
Lemma 2: The OP of U f for the FD C-NOMA network with NL-EH is given by where I 7 and I 8 are expressed in closed form as and , and E 1 (•) denoting the exponential integral of type 1.
Proof: For the NL-EH model, the OP of U f is given by ( 16), where Γ nf, and Γ ff, are given by ( 4) and ( 6), respectively.For a detailed derivation of I 7 and I 8 , refer to the Appendix.
Remark 4: The expression for the OP of FU in the L-EH case can be obtained by substituting Therefore, the OP of FU in the L-EH case is given by (19) Remark 5: At higher transmit powers, the saturation threshold γ th causes an outage floor in FU performance.This outage floor can be established by deriving an asymptotic expression of p f by substituting γ s → ∞ into (16), where I 7 and I 8 are expressed in (17) and (18), respectively.An asymptotic expression for p f is given by p f 1 − exp(− λ nf γ f ηγ th C 2 ).Clearly, the saturation threshold γ th = Q th σ 2 limits the performance of FU at high SNRs.
The throughput of U f in bits per channel use (bpcu) is given by τ f = R f κ(1 − p f ).For CM/NCM switching at NU, the throughput is given by where The EE of the considered C-NOMA system in bpcu per Joule can be expressed by the ratio of sum-throughput (τ j n +τ f ) to the total energy used, and is given by IV.THE OPTIMIZATION PROBLEM Since the NU harvests the energy from S and then uses this harvested energy for communicating the information symbols to FU, when the TS or PS parameter is very small, the harvested energy is very small and sometimes not enough for the U n -U f transmission.While the large value of the EH parameter also results in lower FU throughput.Therefore, the careful choice of the TS or PS parameter is necessary to attain a good QoS at FU while ensuring the desired target QoS at NU.
In order to guarantee the desired target throughput τn at NU, we first substitute τ  determine a n .Unfortunately, with CM/NCM switching at NU, solving for τ switch n = τn does not yield a closed-form expression for a n (numerical techniques need to be used).However, when switching is not used at NU, we solve for τ CM n = τn by linearly approximating the exponential terms in I 1 and I 2 to obtain where can be evaluated.Now, the choice of TS or PS parameter is essential to maximize the FU throughput.Therefore, the optimization problem is where A * 1 (as seen in Table I) denotes the optimal TS/PS parameter that maximizes τ f .Also, τ f is a concave function of A 1 , which can be established by verifying ∂ 2 τ f ∂A 2 1 < 0 (details are omitted for brevity).Due to the presence of complicated logarithmic terms in (16), solving for ∂τ f ∂A 1 = 0 to obtain a closed-form expression of A * 1 is not possible.However, A * 1 can be obtained employing an offline numerical search.
V. SIMULATION RESULTS In this section, accuracy of the derived analytical expressions is validated using extensive Monte Carlo simulations.Unless mentioned otherwise, the used parameters are as follows: Fig. 1(a) and (b) depict the OP vs. P s (dBm) for TS and PS EH protocols, respectively.For NU, the OP is shown for two cases 1) with CM/NCM switching derived in (7), and 2) without CM/NCM switching given by (14).With both TS and PS EH protocols at NU, with CM/NCM switching, NU attains the same performance as with OMA irrespective of the choice of TS/PS parameters.While, for the case without CM/NCM switching, NU outage performance remains inferior to that of OMA.Performance of NU with TS protocol does not get influenced by the choice of the TS parameter, whereas in the case of PS EH, the OP at NU depends on the choice of PS parameter.At FU, for the lower transmit powers, the OP significantly improves, while at higher powers, the saturation threshold γ th causes an outage floor.When compared to the L-EH model at NU, both L-EH and NL-EH result in almost similar performance at low transmit powers, whereas, for higher powers, the transmit power of U n is limited by NL-EH, which causes a diversity loss to FU.Also, the performance of FU significantly relies on the choice of EH parameters α and ρ.Therefore, optimum choice of EH parameters is crucial to achieve the best FU performance.Fig. 2(a) plots NU and FU OP vs. a f for different target rates R n = R f = R.For NU, initially both p switch n and p CM n decrease with increasing a f , and then attain a minimum value at Further increase in a f results in increased p CM n which increases further to 1 at a f = 1.The outage remains 1 for a f < 1 − 1 1+γ f .This is because the SINR at U n to decode the s f decreases when a f decreases below 1 − γn γ f +γn(1+γ f ) and becomes 1 for a f < 1− 1 1+γ f (here the SINR to decode the FU symbol becomes less γ f ).In the case of CM/NCM switching, NU attains the minimum OP at a f = 1 − γn γ f +γn(1+γ f ) and then remains constant for a f larger than this value (this is due to the switching used), which ensures that NU performance is similar to OMA.The performance of FU completely depends on the decoding status at NU. Therefore, for a f < 1 − 1 1+γ f , NU is not able to decode the FU's symbol and cannot cooperate with FU.Similarly, at a f = 1, NU cannot decode its own symbol successfully and does not cooperate with FU, due to which it goes into outage.Fig. 2(b) illustrates the throughput vs. P s (dBm) and compares the performance of both TS and PS EH protocols with α = α * and ρ = ρ * , respectively.For NU, both TS and PS result in similar performance with or without CM/NCM switching.Whereas for FU, PS outperforms TS by a big margin (this is because the throughput of TS is limited by the IT time (1 − α)T ).Fig. 3(a) shows the variation of FU throughput τ f vs. TS or PS parameters for different choices of τn and R t = R n = R f = R at P s = 5dBm.The optimum a n value is obtained by a numerical search.Clearly, the FU throughput is concave w.r.t.both α and ρ.Therefore, τ f can be maximized by optimally choosing the EH parameter.Clearly, for PS-based EH at NU, the CM/NCM switching at NU results in enhanced throughput at FU for higher values of ρ, whereas, with TS-based EH at NU, the throughput at FU remains the same for both CM/NCM switching and without switching at NU.With TS EH protocol, IT time is limited to (1 − α)T , which results in lower FU throughput.
In Fig. 3(b), we plot the EE vs. α and ρ to compare the TS and PS protocols.We observe that with CM/NCM switching, PS completely outperforms TS by a huge margin.With PS at ρ = 0, no energy is harvested at NU so that τ f = 0.However, NU throughput is maximum when ρ = 0. Further increase in ρ results in improvement in τ f while CM/NCM switching Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. .Similarly, without CM/NCM switching and ρ = 1, IT does not take place, so that τ f and τ CM n both become 0 (and so does the EE).However, when ρ = 1 with CM/NCM switching, τ switch n = τ NCM n so that EE does not decrease to zero.On the other hand for TS with α = 0, no energy can be harvested at NU, while NU throughput is maximum.Further increase in α results in improved τ f .With α = 1, IT is not possible, which results in zero throughput at NU as well as FU (EE is therefore zero).
Also, EE decreases dramatically at high RSI levels when switching is not used at NU for both PS and TS EH protocols.In contrast, CM/NCM switching results in higher NU throughput and the effect of RSI is less.

VI. CONCLUSION
This letter the performance of a cooperative NOMA network where full-duplex (FD) near user (NU) assists the transfer to (FU) using energy harvested from the source using time-switch/power-splitting (TS/PS).Considering cooperative mode/non-cooperative mode (CM/NCM) switching ensures that the performance of the NU does not degrade due to cooperation.We considered practical nonlinear EH at NU and derived closed-form expressions for the FU and NU outage probabilities and throughput.We then demonstrated that NL-EH results in a loss of diversity at FU.We also demonstrated that FU throughput could be maximized by choosing the optimum TS/PS parameter after guaranteeing the desired NU throughput.Finally, we demonstrated that using CM/NCM switching with PS results in higher EE than TS, and RSI severely affects the system when switching is not used at NU.In the future, this letter can be extended to multiple users with a multi-antenna source and a battery-assisted FD near user.APPENDIX Proof of Lemma 1: We substitute Q in , Γ nf, and Γ nn, from (2), ( 4) and (5), respectively, into (7).After some mathematical modifications, I 1 can be expressed as where μ 1 = max( γ f ξC 1 −ηA 1 γ f λnn , γn anC 1 −ηA 1 γnλnn ).Since X is exponentially distributed, I 1 as can be evaluated as On solving the above integral, we obtain I 1 as in (8).Similarly, we obtain the expressions for I 2 -I 6 as given in ( 9)- (13).

jn
= τn (with j ∈ {switch, CM}) to Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.