Unambiguous 2-D Angle-of-Arrival Estimation Receiver Based on a 16-Port Interferometer

Multiport interferometer (MPI) techniques are getting more and more attention, especially for passive receiver (Rx) beyond 24 GHz. However, MPIs with more than six ports are rarely been studied. And the existing MPI techniques only can achieve 2-D angle-of-arrival (AOA) estimation in a narrow range of angle, which means they have an ambiguous problem. In this article, an unambiguous 2-D AOA estimation Rx based on a 16-port interferometer is proposed and demonstrated. It has three main components: eight antennas, a 16-port interferometer, and a signal processor. The 16-port interferometer with eight input ports and eight output ports is the key part and the main point of this article. The eight input signals are superposed on eight output port signals in the interferometer. First, a 16-port interferometer and the corresponding AOA estimation algorithm are proposed. The algorithm transposes the phase differences between the antenna elements into the power relationship of the output signals. Then, the Rx error models are established to obtain the systematic errors. After that, a method for reducing angle ambiguity is introduced. The method allows for the distance between the antenna elements to be larger than $\lambda $ /2, and the angle detection range is theoretically–90° to 90°. An Rx operating at 31 GHz was fabricated. The measurements demonstrate that the system operates as expected, with AOAs ranging from–40° to 40° and a mean squared error (MSE) of approximately 1°.


I. INTRODUCTION
NTERFEROMETERS have a wide range of applications in direction-finding algorithms [1], [2], such as sun fringe observations [3], airborne single observer passive locations [4], and threat determination signal detection [5].Interferometric receivers (Rxs) estimate the angle of arrival (AoA) based on the phase relationships between the signals received by the antenna elements at several different positions [6].If the impinging wave is planar, the AoA can be specified by the direction of the Poynting vector [7].
In most cases, for interferometer Rxs, multielement arrays are required to achieve both good angular resolution and a low probability of ambiguity for realistic values of receiving channel phase errors [8].This means that two or more phase comparators are needed to measure the phase differences between each element [1].
Multiport interferometer (MPI) techniques can be used to decrease the number of phase comparators, as discussed in [9], [10].MPI techniques have advanced since the six-port Manuscript received Feb. 26, 2022.This work was supported by the National Natural Science Foundation of China 61671439 and 61731021.
reflectometer was developed in the early 1970s [11], [12].The six-port reflectometer has two input ports and four output ports that superimpose the two input signals with four different relative phases.At the time, the six-port reflectometers were a simple and accurate current, voltage, power and impedance measurement setup.This concept was also used to determine the relative permittivity of a material [13], adaptive load-and source-pulling [14] and antenna near-field characterization [15].The six-port concept was first used in Rxs in [16], [17].After that, the concept gained widespread attention, such as in [18]- [22], and evolved into MPI techniques.
MPIs are a passive component network.In an MPI, incoming signals are superposed in the analogy domain with multiple output port signals.MPI techniques handle high-power signals better than other techniques [23], allowing the setup of largesignal analysis systems for power amplifiers or semiconductor circuits [24], as well as precise phase measurements [25].
However, a six-port interferometer can only estimate one dimension of the AoA because it has a maximum of two receiving channels.Some solutions for obtaining azimuth and elevation (2-D) AoAs have been proposed: incorporating downconverted mixers [35], measuring the time difference of arrival (TDOA) [36], and adding more signal channels (at least two six-port junctions) [37], [38].However, these are not attractive schemes in terms of cost and size [39].
In 2017, [39] showed a 2-D AoA estimation system based on an eight-port interferometer for the first time through specific theoretical analyses and simulations.It combined the signals received by an area array with four antennas through one interferometer.However, in this system, the unambiguous angle range in the elevation and azimuth planes is narrow.

I
where the phase is defined as the phase within half a wavelength.Ambiguity issues occur when the measured distance is larger than half the wavelength.The ambiguity is due to the periodic repetition of the distance variation.This causes the distance between the antenna elements to be short, which limits the shape and gain of the antenna.The most common method for broadening the unambiguous detection range is to measure the same dimensional angle information at different relative distances between the receiving antennas, with each distance referred to as the baseline.Reference [40] proposed an easy, wide-unambiguous-range method that has been applied in an AoA detection system based on two six-port interferometers.This method has a high resolution.
In this paper, an unambiguous 2-D AoA estimation receiver based on a new 16-port interferometer is proposed.
The three major goals of this paper are to 1) Introduce the proposed 16-port interferometer and develop the corresponding 2-D AoA estimation algorithm when the antenna elements are arranged in the same plane in a concentric-square-shaped configuration (Section II). 2) Resolve the phase ambiguities of the designed 2-D AoA estimation receiver by extending the 1-D method from [40] to 2-D by adding four more antennas (Section III).3) Establish a mathematical model for calibrating the system error to improve the accuracy (Section IV).The prototyping receiver is fabricated in Section V, and the measurements verify the theory.

A. 16-port Interferometer
The antenna spacing for a signal frequency six-port interferometer Rx must be less than half the wavelength to cover a wide unambiguous detection range since the phase difference can only be measured in modulo 2π [1,39].To overcome this limitation and achieve a 2-D AoA estimation, at least three antenna elements are required on the horizontal axis and the vertical axis.Thus, a 16-port interferometer with eight input and eight output ports is proposed in this paper.
The topology of the 16-port interferometer is shown in Fig. 1.The 16-port interferometer consists of eight 3 dB 180° rat-race couplers (RRCplrs) and four 45° phase shifters.P in represents the input port connected to the receiving antenna.P out represents the output port connected to the detector.The indices in and out range between (1, 2, ⋯, 8) and (9, 10,⋯, 16), respectively.a IN = a 1 , a 2 , ⋯, a 8 T represents the independent power waves that enter port P in .b OUT = b 9 , b 10 , ⋯, a 16 T represents the dependent power waves that exit port P out .
The S-parameter network of the 16-port interferometer is represented by the matrix relationship shown in (1), where a OUT = a 9 , a 10 , ⋯, a 16 T represents the independent power waves that enter port P out and b T represents the dependent power waves that exit port P in .
The 16-port interferometer's scattering matrix S can be divided into four submatrices, as shown in (2).The subscripts (8 × 8) The transfer coefficient matrix S II, I shown in (3) is a solely concerned submatrix that explains the phase and amplitude changes as the input signals from the antennas travel through the passive network.
S II, I satisfies two conditions: the amplitude relationships and the phase relationships, shown in Table I and Table II, respectively.These two tables take the amplitude and phase of the transmission parameters S 9, 1 , |S 9, 1 | and ∠S 9, 1 as the reference parameters.The row headers indicate the serial number of the output ports, and the column headers indicate the input ports.

B. Topology of the Antenna Elements
The antenna elements shown in Fig. 2 are arranged in the same plane in a concentric-square-shaped configuration.β is the Poynting vector of the incoming wave.Taking the 7th element as the reference element, the element locations in the x-y-z coordinate system can be expressed as The Poynting vector is an algebraic column unit vector u= [cos θE sin θH, cos θE cos θH, sin θE ] T , where θE and θH are the altitude and azimuth, respectively [7,39].The antenna element phases are Let F ( θE, θH) and A be the pattern factor of the antenna and the amplitude of the incoming wave, respectively [41].The wave incident on the input port of the 16-port interferometer can be expressed as a IN = A F exp ( j φin).It should be noted that φ7 = 0. Therefore, a 7 = A F.

C. 2-D AoA Estimation
After the mathematical modeling of the interferometer and the received signals, the output waves of the 16-port interferometer can be calculated as ( ) = exp Let Bout= bout bout* be the output power.The output powers can be expressed by (13) in Appendix A.
The relationship in ( 7) can be obtained immediately because the sum of each column of E in (16e) except the first column is zero.This means that the total power of the output is equal to the total power of the input, and when the power received by each antenna unit is equal, the total power of the output is eight times that of the power received by each unit.This also means that there is no need to consider the pattern factor of antenna F ( θE, θH) in theory.
After some algebraic operations, the four phase differences can be solved by      Let φ2z0 and φ2x0 be the unambiguous phase differences in the vertical and horizontal directions on the baseline d2 , respectively.They can be solved using the angle ambiguityresistant method shown in Section III and the four phase differences calculated from (8).

III. ANGLE AMBIGUITY-RESISTANT METHOD
The algorithm shown in the last section can only be used to measure a narrow range of angles because of angle ambiguity [39].In this paper, to suppress the ambiguity, the 1-D method from [40] is extended to 2-D by adding four more antennas, which establish two baselines, d1 and d2, as shown in Fig. 2.
The two baselines are related by d2 = v d1 , where v is a noninteger positive number; this relationship improves the unambiguous range.The unambiguous range could extend to (-90°, 90°).The values of d1 and d2 are flexible, as long as the condition for v is satisfied and d1 > λ / 2 to leave enough space for the antennas.

A. Unambiguous Altitude θ
With d1 = 9 mm and a signal frequency f of 31 GHz, there is still an unknown parameter v .This parameter was selected based on the step-like phase difference, which will be introduced later, and its value is almost arbitrary as long as it is a noninteger.Here, v was chosen to be 3.33 to describe the stepshaped phase difference.
When the real azimuth θE ranges over (-90°, 90°) and no method to improve angle ambiguity is used, the detected azimuth θE i under different baselines is sin -1 [φi z / (β0 di)] , i = 1, 2, as shown in Fig. 3 (a) and Fig. 3 (b).It can be seen from the figure that θE i is equal to θE only in the small range of the red lines, indicating that only a narrow range of AoAs can be measured in the system.
However, the difference θE1 -θE2 constantly changes [40]; when plotted, it had unambiguous step-like sections with the observation range of θE shown in Fig. 3(b).For each section, a static offset was defined.There are nine 'steps' in total, numbered from left to right, and the specific data are shown in Table III.Based on this, φ2z can be divided into nine segments, with e = 1, 2, …, StallE, where StallE indicates the total number of 'steps', Ste indicates the step number to which θE1 -θE2 belongs, and t is a positive integer related to v: t = 1 when v ranges from 1 to 3 and t = 2 when v ranges from 3 to 5. The symbol '< >' denotes rounding.

B. Unambiguous Azimuth θH
The step-like diagrams in the horizontal direction are different at different vertical angles θE.θH i = sin -1 [φi x/ (β0 di cos θE) is the detected horizontal azimuth when no angle-ambiguity-improving approach is used.The steps in the horizontal direction θH2 -θH1 for some typical values of θE (20°, 40°, 58°, 75°) are shown in Fig. 4.
There are four kinds of step numbers based on different θE: there are at most 9 steps when θE ranges from -33.5° to 33.5°, and there are at least 3 steps when θE ranges from -90° to -60° and 60° to 90°, as shown in Table IV (10) with h = 1, 2, …, StallH|θE , where StallH|θE indicates the total number of 'steps' for a specific θE, and Sth|θE indicates the step number to which θH2 -θH1 belongs for a specific θE.

IV. CALIBRATION TECHNIQUE
Calibration is an essential step in the measurement system because the impact of imperfections in various components on the measurement results can be catastrophic.Fortunately, the errors caused by nonideal devices are systematic errors.Thus, these errors are constant and measurable [39].

A. Systematic Errors Mathematical Model
The AoA detection system in this paper, shown in Fig. 5, consists of eight antennas, a 16-port interferometer, eight Schottky detectors, eight operational amplifiers (OpAmps) and a digital processing unit with a micro control unit (MCU) and a PC interface.αin and γin are the amplitude and phase deviations caused by the antennas and the transmission line between the antenna and the interferometer, respectively.αout,in and γout,in indicate the deviation from the ideal amplitude and phase difference in the 16-port interferometer from P in to P out , respectively.K out denotes the voltage gain of the detector.G out is the gain of the operational amplifier.
A receiver with LNAs would improve the noise figure and the signal-to-noise ratio (SNR), and hence improve measurement precision [42].However, this receiver needs at least eight LNAs, increasing the system's cost and volume.In this paper, a method that improves the power of an analog signal generator was selected to ensure that the OpAmps detect the signal, and a system error mathematical model was established to improve measurement precision.
The error model can be determined from the main algorithm  Then, the output power B out after the OpAmps with error factors can be expressed as (12)., , , where X is the phase vector shown and E = [e 9, e 10, …, e 16] T is the error matrix.Each element in E is a different combination of system errors: αin, γin, αout,in , γout,in, K out , and G out .Given that they are constant errors, the combinations could be ignored and every element of E is treated as an unknown number here.Parameters in (12) are shown in ( 14) in Appendix B.
The values for the elements of E can be obtained after several calibration measurements when the angle of arrival is known based on the least squares technique (LS).For example, the estimated error vector e 9 T of the 9th signal channel would be After estimating the error vector, φ1x, φ2x, φ1z, and φ2z can be obtained by solving (12).

V. EXPERIMENTAL RESULTS
A prototype that achieved unambiguous 2-D AoA estimations was fabricated, as shown in Fig. 6.This prototype was an eight-layer board with four 0.254 mm Rogers RO4350B substrates.

A. Antenna
The patch antennas shown in Fig. 6(a) were fabricated on the first copper layer (L1).The numbers next to the elements correspond to the port of the interferometer; for example, antenna ① is connected to input port P 1 of the interferometer.Eight meandering lines with the same length were used to maintain the same phase difference between the receiving signal from the antenna element and the associated input port of the multiport network.The antenna simulation and measured results are shown in Fig. 7.A -10 dB bandwidth was achieved from 30.6 to 31.2 GHz.The radiation at 31 GHz in the E-plane was larger than that in the H-plane: a 120° 3 dB beamwidth was achieved in the E-plane, while a 100° 3 dB beamwidth was achieved in the H-plane.To obtain high reliability data, the system measured the AoA from -30° to 30°.

B. 16-port Interferometer
The 16-port interferometer shown in Fig. 8(b) was fabricated on the 5th copper layer (L5).The 3 λ / 4 section of the 180° RRCplr was arranged inside the coupler for miniaturization, which is different from the classic structure.Fig. 9 shows the simulation and measured results of the amplitude and phase components of the 16-port interferometer scattering matrix.The

C. Detector
A SMS7630-061 silicon, zero bias Schottky detector diode was used for the detector circuit, as shown in Fig. 10.As shown in Fig. 11, the simulation and the measurement produced similar results.The detected voltage was linear for input powers ranging from -30 dBm to -10 dBm.Thus, this detector was acceptable to be used in the proposed system.

D. Other Parts
The remaining parts were on the 8th copper layer (L5).A THS4551 OpAmp was used to achieve 90 V/V signal amplification with signal-ended differential gain.A STM32L476 microcontroller was used to process the received signal, which includes analog-to-digital conversion and simple calculations.The FT230X is a USB-to-serial UART interface that was used to transmit data from the MCU to the laptop.The whole board, including the antennas, was designed by the author.

E. Link Budget
The minimum input voltage of the OpAmps in this prototype was 0.1 mV.This means that differences in detector output voltages greater than 0.1 mV would be favorable.In that case, based on a system-level simulation by Keysight ADS, the signals entering the 16-port interferometer input ports should be greater than -30 dBm.The free space loss − 57.8 dB was calculated by: 92.4 + 20 log f + 20 log R [44].R = 6 × 10 -4 is the distance between the receiver and the Tx antenna in kilometers.Therefore, a 5 dBm transmitted signal before a 25 dB horn Tx antenna is sufficient for measurement.

F. Measurement
The test bed is shown in Fig. 12.The best system performance upon calibration was obtained at 31 GHz, which is higher than the designed frequency of 30 GHz.This is mainly because the dielectric constant and thickness of the multilayer substrate after the actual production process are lower than the design values.A KEYSIGHT E8257D PSG analog signal generator was used to generate a 31 GHz signal with a 5 dBm analogy signal.A RIGOL DP832 power supply was used to supply a 3.3 V voltage.A HENGDA MICROWAVE HD-320SGAH25 K horn antenna with a 25 dB gain was used as the Tx antenna, which was connected to an FUYU three-axis linear workbench to simulate signals in any direction.
The unambiguous AoA detection range is -90° to 90° in theory.Given that the beamwidth of the antennas used here is narrow, the highly reliable beamwidth of this systems is 60°.Thus, in the range of -30° to 30°, the measurement was performed at 1° step intervals.The test bed moved both horizontally and vertically.
The measurement process is shown in Fig. 13.Some calibration measurements were performed first to obtain the error matrix E , which was calculated with the PC.The calibration must be done once and then be used for ever because of the constant system errors.In the formal test, the DC raw data at the output of the detectors were amplified by the OpAmps and received by the ADCs of the STM32 microcontroller.The MCU solved ( 13) and ( 14) to obtain φ1x, φ2x, φ1z, and φ2z.After that, the unambiguous azimuth θE and altitude θH were estimated by ( 8), (9), and (10).
Finally, the measurement results and the mean squared error

VI. CONCLUSION
An unambiguous 2-D AoA estimation receiver operating at 31 GHz is demonstrated in this work.The receiver determines the incoming wave angle with the different phase offset characteristics of the ports, which are caused by the 16-port interferometer proposed in this paper.The 2-D AoA estimation algorithm is described first.Then, an ambiguity-resistant method is introduced.This allows for greater flexibility in antenna spacing and size; theoretically, the unambiguous angle range is from -90° to 90° in both the horizontal and vertical directions.The system measures the range from -30° to 30° due to the beamwidth of the receiving antenna.The MSE values of the measured results are approximately 0.4°.Table V compares the receiver presented in this work with AoA estimation MPRs in the main references.
In future work, an interferometer with more ports and a wider bandwidth can be designed, and the emission source can be integrated into the system to achieve multitarget AoA estimation.This kind of multiple distributed MPR can be used to perform more complex functions, such as multitarget tracking [45].In addition, a wideband interferometer can provide absolute measurements of the target distance.

Fig. 2 .
Fig. 2. Concentric-square layout of the 8 antennas and the relationship to the incoming wave.

Fig. 7 .
phase differences at 30.5 GHz were approximately 45°, 90°, Antenna simulation and measured results in HFSS.(a) Return loss; (b) Antenna gain in the E-plane (peaks at 6.3 dB) and H-plane (peaks at 5.2 dB).

Fig. 11 .Fig. 8 .Fig. 9 .
Fig. 11.Simulated and measured detected voltage v d versus RF power at 30 GHz: the y-coordinates of the blue lines have a base-10 logarithmic scale; the y-coordinates of the red lines have a linear scale.
Multiport interferometer techniques are based on phase analysis, XiaoWei Sun is with the Shanghai Institute of Microsystem and Information Technology of Chinese Academy of Science, Shanghai, China (e-mail: xwsun@mail.sim.ac.cn).Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

TABLE II PHASE
RELATIONSHIPS OF S II, I

TABLE V A
COMPARISON BETWEEN THIS WORK AND THE AOA ESTIMATION MPRS IN THE MAIN REFERENCES In this table, '±' means the range, e.g.'±3' means 'from −3 to 3.'and the symbol ' ' indicates the Hadamard product.Each unit in E is a different combination of system errors αin, γin, αout,in , γout,in, K out , and G out , e.g.: