Hardware Prototype Demonstration of ACognitive Radar with Sparse Array Antennas

Rong Fu, Satish Mulleti, Tianyao Huang, Yimin Liu, Yonina C.Eldar

As a typical signal processing problem, direction-of-arrival (DOA)estimation has been adapted to a wide range of applications in radar-based systems. A high DOA resolution requires a large number of antennaelements which increases the overall cost. To minimize the cost, it isdesirable to choose an optimum sub-array from a full array. To enablecognition, the subarrays are selected based on the present target scenario.By using deep learning (DL) based techniques, we show a cognitive sparsearray selection technique. By using hardware simulations, we demonstratethe applicability of the DL-based sparse antenna selection network inDOA estimation problems. We show that the DL-based sub-arrays leads toa higher DOA estimation accuracy by 6 dB over random array selection.

Introduction: With the growing complexity of the dynamically changingelectromagnetic environment, the concept of cognitive radar has gainedever-increasing attention in recent years, due to its flexibility of responseto various environmental changes. For example, in the automotive radarapplication, the bandwidth available for the radars is fixed. Dependingupon the number of radars needs to operate at any given instant, thebandwidth has to be adaptively shared among the radars without causinginterference [1].

Another critical resource in a radar system is the number of elementsin an antenna array, which determines the array resolution as well asthe accuracy of the direction of arrival (DOA) estimation. For a givenwavelength, high DOA resolution requires a large aperture array whichleads to a large number of array elements [2]. As each array elementrequires its own dedicated hardware, the overall cost of the systemincreases. Moreover, the computational cost of processing the data streamfrom multiple array elements is very high. To build an economic system interms of cost and power consumption, it is desirable to choose a subset ofarray elements instead of a full array at the expense of resolution. As onlya few array elements are considered from the full array, we denote the sub-array as a sparse array. By assuming that the degradation of the resolutionis within the acceptable limits, working with sparse arrays has two distinctadvantages. First, as mentioned, the computational cost reduces as onehas to work with a smaller amount of received data. Second, it facilitatescognition. For example, consider the following two cognitive systems: (a)one can choose the subset of array elements from the full array based onthe current target scenario such that accuracy of DOA estimation is high;(b) different non-overlapping subsets of array elements can be assignedadaptively to track different targets. In this paper, we consider the firstscenario and demonstrate a hardware prototype for the same.

The problem of sparse antenna array selection has been a very activeresearch topic in recent years. In the literature, nearly most of the antennaselection algorithms adopt an optimization-based algorithm or a greedysearch algorithm, which will take a long time and obtain sub-optimumsolutions [3]. Recently, Elbir et al. [4] proposed a DL based sparse antennaarray selection method by assuming a single-target scenario. The work hasbeen extended to two target case [5]. To select antennas in a cognitiveradar, Elbir et al. constructed a convolution neural network (CNN) modelas a multiclass classification framework where each class designates apossible sub-array. Numerical experiments have shown that the CNNclassification network provides more accurate DOA estimates than randomarray selection (RAS).

In this paper, we propose a hardware prototype demonstrating theapplicability of the DL approach as developed in [5]. Specifically, wedemonstrate a DL-based sparse sub-array selection technique based onthe current target scenario. We show that the sub-array chosen by thetrained antenna selection network can achieve almost the same estimationaccuracy as the best sub-array with the lowest Cramér-Rao lower bound(CRB). Using hardware simulations, we demonstrate the applicabilityof cognitive antenna selection for DOA estimation and its accurateperformance over RAS. Next, we describe our cognitive radar system,followed by the details of the hardware and the simulation results.

Antenna Selection in Cognitive Radar System: In [5], an optimal K-element sparse array is chosen to minimize the CRB of DOA estimation.

Alternatively, choosing K antenna elements from a total of N elementscan also be viewed as a classification problem wherein each class denotes apossible sub-array. Once the optimum sparse sub-array is obtained, we canestimate the DOAs based on the noisy observed signals from the selectedantennas.

In this work, we assume the following scan mechanism. Generally, thetargets move slowly compared to the high-speed switch antenna array. Inthe first scan, we assume that all the receive antennas are active and feedtheir received signals to the CNN classification network. Then the output ofthe network determines an optimal antenna array where only K antennaswill be used and cognitive systems will continue to use this sub-array for apredetermined number of scans before switching back to the full array [4].Our hardware prototype is designed to address this setting. We apply thefollowing three antenna selection methods and compare their performancewith that of full array.

• Best sub-array: the beam forming performance gives the lowest CRB.• Random sub-array: it is selected by random array selection.• CNN sub-array: it is selected by a trained CNN, whose input datasets are

three real-valued channels while the output is the best sub-array indexamong all the possible sub-arrays.

Once the antenna array is selected, the DOA is estimated from the signalsfrom the sub-array elements by applying multiple signal classificationalgorithm (MUSIC).

Mathematical Modeling: Consider an N -element antenna array systemwith the elements located at

{pnd|pn ∈N3

}where d is the inter-element

spacing as half the carrier wavelength λ and n is the index of antennasranging from 1 to N . The position vector pn in the Cartesian coordinatesystem takes integer value.

We assume that there are K narrow-band signals impinging on theN -element array from K distinct DOAs {θk, φk}Kk=1 which denote theelevation and azimuth angles in spherical coordinates, respectively. Foreach antenna, the received signal at snapshot time t yields a sum of Kexponential components as follows.

yn (t) =

K∑k=1

xk (t) exp

(−j

2π

λdpTnκ(θk, φk)

), 1≤ n≤N. (1)

Here xk (t) is the complex amplitude of the k-th source signal and itscorresponding Cartesian coordinate is κ(θk, φk) which can be calculatedas κ(θk, φk) = [sin(φk) cos(θk), cos(φk) cos(θk), cos(θk)]

T.As we discretize the angle space into M grids (K�M ) with the

assumption that each source DOA lies on the prescribed grid points, thenoise-corrupted received signal vector of the whole sparse array can bemodeled as

y (t) =

M∑k=1

xk (t)a (θk, φk) +w (t) (2)

where a (θk, φk) is the steering vector of the sparse array whose elementis computed as an (θk, φk) = exp

(−j 2π

λdpTnκ(θk, φk)

). Here w (t) =

[w1 (t) , w2 (t) , · · · , wN (t)]T is the additive noise vector. The targetsignal x (t) = [x1 (t) , x2 (t) , · · · , xM (t)]T is a K-sparse vector whichmeans that only K elements of source angles are nonzero values andother (M −K) elements of nonexistent angles are zero. For the sakeof clarity, hereafter we neglect the time index t and rewrite (2) intoy=Ax+w where the array manifold matrix A can be written as A=[a (ω1) ,a (ω2) , · · · ,a (ωM )].

Based on the spatial sparsity of sources, many sparse recoveryalgorithms such as fast iterative shrinkage-thresholding algorithm (FISTA)have been widely applied to single-snapshot DOA estimation [6, 7].However, as aggregated data across multiple snapshots leads to a morestable estimate, we will put more emphasis on the multiple-snapshot DOAestimation. We provide the DOA estimation results by using MUSICalgorithm as described in [5].

Hardware Prototype: A schematic of the proposed hardware is shown inFig. 1(a) which consists of following main blocks: a receive (Rx) antennaarray, a receiver board (Rx board) and a personal computer (PC) controller.The hardware is shown in Fig. 1(b). The Rx antenna array operates at2.4 GHz and it is fixedly divided into 16 sets of 4 patch antennas each.Only one antenna of each set can be selected at a time, via 4 to 1 high-speed selector. The receiver board consists of a downconverter board, two

ELECTRONICS LETTERS September 7, 2020 Vol. 00 No. 00

16 ch Rx

Rx Ant Array

8 ch ADC

8 ch ADC

FPGA PC

controller

Rx Board

analog

front end

(a)

(b)

(c)

Fig. 1 A hardware prototype of the sparse array demo: (a) Flowchart of theproposed demo prototype; (b) full prototype with indications corresponding tothe flowchart; (c) a screen shot of GUI.

analog to digital converter (ADC) cards and a field-programmable gatearray (FPGA) board, where the received analog signal is converted tothe baseband digital signal. Its first step is to down-convert the amplifiedanalog signal to baseband by a downconverter board which will mix thereceived signal with a local oscillator and pass it through a basebandfilter. After analog down conversion, an eight-channel FMC168 ADCcard is adopted to sample the analog baseband signal. Then the VC707FPGA-based processing board transmits the digital outputs to the host PCcontroller in a high-speed mode where they are utilized for estimating thetarget DOAs.

The graphical user interface (GUI) is shown in Fig.1(c), wherein asingle sparse array is presented in both the plane and 3D view. In thesparse array demo, the full array is formed by N = 16 antennas in theshape of either uniform rectangular array (URA), diamond or a randompattern. To address adaptation in dynamic automotive environments, weimplement various options in the demonstration. For example, users canchoose a combination of the following configurations: six different targetscenarios, three different antenna array patterns, three different numbersof antennas used in each sub-array and four decreasing noise levels. Thedetail view at the bottom shows the antenna patterns and beam patterns forthe full array and three sub-arrays based on the configurations presentedabove. On the right side, we compare the performance of the full array andthree selected sub-arrays in terms of the estimated DOAs as well as theroot mean square error (RMSE), simultaneously for all the targets.

Next, we compare the performance of different antenna selectionmethods. To avoid interference due to wireless networks, specifically WiFioperating at 2.4 GHz, the data is transmitted through cables instead of overthe air. In particular, we employ a 16 channel transmit-board, similar to theRx board shown in Fig. 1(a), to transmit the signals generated in MATLAB.

0 5 10 15

SNR, [dB]

10 -1

10 0

RM

SE

-Do

A,(

De

gre

es)

MUSIC with BEST Subarray

MUSIC with CNN Subarray

MUSIC with Random Subarray

MUSIC with Full Array

Fig. 2 Simulation result of multiple-snapshot DOA estimation by applyingMUSIC algorithm.

The signals are generated as in [5] and the DOAs from the received signalsare estimated by applying MUSIC algorithm. The performance of theproposed cognitive array selection strategy under different signal to noiseratio (SNR) values is shown in Fig. 2. Comparing the DOA estimationperformance of three sub-arrays, the proposed CNN approach effectivelyselects the best sub-array for a large range of SNRs and it provides effectiveperformance as compared to RAS. Especially, the CNN-based method has6 dB lower RMSE compared with RAS in the case of MUSIC estimationresults.

Conclusion: A high DOA resolution requires a large number of antennas,which usually entails dedicated hardware equipment for each radar receiveantennas and results in high cost. In many radar applications, instead of theentire array, a cognitively selected sub-array offers potential advantages ofbalancing hardware cost and high resolution. To optimally choose the sub-arrays based on the target DOAs, we use a convolutional network whichaccepts the array covariance matrix as its input and selects the best sparsesub-array which minimizes the RMSE. This approach aids in cognitionwhere multiple antennas are simultaneously operating to track differenttargets in different directions based on the current target scenario.

Acknowledgment: This project has received funding from the EuropeanUnion’s Horizon 2020 research and innovation program undergrant No. 646804-ERC-COG-BNYQ, Air Force Office of ScientificResearch under grants No. FA9550-18-1-0208, and from the IsraelScience Foundation under grant No. 0100101. We would like to thankMoshe Namer and Maxim Meltsin for their help in realizing thehardware prototype.1Rong Fu, 2Satish Mulleti, 1Tianyao Huang, 1Yimin Liu, and 2YoninaC. Eldar ( 1Department of Electrical Engineering, Tsinghua University,Beijing, China; 2Faculty of Mathematics and Computer Science,Weizmann Institute of Science, Rehovot, Israel)

E-mail: fu-r16@mails.tsinghua.edu.cn, mulleti.satish@gmail.com,yonina.eldar@weizmann.ac.il

References

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2 C. Hu, Y. Liu, H. Meng, and X. Wang, “Randomized switched antennaarray FMCW radar for automotive applications,” IEEE Trans. Veh.Technol., vol. 63, no. 8, pp. 3624–3641, 2014.

3 Y. Gao, A. J. H. Vinck, and T. Kaiser, “Massive MIMO antenna selection:Switching architectures, capacity bounds and optimal antenna selectionalgorithms,” IEEE Trans. Signal Process., vol. PP, no. 99, pp. 1–1, 2018.

4 A. M. Elbir, K. V. Mishra, and Y. C. Eldar, “Cognitive radar antennaselection via deep learning,” IET Radar, Sonar & Navigation, 2019, inpress.

5 A. M. Elbir, S. Mulleti, R. Cohen, R. Fu, and Y. C. Eldar, “Deep-sparse array cognitive radar,” in Proc. Int. Conf. Sampling Theory Appl.(SampTA), 2019.

6 R. D. Balakrishnan and H. M. Kwon, “A new inverse problem basedapproach for azimuthal doa estimation,” in Proc. IEEE Global Commun.Conf. (IEEE GLOBECOM), vol. 4, 2004, pp. 2187–2191.

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