Network DesignMotivation and Contributions

Signal Model Antenna Selection and DOA Estimation

User Interface Results

High DOA resolution requires large number of antennas. Multiple antennas usually entails dedicated hardware

equipment for each radar receive antennas which results in

high cost.

To achieve a balance between hardware cost and

resolution, it is often desirable to choose an optimum

subarray from a full array based on the target scenario.

To optimally choose the subarrays based on the target.

DOAs, we design a convolutional network which accepts

the array covariance matrix as an input and selects the best

sparse subarray that minimizes the mean square error.

This approach aids in cognition where multiple antennas

are simultaneously operate to track different targets in

different directions based on the current target scenario.

We design a deep neural network which consists of 9 layers. The CNN accepts the two-dimensional inputs in three

real-valued channels.

There are rectified linear units (ReLU) after each convolutional and fully connected layers.

At the output layer, there are Q units wherein the network classifies the given input data using a softmax function and

reports the probability distribution of the classes to provide the best subarray.

Deep Sparse Antenna Array Selection And DOA Estimation DemoSatish Mulleti1, Regev Cohen2, Ahmet M. Elbir3, Rong Fu4, Moshe Namer2, Maxim Meltsin2, Harel Moalem2,

Eli Laks2, Eli Shoshan2, Tinayao Huang4, Yimin Liu4, Yonina C. Eldar1

1 Faculty of Mathematics and Computer Science, Weizmann institute of Science, Rehovot, Israel2 Andrew and Erna Viterbi Faculty of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.

3 Department of Electrical and Electronics Engineering, Duzce University, Duzce, Turkey.4 Department of Electronic Engineering, Tsinghua University, Beijing, China.

* e-mail: mulleti.satish@gmail.com

Demo System

The 16 Tx and Rx signals from the up-converters, are amplified and

connected 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. For high

speed operation there is a local FPGA, enabling to run pre-defined

cyclic scenarios and select specific antennas.

Three antenna selection methods are applied

Best subarray gives lowest CRB.

Random subarray is selected by random array

selection (RAS).

CNN subarray is selected by trained CNN network,

which input dataset are three real-valued channels

where, 𝑅 is the sample data covariance

Two DOA estimation algorithms:

MUSIC

𝒂 Θ : the steering vector,

𝑮:the noise subspace eigenvector matrix of the sample data covariance

FISTA

𝒑: K-sparse vector with the same support as of target signal

𝑩=𝑨⊙𝑨, 𝑤ℎ𝑒𝑟𝑒 𝑨 is the array manifold matrix

𝒓: the vectorization of the sample data covariance 𝑅

Once the optimum sparse subarray is obtained, the

signals from the selected antennas are used to estimate

the DOAs. We provide numerical simulations to validate

the performance of the proposed cognitive array selection

strategy and different DOA estimation algorithm.

The RMSE vs SNR plots for MUSIC and FISTA are shown

in Fig. A and B, respectively.

The proposed CNN approach effectively selects the best

subarray for a large range of SNRs and it provides

effective performance as compared to RAS.

For a given antenna selection method, comparing the

DOA estimation performance of MUSIC and FISTA, it is

observed that the MUSIC algorithm performs better than

FISTA. The RMSE of FISTA does not reduce for high SNR

while MUSIC provides much better precision.

𝑃 Θ =1

𝒂𝐻 Θ 𝑮𝑮𝐻𝒂 Θ

ෝ𝒑 = 𝑎𝑟𝑔𝑚𝑖𝑛𝒑≥𝟎

𝑩𝒑 − 𝒓 22+𝜆 𝒑 1

𝑋1 𝑖,𝑗 = ∠ 𝑅𝑖,𝑗

𝑋2 𝑖,𝑗 = 𝑅𝑒 𝑅𝑖,𝑗

𝑋3 𝑖,𝑗 = 𝐼𝑚 𝑅𝑖,𝑗

𝑦(𝑡) = σ𝑘=1𝑀 𝑥𝑘 𝑡 𝒂 Θ𝑘 + 𝑤(𝑡),

= σ𝑘=1𝑀 𝑨𝑥 𝑡 + 𝑤(𝑡),

where, 𝒂 Θ is the steering vector and 𝑨 is the

array manifold matrix,

𝑨 = [𝒂 Θ1 𝒂 Θ2 …𝒂 Θ𝑀 ]𝑯

For 𝑀 targets, the measurement vector at 𝑡th

snapshot is given as:

Our goal is to estimate DOAs from the

autocorrelation matrix 𝑅 = 𝐸 𝑦 𝑡 𝐻𝑦 𝑡 of the

measurements.

Antenna

array GUI

Rx FPGA

Tx FPGA

Rx antenna array

FPGA and UP/DOWN converters

(A)

(B)