1 Neural Network-Based Multi-Target Detection within Correlated Heavy-Tailed Clutter

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Neural Network-Based Multi-Target Detection

within Correlated Heavy-Tailed Clutter

S. Feintuch, H. Permuter, Senior Member, IEEE, I. Bilik, Senior Member, IEEE, and J. Tabrikian, Fellow, IEEE

Abstract—This work addresses the problem of range-Doppler

multiple target detection in a radar system in the presence of

slow-time correlated and heavy-tailed distributed clutter. Conven-

tional target detection algorithms assume Gaussian-distributed

clutter, but their performance is signiﬁcantly degraded in the

presence of correlated heavy-tailed distributed clutter. Derivation

of optimal detection algorithms with heavy-tailed distributed

clutter is analytically intractable. Furthermore, the clutter dis-

tribution is frequently unknown. This work proposes a deep

learning-based approach for multiple target detection in the

range-Doppler domain. The proposed approach is based on a

uniﬁed NN model to process the time-domain radar signal for a

variety of signal-to-clutter-plus-noise ratios (SCNRs) and clutter

distributions, simplifying the detector architecture and the neural

network training procedure. The performance of the proposed

approach is evaluated in various experiments using recorded

radar echoes, and via simulations, it is shown that the proposed

method outperforms the conventional cell-averaging constant

false-alarm rate (CA-CFAR), the trimmed-mean CFAR (TM-

CFAR), and the adaptive normalized matched-ﬁlter (ANMF)

detectors in terms of probability of detection in the majority

of tested SCNRs and clutter scenarios.

Index Terms—Radar Target Detection, Correlated Heavy-

Tailed Clutter, Neural Networks, Deep Learning, CA-CFAR, TM-

CFAR, ANMF, Range-Doppler, LFM, Multiple Target Detection,

Machine Learning.

I. INTRODUCTION

Target detection in range-Doppler map is one of the major

radar tasks [1], [2]. Conventionally, the decision on target

presence is made by comparing the energy within the cell-

under-test with a threshold, which is calculated according to

the energy at neighboring cells [3]. The presence of spiky

clutter in the cells used for the detection threshold calculation

increases the threshold level, and thus, compromises the target

detection performance [3].

Considering the detector input as a one-dimensional com-

plex signal that contains slow-time samples of received radar

echoes in each range bin, the task of radar target detec-

tion within correlated heavy-tailed clutter is conventionally

formulated as a binary hypotheses decision task. Under this

formulation, the hypotheses H0and H1represent cases where

there is no target and the target is present within the cell-under-

test (CUT), respectively [3]–[22]. In [4]–[10] the problem of

radar target detection was formulated as a binary hypothesis

testing, where the optimum detectors were derived under

certain conditions. The design for a regularized covariance

Stefan Feintuch, Haim H. Permuter, Igal Bilik, and Joseph Tabrikian

are with the School of Electrical and Computer Engineering, Ben Gurion

University of the Negev, Beer Sheva, Israel. (e-mails: stefanfe@post.bgu.ac.il,

haimp@bgu.ac.il, bilik@bgu.ac.il, joseph@bgu.ac.il). This work was partially

supported by the Israel Science Foundation under Grants 2666/19 and

1895/21.

matrix estimation in the adaptive normalized matched-ﬁlter

(ANMF) was introduced in [11] to maximize the asymptotic

probability of detection, while retaining a constant false-

alarm rate (CFAR). The properties of CFAR detectors in

the presence of correlated heavy-tailed clutter were studied

in [18]. The problem of range-migrating target detection within

heavy-tailed clutter was addressed in [16], in which a fast-

converging amplitude estimation algorithm for target detection

was proposed. An orthogonal-projection-based approach to

suppress the sea clutter at each range cell in combination

with cell-averaging CFAR (CA-CFAR), was proposed in [22].

The authors in [21] addressed the target detection within

heavy-tailed clutter using massive multiple-input multiple-

output (mMIMO) radar. Therein, a detector was proposed for

the asymptotic regime with increasing number of antennas,

and its robustness to the unknown clutter distribution was

demonstrated.

However, these model-based approaches were designed con-

sidering a speciﬁc measurement model, and their performance

may degrade in the case of model mismatch. Alternatively,

data-driven machine learning (ML) approaches have been

proposed in [12]–[15], [19], [20], [23]. In these approaches,

target detection is performed using features extracted from the

data. Thus, they enable detectors’ robustness to environmental

and clutter statstics’ variations. K-nearest neighbors (KNN)

based approaches using various feature space transforms of the

raw one-dimensional complex signal were proposed in [12]–

[15], [19] to address the binary hypothesis decision task. In

particular, the authors in [12], [14] proposed to obtain a KNN-

based decision rule from simulated data, and evaluated the

proposed methods using the IPIX database [24] of recorded

radar echoes that contain correlated heavy-tailed sea clutter.

Authors in [23] used support vector machine to switch between

conventional CFAR methods and perform target detection

in an environment containing clutter edges and/or multiple

interfering targets under white Gaussian noise. The work

in [20] extended the work in [21] to angle dimension and

proposed a reinforcement learning (RL) based approach to

design the beamforming matrix in a cognitive radar (CR)

setup.

The binary hypothesis-based approaches in [4]–[22] as-

sume under the H1hypothesis a) the presence of a single-

target within each CUT and b) the availability of target-free

secondary data, which is used for clutter covariance matrix

estimation. However, practical scenarios may include multiple

targets with similar azimuth, range, and Doppler. Therefore,

the performances of these methods degrade in such scenarios.

In addition, the methods in [4]–[10], [12]–[19], [22], [23] use

the data after range matched-ﬁlter processing, which linearly

arXiv:2210.12042v2 [eess.SP] 8 Apr 2023

projects each fast-time received pulse to range bins [3]. This

linear transformation fails to suppress the clutter echo signals,

since these are not orthogonal to the projection signals that

correspond to each range bin.

Recently, deep neural networks (DNNs) with various net-

work architectures have been introduced for radar target de-

tection, where the network input consists of the samples of

the received radar echo [17], [25]–[27]. Considering a one-

dimensional problem with a-priori known signal, a multi-

layer perceptron (MLP) based detector for binary hypothesis

detection within non-Gaussian noise was proposed in [17].

A fully-connected architecture for multiple target detection

in the presence of homogeneous Rayleigh-distributed clutter

was utilized in [25]. A single-target detection within additive

white Gaussian noise (AWGN) using convolutional neural

network (CNN) based architecture for range-Doppler target de-

tection and azimuth-elevation estimation was proposed in [26].

However, the works in [25]–[27] assume white Gaussian-

distributed clutter, whereas a more realistic clutter model

would be correlated and non-Gaussian. Although the work

in [17] addresses the non-Gaussian clutter, it also assumes

the binary hypothesis decision task, which has limitations as

previously mentioned.

Neural network (NN) based processing using range-Doppler

map input was also studied in the literature, the majority

of these works invoke computer vision methods for radar

target detection within AWGN [28]–[31]. A fully connected

NN architecture for multiple target detection within heavy-

tailed clutter was proposed in [32]. A residual block [33] was

proposed in [29] for background noise estimation in the range-

Doppler map for the conventional CFAR detector. In [30]

a model-based data augmentation technique was proposed

for linear frequency modulated (LFM) radar detector in the

3D range-Doppler-angle domain. The proposed technique was

used to generate a synthetic dataset for U-net [34] training,

considering a single target in the azimuth-elevation domain at

each range-Doppler region-of-interest (ROI). The work in [31]

extended [30], by utilizing the absolute value of the range-

Doppler map for additional data augmentation.

Contrary to previous works described above, which address

the radar target detection within heavy-tailed clutter as a

one-dimensional binary hypothesis decision task for each

range bin, this work addresses the problem of radar target

detection within heavy-tailed clutter as a two-dimensional

(range-Doppler) detection problem with multiple targets in

unknown ranges and radial velocities (Doppler). Furthermore,

in practical radar scenarios characterized by correlated clutter,

the conventional range-Doppler transform designed for AWGN

model fails to suppress the clutter, since the clutter signal

is correlated in slow-time and can be spread over multiple

range bins. Therefore, the range-Doppler map-based DNN

approaches mentioned above, do not fully exploit the power

of DNNs to learn highly abstract nonlinear transformations

for suppressing the clutter. To that aim, this work proposes

to leverage DNN’s ability to learn highly complex nonlinear

functions in order to transform the complex time-domain

radar echo samples into the range-Doppler domain while

suppressing the correlated clutter.

The contributions of this work are:

1) A novel neural processing block named dimensional-

alternating fully connected (DAFC) block, is proposed

to process raw time-domain radar echoes for the task

of multiple target detection. A DNN architecture that

utilizes this block is proposed to map radar signals

to either range or Doppler domains while suppressing

correlated heavy-tailed clutter.

2) The proposed DNN architecture is utilized as part of

a novel range-Doppler multiple target detector, that is

evaluated in the presence of correlated heavy-tailed

clutter.

3) The proposed method signiﬁcantly outperforms con-

ventional methods and proves to be more robust in

various aspects: multiple targets within AWGN and

correlated heavy-tailed clutter, varying clutter condi-

tions/“spikiness” measure, and detection threshold sen-

sitivity to clutter “spikiness”.

4) The proposed method proves to generalize well to un-

seen data, based on experiments involving recorded real

data.

The following notations will be used throughout the paper.

Roman boldface lower-case and upper-case letters represent

vectors and matrices, respectively. Non-bold italic letters

stands for scalars. INand 0Nare the identity matrix and zero

matrix of size N×N, respectively. E, superscript T, and

superscript Hare the expectation, transpose, and Hermitian

transpose operators, respectively. Vec, |·|, and Istand for the

vectorization, set size, and indicator operators, respectively.

(·)and (·,·)denote single argument and double arguments

functions. [a]nand [A]n,m are the n-th and n, m-th elements

of the vector aand the matrix A, respectively. [A][·,:] and

[A][:,·]represent an arbitrary row and column in the matrix

A, respectively.

The remainder of this paper is organized as follows: The

addressed problem is stated in Section II. Section III presents

the proposed DAFC-based radar target detection approach.

The performance of the proposed approach is evaluated via

simulated data and recorded real data in Section IV, and our

conclusions are summarized in Section V.

II. PROBLEM STATEMENT

The measurement model is described in Subsection II-A,

and the multiple target detection problem in the range-Doppler

domain is formulated in Subsection II-B.

A. Measurement Model

Consider the baseband fast-time ×slow-time model of a

single received radar echo:

X=S(T) + C+W(1)

where X,S(T),C,W∈CN×K,T=

{(rj, vj) : (rj, vj)∈[rmin, rmax]×[vmin, vmax]}denotes

the set of targets present in the frame, and [rmin, rmax]

and [vmin, vmax]are intervals of targets’ ranges and radial

velocities, respectively. The matrices S(·),C, and W

Figure 1: Example of range-Doppler map containing simulated

targets, clutter, and noise. The targets are circled in red, with

the marked SCNRs. The non-homogeneous clutter is present

at the vicinity of the 4m/s Doppler velocity in the majority

of the range bins.

represent the target echo signal, the clutter, and the additive

noise. The targets’ matrix S(·)is deﬁned as:

S(T) = (P(r,v)∈T e

S(r, v),T 6=∅

0N×K,T=∅(2)

where e

S(r, v)is the radar echo matrix received from a single

target at range rand radial velocity v, and is deﬁned as [3]:

S(r, v) =Arv ejφrv r(r)vT(v)(3)

where 0N×Kdentoes the N×Kzero matrix, φrv ∼

U([0,2π]) is unknown phase, Arv ∈R+represents the

received signal amplitude and depends on the target radar cross

section (RCS) and the propagation path loss.

Notice that the model in (1) represents the radar echo of

both the pulse-Doppler and the LFM-CW radars with the

appropriate range and radial velocity steering vectors, r(·)and

v(·). Thus, for LFM-CW radar:

r(r) = h1e−j2π2Br

cN . . . e−j2π2Br

cN (N−1)iT,(4)

v(v) = h1e−j2π2fcv

cT0. . . e−j2π2fcv

cT0(K−1)iT,

where Nis the number of samples per LFM chirp, Kis

the number of chirps per dwell, Bis the transmit signal

bandwidth, fcis the carrier frequency, cis the speed of light,

and T0stands for the pulse repetition interval (PRI).

Conventionally, slow-time radar clutter is statistically mod-

eled as a random vector at each range bin [12], [24], [35]. Let

{cr∈CK}r∈R denote the group of one-dimensional slow-

time clutter vectors. Then, the clutter matrix Cin (1) can

be obtained by converting {cr}rto the fast-time ×slow-time

representation by:

C=X

r∈R

r(r)cT

r,(5)

where Ris the set of range bins, that partition the continuous

range space to grid points spaced by the range resolution ∆r=

c/(2B). The clutter signal matrix Cin (1) is a sum of |R|

“clutter echoes”, one per range bin. According to (5), each

column in Cis a linear combination of the range steering

vectors corresponding to the range bins in R. Therefore, by

projecting the fast-time vectors (i.e. columns) in (5) to the

range steering vectors representing the range bins in R, we

will obtain the set of original clutter vectors {cr}r, one per

range-bin.

The fast-time×slow-time noise matrix Win (1) is deﬁned

by e

w=Vec (W), where e

wis modeled as an AWGN vector:

w∼ CN 0N K , σ2IN K .(6)

Let ˜

s(r, v),Vec(e

S(r, v)) and ˜

c,Vec(C)be the

vectorizations of a target and clutter matrices in (3) and (5),

respectively. The clutter-to-noise ratio (CNR) for a given frame

and signal-to-clutter-plus-noise ratio (SCNR) for a given target

within the frame are deﬁned as:

CNR =Ek˜

ck2

E[k˜

wk2],(7)

SCNR =Ek˜

s(r, v)k2

E[k˜

c+˜

wk2].

B. Range-Doppler Detection Formulation

The sets of range and Doppler bins are denoted by Rand

V, respectively. The range bins deﬁned earlier and the Doppler

bins Vpartition the continuous Doppler space to grid points

spaced by the Doppler resolution ∆v=c/(2fcKT0). The set

of range-Doppler bins is obtained by the Cartesian product R×

V. A range-Doppler detector can be formulated as a mapping

between the received signal in (1) to a per-bin decision in the

range-Doppler domain:

Y=H(X)∈ {0,1}dR×dV,(8)

where dR=|R|,dV=|V| and H(·)is a mapping from a fast-

time ×slow-time input frame Xto a range-Doppler decision

matrix ˆ

Let [m, l]denote a coordinate in the discrete range-Doppler

space R × V. The decision on target presence in the range-

Doppler bin corresponding to the coordinate [m, l]is deﬁned

using entries in the range-Doppler decision matrix ˆ

(Target,[ˆ

Y]m,l = 1

No target,[ˆ

Y]m,l = 0 .

An optimum detector, maximizes the probability of detection

PDfor a ﬁxed probability of false-alarm PF A.

The conventional range-Doppler transform, which maps the

received signal in (1) to the range-Doppler domain, can be ob-

tained by taking the absolute squared value of the 2D-FFT of

X. Fig. 1shows an example of the conventional range-Doppler

transform of simulated radar signal consisting of multiple

targets, correlated heavy-tailed clutter, and AWGN. Note that

there is a non-homogeneous clutter that is observed around the

Doppler velocity of 4m/s, and is present in the majority of the

range bins. This example visually exempliﬁes the limitations

of conventional range-Doppler processing in suppression of

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1NeuralNetwork-BasedMulti-TargetDetectionwithinCorrelatedHeavy-TailedClutterS.Feintuch,H.Permuter,SeniorMember,IEEE,I.Bilik,SeniorMember,IEEE,andJ.Tabrikian,Fellow,IEEEAbstractThisworkaddressestheproblemofrange-Dopplermultipletargetdetectioninaradarsysteminthepresenceofslow-timecorrelatedandheavy-t...

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