Elsevier

Signal Processing

Volume 84, Issue 9, September 2004, Pages 1667-1675
Signal Processing

Robust approximate median beamforming for phased array radar with antenna switching

https://doi.org/10.1016/j.sigpro.2004.05.007Get rights and content

Abstract

We propose a new robust beamformer for estimating movement parameters in impulsive noise environments using a phased array radar with antenna switching. The radar system is composed of a single transmitter, M receiving antennas, and a single receiver. The proposed beamformer is implemented as an approximate median algorithm and uses a three-dimensional power function. Maximum peaks of this power function are used for estimation of the angle, velocity and range of multiple moving targets. It is shown in simulation experiments that the new robust beamformer demonstrates a high accuracy in estimation of movement parameters and has a decreased sensitivity of the estimates with respect to noise components having heavy-tailed distributions.

Introduction

A great deal of interest has been given in recent years to the development of advanced radars with arrays of antennas as an essential component of the system [22]. Most of the earlier theoretical works in detection and estimation for radar focused on the case where the ambient noise is additive white Gaussian [14]. In many physical radar environments, however, it is shown that the ambient noise is mainly essentially non-Gaussian in the following applications: airborne applications [2], [4], [7], [12], [18], [19], [21] related to air-to-ground military radars such as millimeter-wave (MMW) seekers (94GHz) and obstacle detection radars (35GHz) mounted on helicopters, and automotive applications related to MMW car radars (77GHz) and traffic monitoring radars (24GHz) [16]. These applications are also our interests. The radar systems in such impulsive noise environments receive spiky clutter returns that give rise to non-Gaussian observations. The non-Gaussian heavy-tailed noise can be quite detrimental to the performance of conventional systems based on the Gaussian assumption [8], [15], [20]. The Laplace, Cauchy, and α-stable distributions are examples of such non-Gaussian distributions. The most important characteristic of a heavy-tailed distribution is its tail which is significantly thicker (heavier) than the exponential tail of the Gaussian distribution.

Standard high-resolution array signal processing techniques are based on simultaneous sampling of the whole multiple-sensor array and, hence, require that the number of receivers should be equal to the number of receiving antennas [6]. This, in turn, may render the applicability of these techniques very unattractive as the system is complex, bulky and costly. Moreover, a difference in gain and phase between the receiving channels deteriorates the accuracy significantly. A solution of simple structure with fewer receivers than antennas is an important issue in the design of array systems. A radar array system with antenna switching is a promising substitute for the multiple-channel array due to its lower cost and simpler front-end circuitry. New switch-type systems for radar and wireless communications have been proposed recently [1], [3], [11], [23]. Particularly in [3], the authors propose an antenna array integrated with a p–i–n diode multiplexing feed network for smart antennas. This scheme can be also applied to radar systems.

This paper is focused on signal processing issues. We consider a switching radar system composed of a single transmitter, a single transmitting antenna, M receiving antennas, and a single receiving channel, as shown in Fig. 1 [11]. The receiving antennas are switched to the single receiving channel periodically, once per cycle. Echo signals acquired in a number of these cycles are used for estimation of the movement parameters. Recently, several beamforming algorithms for such switching-type radar systems have been proposed [1], [11], [23]. It is assumed in these studies that the ambient noise is Gaussian, and thus the techniques developed in [1], [11], [23] perform poorly when the noise is non-Gaussian.

In this paper, we propose a new robust beamforming algorithm for estimating movement parameters using a phased array radar with antenna switching in an impulsive non-Gaussian noise environment. This beamformer is an extension to the switching system of the approximate median algorithm introduced in [9] for robust beamforming. This new robust beamformer forms a power distribution which is a 3D function of the azimuth angle, radial velocity and range. Maximization of the power distribution provides estimates of the movement parameters. 1D and 2D projections of this 3D function are exploited for 1D and 2D visualizations of movement in subspaces of angle, velocity and range parameters. Simulation experiments confirm a high-accuracy performance of the proposed algorithm in Gaussian and non-Gaussian environments while the conventional least-squares (LS) beamformer completely fails when the noise is heavy-tailed non-Gaussian. It demonstrates that the proposed beamformer has a strong resistance with respect to heavy-tailed noise distributions.

The rest of this paper is organized as follows. In Section 2, a switching-array system model is presented. The conventional LS based beamformer for the switching-array system is described in Section 3. The new robust beamformer based on the approximate median algorithm is proposed in Section 4. Simulation experiments are discussed in Section 5.

Section snippets

Problem formulation

Consider a uniform linear array (ULA) of M antennas where all antennas share a single transmitter radiating a frequency modulated continuous wave (FMCW). Assume that the transmitted FMCW signal is of the formx0(t)=exp(j2πϕ(t)),ϕ(t)=α0t+α1t22,0⩽t<T,where T is the pulse period and ϕ(t) is the linear time-varying phase with an initial frequency α0 and a chirp rate α1. The chirp rate α1 is given by α1=BW/T, where BW is the bandwidth. The pulses are transmitted starting at the time instants (l−1)T,

Conventional LS beamforming

Let us express the multiple-target model (9) in the form ‘single-target and interference-plus-noise’ commonly used for beamforming asy(t)=a(θ,v,D,t)s(t)+u(t),where s(t) and a(θ,v,D,t) denote the desired signal and its corresponding time-varying steering vector, respectively, and u(t) refers to ‘other-signals-plus-noise’ vector, u(t)=∑kak,vk,Dk,t)sk(t)+ε(t), where (′) means that one of the components in the sum is omitted.

The conventional LS beamformer for a single target and switching-array

Robust approximate median beamforming

In order to make clear the idea behind our approach, let us start from representation of (16) in the following equivalent form:Jt(s,θ,v,D)=l=1NM[eI,l2(t)+eQ,l2(t)],e(t)=y(t)−a(θ,v,D,t)s,eI(t)=Re{e(t)},eQ(t)=Im{e(t)},where e(t)∈RNM is the vector of residuals and the subscript l means the lth element of this vector. Hereafter, we use the subindexes I and Q for real (inphase) and imaginary (quadrature) components of variables, as done in (21) for the residuals eI,l(t) and eQ,l(t).

Let us replace

Simulation experiments

In this section, we examine the performance of the proposed robust beamformer through computer simulation. We assume a ULA of M=8 antennas with a half-wavelength interelement spacing, and a linear FM signal with α0=24GHz, the bandwidth BW=100MHz, and the pulse period T=0.05ms. A total of 50 snapshots are taken during pulse period T with the fast sampling frequency Tfast=1MHz. We consider N=4 cycles and two moving targets. The movement parameters with respect to the broadside of the array are θ1

Conclusions

The problem of finding the angle, velocity and range in a multitarget and impulsive noise scenario has been addressed for a phased array radar with antenna switching. A simple algorithm implementation of a new robust beamformer has been presented. It has been seen in simulations that the proposed robust approximate median beamformer demonstrates a high accuracy in estimation of the movement parameters and gives a decreased sensitivity of the estimates with respect to noise components having

Acknowledgements

This work was supported by the Brain Korea 21 Project.

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