Performance Analysis of Target Parameters Estimation Using Multiple Widely Separated Antenna Arrays

TL;DR

This paper analyzes the performance of target parameter estimation in radar systems using multiple widely separated antenna arrays, deriving bounds and examining the effects of array configurations on estimation accuracy.

Contribution

It provides new theoretical expressions for CRLB and ML estimator properties for radar with multiple antenna arrays under stochastic and deterministic models.

Findings

ML estimator is consistent and efficient for large array products under stochastic model

Grouping receiving elements into arrays improves estimation accuracy and reduces SNR threshold

Small array products can degrade performance and make CRLB a poor predictor of MSE

Abstract

Target parameter estimation performance is investigated for a radar employing a set of widely separated transmitting and receiving antenna arrays. Cases with multiple extended targets are considered under two signal model assumptions: stochastic and deterministic. The general expressions for the corresponding Cramer-Rao lower bound (CRLB) and the asymptotic properties of the maximum-likelihood (ML) estimator are derived for a radar with $M_t$ arrays of $L_t$ transmitting elements and $M_r$ arrays of $L_r$ receiving elements for both types of signal models. It is shown that for an infinitely large product $M_tM_r$, and a finite $L_r$, the ML estimator is consistent and efficient under the stochastic model, while the deterministic model requires $M_tM_r$ to be finite and $L_r$ to be infinitely large in order to guarantee consistency and efficiency. Monte Carlo simulations further investigate the estimation performance of the proposed radar configuration in practical scenarios with finite $M_tM_r$ and $L_r$, and a fixed total number of available receiving antenna elements, $M_r L_r$. The numerical results demonstrate that grouping receiving elements into properly sized arrays reduces the mean squared error (MSE) and decreases the threshold SNR. In the numerical examples considered, the preferred configurations employ $M_t M_r > 1$. In fact, when $M_t M_r$ becomes too small, due to the loss of the geometric gain, the estimation performance becomes strongly dependent on the particular scenario and can degrade significantly, while the CRLB may become a poor prediction of the MSE even for high SNR. This suggests it may be advantageous to employ approaches where neither $M_tM_r$ nor $L_r$ are too small.