Optimizations of Multisite Radar System with MIMO Radars for Target Detection

Abstract

This paper proposes a novel multisite radar system (MSRS) with multiple-input and multiple-output (MIMO) radars, i.e., MIMO-MSRS system, to improve the detection performance of fluctuating targets. The proposed MIMO-MSRS system increases the local signal-to-noise ratio (SNR) by using digital beamforming (DBF) among all transmitting and receiving channels in a single site. Then it smoothes the target's fluctuation via spatial diversity among the DBF outputs of different sites. For the MIMO-MSRS system, we derive the likelihood ratio test (LRT) detector at first based on the proposed signal model and spatial diversity conditions. Furthermore, with the derived statistics of the LRT detector in the fixed noise background, three optimization problems are discussed on the MIMO-MSRS system configurations, i.e., the numbers of sites and collocated channels in different sites. The first problem is to detect the lowest SNR target with a given probability of false alarm ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PF</i> ), probability of detection ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PD</i> ) and total system degrees of freedom (DOF). The second is to detect a target with the highest <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PD</i> for a given <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PF</i> , target SNR, and system DOF. The third is on the minimal system DOF to detect a target with a given <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PF</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PD</i> , and target SNR. For the uniform MIMO-MSRS system, both the standard optimal site number, i.e., the diversity DOF, and its closed-form approximation of the above three problems are obtained. Finally, some numerical results are also provided to demonstrate the effectiveness of the proposed MIMO-MSRS systems.