Receiver Design With Reduced DOF in Frequency Domain for Target Detection Under Gaussian Clutter

This paper addresses the problem of target detection against a background of Gaussian clutter by using frequency snapshots with reduced degrees of freedom (DOF). We derive the optimal detector and detection performance under the Neyman-Pearson criterion for general frequency snapshot selection with arbitrary DOF. When the clutter statistics are unknown, we use a uniformly random frequency snapshot selection method and show how the DOF employed affects the detection performance. When the clutter return follows a stationary Gaussian distribution with slowly varying power spectral density, the optimal selection is derived. When the clutter is composed of reflected versions of the transmitted waveforms, a greedy-based method for selecting the frequency snapshots is presented. Numerical experiments show that a receiver with reduced DOF can lead to detection performance which is very close to that of the receiver with full DOF.

I. Introduction

The detection of radar targets against clutter is one of the fundamental problems in radar signal processing [1], [2]. It is well known that when the clutter-plus-noise is a white stationary Gaussian random process independent of the target return, the optimal receiver is a matched filter. Sometimes, it may be convenient to process the received signal and analyze the detection performance in the frequency domain [3], [4]. In [3], [4], the optimal Neyman-Pearson (NP) detector and its performance are derived using frequency snapshots, and then waveform design methods are presented based on the detection performance. Although the method proposed in [3], [4] can lead to optimal or quasi-optimal performance, the receivers have to process all frequency snapshots, leading to a high complexity radar with full degrees of freedom (DOF). In order to lower the hardware or software complexity of radar systems, in this paper, we study receiver design with reduced DOF in the frequency domain.