Compressive Sensing for Radar and Radar Sensor Networks

In this project, compressive sensing for radar and radar sensor networks were studied. Significant results have been achieved in the following aspects: Compressive Sensing in Radar Sensor Networks Using Pulse Compression Waveforms; Theoretical Performance Bounds for Compressive Sensing with Random Noise; Compressive Sensing in Radar Sensor Networks for Target RCS Value Estimation; Rate Distortion Performance Analysis of Compressive Sensing; etc. Three PhD students were directly supported by this project, and have graduated. Major recognitions and awards associated with the sponsored research were conferred to the PI. 21 journal papers and 30 conferences papers were published or presented, and a complete list is attached in this report. 1 Most Significant Research Results 1.1 Compressive Sensing in Radar Sensor Networks Using Pulse Compression Waveforms Inspired by recent advances in compressive sensing (CS), we introduce CS to the radar sensor network (RSN) using the pulse compression technique in order to efficiently compress, restore and recover the radar data [7]. For the sake of simplicity but without losing generality, we study an RSN consisting of a number of transmit sensors and one receive sensor. Our idea is to employ a set of Stepped-Frequency waveforms as pulse compression codes for transmit sensors, and to use the corresponding Stepped-Frequency (SF) waveforms as the sparse matrix in the receive sensor due to the orthogonality of the basis. We conclude that the signal samples along the time domain could be largely compressed so that they could be recovered by a small number of measurements. In addition, a diversity gain could also be obtained at the output of the set of the matched filters in the receive sensor. Simulation results show that even if the signal could not be perfectly reconstructed, the probability of miss detection of target could be kept zero. In the future, the reconstructed signal would further be applied to the study of target recognition. 1.2 Theoretical Performance Bounds for Compressive Sensing with Random Noise In [1], we study the performance of compressive sensing theoretically in the presence of random noise. Different from other literature, we consider exact reconstruction of the signal, but not the recovery of the support of the signal. Both the lower bound and upper bound of the probability of error for compressive sensing are provided, with the assumption that both the original signal and the noise follow Gaussian distribution. It has been shown that under some condition, perfect reconstruction of the signal vector is impossible, as there will always be certain error. Our results provide some theoretical reference of noisy compressive sensing.