Robust target estimation in compressive sensing based colocated MIMO radar

A colocated multiple-input multiple-output (MIMO) radar system is considered, in which the transmitters and receivers are nodes of a small scale wireless network. The sparsity of targets in the illuminated space allows target detection based on compressive sensing (CS) techniques. A receive node compresses the received signal via a linear transformation, Φ, referred to in CS theory a measurement matrix. The compressed samples are subsequently forwarded to a fusion center, where an ℓ1-optimization problem is formulated and solved for target information. CS-based MIMO radar achieves the same localization performance as do traditional methods but with many fewer measurements. Unlike previous work, we consider the case in which the targets might be located across several range bins, and the delay of the first reflected signal is unknown and, due to the small number of compressed samples, cannot be estimated accurately. A new measurement matrix is proposed that is constructed based on the transmit signal waveforms and also accounts for all possible discretized delays of target returns within a given time window. It is shown that reduced bandwidth transmit waveforms can lead to a measurement matrix that improves signal-to-interference ratio (SIR), but on the other hand, using waveforms that are too narrowband increases the coherence of the sensing matrix, thus invalidating the conditions for the application of the CS approach. Therefore, the transmit waveforms must be chosen carefully to guarantee the desired performance.