Compressive sampling in array processing

In this paper, we propose a sampling architecture for the efficient acquisition of multiple signals lying in a subspace. We show that without the knowledge of the signal subspace, the proposed sampling architecture acquires the signals at a sub-Nyquist rate. Prior to sampling at a sub-Nyquist rate, the analog signals are diversified using analog preprocessing. The preprocessing step is carried out using implementable components that inject “structured” randomness into the signals. We recast the signal reconstruction from fewer samples as a low-rank matrix recovery problem from generalized linear measurements. Our results also include a sampling theorem that provides the sufficient sampling rate for the exact reconstruction of the signals. We also discuss an application of this sampling architecture in the estimation of the covariance matrix, required for parameter estimation in several important array processing applications, from much fewer samples.