Subspace compressive detection for sparse signals

The emerging theory of compressed sensing (CS) provides a universal signal detection approach for sparse signals at sub-Nyquist sampling rates. A small number of random projection measurements from the received analog signal would suffice to provide salient information for signal detection. However, the compressive measurements are not efficient at gathering signal energy. In this paper, a set of detectors called subspace compressive detectors are proposed where a more efficient detection scheme can be constructed by exploiting the sparsity model of the underlying signal. Furthermore, we show that the signal sparsity model can be approximately estimated using reconstruction algorithms with very limited random measurements on the training signals. Based on the estimated signal sparsity model, an effective subspace random measurement matrix can be designed for unknown signal detection, which significantly reduces the necessary number of measurements. The performance of the subspace compressive detectors is analyzed. Simulation results show the effectiveness of the proposed subspace compressive detectors.