Performance Limits of Sparse Support Recovery Algorithms

Compressed Sensing (CS) is a signal acquisition approach aiming to reduce the number of measurements required to capture a sparse (or, more generally, compressible) signal. Several works have shown significant performance advantages over conventional sampling techniques, through both theoretical analyses and experimental results, and have established CS as an efficient way to acquire and reconstruct a sparse signal with low sampling rate, even below Nyquist. However, apart from the full signal recovery, in some cases only certain features and properties of the signal are required. For instance, in many wireless communication applications, e.g. cognitive radio systems and channel estimation, the indices recovery of the non-zero components of a sparse signal is required. In this work, we study the problem of sparse support recovery from few and noisy signal measurements by examining both fundamental bounds and performance of some of the prevailing practical algorithms for support recovery. After summarizing some algorithm-independent information theoretic limits, we present four frequently used support recovery algorithms with different complexity requirements and recovery capabilities: (i) maximum correlation (MC) algorithm, (ii) a thresholded greedy optimization algorithm, (iii) an `1-constrained quadratic programming approach, and (iv) thresholded basis pursuit (TBP) algorithm. Their performance is simulated and examined for different sparsity levels, number of measurements, signal characteristics (i.e. βmin,MAR) and SNR values. Our simulation results indicate that TBP outperforms the other methods at the expense of higher complexity. In addition, simulation results emphasize the importance of signal characteristics on the success of the support recovery.