Compressive sampling architecture for wideband communication

Abstract

This dissertation proposes a novel Compressive Sampling (CS) scheme for Sub-Nyquist Spectrum Sensing (SNSS) of spectrally sparse wideband signals. A novelty of our proposed SNSS scheme resides in the analog front-end. We show that it can be modeled as a sparse binary-valued measurement matrix. This has allowed us to bring to bear the proven advantages of the Low Density Parity Check (LDPC) matrices in improving the performance of the existing SNSS methods. Specifically, we show that the number of parallel SNSS channels required for a robust CS sparsity detection in our proposal is reduced compared to the existing SNSS methods. We provide new analytic (information-theoretic) lower bounds on this number and show that the LDPC-based measurement matrix is closer to this bound compared to the alternatives.The existing algorithms (such as those based on Matching Pursuit or Basis Pursuit)for CS sparsity detection are not optimal for our proposed architecture giventhe unique (sparse binary-valued) aspect of the measurement matrix. We developtwo new Belief Propagation (BP) algorithms - an Independent Probability Estimates(IPE) algorithm and a Joint Probability Estimates (JPE) algorithm - to solvethe sparsity detection problem. The performance of these algorithms is evaluatedusing Monte-Carlo simulations as well as semi-analytic approaches based onDensity Evolution and EXIT (Extrinsic Information Transfer) methods. We showthat the proposed algorithms outperform several existing algorithms (includingthe well-known Orthogonal Matching Pursuit (OMP) algorithm).Another contribution of our work is in mitigating the problem of noise enhancement (during Zero-Forcing based signal reconstruction) that affects several existing SNSS schemes (such as the Modulated Wideband Converter (MWC)). We provide analytical proofs showing this benefit and confirm the analytical results by simulation.Finally, we demonstrate the signal reconstruction in the proposed CS receiver through simulation. The Bit Error Rate (BER) performance of a QPSK system with the proposed CS receiver is simulated and the performance improvement over the MWC is demonstrated. As an extension of the developed algorithms, a framework of joint compression and denoising application is envisioned and presented with theoretical analysis.