The Application Of Sparse Signal Processing In Wireless Communications

The theme for this thesis is to exploit sparsity in a number of wireless communication problems.We formulate the sparsity property as prior information to be utilized in signal processing problems,and define a broad range of problems applicable to this paradigm as sparse signal processing problems.Sparsity enforcing regularization optimization,fixed sparsity-inducing prior Bayesian methods,parameterized prior Bayesian methods and greedy Matching Pursuit algorithms are introduced in this thesis.We derive Sparse Bayesian Learning(SBL)by applying(?)_p norm regularization to prior parameters,which directly explains why SBL can converge to a sparse solution.We apply sparse signal processing to OFDM channel estimation under impulse noise.We first use e₁ norm regularization to recover the impulse noise component and cancel its impact.Then we developed IFFT approximation algorithm with thresholding,which scarifies a little performance for a big reduction in implementation complexity. Simulation results show that both of our algorithms can improve OFDM channel estimation performance significantly under various impulse noise environments.We apply Sparse Bayesian learning(SBL)to blind OFDM equalization for sparse multi-path channels.We integrate the Sparse Bayesian Learning algorithm into the SMC blind receiver to improve the performance under sparse channels.Based on the observation that increasing the particle number to sample the signal space is inefficient, and that SBL improves trail distribution quality,we propose a novel low complexity deterministic sparse Bayesian blind equalizer.We also use iterative equalization to improve the estimate of the first few symbols in an OFDM symbol,which further reduces BER rate.We apply sparse signal processing to QAM blind equalization.We differentiate the sorted inverse of the QAM signals,to get a sparse signal with only a few non-zero elements.Then we use e₁ norm cost function to encourage sparsity so that equalization output can converge to the constellation points.Our algorithm has a relatively high complexity,but it can converge within one OFDM symbol,which is not possible for many other blind equalization algorithms based on property recovery.