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A Bayesian approach to sparse channel estimation in OFDM systems

In this work, we address the problem of estimating sparse communication channels in OFDM systems in the presence of carrier frequency offset (CFO) and unknown noise variance. To this end, we consider a convex optimization problem, including a probability function, accounting for the sparse nature of the communication channel. We use the Expectation-Maximization (EM) algorithm to solve the corresponding Maximum A Posteriori (MAP) estimation problem. We show that, by concentrating the cost function in one variable, namely the CFO, the channel estimate can be obtained in closed form within the EM framework in the maximization step. We present an example where we estimate the communication channel, the CFO, the symbol, the noise variance, and the parameter defining the prior distribution of the estimates. We compare the bit error rate performance of our proposed MAP approach against Maximum Likelihood.