  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.
