We examine the application of current research in sparse signal recovery to the problem of channel estimation. Specifically, using an Orthogonal Frequency Division Multiplexed (OFDM) transmission scheme with Pilot Symbol Assisted Modulation (PSAM), we consider the problem of identifying a frequency selective channel from a limited number Q out of a possible M tones of an OFDM symbol. The main observation is that if M is chosen as prime, one can identify the channel uniquely if Q ≥ 2T, where T is the number of nonzero taps in the frequency-selective channel. The identifiability result requires the minimization of the l0 norm, leading to an intractable combinatorial search problem. Several methods have been proposed to deal with these issues, and the one we examine involves l1 norm regularization known as basis pursuit . We apply these methods specifically to the problem of estimating a frequency selective channel with PSAM. As a result, the bandwidth efficiency of the system is increased due to the sparsity of the channel.