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Compressed sensing (CS) algorithms for orthogonal frequency division multiplexing (OFDM) channel estimation work best when the pilot subcarrier locations are pseudo random. However, wireless standards such as LTE typically have equi-spaced pilot structures on the downlink to also enable the estimation of various other signal parameters. Here, we propose an iterative CS algorithm for channel estimation in OFDM systems which works well even in the presence of equi-spaced pilots. Simulation results indicate that between the first and second iteration of the proposed CS algorithm, we accrue a 10 dB lower mean square error (MSE) over a SNR range of 0-30 dB. A substantial gain in also observed in the block error rate (BLER) when turbo codes are employed.