Performance analysis of OMP-based channel estimation for OFDM systems with periodical pilots and virtual subcarriers

By exploiting the sparsity of the channel impulse response (CIR), compressive channel sensing methods are capable of recovering the channel state information with overwhelming probability, given that the sensing matrix holds the restricted isometry property (RIP). To this end, random pilot patterns are often assumed to ensure the RIP of the sensing matrix. In practical orthogonal frequency division multiplexing (OFDM) systems, however, periodical pilots and a large amount of virtual subcarriers (VCs) are usually employed to ease frame design and to confront inter-channel interference. The pilot patterns in practical OFDM systems are far from being random, and thus it is necessary to investigate the performance of practical compressive channel sensing methods for such systems. In this paper, we analyze the performance of an orthogonal matching pursuit (OMP) algorithm for practical OFDM systems with periodical pilot patterns and a large number of VCs. In particular, we study the coherence of the channel sensing matrix and present a lower bound for mean squared error performance of the presented OMP algorithm over frequency-selective Rayleigh fading channels. The presented analysis is verified by means of extensive Monte Carlo simulations.