Sparse channel estimation in OFDM systems with virtual sub-carriers

Sparse channel estimation (SCE) in orthogonal frequency division multiplexing (OFDM) systems with large number of virtual sub-carriers and regularly spaced pilots is studied in this paper. Such OFDM systems are present in wireless standards like long term evolution (LTE). We numerically evaluate the performance of popular compressive sensing (CS) algorithms and shows that low complexity CS algorithms like OMP, subspace pursuit etc performs badly in these OFDM systems. We also provide analytical reasoning for this suboptimal performance. This paper points to the need of developing new low complexity CS algorithms for SCE in OFDM systems with large number of virtual sub-carriers and equispaced pilots.