Performance Analysis of OMP-Based Channel Estimations in Mobile OFDM Systems

Abstract

To analyze the performance of orthogonal matching pursuit (OMP)-based compressed channel estimation (CCE) with deterministic pilot patterns, we propose a mathematical framework by defining four normalized mean square errors (NMSEs): the total NMSE (NMSET), the NMSE on dominant channel components (NMSED), the NMSE caused by “lost errors” (NMSEL), and the NMSE caused by “false alarms” (NMSEF). Then, we derive a formula with a closed form for evaluating the upper bound of NMSED in the ideal case (NMSED,UB). Using the proposed analytical framework, the main findings include: 1) the NMSED,UB is determined by the following four parameters: the deterministic pilot pattern, the maximum Doppler shift, the number of dominant multipath components, and the SNR; 2) the NMSED,UB can be viewed as an approximation of practical NMSET in the case that the probability of the successes of OMP exceeds a certain threshold, in which both NMSEL and NMSEF are neglectable; and 3) using linear regression models, the practical bit-error-rate performance also can be predicted well based on the proposed NMSED,UB. We believe that the proposed framework provides a useful tool for adaptively optimizing pilot parameters according to rapidly time-varying channel conditions when using OMP-based CCEs in mobile OFDM systems.