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 (NMSE), the NMSE on dominant channel components (NMSEDT), the NMSE caused by ‘lost errors’(NMSEL) and the NMSE caused by ‘false alarms’ (NMSE). Then, we derive a formula with a closed form for evaluating the upper-bound of NMSED in the ideal case (NMSE). Using the proposed analytical framework, the main findings include: 1) the NMSE 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 NMSETD;UB in case that the probability of the successes of OMP exceeds a certain threshold, in which both NMSEL are neglectable; 3) using linear regression models, the practical bit-error-rate performance also can be predicted well based on the proposed NMSE. 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.