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

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 ( $\textrm {NMSE}_{\textrm s}$ ): the total NMSE ( $\textrm {NMSE}_{\textrm T}$ ), the NMSE on dominant channel components ( $\textrm {NMSE}_{\textrm D}$ ), the NMSE caused by “lost errors” ( $\textrm {NMSE}_{\textrm L}$ ), and the NMSE caused by “false alarms” ( $\textrm {NMSE}_{\textrm F}$ ). Then, we derive a formula with a closed form for evaluating the upper bound of $\textrm {NMSE}_{\textrm D}$ in the ideal case ( $\textrm {NMSE}_{\textrm {D,UB}}$ ). Using the proposed analytical framework, the main findings include: 1) the $\textrm {NMSE}_{\textrm {D,UB}}$ 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 $\textrm {NMSE}_{\textrm {D,UB}}$ can be viewed as an approximation of practical ${\textrm {NMSE}_{\textrm T}}$ in the case that the probability of the successes of OMP exceeds a certain threshold, in which both $\textrm {NMSE}_{\textrm L}$ and $\textrm {NMSE}_{\textrm F}$ are neglectable; and 3) using linear regression models, the practical bit-error-rate performance also can be predicted well based on the proposed $\textrm {NMSE}_{\textrm {D,UB}}$ . 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.