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This paper analyzes the impact of non-Gaussian multipath component (MPC)amplitude distributions on the performance of Compressed Sensing (CS) channelestimators for OFDM systems. The number of dominant MPCs that any CS algorithmneeds to estimate in order to accurately represent the channel ischaracterized. This number relates to a Compressibility Index (CI) of thechannel that depends on the fourth moment of the MPC amplitude distribution. Aconnection between the Mean Squared Error (MSE) of any CS estimation algorithmand the MPC amplitude distribution fourth moment is revealed that shows asmaller number of MPCs is needed to well-estimate channels when thesecomponents have large fourth moment amplitude gains. The analytical results arevalidated via simulations for channels with lognormal MPCs such as the NYUmmWave channel model. These simulations show that when the MPC amplitudedistribution has a high fourth moment, the well known CS algorithm ofOrthogonal Matching Pursuit performs almost identically to the Basis PursuitDe-Noising algorithm with a much lower computational cost.

Compressed Sensing Channel Estimation for OFDM with non-Gaussian Multipath Gains