  This paper analyzes the impact of non-Gaussian multipath component (MPC)
amplitude distributions on the performance of Compressed Sensing (CS) channel
estimators for OFDM systems. The number of dominant MPCs that any CS algorithm
needs to estimate in order to accurately represent the channel is
characterized. This number relates to a Compressibility Index (CI) of the
channel that depends on the fourth moment of the MPC amplitude distribution. A
connection between the Mean Squared Error (MSE) of any CS estimation algorithm
and the MPC amplitude distribution fourth moment is revealed that shows a
smaller number of MPCs is needed to well-estimate channels when these
components have large fourth moment amplitude gains. The analytical results are
validated via simulations for channels with lognormal MPCs such as the NYU
mmWave channel model. These simulations show that when the MPC amplitude
distribution has a high fourth moment, the well known CS algorithm of
Orthogonal Matching Pursuit performs almost identically to the Basis Pursuit
De-Noising algorithm with a much lower computational cost.
