Asymptotic Capacity Lower Bound for an OFDM System With Lasso Compressed Sensing Channel Estimation for Bernoulli-Gaussian Channel

We analyze the asymptotic capacity of an OFDM system with pilot aided channel estimation over a Bernoulli-Gaussian sparse channel, with Lasso compressed sensing (CS) used for channel estimation. In the analysis, we utilize the CS asymptotic performance similarity when using Haar and DFT measurement matrices. We evaluate the mean square estimation error of an augmented Lasso estimator using the replica method results and then use it to obtain an asymptotic capacity lower bound for the OFDM system. For the considered system with equi-power pilot symbols, we optimize the average fraction of pilot subcarriers used for channel estimation and the pilot to data power ratio, given an average symbol power per subcarrier, and evaluate the asymptotic capacity bound increase due to CS.