Generalized spatial modulation (GSM) is a variant of spatial modulation (SM) which offers enhanced spectral efficiency with a moderate increase in signal processing complexity. This paper proposes a novel compressive sensing (CS) aided detection algorithm which offers better performance than traditional CS based detection algorithms. In contrast to widely considered frequency-flat channel models, we have adopted frequency-selective wireless channel models to account for high data-rate applications. Our proposed algorithm offers superior performance over traditional CS based algorithms even in the presence of channel estimation errors. Numerical experiments are conducted to investigate the mathematical analysis under different suppositions on channel state information. Normalized mean-square error (NMSE) and bit-error rate (BER) versus signal-to-noise (SNR) curves are studied to investigate the performance under different detection algorithms.