In this letter, we propose a generalized quadrature spatial modulation technique (GQSM) which offers additional bits per channel use (bpcu) gains and a low complexity greedy detector algorithm, structured orthogonal matching pursuit (S-OMP)- GQSM, based on compressive sensing (CS) framework. Simulation results show that the bit error rate (BER) performance of the proposed greedy detector is very close to maximum likelihood (ML) and near optimal detectors based on convex programming.