Detection of differential spatial modulation (DSM) needs only the received symbols, unlike spatial modulation that requires channel state information at the receiver. The maximum likelihood (ML)-based DSM receiver, though works well for a small number of transmit antennas, is computationally prohibitive for higher number of antennas. The hard-limiter based ML (HL-ML) receiver has low search complexity in the higher signal-to-noise regions only. The authors propose a low-complexity detection technique using compressive sensing for DSM. The detection involves a two-step process, by first finding the antenna index number and then the M-ary phase-shift keying (MPSK) symbol transmitted from that antenna. After performing a correlation between the past and the present received symbol blocks, the index location of the largest elements of this operation reveals the order of antennas that were activated in a symbol duration. The MPSK symbol is found by a pseudo-inverse operation on the columns of the past and the present received symbol blocks, corresponding to the time index and antenna number, which is same as the above indices. The proposed receiver achieves a substantial reduction in computational complexity close to 63%, when compared to the HL-ML receiver and the performance penalty narrows down with higher order MPSK constellations.