In this paper, we propose a novel scheme, which is called generalized precoding-aided quadrature spatial modulation (GPQSM), that extends the conventional quadrature spatial modulation to the receiver side. In GPQSM, spatial modulation works in both the in-phase and quadrature parts of the received signals, thus conveying additional information bits compared with conventional generalized precoding-aided spatial modulation (GPSM). The proposed scheme is general and can degenerate into the conventional multiple-input multiple-output (MIMO) scheme. A closed-form upper bound on the average bit error probability of GPQSM is derived. Simulation results verify the theoretical analysis and show that GPQSM outperforms the conventional GPSM scheme and the MIMO scheme under the same spectral efficiency.