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Spatial modulation (SM) is a multiple-input multiple-output (MIMO) technique that achieves a MIMO capacity by conveying information through antenna indices, while keeping the transmitter as simple as that of a single-input system. Quadrature SM (QSM) expands the spatial dimension of the SM into in-phase and quadrature dimensions, which are used to transmit the real and imaginary parts of a signal symbol, respectively. A parallel QSM (PQSM) was recently proposed to achieve more gain in the spectral efficiency. In PQSM, transmit antennas are split into parallel groups, where QSM is performed independently in each group using the same signal symbol. In this paper, we analytically model the asymptotic pairwise error probability of the PQSM. Accordingly, the constellation design for the PQSM is formulated as an optimization problem of the sum of multivariate functions. We provide the proposed constellations for several values of constellation size, number of transmit antennas, and number of receive antennas. The simulation results show that the proposed constellation outperforms the phase-shift keying (PSK) constellation by more than 10 dB and outperforms the quadrature-amplitude modulation (QAM) schemes by approximately 5 dB for large constellations and number of transmit antennas.

Performance Analysis and Constellation Design for the Parallel Quadrature Spatial Modulation