Abstract
This paper focuses on a noncoherent flat Rayleigh fading wireless communication system with a single transmitter antenna and $N$ receiver antennas, i.e., a single-input-multiple-output (SIMO) system, in which the channel coefficients vary in every one time slot. For such a system, a fast noncoherent maximum likelihood (ML) detection algorithm and a corresponding closed form symbol error probability (SEP) formula are derived. In addition, the lower and upper bounds on SEP are established to quantitatively characterize how quickly SEP decays when $N$ goes to infinity, with two important concepts, full receiver diversity gain and geometrical coding gain, being introduced, showing that any nonnegative pulse amplitude modulation (PAM) constellation enables full receiver diversity for the massive SIMO system. Furthermore, we find that an optimal received constellation that maximizes the geometrical coding gain is the geometrical constellation. Comprehensive computer simulations validate our theoretical analysis and demonstrate that our proposed optimal constellation attains significant performance gains over the currently available constellation design the the same massive SIMO system.
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