Phase modulated communication with low-resolution ADCs

This paper considers a low-resolution wireless communication system in which transmitted signals are corrupted by fading and additive noise. First, a universal lower bound on the average symbol error probability (SEP), correct for all M-ary modulation schemes, is obtained when the number of quantization bits is not enough to resolve M signal points. Second, in the special case of M-ary phase shift keying (M-PSK), the optimum maximum likelihood detector for equi-probable signal points is derived. Third, utilizing the structure of the derived optimum receiver, a general average SEP expression for the M-PSK modulation with n-bit quantization is obtained when the wireless channel is subject to fading with a circularly-symmetric distribution. Finally, an extensive simulation study of the derived analytical results is presented for general Nakagami-m fading channels. It is observed that a transceiver architecture with n-bit quantization is asymptotically optimum in terms of communication reliability if n ≥ log ₂ M + 1. That is, the decay exponent for the average SEP is the same and equal to m with infinite-bit and n-bit quantizers for n ≥ log ₂ M + 1. On the other hand, it is only equal to 1/2 and 0 for n = log ₂ M and n ≥ log ₂ M, respectively. Hence, for fading environments with a large value of m, using an extra quantization bit improves communication reliability significantly.