Low-Resolution Quantization in Phase Modulated Systems: Optimum Detectors and Error Rate Analysis

This paper studies optimum detectors and error rate analysis for wireless systems with low-resolution quantizers in the presence of fading and noise. 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. In the special case of M-ary phase shift keying (M-PSK), the maximum likelihood detector is derived. Utilizing the structure of the derived detector, a general average SEP expression for M-PSK modulation with n-bit quantization is obtained when the wireless channel is subject to fading with a circularly-symmetric distribution. For the Nakagami-m fading, it is shown 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. An extensive simulation study is performed to illustrate the accuracy of the derived results, energy efficiency gains obtained by means of low-resolution quantizers, performance comparison of phase modulated systems with independent in-phase and quadrature channel quantization and robustness of the derived results under channel estimation errors.