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 ≥ lag 2M +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≥ log2M+1. On the other hand, it is only equal to frac 1 2 and 0 for n = log2 M and n < log2 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.