  This paper considers a wireless communication system with low-resolution
quantizers, in which transmitted signals are corrupted by fading and additive
noise. For such wireless systems, 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 optimum maximum
likelihood detector for equi-probable signal points is derived. Utilizing the
structure of the derived optimum receiver, 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. Adopting this
result for Nakagami-m fading channels, easy-to-evaluate expressions for the
average SEP for M-PSK modulation are further derived. It is shown that a
transceiver architecture with n-bit quantization is asymptotically optimum in
terms of communication reliability if n is greater than or equal to 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 is greater than or equal to
log_2(M+1). On the other hand, it is only equal to half and 0 for n = log_2(M)
and n < log_2(M), respectively. An extensive simulation study is performed to
illustrate the derived results and energy efficiency gains obtained by means of
low-resolution quantizers.
