On the symbol error probability for QPSK with quantized observations

Abstract

We consider a single-input-single-output (SISO) system with quadrature phase shift keying (QPSK) modulation and derive an easy-to-evaluate expression for the symbol error probability (SEP) when a general n-bit phase quantization is used at the receiver. We further evaluate the expressions asymptotically to characterize the diversity order and the quantization penalty at high signal-to-noise ratios (SNRs). We observe that the system with n-bit phase quantization achieves full diversity order of one when n > 2. Numerical examples are used to verify the analysis.