Phase Modulated Communication with Low-Resolution ADCs

Abstract

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 equiprobable 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 circularlysymmetric distribution. Finally, an extensive simulation study of the derived analytical results is presented for general Nakagamim 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.Index Terms-Maximum likelihood detection, low-resolution ADC, symbol error probability.

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

“…Our results in Theorem 4 (together with Theorem 1) establishes a fundamental ternary behaviour for the symbol error probability in the high SNR regime for low-resolution ADC based receiver architectures. These results do not appear in our previous work [37] and [38], or exist in any other previous paper in the literature. Further, we present a numerical performance comparison of phase quantization to the situation where the in-phase and quadrature channels are independently quantized.…”

“…We further extend our numerical analysis to evaluate the robustness of our findings to imperfect channel state information. This analysis did not exist in our previous work [37] and [38].…”

“…Furthermore, the same effect to improve channel estimation accuracy can be achieved by using carefully designed training sequences to perform a bisection search during the channel estimate phase. The material in this paper was presented in part at [37] and [38]. In [37] we focus only on QPSK modulation for Rayleigh fading environments and in [38] we generalize the error probability results to M -PSK modulation under any circularly symmetric fading distributions.…”

“…The material in this paper was presented in part at [37] and [38]. In [37] we focus only on QPSK modulation for Rayleigh fading environments and in [38] we generalize the error probability results to M -PSK modulation under any circularly symmetric fading distributions. The present paper expands upon the results presented in [37] and [38] and provides a rigorous error probability performance and diversity order analysis under Nakagami-m fading.…”

“…In [37] we focus only on QPSK modulation for Rayleigh fading environments and in [38] we generalize the error probability results to M -PSK modulation under any circularly symmetric fading distributions. The present paper expands upon the results presented in [37] and [38] and provides a rigorous error probability performance and diversity order analysis under Nakagami-m fading. Our results in Theorem 4 (together with Theorem 1) establishes a fundamental ternary behaviour for the symbol error probability in the high SNR regime for low-resolution ADC based receiver architectures.…”