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

Abstract

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.

Reliability Characterization for SIMO Communication Systems With Low-Resolution Phase Quantization Under Rayleigh Fading

“…We also assume that full channel state information (CSI) is available at the receiver. Similar to our previous work in [8], the motivation behind our model with full-precision CSI is two-fold. First, in [42], it was shown that it is possible to attain a high channel estimation precision with the use of low-resolution ADCs by increasing the number of training symbols in the closed-loop estimation process.…”

“…By using DVO as our main performance metric, we determine communication reliability to first order. We propose three lowcomplexity antenna selection strategies for data detection and we obtain reliability regimes for the proposed strategies, analogous to those obtained in the case of SISO systems in [8]. We establish their asymptotic optimality properties as a function of the quantization bits in terms of DVO, and compare their performance with the one achieved by the derived maximum likelihood (ML) detector.…”

“…approach, where we first select an antenna that will give us a favourable diversity branch based on the observed channel states, and then use the single antenna ML detector to estimate the transmitted symbols over the selected antenna. The single antenna ML detector, unlike the multi-antenna one given in Theorem 1, is a simple low-complexity distance calculator [8]. We illustrate the antenna selection approach in Fig.…”

“…As an important step to characterize communication reliability with low-resolution ADCs, three reliability regimes were established in [8]. They can be called quantization plateau, slow-decay and quantization invariance regimes.…”

“…In the quantization invariance regime, n is larger than the logarithm of the input alphabet size and the DVO does not change with n. In this regime, we achieve the same DVO that can be achieved by means of a high-resolution quantizer. These fundamental structural results were only obtained for single-input single-output (SISO) low-resolution ADC communication systems in [8], and their extension to the multi-antenna systems is a completely open problem in the literature.…”