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 ( $\mathsf {SEP}$ ), 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 $\mathsf {SEP}$ 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 $n \geq \log _{2}M +1$ . That is, the decay exponent for the average $\mathsf {SEP}$ is the same and equal to $m$ with infinite-bit and $n$ -bit quantizers for $n\geq \log _{2}M+1$ . On the other hand, it is only equal to $\frac {1}2$ 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.

中文翻译：

---

调相系统中的低分辨率量化：最佳检测器和误码率分析

本文研究了在存在衰落和噪声的情况下，具有低分辨率量化器的无线系统的最佳检测器和误码率分析。一种普遍 平均符号错误概率的下限（ $ \ mathsf {SEP} $ ），所有内容均正确 $ M $ 当量化位数不足以解析时获得二进制调制方案 $ M $ 信号点。在特殊情况下 $ M $ -ary相移键控（ $ M $ -PSK），则得出最大似然检测器。利用派生的检测器的结构，共同平均值 $ \ mathsf {SEP} $ 表达 $ M $ -PSK调制与 $ n $ 当无线信道经受圆形对称分布的衰落时，获得比特量化。对于中神 $ m $ 衰落，表明具有 $ n $ 位量化是 渐近地 如果通信可靠性最佳 $ n \ geq \ log _ {2} M + 1 $ 。也就是说，平均值的衰减指数 $ \ mathsf {SEP} $ 等于等于 $ m $ 与无限位和 $ n $ 位量化器 $ n \ geq \ log _ {2} M + 1 $ 。另一方面，它仅等于 $ \ frac {1} 2 $ 和0代表 $ n = \ log _ {2} M $ 和 $ n <\ log _ {2} M $ ， 分别。进行了广泛的仿真研究，以说明得出的结果的准确性，通过低分辨率量化器获得的能效增益，具有独立同相和正交信道量化的相位调制系统的性能比较以及信道下得出的结果的鲁棒性估计误差。