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 ( $\mathsf {SEP}$ ), 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 , 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.
Highlights
Massive MIMO systems use hundreds of antennas where each antenna is connected to a dedicated radio frequency (RF) chain equipped with high-resolution AND MOTIVATIONA NALOG-TO-DIGITAL converters (ADCs)
In [29], the authors propose a linear minimum mean square error (LMMSE) receiver when in-phase and quadrature components of the received signal are independently quantized by using a low-resolution ADC
While clearly 2-bit phase quantization is identical to using 1-bit quantization on each of the I and Q arms, we show that 3-bit phase quantization performs very to the optimized independent I and Q quantization using 4-bits
Summary
A NALOG-TO-DIGITAL converters (ADCs) are known to consume most of the power dissipated at a base station [1]. In [29], the authors propose a linear minimum mean square error (LMMSE) receiver when in-phase and quadrature components of the received signal are independently quantized by using a low-resolution ADC They provide an approximation for the mean squared error between the transmitted symbol and the received one, and derive an optimized linear receiver which performs better than the conventional Weiner filter. 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. This analysis did not exist in our previous work [37] and [38]
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