Diversity Order Analysis for Quantized Constant Envelope Transmission

Quantized constant envelope (QCE) transmission is a popular and effective technique to reduce the hardware cost and improve the power efficiency of 5G and beyond systems equipped with large antenna arrays. It has been widely observed that the number of quantization levels has a substantial impact on the system performance. This paper aims to quantify the impact of the number of quantization levels on the system performance. Specifically, we consider a downlink single-user multiple-input-single-output (MISO) system with M -phase shift keying (PSK) constellation under the Rayleigh fading channel. We first derive a novel bound on the system symbol error probability (SEP). Based on the derived SEP bound, we characterize the achievable diversity order of the quantized matched filter (MF) precoding strategy. Our results show that full diversity order can be achieved when the number of quantization levels L is greater than the PSK constellation order M, i.e., L>M , only half diversity order is achievable when L=M , and the achievable diversity order is 0 when L<M . Simulation results verify our theoretical analysis.

Introduction

Large antenna array is a promising technology to achieve high data rate and high reliability of wireless communication systems [1], [2], [3]. However, the power consumption and hardware cost of the system also grow with the number of antennas, which is a major concern for the practical implementation of the large antenna array technology. To address such issues, it is necessary to employ low-cost and energy-efficient hardware components at the base station (BS). It is well known that the most power hungry components at the BS are the power amplifiers (PAs) [4]. To improve the efficiency of the PAs, transmit signals with low peak-to-average power ratios (PAPRs) are desirable. In particular, constant envelope (CE) transmission, where the transmit signals from each antenna are restricted to have the same amplitude, has attracted a lot of research interests as it facilitates the use of the most efficient and cheapest PAs. It has been shown in the pioneering works [5], [6] that with  N  transmit antennas at the BS, an  O(N)  array power gain is achievable for CE transmission, as in the case of conventional transmission schemes without the CE constraint.