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.