  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.
