Analytical Solution of Optimal Symbol Error Rate for Multilevel Pulse-Amplitude-Modulated Signals With One-Bit Quantization

Low-resolution ADC is a promising solution to reduce circuit cost and energy consumption in 6G wireless communication systems. There are few analytical results on symbol error performance with low-resolution quantization. In this letter, novel, analytical solution for the optimal symbol error rate (SER) of $M$ -ary pulse amplitude modulated ( $M$ -PAM) signals with one-bit quantization over additive white Gaussian noise (AWGN) channel is derived. The SER expression is shown to be the function of quantization thresholds, modulated symbol levels and sampling numbers by utilizing the asymptotic distribution of the quantized outputs. The new solution shows that temporal oversampling compensates for 1-bit quantization and the SER performance bound when sampling number goes to infinity degrades by a factor of $2/\pi $ compared to the unquantized case. These results allow for a rapid and accurate evaluation of the system performance when using 1-bit ADCs, and thus offer a useful tool for system design, analysis and optimization.