Achievable rate of single-carrier systems with optimal uniform quantization at the receiver

The performance of digital communications systems can be affected by limitations of the analog-to-digital conversion at the receiver. To cope with finite sampling frequency and limited quantization resolution it is important to know about the impact on the achievable rate. This paper studies the achievable rate of single-carrier systems that employ analog-to-digital-conversion with uniform quantization. The achievable rate is evaluated in terms of the average mutual information between the transmitted symbols and the quantized received samples. Complex-valued modulation schemes are considered and a phase offset between the transmitter and the receiver is taken into account. System design constraints that derive from general upper bounds are discussed, and the achievable rate with optimal uniform quantization is evaluated numerically. The results show that a phase offset can significantly degrade the performance even in case of optimal quantization. This degradation cannot be compensated by means of any digital post-processing but requires either sufficiently high quantization resolution or an analog compensation, both of which has to be traded off for receiver complexity.