1-Bit Quantization and Oversampling at the Receiver: Communication Over Bandlimited Channels With Noise

Abstract

A bandlimited additive white Gaussian noise channel is considered where the output is 1-bit quantized and oversampled with respect to the Nyquist rate. We consider root raised cosine filters at the transmitter and receiver. In particular, we focus on a roll-off factor equal to 1 and 0. Because of the oversampling the channel has infinite memory. An auxiliary channel law is proposed which describes the resulting received sequences based on a truncated waveform. The random distortion due to the residual sidelobes can be considered as an additional noise term in the auxiliary channel law. The auxiliary channel law is utilized for computing a lower bound on the achievable rate and in a further step for optimizing a Markov source model. Different signaling schemes have been considered, such as BPSK and ASK. Moreover, Nyquist signaling and faster-than-Nyquist signaling are considered. The resulting achievable rates are superior as compared with results from the literature on bandlimited channels with noise, 1-bit quantization, and oversampling at the receiver.