On the achievable rate of bandlimited continuous-time 1-bit quantized AWGN channels

Abstract

We consider a continuous-time bandlimited additive white Gaussian noise channel with 1-bit output quantization. On such a channel the information is carried by the temporal distances of the zero-crossings of the transmit signal. The set of input signals is constrained by the bandwidth of the channel and an average power constraint. Under a set of assumptions, we derive a lower bound on the capacity by lower-bounding the achievable rate for a given set of waveforms with exponentially distributed zero-crossing distances. We focus on the behaviour in the high signal-to-noise ratio regime and characterize the achievable rate depending on the available bandwidth and the signal-to-noise ratio.