Transceiver Design with Low-Precision Analog-to-Digital Conversion : An   Information-Theoretic Perspective
  Modern communication receiver architectures center around digital signal processing (DSP), with the bulk of the receiver processing being performed on digital signals obtained after analog-to-digital conversion (ADC). In this paper, we explore Shannon-theoretic performance limits when ADC precision is drastically reduced, from typical values of 8-12 bits used in current communication transceivers, to 1-3 bits. The goal is to obtain insight on whether DSP-centric transceiver architectures are feasible as communication bandwidths scale up, recognizing that high-precision ADC at high sampling rates is either unavailable, or too costly or power-hungry. Specifically, we evaluate the communication limits imposed by low-precision ADC for the ideal real discrete-time Additive White Gaussian Noise (AWGN) channel, under an average power constraint on the input. For an ADC with K quantization bins (i.e., a precision of log2 K bits), we show that the Shannon capacity is achievable by a discrete input distribution with at most K + 1 mass points. For 2-bin (1-bit) symmetric ADC, this result is tightened to show that binary antipodal signaling is optimum for any signal-to-noise ratio (SNR). For multi-bit ADC, the capacity is computed numerically, and the results obtained are used to make the following encouraging observations regarding system design with low-precision ADC : (a) even at moderately high SNR of up to 20 dB, 2-3 bit quantization results in only 10-20% reduction of spectral efficiency, which is acceptable for large communication bandwidths, (b) standard equiprobable pulse amplitude modulation with ADC thresholds set to implement maximum likelihood hard decisions is asymptotically optimum at high SNR, and works well at low to moderate SNRs as well. 
Jaspreet Singh, Onkar Dabeer, Upamanyu Madhow