On the limits of communication with low-precision analog-to-digital conversion at the receiver

Abstract

Abstract-As communication systems scale up in speed and bandwidth, the cost and power consumption of high-precision (e.g., 8-12 bits) analog-to-digital conversion (ADC) becomes the limiting factor in modern transceiver architectures based on digital signal processing. In this work, we explore the impact of lowering the precision of the ADC on the performance of the communication link. Specifically, we evaluate the communication limits imposed by low-precision ADC (e.g., 1-3 bits) for transmission over the 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 log 2 K bits), we show that the input distribution need not have any more than K+1 mass points to achieve the channel capacity. For 2-bin (1-bit) symmetric quantization, this result is tightened to show that binary antipodal signaling is optimum for any signal-tonoise ratio (SNR). For multi-bit quantization, a dual formulation of the channel capacity problem is used to obtain tight upper bounds on the capacity. The cutting-plane algorithm is employed to compute the capacity numerically, and the results obtained are used to make the following encouraging observations : (a) up to a moderately high SNR of 20 dB, 2-3 bit quantization results in only 10-20% reduction of spectral efficiency compared to unquantized observations, (b) standard equiprobable pulse amplitude modulated input with quantizer thresholds set to implement maximum likelihood hard decisions is asymptotically optimum at high SNR, and works well at low to moderate SNRs as well.

Multi-Gigabit communication: the ADC bottleneck¹

“…We begin by recalling some results we obtained last year while investigating these issues for the classical bandlimited Additive White Gaussian Noise (AWGN) channel [3], [4]. Apart from its fundamental significance, the AWGN channel model also forms an excellent approximation for the near line-of-sight, 60 GHz "point-and-shoot" links, where the use of directional antennas (possibly fixed beam) at each end can cut down drastically on multipath.…”

Capacity of the discrete-time AWGN channel under output quantization

“…Specifically, in [2], we have shown analytically that for the extreme scenario of 1-bit symmetric quantization, binary antipodal signaling achieves the capacity (at any SNR). Multi-bit quantization has been considered in [3], [10], where we show that the cutting-plane algorithm [11] can be employed for computing the capacity and obtaining optimal input distributions.…”

“…{jsingh, madhow}@ece.ucsb.edu, onkar@tcs.tifr.res.in capacity for any signal-to-noise ratio (SNR) [2]. For multibit quantization [3], we provided a duality-based approach to bound the capacity from above, and employed the cuttingplane algorithm to generate input distributions that nearly achieved these upper bounds. Based on our results, we conjectured that a discrete input with cardinality not exceeding the number of quantization bins achieves the capacity of the average power constrained AWGN-QO channel.…”

On the Capacity of Quantized Gaussian MAC Channels with Finite Input Alphabet

“…In [2], it has been shown that quantization causes floors in the bit error performance in single-input multiple-output (SIMO) fading channels. In [3], it is shown that for a single-input single-output (SISO) pointto-point single user system with additive white Gaussian noise (AWGN), receiver quantization with low precision ADC results in significant loss of capacity when compared to an unquantized receiver.…”

“…In [3], the optimum input distribution for a point-to-point single-user SISO AWGN This work was supported in part by the DRDO-IISc Program on Advanced Research in Mathematical Engineering. channel with quantized output was shown to be non-Gaussian with a finite support set.…”