New Equivalent Model of a Quantizer With Noisy Input and Its Applications for MIMO System Analysis and Design

Abstract

We propose a novel equivalent model for a quantizer with noisy input (the desired signal corrupted by measurement noise). It presents the quantizer output as a sum of the desired signal after it passes through a nonlinear element with a known equivalent transfer function and an equivalent additive white noise. The equivalent transfer function takes the form of a conditional expectation of the quantizer output given the desired signal portion of its input. The proposed model proves to be effective for the analysis and design of MIMO systems employing low-resolution quantizers (analog to digital and digital to analog converters, ADCs and DACs, respectively). We also demonstrate the efficacy of the model through several example applications for 1) the design of digital dither that mitigates the effect of DAC quantization error in a MIMO transmitter and significantly reduces the DAC resolution requirement; 2) the determination of the minimal ADC resolution required for operation of conventional MIMO receivers designed for infinite-resolution ADC arrays, without incurring significant performance degradation; and 3) the design of simple MIMO receivers (ML and MMSE) that mitigate the effect of insufficient ADC resolution, thereby extending the receiver SNR operating range without an undue complexity increase.