Performance Analysis of Distributed Quantization Aware LMS Algorithm with Quantized Measurements

This paper analyzes the mean-square performance of a distributed quantization-aware framework for adaptive Internet of Things (IoT) networks where agents use coarsely quantized measured data. Smart agents in the IoT networks contain many sensors to interact with the physical world by using analog-to-digital converters (ADCs). The distributed quantization-aware Least Mean Square (DQA-LMS) algorithm that can learn parameters in an energy-efficient fashion using measurements quantized by low-resolution ADCs with few bits is investigated. The DQA-LMS algorithm uses a bias compensation strategy to further improve its performance. We carry out a statistical analysis of the DQA-LMS algorithm and derive an expression for the mean square deviation (MSD). Numerical results show that the proposed analytical formulas are very accurate to predict the performance of the DQA-LMS algorithm.