Formulation and Analysis of LMS Adaptive Networks for Distributed Estimation in the Presence of Transmission Errors

Wireless sensor network (WSN) technologies and distributed processing are essential to develop ubiquitous sensing in the Internet of Things (IoT) paradigm, wherein sensors pervasively collect data and perform information processing and communication tasks to achieve a common objective. This paper presents the formulation and analysis of distributed estimation algorithms based on the diffusion cooperation scheme in the presence of errors due to the unreliable data transfer among nodes. In particular, we highlight the impact of transmission errors on the least-mean squares (LMS) adaptive networks. We develop the closed-form expressions for the steady-state mean-square deviation (MSD), which is helpful to assess the effects of the imperfect information flow on the behavior of diffusion LMS algorithms in terms of steady-state error. The model is then validated by performing Monte Carlo simulations. It is shown that local and global steady-state MSD values are not necessarily monotonic increasing functions of the error probability. We also assess sufficient conditions that ensure mean and mean-square stability of diffusion LMS strategies in the presence of transmission errors. We examine a practical scenario where errors occur at the medium access control (MAC) level. To overcome the problem of unreliable data exchange, we implement a random pairwise strategy that improves the performance of the estimation algorithm in the presence of high transmission error rates. Moreover, issues such as scalability in the sense of network size and regressor size, convergence behavior during the transient phase, spatially correlated observations, as well as the effect of the distribution of the noise variance are studied.