Performance of estimation and detection algorithms in wireless networks

© 2007 Dr. Alex Seak Chon LeongThis thesis focuses on techniques for analyzing the performance of estimation and detection algorithms under conditions which could be encountered in wireless networks, with emphasis on wireless sensor networks. These include phenomena such as measurement losses, fading channels, measurement delays and power constraints. We first look at the hidden Markov model (HMM) filter with random measurement losses. The loss process is governed by another Markov chain. In the two-state case we derive analytical expressions to compute the probability of error. In the multi-state case we derive approximations that are valid at high signal-to-noise ratio (SNR). Relationships between the error probability and parameters of the loss process are investigated. We then consider the problem of detecting two-state Markov chains in noise, under the Neyman-Pearson formulation. Our measure of performance here is the error exponent, and we give methods for computing this, firstly when channels are time-invariant, and then for time-varying fading channels. We also characterize the behaviour of the error exponent at high SNR. We will look at the fixed lag Kalman smoother with random measurement losses. We investigate both the notion of estimator stability via expectation of the error covariance, and a probabilistic constraint on the error covariance. A comparison with the Kalman filter where lost measurements are retransmitted is made. Finally we consider the distributed estimation of scalar linear systems using multiple sensors under the analog forwarding scheme. We study the asymptotic behaviour of the steady state error covariance as the number of sensors increases. We formulate optimization problems to minimize the sum power subject to error covariance constraints, and to minimize the error covariance subject to sum power constraints. We compare between the performance of multi-access and orthogonal access schemes, and for fading channels the effects of various levels of channel state information (CSI)