COMMUNICATION AND ESTIMATION IN NOISY NETWORKS

In this thesis, we present a study of two problems relevant to sensor networks. We first study a new form of sensor networks where the parameters of interest are the inter-node time-varying channel(s) and then study the problem of determining the optimal location of a mobile relay node to optimize a certain cost function for the sensor network. Networks which collect information about the channels are becoming relevant in environmental monitoring systems, like underwater tsunami detecting networks. We first present two examples to drive home the point that joint channel estimation and communication can outperform training based schemes. First, the binary symmetric channel is examined; an achievable capacity-distortion trade-off is derived for both joint and time-orthogonal protocols. For the flat fading, additive, white, Gaussian noise channel, a novel joint communication and estimation scheme using low correlation sequences is presented. It is observed that in most situations, joint communication and estimation performs better than a scheme where communication and estimation are performed individually, furthermore, the gains of joint communication and estimation over individual communication and estimation can be significant as the distortion tolerance increases. It is also observed that even a slight tolerance to errors in the channel parameters close to the theoretical lower bounds yield significant improvements in the rate at which reliable communication is achievable. We then formulate a joint communication and estimation problem : simultaneous communication over a one-hop noisy channel and estimation of certain channel parameters. The trade-off between the achievable rate and distortion in estimating the channel parameters is then quantified x for a variety of channels. Finally, we formulate the information theoretic problem corresponding to maximizing the achievable rate while simultaneously meeting the distortion constraint for channel estimation at the destination. The capacity for this problem is evaluated and the theory applied to examples to highlight the results presented. These results are then extended from the one-hop scenario to the multiple access channel (MAC) and the two-hop relay – though we only present achievable and outer-bounds for the latter network. It is also noted that these bounds coincide for particular networks and one particular class of these networks is presented. Each ideas for the theoretical results presented are bolstered with examples as appropriate. More general networks are then studied where the only objective at the destination is to minimize the end-to-end distortion of collecting channel estimates for all inter-node channels. Two particular protocol classes: amplify-and-forward and encode-and-forward are analyzed in this study. First we show that asymptotically in SNR, amplify-and-forward can outperform encodeand-forward and in fact can achieve the maximum possible distortion diversity order of unity. Second, we compare two topologies, a linear network and a tree network operating with orthogonal access, and conclude that fewer hops are beneficial to achieve better end-to-end distortion performance. We derive lower and upper bounds on distortion for both protocols and both networks, which can be used to optimize finite SNR performance. Finally, we study the problem of determining the optimal location of a mobile relay node in a sensor network to optimized some end-to-end metric. Three such metrics are considered: distortion, delay and energy. For each of these cases when we want to optimize the end-to-end metric in the estimation of a certain phenomenon, the problem is reduced to some problems which have already been solved and the results are applied to gain intuition about the results. We also study problems with multiple cost constraints – like minimizing end-to-end distortion while imposing an upper bound on the delay across the network. It is observed that the mobility of the relay node gives us additional degrees of freedom to optimize over while simultaneously making the optimization problem hard as the number of nodes in the network increases. xi