This thesis consists of two parts addressing two different problems in fading channels. The first part deals with asynchronous cooperative relay communication. The assumption of nodes in a cooperative communication relay network operating in synchronous fashion is often unrealistic. In this work we consider two different models of asynchronous operation in cooperative-diversity networks experiencing slow fading and examine the corresponding Diversity-Multiplexing Tradeoffs (DMT). For both models, we propose protocols and distributed space-time codes that asymptotically achieve the transmit diversity bound on DMT for all multiplexing gains and for number of relays N ≥ 2. The distributed space-time codes for all the protocols considered are based on Cyclic Division Algebras (CDA). The second part of the work addresses the DMT analysis of diversity embedded codes for MIMO channels. Diversity embedded codes are high rate codes that are designed so that they have a high diversity code embedded within them. This allows a form of opportunistic communication depending on the channel conditions. The high diversity code ensures that at least a part of the information is received reliably, whereas the embedded high rate code allows additional information to be transferred if the channel is good. This can be thought of coding the data into two streams: high priority and low priority streams so that the high priority stream gets a better reliability than the lower priority stream. We show that superposition based diversity embedded codes in conjunction with naive single stream decoding is sub-optimal in terms of the DM tradeoff. We then construct explicit diversity embedded codes by the superposition of approximately universal space-time codes from CDAs. The relationship between broadcast channels and the diversity embedded setting is then utilized to provide some achievable Diversity Gain Region (DGR) for MIMO broadcast Channels.

This thesis proposes and analyzes data fusion algorithms that operate on the physical layer of a wireless sensor network, in the context of three applications of cognitive radios: 1. Cooperative spectrum sensing via binary consensus; 2. Multiple transmitter localization and communication footprint identification; 3.Target self-localization using beacon nodes. For the first application, a co-phasing based data combining scheme is studied under imperfect channel knowledge. The evolution of network consensus state is modeled as a Markov chain, and the average transition probability matrix is derived. Using this, the average hitting time and average consensus duration are obtained, which are used to determine and optimize the performance of the consensus procedure. Second, using the fact that a typical communication footprint map admits a sparse representation, two novel compressed sensing based schemes are proposed to construct the map using 1-bit decisions from sensors deployed in a geographical area. The number of transmitters is determined using the K-means algorithm and a circular fitting technique, and a design procedure is proposed to determine the power thresholds for signal detection at sensors. Third, an algorithm is proposed for self-localization of a target node using power measurements from beacon nodes transmitting from known locations. The geographical area is overlaid with a virtual grid, and the problem is treated as one of testing overlapping subsets of grid cells for the presence of the target node. The column matching algorithm from group testing literature is considered for devising the target localization algorithm. The average probability of localizing the target within a grid cell is derived using the tools from Poisson point processes and order statistics. This quantity is used to determine the minimum required node density to localize the target within a grid cell with high probability. The performance of all the proposed algorithms is illustrated through Monte Carlo simulations.