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.