Chair and Varshney have derived an optimal rule for fusing decisions based on the Bayesian criterion. To implement the rule, probabilities of detection P_D and false alarm P_F for each detector must be known, which is not readily available in practice. This dissertation presents an adaptive fusion model which estimates the P_D and P_F adaptively by a simple counting process. Since reference signals are not given, the decision of a local detector is arbitrated by the fused decision of all the other local detectors. Adaptive algorithms for both equal probable and unequal probable sources, for independent and correlated observations are developed and analyzed, respectively. The convergence and error analysis of the system are analytically proven and demonstrated by simulations. In addition, in this dissertation, the performance of four practical fusion rules in both independent and correlated Gaussian noise is analyzed, and compared in terms of their Receiver Operating Characteristics (ROCs). Various factors that affect the fusion performance are considered in the analysis. By varying the local decision thresholds, the Rocs under the influence of the number of sensors, signal-to-noise ratio (SNR), the deviation of local decision probabilities, and correlation coefficient, are computed and plotted, respectively. Several interesting and key observations on the performance of fusion rules are drawn from the analysis.

As an application of the above theory, a decentralized or distributed scheme in which each fusion center is connected with three widely spaced base stations is proposed for digital cellular code-division multi-access communications. Detected results at each base station are transmitted to the fusion center where the final decision is made by optimal fusion. The theoretical analysis shows that this novel structure can achieve an error probability at the fusion center which is always less than or equal to the minimum of the three respective base station. The performance comparison for binary coherent signaling in Rayleigh fading and log-normal shadowing demonstrates that the decentralized detection has a significant increased system capacity over conventional macro selection diversity. This dissertation analyzes the performance of the adaptive fusion method for macroscopic diversity combination in the wireless cellular environment when the error probability information from each base station detection is not available. The performance analysis includes the derivation of the minimum achievable error probability. An alternative realization with lower complexity of the optimal fusion scheme by using selection diversity is also proposed. The selection of the information bit in this realization is obtained either from the most reliable base station or through the majority rule from the participating base stations.