| Summary: | 碩士 === 國立清華大學 === 通訊工程研究所 === 99 === For wireless relay networks, this work focuses on the convergence analysis of adaptive distributed beamforming schemes that can be reformulated as local random search algorithms via a random search framework. Once reformulated in our random search framework, it is proved that under two sufficient conditions: a) the objective function of the random search algorithm is continuous and all its local maxima are global maxima in the considered feasible set, and b) the origin is an interior point within the support of the probability measure for the random perturbation, the corresponding adaptive distributed beamforming schemes converge almost surely. If the objective function is non-negative, it can be further proved that the corresponding adaptive distributed beamforming schemes converge in mean. This proof of convergence is general since it can be applied to analyze randomized adaptive distributed beamforming schemes with any type of objective functions with different feasible sets and probability measures as long as both the sufficient conditions are satisfied. Examples of objective functions along with different feasible sets that satisfy the first sufficient condition are demonstrated by analyzing the signal-to-noise ratio (SNR) functions for the adaptive distributed beamforming problems in the decode-and-forward and the amplify-and-forward relay networks under two different power constraint assumptions, i.e. an individual and a total power constraint, respectively. It is also shown that the convergence time of the considered local random search algorithms in both relay network settings scale linearly with respect to the number of relays in the network. Finally, this framework is extended to analyze adaptive distributed beamforming schemes in an asynchronous scenario where relays can only update their beamforming coefficients asynchronously. Simulation results are provided to validate our analyses.
|
|---|
