Considerable works on adaptive schemes for transmit beamforming in distributed networks have emerged in the past years. In all these works, it was assumed that channels between all transmitters and the re- ceiver experience frequency flat slow-fading and a static environment was often considered. In practical environments, however, system uncertainties such as channels fluctuations, networks random node ad- dition and random node removal may rise and the aforementioned ideal assumptions may fail in these settings. Therefore, we focus on robust designs in this thesis and proposed a systematic analytical framework where stochastic stability is employed to demonstrate the tracking capability of the general adaptive schemes when channels are subject to fast variations in time. In addition, for time-varying channel and time-varying network topology, we defined a set of robustness criteria that can be used as comparison metrics for existing adaptive schemes. By utilizing the proposed analytical frameworks and metrics, we develop an bio-inspired scheme, BioRARSA2, that possess significantly superior ro- bustness with respect to environmental variations and system uncertainties. The improved robustness of the proposed algorithm is further validated through extensive numerical simulations.

Considerable works on adaptive schemes for transmit beamforming in distributed networks have emerged in the past years. In all these works, it was assumed that channels between all transmitters and the re- ceiver experience frequency flat slow-fading and a static environment was often considered. In practical environments, however, system uncertainties such as channels fluctuations, networks random node ad- dition and random node removal may rise and the aforementioned ideal assumptions may fail in these settings. Therefore, we focus on robust designs in this thesis and proposed a systematic analytical framework where stochastic stability is employed to demonstrate the tracking capability of the general adaptive schemes when channels are subject to fast variations in time. In addition, for time-varying channel and time-varying network topology, we defined a set of robustness criteria that can be used as comparison metrics for existing adaptive schemes. By utilizing the proposed analytical frameworks and metrics, we develop an bio-inspired scheme, BioRARSA2, that possess significantly superior ro- bustness with respect to environmental variations and system uncertainties. The improved robustness of the proposed algorithm is further validated through extensive numerical simulations.

1 Introduction 1
2 Problem Formulation 5
2.1 Distributed Beamforming with Limited Feedback .................... 6
2.2 Adaptive Distributed Beamforming with Time-Varying Channels and Network Topology 8
3 Analytical Frameworks and Robustness Criteria 10
3.1 Random Search in Static Environments ......................... 10 3.2 Random Search with Time-Varing Objective Function. . . . . . . . . . . . . . . . . . 12
4 Proposed Algorithm 19
4.1 Algorithm Description .................................. 21 4.2 Convergence for Noiseless Measurement......................... 24
4.3 Important Characteristic of BioRARSA2......................... 25
5 Simulation result 27
5.1 Noise-free static environments .............................. 28
5.2 Noise-freeTime-varying Environments ......................... 30
6 Conclusion Appendix
34

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