**Adaptive Diversity Communications:** Hybrid diversity techniques are reduced-complexity diversity methods where only a subset of the available diversity branches is utilized. These techniques are applicable to the many different forms in which diversity arises. Our contributions have focused on spatial diversity through multiple antennas or relays, and multipath diversity due to wideband transmission. Specific contributions include:

**MIMO Systems:**Developed an analytical framework for the performance of MIMO systems operating in multipath-fading environments, where a subset of antennas is chosen at both the transmit and receive sides. Derived simple, yet tight, bounds on the performance of such system**Hybrid Selection/Maximal-ratio Combining (H-S/MRC) Diversity Systems:**Developed an analytical framework to study the performance of H-S/MRC in a multipath fading environment. In H-S/MRC, the best L out of N diversity branches are selected and combined using MRC, yielding improved performance over L branch MRC.**Efficient Evaluation of Error Rate for Hybrid Diversity Systems:**Derived simple explicit bounds for assessing the error rate of hybrid diversity systems. The bounds are tight and valid for all values of signal-to-noise ratios; thus alleviating the need for complicated analysis and multiple numerical integrals. Contrary to a previous conjecture, the penalty of a hybrid diversity system relative to MRC diversity was shown not to be a constant; it is not independent of the SNR and the target symbol error probability.**Reduced-Complexity Rake Receivers:**Quantified the effects of spreading bandwidth on spread spectrum systems in dense multipath environments in terms of performance, complexity, and channel parameters. Developed an analytical framework that provides fundamental insights on how wideband reduced-complexity Rake receivers can best take advantage of multipath, and theoretical basis for deciding how many fingers should be included in the receiver architecture**Hybrid Diversity with Practical Channel Estimation:**Developed an analytical framework for evaluating the performance of subset diversity schemes in the presence of channel estimation error. Showed that such a system preserves the full diversity order. The study revealed that the asymptotic performance loss due to estimation error has a surprising lack of dependence on the number of combined branches or the total number of available diversity branches.**Outage-Optimal Opportunistic Relaying:**Put forth simple opportunistic relaying strategies under an aggregate power constraint. Developed a distributed relay-selection algorithms requiring only local channel knowledge. Proved that opportunistic decode-and-forward relaying is outage-optimal, that is, it is equivalent in outage behavior to the optimal strategy that employs all potential relays. The results revealed that cooperation offers diversity benefits even when cooperative relays choose not to transmit but rather choose to cooperatively listen.