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This paper proposes a method for determining the antenna element radiation characteristics that maximize diversity gain given a specific power angular spectrum of the propagation environment. The method numerically constructs the eigenfunctions of the covariance operator for the scenario subject to constraints on the radiated power and allowable level of supergain. The discussion also focuses on how the resulting radiation characteristics approximately optimize average capacity for multiple-input multiple-output communications. Computational results reveal that optimal antenna characteristics can provide significantly more diversity gain than that offered by the characteristics of a simple design. An example computation using genetic algorithm optimization demonstrates that a numerically optimized practical design can be designed whose performance is relatively close to that of the optimal array.