Multiple-input-multiple-output (MIMO) wireless systems use multiple antenna elements at the transmitter and receiver to offer improved spectral efficiency over traditional single antenna systems. In these systems, properties of the transmit and receive antenna arrays play a key role in determining the overall performance of the system. This thesis derives an upper bound on ergodic (average) channel capacity which formally links good antenna diversity performance with good ergodic capacity. As a result of this derivation, antenna arrays with good ergodic capacity performance are designed in this thesis by designing antenna arrays with near-optimal diversity gain. Several approaches are developed to design antenna array elements which achieve near-optimal diversity. These design methods only require an array geometry and the power azimuth spectrum of the propagation environment. Examples and analysis are included that illustrate advantages and disadvantages of each design technique. Three different array geometries are also investigated. Diversity performance results for each design technique and array geometry, averaged over an ensemble of typical power azimuth spectrums, are presented and compared. This analysis shows that the diversity gain achieved by the best design approach is, on average, less than 1.5 dB below the optimal diversity gain.