We perform analysis and design for multiple-input multiple-output (MIMO) wireless systems in ultra-wideband (UWB), mobile-to-mobile channels, and relay channels. We analyze the bit error rate (BER) performance in the IEEE 802.15.3a and 802.15.4a UWB channel models and present an analytical expression for the signal-to-noise ratio (SNR) of the pulse position modulated (PPM) signal in a UWB channel. We derive the autocorrelation function (ACF), level crossing rate (LCR), and average fade duration (AFD) of the mobile-to-mobile Rician fading channel. We suggest a sum-of-sinusoid MIMO mobile-to-mobile channel simulation method.