Random matrix processes: Quantifying rates of change in MIMO systems

The rates of change of a wide variety of MIMO metrics are evaluated by differentiating the relevant random processes. Moments, distributions and simplified representations are derived where possible for the resulting derivatives. Fundamental metrics such as the channel coefficients, channel correlation matrices and eigenvalues are considered in addition to performance metrics such as bit-error-rate and the condition number. The analysis presents a comprehensive framework for studying the time-varying nature of MIMO systems in independent Rayleigh fading and leads to insights into the relative rates of change of the various metrics. For example, we show that there is a difference of several orders of magnitude between the moderate rates of change of channel elements and eigenvalues and the extremely rapid variations of the channel condition number. The channel eigenvectors are also shown to experience rapid fluctuations.