Frequency Domain Variation of Eigenvalues in Adaptive MIMO OFDM Systems

We consider the effects of the frequency variation of frequency selective fading channels on adaptive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The magnitude of this variation has important effects on system performance and design as well as applications to temporal variation, feedback delay and channel estimation.We first examine the variation of the eigenvalues and eigenvalue sums across the frequency bins of a MIMO OFDM system focusing on the changes in the ordered eigenvalues and the eigenvalue sum or link gain between two distinct frequency bins. Here we derive distributions and moments for changes in the link gain and maximum eigenvalue and autocorrelation functions for the link gain and maximum eigenvalue as well as simple approximate results for the ordered eigenvalue differences. We then consider variations in performance via the level crossing rates (LCRs) of the bit error rates (BERs) across the frequency bins of the MIMO OFDM system operating over a Rayleigh fading channel. Each eigenmode constitutes a random process in the frequency domain and we compute the LCR for the BER of transmission down the eigenchannels of the MIMO OFDM channel. We finally verify our analysis using Monte Carlo simulations.