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.

I. Introduction

To provide spatial diversity to combat fluctuations in signal strength or fading in wireless channels, multiple antennas at the transmitter and receiver can be used [1], [2], [3], [4]. Such MIMO wireless systems have been shown to provide a diversity gain equal to the product of the number of transmit antennas and the number of receive antennas in narrowband channels. For the case of complete knowledge of the channel state information (CSI) at the transmitter, full diversity can be achieved using transmit beamforming and receive combining [5], [6], [7]. Compared to space-time block codes, beamforming and combining provide additional array gain and a low-complexity and flexible receiver structure. The CSI at the transmitter may be obtained from the receiver using a feedback control channel. The particular case of beamforming and combining using a feedback channel to convey the CSI has been investigated in [8], [9]. In this paper we consider MIMO OFDM systems operating over frequency selective Rayleigh and Rician fading environments. Such systems form the mainstay of next-generation wireless standards such as WiMax and LTE. We focus on an adaptive beamforming combining MIMO OFDM system using a feedback control channel.