Abstract

In this paper we consider the variation of eigenvalues and eigenvalue sums across the frequency bins of a MIMO OFDM system. In particular, we consider the changes in the ordered eigenvalues and the eigenvalue sum or page link gain, between two distinct frequency bins. The size of such changes has an important effect both on system performance and design. In addition these results have applications in other areas, including temporal variation, feedback delay and channel estimation. Novel results presented include distributions and moments for changes in page link gain and the maximum eigenvalue and autocorrelation functions for the page link gain and maximum eigenvalue. Furthermore, some very simple approximate results for the ordered eigenvalue differences are presented and the accuracy of the analysis is verified by Monte Carlo simulations. In addition, we consider each eigenmode as a random process in the frequency domain and compute the LCR for the BER of transmission down the eigenchannels of the MIMO OFDM channel. Many extensions to this work are possible including LCRs in time as well as in frequency. The accuracy of the analytical approximations are verified by Monte Carlo simulations. ion for Research, Science and Technology of New Zealand.

INTRODUCTION

In this paper we consider a multiple-input multiple-output (MIMO) system in conjunction with orthogonal frequency division multiplexing (OFDM) operating over frequency selective Rayleigh and Rician fading environments. In particular we focus on the eigenvalues of the complex Wishart matrices defined for each OFDM subcarrier and investigate their variation across frequency. Since the throughput and performance of such a system are heavily dependent on the eigenvalues, the results and analysis presented have many applications. Examples include the performance of beamforming systems which is governed by the maximum eigenvalue and the page link gain which is characterized by the sum of the eigenvalues.

The throughput and performance of adaptive MIMO-OFDM systems heavily depends on the eigenvalues of the complex Wishart matrices defined for each OFDM subcarrier across frequency. In this chapter, we consider these variations over both Rayleigh and Rician fading channels. In particular, analysis for the differences between eigenvalues and between eigenvalue sums across the OFDM frequency bins is provided. This work leads to the study of eigenvalue autocorrelation functions (ACFs) and various joint distributions in frequency. The main contributions of this work are the following:
-Maximum eigenvalue results including the joint PDF of the maximum eigenvalue in two frequency bins, the ACF of the maximum eigenvalue, the distribution and variance of the difference between the two maximum eigenvalues.
- Link gain results including the PDF, the CDF and variance of the page link gain difference, and the ACF of the page link gain.
-Simple approximations to the ACF of the maximum eigenvalue and to the variance of the maximum eigenvalue difference.

The second part of this paper focuses on the level crossing rates (LCRs) of BERs across the frequency bins of a MIMO-OFDM system operating over frequency selective Rayleigh fading environments. Using the results in [1], here we develop analysis for calculating the LCR of BER in an adaptive MIMO-OFDM system which may use multiple eigenvalues. The results presented in this paper provide new insights into the BER analysis of an adaptive system. It is worth reiterating that we focus on BER as a process in frequency across the OFDM block. Hence we consider variations in BER across the bins and not over time. In particular, we consider each eigenmode as a random process in the frequency domain and compute the LCR for the BER of transmission down the eigenchannels of the MIMO-OFDM channel.