Karhunen-Loeve Transform Based Low-Rank Estimation of ICI Matrices in High-Mobility Doubly-Dispersive OFDM Systems

We propose a novel method for estimating inter-carrier interference (ICI) matrices for orthogonal frequency division multiplexing (OFDM) on doubly-dispersive (DD) channels using the Karhunen–Loève transform (KLT). Existing methods using KLT and basis-expansion models (BEM) typically focus on estimating the time-domain channel impulse response. In contrast, our work establishes the statistical relationship between the time-domain (TD) representation and the frequency-domain ICI matrix by linking their respective autocorrelation matrices. We demonstrate that for a channel of a given impulse response length, the diagonals of the ICI matrix are stationary even when the underlying time-domain channel is non-stationary. For the Jakes wide-sense-stationary-uniform-scattering (WSSUS) channel model, the number of basis functions required for time-domain estimation grows linearly with the normalized Doppler spread. By contrast, we demonstrate that the rank of our ICI matrix model is fixed and equal to the channel length. This provides a significant reduction in complexity compared to time-domain BEM estimation, especially for the high Doppler conditions considered here. We design a system for joint KLT-based estimation of the ICI matrix and turbo-equalization for OFDM systems operating over DD channels. The system employs a maximum a posteriori (MAP)-based channel equalizer with a convolutional error correction code; channel estimation and bit error rate (BER) are improved by iterating between the channel estimator, equalizer, and channel decoder. We evaluate the system’s BER for various channel lengths and normalized Doppler frequency values. We compare our approach with orthogonal matching pursuit (OMP), a common method for estimating sparse channels, and a previous KLT-based approach that estimates the TD channel. Simulations show that the proposed approach significantly outperforms OMP in terms of BER and the previous TD KLT estimation method in terms of mean squared error (MSE), and that the proposed approach achieves significant complexity savings over a more recently proposed TD BEM channel estimation method.