On the Cramer-Rao Lower Bound for Spatial Correlation Matrices of Doubly Selective Fading Channels for MIMO OFDM Systems

Abstract

In this paper, the Cramér-Rao lower bound (CRLB) of the sample frequency correlation matrices (SFCM) is derived based on a rigorous model of the doubly selective fading channel for orthogonal frequency division multiplexing (OFDM) systems with pilot-symbol-aided modulation. By assuming a fixed pilot sequence and independent samples, SFCM is complex Wishart distributed. Then, the maximum likelihood estimator (MLE) and the exact expression of CRLB are obtained. From CRLB, the lower bounds of total mean squared error (TMSE) and average mean squared error (AvgMSE) independent of the pilot sequence are deduced, which reveal that the amount of samples is the dominant factor affecting AvgMSE while the signal-to-noise ratio and the maximum Doppler spread have negligible effect. Numerical simulations demonstrate the analytic results.

Spatial correlation coefficient estimator for frequency selective MIMO channels

“…Therefore, it is challenging to obtain an estimator of the SCC over frequency selective MIMO channels with a finite delay spread and a limited bandwidth. In [4], the Cramér–Rao lower bound (CRLB) of the SCC estimator in frequency selective time invariant MIMO channels is derived. Inspired by this piece of work, an optimal SCC estimator for frequency selective time invariant MIMO channels is proposed following the maximum‐likelihood (ML) principle in this Letter.…”

“…In practice, spatial correlation coefficient (SCC) among wireless channels worsen the transmission performance [2,3]. Knowledge of the SCC is critical for system evaluation and design [4]. The SCCs of MIMO wireless channels have been estimated through measurements in various propagation scenarios [5][6][7][8][9][10].…”

“…While estimating SCC, if we predict the real SCC is relatively low, we have to increase t RMS B to guarantee an acceptable accuracy. (4) We note that t RMS is determined by the scattering environment, and is not configurable in system design. Therefore, we have to enlarge the bandwidth B to increase the t RMS B.…”