University of Minnesota


Equalization of Rapidly Varying Channels with Antenna Arrays

Research in this project focuses on development and testing of efficient algorithms for:

  1. explicit modeling and estimation of rapidly varying communication channels, and
  2. the resulting self-recovering antenna receivers and equalizers in rapidly fading mobile battlefield scenarios (experimental evaluation is also to be performed on a testbed).

So far we have established that finitely parameterized basis expansions render single-input single-output (SISO) time-varying (TV) channels equivalent to multivariate time-invariant (TI) channels with inputs formed by modulating a single input with the bases. SISO-TV fading channels are of paramount importance both for commercial as well as for military communications because they capture phase noise, oscillator drifts, Doppler effects caused by relative motion between transmitters and receivers, and varying multipath propagation encountered with mobile wireless links in the battlefield. They cause time- and frequency-selective intersymbol interference (ISI) which has been traditionally modeled via random (Rayleigh or Rician) channels; however, by establishing links with existing physical channel measurements, we have shown that deterministic Fourier bases expansions are well motivated for modeling rapidly fading mobile communication channels when multipath propagation caused by a few dominant reflectors gives rise to (Doppler induced) linearly varying path delays. Our algorithms estimate Doppler frequencies blindly using cyclic statistics and determine the channel orders relying upon rank properties of a received data matrix. By complementing channel (or Doppler) diversity with temporal, or, spatial diversity (available with oversampling or multiple antennas), we have derived blind estimators of TV channels along with direct equalizers under with minimal (persistence-of-excitation) assumptions on the input and the bases. Two deterministic blind equalization algorithms have been derived: one determines the channels first and then the equalizers, whereas the other estimates the equalizers directly. The equalizers are time-invariant, multivariate, zero-forcing, and lend themselves to optimally weighted and adaptive extensions. We have also proved that exploitation of the input's whiteness reduces the amount of spatio/temporal diversity (only two sensors) needed to identify blindly TV channels and mitigate their effects using minimum mean-square error equalizers. Sensitivity to order and model mismatch have been studied briefly.

Work in progress on the algorithmic tasks of our project focuses on: performance analysis of the channel estimators especially when model perturbations due to synchronization effects and Doppler frequency drifts are present; exploitation of input redundancy in the form of time-varying precoding filterbanks, for estimating TV channels with antenna arrays;

Detailed exposition of our work in this project can be found in:

  1. G. B. Giannakis and C. Tepedelenlioglu, "Basis Expansion Models and Diversity Techniques for Blind Equalization of Time-Varying Channels," Proceedings of the IEEE, vol. 86, pp. 1969-1986, October 1998.
  2. H. Liu and G. B. Giannakis, "Deterministic approaches for blind equalization of time-varying channels with antenna arrays," IEEE Transactions on Signal Processing, vol. 46, no. 11, pp. 3003-3013, November 1998.
  3. A. Scaglione, S. Barbarossa, and G. B. Giannakis, "Self-recovering equalization of time-selective fading channels using redundant filterbank precoders," Proc. of Digital Signal Proc. Workshop, Bryce Canyon, Utah, August 9-12, 1998.


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