Uppsala universitet

The Structure and Design of Realizable Decision Feedback Equalizers for IIR Channels with Coloured Noise

Mikael Sternad and Anders Ahlén

IEEE Transactions on Information Theory,
vol IT-36, pp 848-858, July 1990. © 1990 IEEE.

Paper available In Pdf.

When digital data are transmitted over a dispersive channel, a decision feedback equalizer can be utilized to estimate transmitted symbols. This detector subtracts an estimate of the intersymbol interference caused by previous symbols, before making symbol-by-symbol decisions. The paper discusses the model-based design of the filters included in the device.

A simple algorithm for optimizing decision feedback equalizers by minimizing the mean square error (MSE) is presented. A complex baseband channel and correct past decisions are assumed. The dispersive channel may have infinite impulse response and the noise may be coloured. We consider optimal realizable (stable and finite-lag smoothing) forward and feedback filters in discrete time. They are parametrized as recursive filters. In the special case of transmission channels with finite impulse response and autoregressive noise, the minimum MSE can be attained with transversal feedback and forward filters. In general, the forward part should include a noise-whitening filter (the inverse noise model).

The finite realizations of the filters are calculated using a polynomial equation approach to the linear quadratic optimization problem. The equalizer is optimized essentially by solving a system of linear equations Ax=B, where A contains transfer function coefficients from the channel and noise model. No calculation of correlations are required with this method.

A simple expression for the minimal MSE is presented. The DFE is compared to MSE-optimal linear recursive equalizers. Expressions for the equalizer in the limiting case of infinite smoothing lags are also discussed.

Matlab m-file
for model-based design of MSE-optimal IIR Decision Feedback Equalizers
(written by Stefano Bigi):

Related publications:
Licentiate Thesis by S Bigi, who considers data-based design when the data record is short.
Licentiate Thesis by E Lindskog, where robust design and multiple measurements are considered.
Conference paper, ICASSP'93, on robustness against model errors and erroneous past decisions.
Multivariable (MIMO) case with both multiple sensors and multiple users.
Conference paper on MIMO fractionally spaced DFE's as DS-CDMA multiuser detectors .
PhD Thesis by L Lindbom 1995, with MIMO time-varying DFE for FIR channels in Chap. 7.

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