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On Finite Word Length Effects for the FIR MMSEDFE Naofal AlDhahir \Lambda

Summary: On Finite Word Length Effects for the FIR MMSE­DFE
Naofal Al­Dhahir \Lambda
, Member IEEE
EDICS Category CL1:5:3 (Equalization)
An analytical upper--bound on the degradation in the decision--point SNR of the FIR MMSE--DFE due to
finite--precision implementation of its optimum filter coefficients is derived. Simulation results demonstrate the
tightness of the analytical bound for scenarios of most practical interest.
I. Introduction
In a digital implementation of the finite--impulse--response (FIR) minimum--mean--square--error decision--feedback
equalizer (MMSE--DFE), the optimum coefficients of its feedforward and feedback filters are quantized to a
certain finite precision. Choosing the number of bits used in coefficient quantization (also called word length
size) represents a design tradeoff between implementation cost and achievable performance. This letter analyzes
and quantifies this tradeoff.
II. Analysis
We assume the following standard vector representation of a linear dispersive additive--noise channel
y k+N f \Gamma1:k = Hx k+N f \Gamma1:k\Gammaš + n k+N f \Gamma1:k ; (1)
where y k+N f \Gamma1:k is a block of N f output symbols and x k+N f \Gamma1:k\Gammaš and n k+N f \Gamma1:k are the corresponding input
and noise blocks. H is a Toeplitz channel matrix whose first row is equal to the channel impulse response (CIR)
appended by (N f \Gamma 1) zeros and š is the channel memory. Both the input and noise sequences are assumed to


Source: Al-Dhahir, Naofal - Department of Electrical Engineering, University of Texas at Dallas


Collections: Engineering