 
Summary: On Finite Word Length Effects for the FIR MMSEDFE
Naofal AlDhahir \Lambda
, Member IEEE
EDICS Category CL1:5:3 (Equalization)
Abstract
An analytical upperbound on the degradation in the decisionpoint SNR of the FIR MMSEDFE due to
finiteprecision 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 finiteimpulseresponse (FIR) minimummeansquareerror decisionfeedback
equalizer (MMSEDFE), 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 additivenoise 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
