Micro-programmed Adaptive Filtering Applications - Digital Design of Signal Processing Systems: A Practical Approach - page 462

Unequalized Received Signal Equalized Signal

(a) (b)

Figure 11.5 Equalizer example. (a) Unequalized received signal. (b) Equalized QAM signal at the
receiver

Figure 11.5 shows a comparison between an unequalized QAM signal and an equalized signal
using the NLMS algorithm.
Usually divisions in the algorithm are avoided while selecting algorithms for implementation in
hardware. For the case of NLMS, The Newton Repson method can be used for computing 1 =x n x

T
n

.

Modified MATLAB code of the NLMS loop of the implementation is given here:

for i=MAX_SPREAD:Length_Training
xn=Training_Data(i:-1:i-MAX_SPREAD+1);
y(i)=xn*hn;
d(i)=Training(i);
e(i)=d(i)-y(i);
Energy=(norm(xn)^2);
% Find a good initial estimate
if Energy > 10
invEnergy = 0.01;
elseif Energy > 1
invEnergy = 0.1;

else

invEnergy = 1;

end

% Compute inverse of energy using Newton Raphson method
for iteration = 1:5
invEnergy = invEnergy*(2-Energy*invEnergy);

end

hn = hn + mue*e(i)*xn'*invEnergy;

end

To avoid division a simple LMS algorithm can be used. For the LMS algorithm, the equation for
updating the coefficients need not perform any normalization and the MATLAB code for
adaptation is given here: