mmseweights

Linear equalizer MMSE tap weights

Syntax

weights = mmseweights(eq,chTaps,EbN0)

Description

weights = mmseweights(eq,chTaps,EbN0) calculated minimum mean squared error (MMSE) solution for the linear equalizer, eq System object™ given the channel delay taps, chTaps, and signal to noise ratio, EbN0.

Examples

Calculate MMSE Weights for Linear Equalizer

Calculate the minimum mean squared error (MMSE) solution and use the weights for the linear equalizer taps weights.

Initialize simulation variables.

M = 4; % QPSK
numSymbols = 10000;
numTrainingSymbols = 1000;
chtaps = [1 0.5*exp(1i*pi/6) 0.1*exp(-1i*pi/8)];
EbN0 = 20;

Generate QPSK modulated symbols. Apply delayed multipath channel filtering and AWGN impairments to the symbols.

data = randi([0 M-1], numSymbols, 1);
tx = pskmod(data, M, pi/4);
rx = awgn(filter(chtaps,1,tx),25,'measured');

Create a linear equalizer System object configured to use CMA algorithm and input the taps weights. Calculate the MMSE weights. Set the initial tap weights to the calculated MMSE weights. Equalize the impaired symbols.

eq = comm.LinearEqualizer('Algorithm','CMA','AdaptWeights',false,'InitialWeightsSource','Property')

eq = 
  comm.LinearEqualizer with properties:

                Algorithm: 'CMA'
                  NumTaps: 5
                 StepSize: 0.0100
            Constellation: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
    InputSamplesPerSymbol: 1
       AdaptWeightsSource: 'Property'
             AdaptWeights: false
     InitialWeightsSource: 'Property'
           InitialWeights: [5×1 double]
       WeightUpdatePeriod: 1

wgts = mmseweights(eq,chtaps,EbN0)

wgts = 5×1 complex

   0.0005 - 0.0068i
   0.0103 + 0.0117i
   0.9694 - 0.0019i
  -0.3987 + 0.2186i
   0.0389 - 0.1756i

eq.InitialWeights = wgts;

[y,err,weights] = eq(rx);

Plot constellation of impaired and equalized symbols.

constell = comm.ConstellationDiagram('NumInputPorts',2);
constell(rx,y)

Plot the equalizer error signal and compute the error vector magnitude of the equalized symbols.

plot(abs(err))
grid on; xlabel('Symbols'); ylabel('|e|')

errevm = comm.EVM;
evm = errevm(tx,y)

evm = 
139.0863

Plot equalizer tap weights.

subplot(3,1,1); stem(real(weights)); ylabel('real(weights)'); xlabel('Tap'); grid on; axis([1 8 -0.5 1])
line([eq.NumTaps+0.5 eq.NumTaps+0.5], [-0.5 1], 'Color', 'r', 'LineWidth', 1)
title('Equalizer Tap Weights')
subplot(3,1,2); stem(imag(weights)); ylabel('imag(weights)'); xlabel('Tap'); grid on; axis([1 8 -0.5 1])
line([eq.NumTaps+0.5 eq.NumTaps+0.5], [-0.5 1], 'Color', 'r', 'LineWidth', 1)
subplot(3,1,3); stem(abs(weights)); ylabel('abs(weights)'); xlabel('Tap'); grid on; axis([1 8 -0.5 1])
line([eq.NumTaps+0.5 eq.NumTaps+0.5], [-0.5 1], 'Color', 'r', 'LineWidth', 1)

Input Arguments

eq — Equalizer object

System object

Equalizer object, specified as a comm.LinearEqualizer System object.

chTaps — Channel delay taps

vector

Channel delay taps, specified as a vector.

Data Types: double
Complex Number Support: Yes

EbN0 — Signal to noise ratio

scalar

Signal to noise ratio of the channel, specified as a scalar.

Data Types: double

Output Arguments

weights — Weights for linear equalizer

vector

Weights for linear equalizer, returned as a vector.

Version History

Introduced in R2019a