<p>Run the MLSE equalizer with an imperfect channel estimate, and plot the BER and the burst error performance for each data         block.  These results align fairly closely with the ideal MLSE results.  (The channel estimation algorithm is highly dependent         on the data, such that an FFT of a transmitted data block has no nulls.)  Note how the estimated channel plots compare with         the actual channel spectrum plot.      </p>      <p>See <a href="eqber_mlse.html">eqber_mlse</a> for a listing of the simulation code for the MLSE equalizers.      </p><pre class="codeinput">mlseType = <span class="string">'imperfect'</span>;eqber_mlse;</pre><img vspace="5" hspace="5" src="eqberdemo_11.png"> <img vspace="5" hspace="5" src="eqberdemo_12.png"> <img vspace="5" hspace="5" src="eqberdemo_13.png"> <p class="footer">Copyright 1996-2004 The MathWorks, Inc.<br>         Published with MATLAB&reg; 7.0<br></p>      <!--##### SOURCE BEGIN #####%% BER Performance of Several Equalizer Types% This script shows the BER performance of several types of equalizers in a% static channel with a null in the passband.  The script constructs and% implements a linear equalizer object and a decision feedback equalizer (DFE)% object.  It also initializes and invokes a maximum likelihood sequence% estimation (MLSE) equalizer.  The MLSE equalizer is first invoked with perfect% channel knowledge, then with a straightforward but imperfect channel% estimation technique.%% As the simulation progresses, it updates a BER plot for comparative analysis% between the equalization methods.  It also shows the signal spectra of the% linearly equalized and DFE equalized signals.  It also shows the relative% burstiness of the errors, indicating that at low BERs, both the MLSE algorithm% and the DFE algorithm suffer from error bursts.  In particular, the DFE error% performance is burstier with detected bits fed back than with correct bits fed% back.  Finally, during the "imperfect" MLSE portion of the simulation, it% shows and dynamically updates the estimated channel response.%% This script relies on several other scripts and functions to perform link% simulations over a range of Eb/No values.  These files are as follows:%% <eqber_adaptive.html eqber_adaptive> - a script that runs link% simulations for linear and DFE equalizers%% <eqber_mlse.html eqber_mlse> - a script that runs link simulations% for ideal and imperfect MLSE equalizers%% <eqber_siggen.html eqber_siggen>   - a script that generates a BPSK% signal with no pulse shaping, then processes it through the channel and adds% noise%% eqber_graphics - a function that generates and updates plots showing the% performance of the linear, DFE, and MLSE equalizers.  Type "edit% eqber_graphics" at the MATLAB command line to view this file.%% The scripts eqber_adaptive and eqber_mlse illustrate how to use adaptive and% MLSE equalizers across multiple blocks of data such that state information is% retained between data blocks.%% To experiment with this demo, you can change such parameters as the channel% impulse response, the number of equalizer tap weights, the recursive least% squares (RLS) forgetting factor, the least mean square (LMS) step size, the% MLSE traceback length, the error in estimated channel length, and the maximum% number of errors collected at each Eb/No value.%   Copyright 1996-2004 The MathWorks, Inc.%   $Revision: 1.1.4.1 $  $Date: 2004/06/30 23:03:16 $%% Signal and channel parameters% Set parameters related to the signal and channel.  Use BPSK without any pulse% shaping, and a 5-tap real-valued symmetric channel impulse response.  (See% section 10.2.3 of Digital Communications by J. Proakis for more details on the% channel.)  Set initial states of data and noise generators.  Set the Eb/No% range.% System simulation parametersFs      = 1;      % sampling frequency (notional)nBits   = 2048;   % number of BPSK symbols per vectormaxErrs = 50;     % target number of errors at each Eb/NomaxBits = 1e8;    % maximum number of symbols at each Eb/No% Modulated signal parametersM          = 2;            % order of modulationRs         = Fs;           % symbol ratenSamp      = Fs/Rs;        % samples per symbolRb         = Rs * log2(M); % bit ratedataState  = 999983;       % initial state of data generator% Channel parameterschnl       = [0.227 0.460 0.688 0.460 0.227]';  % channel impulse responsechnlLen    = length(chnl);      % channel length, in samplesEbNo       = 0:14;              % in dBBER        = zeros(size(EbNo)); % initialize valuesnoiseState = 999917;            % initial state of noise generator%% Adaptive equalizer parameters% Set parameter values for the linear and DFE equalizers.  Use a 31-tap linear% equalizer, and a DFE with 15 feedforward and feedback taps.  Use the recursive% least squares (RLS) algorithm for the first block of data to ensure rapid tap% convergence.  Use the least mean square (LMS) algorithm thereafter to ensure% rapid execution speed.% Linear equalizer parametersnWts         = 31;       % number of weightsalgType1     = 'rls';    % RLS algorithm for first data block at each Eb/NoforgetFactor = 0.999999; % parameter of RLS algorithmalgType2     = 'lms';    % LMS algorithm for remaining data blocksstepSize     = 0.00001;  % parameter of LMS algorithm% DFE parameters - use same update algorithms as linear equalizernFwdWts      = 15;       % number of feedforward weights nFbkWts      = 15;       % number of feedback weights%% MLSE equalizer and channel estimation parameters, and initial visualization% Set the parameters of the MLSE equalizer.  Use a traceback length of six times% the length of the channel impulse response.  Initialize the equalizer states.% Set the equalization mode to "continuous", to enable seamless equalization% over multiple blocks of data.  Use a cyclic prefix in the channel esimation% technique, and set the length of the prefix.  Assume that the estimated length% of the channel impulse response is one sample longer than the actual length.% MLSE equalizer parameterstbLen      = 30;                 % MLSE equalizer traceback lengthnumStates  = M^(chnlLen-1);      % number of trellis states[mlseMetric, mlseStates, mlseInputs] = deal([]);const      = pskmod(0:M-1, M);   % signal constellationmlseType   = 'ideal';            % perfect channel estimates at firstmlseMode   = 'cont';             % no MLSE resets% Channel estimation parameterschnlEst = chnl;         % perfect estimation initiallyprefixLen = 2*chnlLen;  % cyclic prefix lengthexcessEst = 1;          % length of estimated channel impulse response                        % beyond the true length% Initialize the graphics for the simulation.  Plot the unequalized channel% frequency response, and the BER of an ideal BPSK system.idealBER = berawgn(EbNo, 'psk', M, 'nondiff');[hBER, hLegend, legendString, hLinSpec, hDfeSpec, hErrs, ...    hText1, hText2, hFit, hEstPlot] = eqber_graphics('init', chnl, EbNo, ...                                               idealBER, nBits);%% Construct RLS and LMS linear and DFE equalizer objects.% The RLS update algorithm is used to initially set the weights, and the LMS% algorithm is used thereafter for speed purposes.alg1 = eval([algType1 '(' num2str(forgetFactor) ')']);linEq1 = lineareq(nWts, alg1);alg2 = eval([algType2 '(' num2str(stepSize) ')']);linEq2 = lineareq(nWts, alg2);[linEq1.RefTap, linEq2.RefTap] = ...    deal(round(nWts/2));    % Set reference tap to center tap[linEq1.ResetBeforeFiltering, linEq2.ResetBeforeFiltering] = ...    deal(0);                % Maintain continuity between iterationsdfeEq1 = dfe(nFwdWts, nFbkWts, alg1);dfeEq2 = dfe(nFwdWts, nFbkWts, alg2);[dfeEq1.RefTap, dfeEq2.RefTap] = ...    deal(round(nFwdWts/2)); % Set reference tap to center forward tap[dfeEq1.ResetBeforeFiltering, dfeEq2.ResetBeforeFiltering] = ...    deal(0);                % Maintain continuity between iterations%% Linear equalizer% Run the linear equalizer, and plot the equalized signal spectrum, the BER, and% the burst error performance for each data block.  Note that as the Eb/No% increases, the linearly equalized signal spectrum has a progressively deeper% null.  This highlights the fact that a linear equalizer must have many more% taps to adequately equalize a channel with a deep null.  Note also that the% errors occur with small inter-error intervals, which is to be expected at such% a high error rate.%% See <eqber_adaptive.html eqber_adaptive> for a listing of the simulation code% for the adaptive equalizers.firstRun = true;  % flag to ensure known initial states for noise and dataeqType = 'linear';eqber_adaptive;%% Decision feedback equalizer% Run the DFE, and plot the equalized signal spectrum, the BER, and the burst% error performance for each data block.  Note that the DFE is much better able% to mitigate the channel null than the linear equalizer, as shown in the% spectral plot and the BER plot.  The plotted BER points at a given Eb/No value% are updated every data block, so they move up or down depending on the number% of errors collected in that block.  Note also that the DFE errors are somewhat% bursty, due to the error propagation caused by feeding back detected bits% instead of correct bits. The burst error plot shows that as the BER decreases,% a significant number of errors occurs with an inter-error arrival of five bits% or less.  (If the DFE equalizer were run in training mode at all times, the% errors would be far less bursty.)  %% For every data block, the plot also indicates the average inter-error interval% if those errors were randomly occurring.%% See <eqber_adaptive.html eqber_adaptive> for a listing of the simulation code% for the adaptive equalizers.eqType = 'dfe';eqber_adaptive; %% Ideal MLSE equalizer, with perfect channel knowledge% Run the MLSE equalizer with a perfect channel estimate, and plot the BER and% the burst error performance for each data block.  Note that the errors occur% in an extremely bursty fashion.  Observe, particularly at low BERs, that the% overwhelming percentage of errors occur with an inter-error interval of one or% two bits.%% See <eqber_mlse.html eqber_mlse> for a listing of the simulation code% for the MLSE equalizers.eqType = 'mlse';mlseType = 'ideal';eqber_mlse;%% MLSE equalizer with an imperfect channel estimate% Run the MLSE equalizer with an imperfect channel estimate, and plot the BER% and the burst error performance for each data block.  These results align% fairly closely with the ideal MLSE results.  (The channel estimation algorithm% is highly dependent on the data, such that an FFT of a transmitted data block% has no nulls.)  Note how the estimated channel plots compare with the actual% channel spectrum plot.%% See <eqber_mlse.html eqber_mlse> for a listing of the simulation code% for the MLSE equalizers.mlseType = 'imperfect';eqber_mlse;##### SOURCE END #####-->   </body></html>