Problem with LMS Linear Equalization Algorithm

Hello,

I am trying to equalize a pseudorandom binary sequence (PRBS) signal passed through a band limited channel with the LMS algorithm for Linear structure but it doesn´t equalize my signal. I have tried to equalize it with the RLS algorithm and it worked, I don´t know if I am missing something when creating the equalizer object. The code is the following:

% Initialize system parameters
Fs = 5e11;             % Sample rate
Rs = 5e9;               % Symbol rate (Sps)
sps = Fs/(Rs);            % Number of samples per symbol
SNR = 110;             % Signal to noise ratio (dB)
Trise = 0.2/(Rs);       % Rise time of the NRZ signal
Tfall = 0.2/(Rs);       % Fall time of the NRZ signal
frameLen = 500;        % Number of symbols in a frame

%% NRZ signal generation
%************************************************************************%
% Set up the pattern generator
src = commsrc.pattern('SamplingFrequency', Fs, ...
                      'SamplesPerSymbol', sps, ...
                      'RiseTime', Trise, ...
                      'FallTime', Tfall) %#ok

% Generate NRZ signal
signal = generate(src, frameLen);

%% Band limited channel generation
%************************************************************************%
fc=2
fs=1000
order=2
w = 0:pi/1000:pi;
wn1= fc/(fs/2); % Relative frequency (0-1 range)
[n1,d1]=butter(order,wn1); % Filter coefficients
freqz(n1,d1,w); % Frequency response

%% RxSignal
%************************************************************************%
rxsignal = filter(n1,d1,signal);

So I am working in a channel attenuation of -27.97 dB.

Now I use a Linear LMS equalizer with the signal as train signal to obtain the coefficients for the taps. With those coefficients I create my own filter to equalize the signal.

%% Linear LMS
%************************************************************************%
x = [-1, 1];
eqlinear_lms_signal = comm.LinearEqualizer('Algorithm','LMS','NumTaps',4,...
    'ReferenceTap',2,'StepSize',0.2,...
    'Constellation',x);
[signal_eq_lms , err_l_lms_signal, w_l_lms_signal] = eqlinear_lms_signal(rxsignal, signal);

fir = dfilt.dffir(w_l_lms_signal);
rxsignal_eq_llms = filter(fir, rxsignal);

With this code the signal equalized remains like this with some zoom (it is not represented in time domain, in time domain it will be t = 1/Fs:1/Fs:length(signal)/Fs which would be a signal of 10^(-7) seconds):

While equalizing with a Linear RLS equalizer my signal its completely equalized:

%Linear RLS
%************************************************************************%
x = [min(rxsignal), max(rxsignal)];
eqlinear_rls_signal = comm.LinearEqualizer('Algorithm','RLS','NumTaps',4,...
    'ReferenceTap',2,'TrainingFlagInputPort',true,'ForgettingFactor',0.99,'Constellation',x);
[signal_eq_rls, err_l_rls_signal, w_l_rls_signal] = eqlinear_rls_signal(rxsignal, signal, true);

eq_lrls_signal = dfilt.dffir(w_l_rls_signal);
rxsignal_eq_lrls = filter(eq_lrls_signal, rxsignal);

I have read that RLS algorithm converges faster than LMS. But I have also tried with larger signals but still LMS algorithm cannot equalize the signal. Does anyone know which can be the problem?