Filter Design Toolbox

adaptfilt.qrdlsl

Return a QR-decomposition-based least squares lattice adaptive filter object

Syntax

• ha = adaptfilt.qrdlsl(l,lambda,delta,coeffs,states)
  

Description

ha = adaptfilt.qrdlsl(l,lambda,delta,coeffs,states) returns a QR-decomposition-based least squares lattice adaptive filter ha.

Input Arguments

Entries in the following table describe the input arguments for adaptfilt.qrdlsl.

Input Argument	Description
l	Length of the joint process filter coefficients. It must be a positive integer and must be equal to the length of the prediction coefficients plus one. L defaults to 10.
lambda	Forgetting factor of the adaptive filter. This is a scalar and should lie in the range (0, 1]. lambda defaults to 1. lambda = 1 denotes infinite memory while adapting to find the new filter.
delta	Soft-constrained initialization factor in the least squares lattice algorithm. It should be positive. delta defaults to 1.
coeffs	Vector of initial joint process filter coefficients. It must be a length l vector. coeffs defaults to a length l vector of all zeros.
states	Vector of the angle normalized backward prediction error states of the adaptive filter

adaptfilt.qrdlsl Object Properties

Since your adaptfilt.qrdlsl filter is an object, it has properties that define its behavior in operation. Note that many of the properties are also input arguments for creating adaptfilt.qrdlsl objects. To show you the properties that apply, this table lists and describes each property for the filter object.

Name	Range	Description
Algorithm	None	Defines the adaptive filter algorithm the object uses during adaptation
FilterLength	Any positive integer	Reports the length of the filter, the number of coefficients or taps
Coefficients	Vector of elements	Vector containing the initial filter coefficients. It must be a length l vector where l is the number of filter coefficients. coeffs defaults to length l vector of zeros when you do not provide the argument for input.
States	Vector of elements, data type double	Vector of the adaptive filter states. states defaults to a vector of zeros which has length equal to l -1
ForgettingFactor		Forgetting factor of the adaptive filter. This is a scalar and should lie in the range (0, 1]. It defaults to 1. Setting forgetting factor = 1 denotes infinite memory while adapting to find the new filter. Note that this is the lambda input argument.
InitFactor
FwdPrediction
BkwdPrediction
ResetBeforeFiltering	off or on	Determine whether the filter states get restored to their starting values for each filtering operation. The starting values are the values in place when you create the filter if you have not changed the filter since you constructed it. ResetBeforeFiltering returns to zero any state that the filter changes during processing. States that the filter does not change are not affected. Defaults to 'on'.
NumSamplesProcessed	Any integer	Returns the number of samples processed during filtering. As a check, the number of samples reported processed plus the number of nonprocessed samples should be the total number of input samples. Defaults to zero.

Examples

Implement Quadrature Phase Shift Keying (QPSK) adaptive equalization using a 32-coefficient adaptive filter.

• D  = 16;                       % Number of samples of delay
  b  = exp(j*pi/4)*[-0.7 1];     % Numerator coefficients of channel
  a  = [1 -0.7];                 % Denominator coefficients of channel
  ntr= 1000;                     % Number of iterations
  s  = sign(randn(1,ntr+D))+j*sign(randn(1,ntr+D)); % Baseband QPSK 
                                 % signal
  n  = 0.1*(randn(1,ntr+D) + j*randn(1,ntr+D));   % Noise signal
  r  = filter(b,a,s)+n;          % Received signal
  x  = r(1+D:ntr+D);             % Input signal (received signal)
  d  = s(1:ntr);                 % Desired signal (delayed QPSK signal)
  lam = 0.995;                  % Forgetting factor
  del = 1;                       % Soft-constrained initialization 
  factor
  ha = adaptfilt.qrdlsl(32,lam,del);
  [y,e] = filter(ha,x,d); 
  subplot(2,2,1); plot(1:ntr,real([d;y;e]));
  title('In-Phase Components');
  legend('Desired','Output','Error');
  xlabel('Time Index'); ylabel('Signal Value');
  subplot(2,2,2); plot(1:ntr,imag([d;y;e]));
  title('Quadrature Components');
  legend('Desired','Output','Error');
  xlabel('Time Index'); ylabel('Signal Value');
  subplot(2,2,3); plot(x(ntr-100:ntr),'.'); axis([-3 3 -3 3]);
  title('Received Signal Scatter Plot'); axis('square'); 
  xlabel('Real[x]'); ylabel('Imag[x]'); grid on;
  subplot(2,2,4); plot(y(ntr-100:ntr),'.'); axis([-3 3 -3 3]);
  title('Equalized Signal Scatter Plot'); axis('square');
  xlabel('Real[y]'); ylabel('Imag[y]'); grid on;
  

See Also

adaptfilt.qrdrls, adaptfilt.gal, adaptfilt.ftf, adaptfilt.lsl

References

S. Haykin, Adaptive Filter Theory, 2nd Edition, Prentice Hall, N.J., 1991

adaptfilt.pbufdaf

adaptfilt.qrdrls