FIR adaptive filter that uses direct matrix inversion
adaptfilt.ap
will be removed in a future
release. Use dsp.AffineProjectionFilter
instead.
ha = adaptfilt.ap(l,step,projectord,offset,coeffs,states,...
errstates,epsstates)
ha = adaptfilt.ap(l,step,projectord,offset,coeffs,states,...
constructs an affine projection
FIR adaptive filter
errstates,epsstates)ha
using direct matrix inversion.
For information on how to run data through your adaptive filter
object, see the Adaptive Filter Syntaxes section of the reference
page for filter
.
Entries in the following table describe the input arguments
for adaptfilt.ap
.
Input Argument  Description 

 Adaptive filter length (the number of coefficients or
taps) and it must be a positive integer. 
 Affine projection step size. This is a scalar that should
be a value between zero and one. Setting 
 Projection order of the affine projection algorithm. 
 Offset for the input signal covariance matrix. You should
initialize the covariance matrix to a diagonal matrix whose diagonal
entries are equal to the offset you specify. 
 Vector containing the initial filter coefficients. It
must be a length 
 Vector of the adaptive filter states. states defaults
to a vector of zeros which has length equal to ( 
 Vector of the adaptive filter error states. 
 Vector of the epsilon values of the adaptive filter. 
Since your adaptfilt.ap
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.ap
objects.
To show you the properties that apply, this table lists and describes
each property for the affine projection filter object.
Name  Range  Description 

 None  Defines the adaptive filter algorithm the object uses during adaptation 
 Any positive integer  Reports the length of the filter, the number of coefficients or taps 
 1 to as large as needed.  Projection order of the affine projection algorithm. 
 Matrix of values  Contains the offset covariance matrix 
 Vector of elements  Vector containing the initial filter coefficients. It
must be a length 
 Vector of elements, data type double  Vector of the adaptive filter states. states defaults
to a vector of zeros which has length equal to ( 
 Vector of elements  Vector of the adaptive filter error states. 
 Vector of elements  Vector of the epsilon values of the adaptive filter. 
 Any scalar from zero to one, inclusive  Specifies the step size taken between filter coefficient updates 

 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. 
Quadrature phase shift keying (QPSK) adaptive equalization using a 32coefficient FIR filter. Run the adaptation for 1000 iterations.
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 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) mu = 0.1; % Step size po = 4; % Projection order offset = 0.05; % Offset for covariance matrix ha = adaptfilt.ap(32,mu,po,offset); [y,e] = filter(ha,x,d); subplot(2,2,1); plot(1:ntr,real([d;y;e])); title('InPhase 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(ntr100: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(ntr100:ntr),'.'); axis([3 3 3 3]); title('Equalized Signal Scatter Plot'); axis('square'); xlabel('Real[y]'); ylabel('Imag[y]'); grid on;
The four plots shown reveal the QPSK process at work.
[1] Ozeki, K. and Umeda, T., "An Adaptive Filtering Algorithm Using an Orthogonal Projection to an Affine Subspace and Its Properties," Electronics and Communications in Japan, vol.67A, no. 5, pp. 1927, May 1984
[2] Maruyama, Y., "A Fast Method of Projection Algorithm," Proc. 1990 IEICE Spring Conf., B744