Filter Design Toolbox

adaptfilt.ap

Construct an affine projection FIR adaptive filter object that uses direct matrix inversion

Syntax

• ha = adaptfilt.ap(l,step,projectord,offset,coeffs,states,...
  errstates,epsstates)
  

Description

ha = adaptfilt.ap(l,step,projectord,offset,coeffs,states,...
errstates,epsstates) constructs an affine projection FIR adaptive filter ha using direct matrix inversion.

Input Arguments

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

Input Argument	Description
l	Adaptive filter length (the number of coefficients or taps) and it must be a positive integer. l defaults to 10.
step	Affine projection step size. This is a scalar that should be a value between zero and one. Setting step equal to one provides the fastest convergence during adaptation. step defaults to 1.
projectord	Projection order of the affine projection algorithm. projectord defines the size of the input signal covariance matrix and defaults to two.
offset	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. offset should be positive. offset defaults to one.
coeffs	Vector containing the initial filter coefficients. It must be a length l vector, 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 the adaptive filter states. states defaults to a vector of zeros which has length equal to (l + projectord - 2).
errstates	Vector of the adaptive filter error states. errstates defaults to a zero vector with length equal to (projectord - 1).
epsstates	Vector of the epsilon values of the adaptive filter. epsstates defaults to a vector of zeros with (projectord - 1) elements.

adaptfilt.ap Object Properties

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
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
NumSamplesProcessed	Any positive integer	Specifies the number performed during the adaptation process
ProjectionOrder		Projection order of the affine projection algorithm. projectord defines the size of the input signal covariance matrix and defaults to two.
OffsetCov		Contains the offset covariance matrix
Coefficients	Vector of elements	Vector containing the initial filter coefficients. It must be a length l vector, 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 + projectord - 2).
ErrorStates	Vector of elements	Vector of the adaptive filter error states. errstates defaults to a zero vector with length equal to (projectord - 1).
EpsilonStates	Vector of elements	Vector of the epsilon values of the adaptive filter. epsstates defaults to a vector of zeros with (projectord - 1) elements.
StepSize	Any scalar from zero to one, inclusive	Specifies the step size taken between filter coefficient updates
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. 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'.

Example

Quadrature phase shift keying (QPSK) adaptive equalization using a 32-coefficient FIR filter. Run the adaptation for 1000 interations.

• 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)
  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('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

msesim

References

[1]  K. Ozeki and Umeda, T., "An Adaptive Filtering Algorithm Using an Orthogonal Projection to an Affine Subspace and Its Properties," Electronics and Communications in Japan, vol.67-A, no. 5, pp. 19-27, May 1984

[2]  Y. Maruyama, "A Fast Method of Projection Algorithm," Proc. 1990 IEICE Spring Conf., B-744

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