QR-decomposition-based least-squares lattice adaptive filter
ha = adaptfilt.qrdlsl(l,lambda,delta,coeffs,states)
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.qrdlsl.
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.
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.
Soft-constrained initialization factor in the least squares lattice algorithm. It should be positive. delta defaults to 1.
Vector of initial joint process filter coefficients. It must be a length l vector. coeffs defaults to a length l vector of all zeros.
Vector of the angle normalized backward prediction error states of the adaptive filter
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.
Defines the adaptive filter algorithm the object uses during adaptation
Returns the predicted samples generated during adaptation. Refer to  in the bibliography for details about linear prediction.
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.
Any positive integer
Reports the length of the filter, the number of coefficients or taps
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.
Returns the predicted samples generated during adaptation in the forward direction. Refer to  in the bibliography for details about linear prediction.
Soft-constrained initialization factor. This scalar should be positive and sufficiently large to prevent an excessive number of Kalman gain rescues. delta defaults to one.
false or true
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. PersistentMemory returns to zero any state that the filter changes during processing. States that the filter does not change are not affected. Defaults to false.
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
Implement Quadrature Phase Shift Keying (QPSK) adaptive equalization using a 32-coefficient adaptive filter. To see the results of the equalization process in this example, look at the figure that follows the example code.
D = 16; % Number of samples of delay b = exp(1j*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))+1j*sign(randn(1,ntr+D)); % Baseband QPSK signal n = 0.1*(randn(1,ntr+D) + 1j*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;