## DSP System Toolbox |

This example shows how to track the time-varying weights of a nonstationary channel using the Recursive Least Squares (RLS) algorithm.

The channel is modeled using a time-varying fifth-order FIR filter. The RLS filter and the unknown, nonstationary channel process the same input signal. The output of the channel with noise added is the desired signal. From this signal the RLS filter attempts to estimate the FIR coefficients that describe the channel. All that is known *a priori* is the FIR length.

When you run the model, a plot is made of each weight over time, with the "true" filter weights drawn in yellow, and the estimates of those weights in magenta. Each of the five weights is plotted on a separate axis.

RLS is an efficient, recursive algorithm that converges to a good estimate of the FIR coefficients of the channel if the algorithm is properly initialized. Experiment with the value of the tunable **Forgetting factor** parameter in the RLS Filter block. A good initial guess is *(2N-1)/2N* where *N* is the number of weights. The **Forgetting factor** is used to indicate how fast the algorithm "forgets" previous samples. A value of 1 specifies an infinite memory. Smaller values allow the algorithm to track changes in the weights faster. However, a value that is too small will cause the estimates to be overly influenced by the channel noise.

For more information on the Recursive Least Squares algorithm, see S. Haykin, **Adaptive Filter Theory**, 3rd Ed., Prentice Hall, 1996.