A design challenge in AEC algorithms is the dual between fast convergence and cancellation accuracy in terms of ERLE. Whilst choosing a small step size will enhance the accuracy results, the convergence rate will be long which makes it quite impractical for RTOSs. A compromise has been the variable descent step size affine projection based algorithms. Consider the systems depicted in Figure 1 below:
Figure 1: Single line AEC architecture
Consider a classical affine projection algorithm which proceeds as:
where is the desired signal, is the input matrix with each vector of length . is a vector of the filter weights and is the variable descent step size. It should be noted that is the apriori error and the output of the system is the a posterior error defined as:
Replacing in (2) with (1) we get:
In the case where there is no near end speech, , which is the classical set up. However, in a more practical scenario, there is always near end signal. Denote the near end signal as , then, using the second order statistics,
A heuristic is employed in estimating the second order statistics of both the near end speech and the error signal.
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