For non-sparse response, we have proposed an IMPNLMS + algorithm [7] by applying time variable parameter μ, which does not perform worse than NLMS even for dispersive channels. It can be applied in time-varying environment as well. In this section, the IMPNLMS + algorithm is recalled.
The steepest descent algorithm with step-size control matrix using μ-law [4] in IMPNLMS + algorithm can be written as:
(1)
The step-size control matrix (L x L):
(2)
The l th coefficient g
l
(k) has been presented in [6]:
(3)
Where, logarithmic function in IMPNLMS + differs from [6]:
(4)
Here, μ (k) [8] is a time variable parameter instead of constant:
(7)
The parameter α (k) in IMPNLMS + can be described as:
(9)
(10)
In IMPNLMS + algorithm, thanks to the adaptation of μ (k), the algorithm is more flexible to minimize the MSE related to the time-varying μ (k). The IMPNLMS + algorithm can achieve better convergence even in time-varying environment where the echo path changes obviously. However, the computation of step-size control matrix with μ-law in IMPNLMS + algorithm is expensive. In the next section, we analyze the computational complexity based on IMPNLMS + algorithm. Non-normalized technology is discussed to reduce the computational complexity of IMPNLMS+, which can be also applied to all proportionate NLMS algorithms.