1753 words - 8 pages

VARIABLE LEAKY LEAST MEAN SQUARE (VLLMS)

The cost function of conventional LMS [15] does not take care of drifting the Wn in presence of external disturbance. Therefore to overcome from this problem we have consider Leaky LMS with the cost function as

Jn=e_n^2+γw_n^T w_n (9)

Where γ should be choose between 0 and 1 so that to avoid drifting parameter. γ is selected as constant leakage factor which result in over/under parameterization [12],[17]. But by using the variable leakage factor, we can avoid the over/under parameterization which may require to modified the cost function as

Jn=e_n^2+γ_n w_n^T w_n (10)

In order to update the leakage factor we can use the same steepest decent rule as the parameter drift [18] is not required to control, so one can updated the variable leakage factor as

γ(n+1)=γ(n)-2μ(n)〖pe(n)x〗^T (n)w(n-1) (11)

Where p is variable must be greater than 1. By using the variable step-size updatation scheme for μ that yields a fast convergence given by

μ(n+1)=λμ(n)+γ(n)e_n^2 (12)

As we know that the desired signal dn may contain noise which is arises from the external disturbance like multipath, path loss etc, so it will be better to incorporate a robust step size variable algorithm rather than the above equation which modified the variable step size as

μ(n+1)=λμ(n)+γ(n)p_n^2 (13)

Where p is the autocorrelation of e(n) that can be computed by time average of it as

p(n+1)=βp(n)+(1-β)e(n)e(n-1) (14)

Where 0

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