A variable step-size diffusion LMS algorithm with a quotient form

A new variable step-size strategy for the least mean square (LMS) algorithm is presented for distributed estimation in adaptive networks using the diffusion scheme. This approach utilizes the ratio of filtered and windowed versions of the squared instantaneous error for iteratively updating the step-size. The result is that the dependence of the update on the power of the error is reduced. The performance of the algorithm improves even though it is at the cost of added computational complexity. However, the increase in computational complexity can be minimized by careful manipulation of the update equation, resulting in an excellent performance-complexity trade-off. Complete theoretical analysis is presented for the proposed algorithm including stability, transient and steady-state analyses. Extensive experimental analysis is then done to show the performance of the proposed algorithm under various scenarios.