Implementation of median-LMS adaptive filters using power-of-two multiplication in the adaptation arithmetic

There are many existing methods for reducing the VLSI implementation cost of the adaptation arithmetic in stochastic gradient adaptive filters. Some of them cause significant performance impairments (such as slower convergence or increased misadjustment noise). However the replacement of multiplications by Power-of-Two Quantisers (PTQ), together with shifters, has been shown to reduce cost with very little performance impairment. This paper reviews an older method, Power-of-Two Multiplication (PTM), which is equivalent to exponent-only floating-point multiplication. We show that although it has little or no advantage over the PTQ approach for the LMS, NLMS, and GAL algorithms, the PTM method has significant advantages for implementing the median-LMS adaptive filter algorithm.