Training sequence for low latency lms implementation

Abstract

Use of a training sequence having terms that are orthogonal to each other are employed to considerably speed up execution of the LMS algorithm. Such orthogonal sequences are developed for a channel that is described as a finite impulse response (FIR) filter having a length Mfrom the already existing orthogonal training sequences for at least two channels that have respective lengths Mand Meach that is less than Msuch that the product of Mand Mis equal to Mwhen Mand Mhave no common prime number factor. More specifically, a set of initial existing orthogonal training sequences is found, e.g., using those that were known in the prior art or by performing a computer search over known symbol constellations given a channel of length M. Thereafter, an orthogonal training sequence of length Mis developed, where the product of Mand Mis equal to Mby repeating the training sequence old1 Mnumber of times to form a first concatenated sequence and repeating the training sequence old2 Mnumber of times to form a second concatenated sequence, so that both the first concatenated sequence and the second concatenated sequence have the same length. Each term of the first concatenated sequence is multiplied by the correspondingly located term in the second concatenated sequence which is placed in the same location in a new sequence made up of the resulting Mproducts. This new sequence is an orthogonal sequence of length M.