Training sequence for low latency LMS implementation
View Patent ↗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 M new from the already existing orthogonal training sequences for at least two channels that have respective lengths M old1 and M old2 each that is less than M new such that the product of M old1 and M old2 is equal to M new when M old1 and M o1d2 have 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 M new is developed, where the product of M old1 and M old2 is equal to M new by repeating the training sequence old1 M old2 number of times to form a first concatenated sequence and repeating the training sequence old2 M old1 number 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 M new products. This new sequence is an orthogonal sequence of length M new .
1. A method for forming an electromagnetic signal embodying a new orthogonal sequence, said signal being adapted for use in a channel, the channel having a length M new , said method comprising the steps of:
selecting first and second existing orthogonal sequences old1 and old2 for at least two channels that have respective lengths M old1 and M old2 , the product of M old1 and M old2 being equal to M new and M old1 and M old2 having no common prime number factor;
repeating the sequence old1 M old2 number of times to form a first concatenated sequence;
repeating the sequence old2 M old1 number of times to form a second concatenated sequence;
multiplying each term in said first concatenated sequence by a correspondingly located term in said second concatenated sequence;
forming said new sequence by placing each product produced in said multiplying step into a corresponding location therein; and
converting said new orthogonal sequence into an electromagnetic signal representative of the information within said resulting orthogonal sequence.
2. The invention as defined in claim 1 further comprising the step of performing a search over each possible combination for a particular modulation scheme's alphabet and a given channel length to determine the existence of an orthogonal sequence for use in said selecting step.
3. The invention as defined in claim 1 wherein at least one of said first existing orthogonal sequence, said second existing orthogonal sequence, and said new orthogonal sequence is employed as a training sequence.
4. The invention as defined in claim 1 wherein at least one of said first existing orthogonal sequence, said second existing orthogonal sequence, and said new orthogonal sequence is employed as a synchronization sequence.
5. The invention as defined in claim 1 wherein first and second existing orthogonal sequences each have a length that has no common prime number factor with the other.
6. The invention as defined in claim 1 wherein said electromagnetic signal is in a modulated format suitable for wireless transmission.
7. A method for forming an electromagnetic signal embodying a new orthogonal sequence, said signal being adapted for use in a channel, the channel having a length M new , said method comprising the steps of:
selecting first and second existing orthogonal sequences old1 and old2 for at least two channels that have respective lengths M old1 and M old2 , the product of M old1 and M old2 being equal to M new and M old1 and M old2 having different lengths;
repeating the sequence old1 M old2 number of times to form a first concatenated sequence;
repeating the sequence old2 M old1 number of times to form a second concatenated sequence;
multiplying each term in said first concatenated sequence by a correspondingly located term in said second concatenated sequence;
forming said new sequence by placing each product produced in said multiplying step into a corresponding location therein; and
converting said new orthogonal sequence into an electromagnetic signal representative of the information within said resulting orthogonal sequence.