Channel equalisers

In a filter for a non-ideal channel having a delay line with N stages and M connections with variable coefficient values, where M<N, a method of determining the filter tap characteristics comprising the steps of:

• connecting a pivot tap to a first tap of the delay line;
• replacing the pivot tap with a variable filter tap and connecting the pivot tap to one of the N−1 locations remaining;
• and,
• at each remaining pivot location optimising a first co-efficient value according to a selected optimality criterion until a best location for the pivot tap has been determined;
• determining a subset of optimal locations;
• determining filter tap values for said optimal locations wherein, for each sequential step of the process, m−1 variable coefficients and one pivot are provided;
• and the variable coefficients are connected to a subset of delay line taps which were determined to be optimal in step m−1;
• wherein the mth pivot tap is scanned through the unused N−m−1 delay line taps remaining and a best location is found as before.

A digital filter having a plurality of filter taps wherein the filter is operable such that a sparse subset of filter taps may be determined according to the following steps:

• obtaining impulse response values {h0, h1, h2, . . . hN} to create a channel response matrix H;
• applying Givens' rotation algorithm to the matrix H comprising the sub-steps of:
• i) using a sequence of N−1 2×2 rotation operations a top row of the matrix is made zero to the right of a first diagonal element of the matrix;
• ii) copying and applying identical sequences of rotations in the same order to second and subsequent rows of the matrix;
• and
• iii) permuting the matrix to achieve a best value for a second diagonal element of the matrix;
• iv) repeating steps i) and ii) for the second row with a corresponding reduction to zero of elements of each row to the right of the diagonal of the matrix;
• v) repeating steps iii) and iv) for subsequent rows up to a limit so as to produce a lower triangular matrix L;
• inverting the matrix L;
• and extracting a leading column of the inverted matrix and mapping element locations in the inverted matrix back through an inverse pivot map,
• such that for each element of the leading column the mapped value of a permuted row number corresponds to the number of a selected tap to be employed of the filter and the element of the leading column corresponds to the desired weight for that tap of the filter.

A filter for a non-ideal channel having a delay line with N stages and M connections with variable coefficient values, where M<N , the filter being operable to determine the filter tap characteristics comprising the method steps of:

• connecting a pivot tap to a first tap of the delay line;
• replacing the pivot tap with a variable filter tap and connecting the pivot tap to one of
• the N−1 locations remaining;
• and,
• at each remaining pivot location optimising a first co-efficient value according to a selected optimality criterion until a best location for the pivot tap has been determined;
• determining a subset of optimal locations;
• determining filter tap values for said optimal locations wherein, for each sequential step of the process, m−1 variable coefficients and one pivot are provided;
• and the variable coefficients are connected to a subset of delay line taps which were determined to be optimal in step m−1;
• wherein the mth pivot tap is scanned through the unused N−m−1 delay line taps remaining and a best location is found as before.

A signal having been processed by a digital filter havirig a plurality of filter taps wherein the filter is operable such that a sparse subset of filter taps may be determined according to the following steps:

• obtaining impulse response values {h0, h1, h2, . . . hN} to create a channel response matrix H;
• applying Givens' rotation algorithm to the matrix H comprising the sub-steps of:
• i) using a sequence of N−1 2×2 rotation operations a top row of the matrix is made zero to the right of a first diagonal element of the matrix;
• ii) copying and applying identical sequences of rotations in the same order to second and subsequent rows of the matrix;
• and
• iii) permuting the matrix to achieve a best value for a second diagonal element of the matrix;
• iv) repeating steps i) and ii) for the second row with a corresponding reduction to zero of elements of each row to the right of the diagonal of the matrix;
• v) repeating steps iii) and iv) for subsequent rows up to a limit so as to produce a lower triangular matrix L;
• inverting the matrix L;
• and extracting a leading column of the inverted matrix and mapping element locations in the inverted matrix back through an inverse pivot map,
• such that for each element of the leading column the mapped value of a permuted row number corresponds to the number of a selected tap to be employed of the filter and the element of the leading column corresponds to the desired weight for that tap of the filter.

In a filter for a non-ideal channel having a delay line with N stages and M connections with variable coefficient values, where M<N, a method of determining the filter tap characteristics comprising the steps of:

• a first step of connecting a pivot tap to a first tap of the delay line;
• a second step of replacing the pivot tap with a first variable filter tap and scanning the pivot tap through the N−1 locations remaining and at each remaining pivot location optimising the co-efficient value of the first variable filter tap according to a selected optimality criterion until a best location for the pivot tap has been determined;
• and
• an mth step of determining a subset of m−1 previously selected optimal locations and the last determined best pivot tap location;
• connecting the variable coefficients to said sub-set of optimal locations and replacing the last pivot tap with an mth variable filter tap;
• and scanning the pivot tap through N−m−1 locations remaining and optimising the co-efficient value of the mth variable filter tap until a best location for the pivot tap has been determined as before.

A filter for a non-ideal channel having a delay line with N stages and M connections with variable coefficient values, where M<N the filter being operable to determine the filter tap characteristics comprising the method steps of:

• a first step of connecting a pivot tap to a first tap of the delay line;
• a second step of replacing the pivot tap with a first variable filter tap and scanning the pivot tap through the N−1 locations remaining and at each remaining pivot location optimising the co-efficient value of the first variable filter tap according to a selected optimality criterion until a best location for the pivot tap has been determined;
• and
• an mth step of determining a subset of m−1 previously selected optimal locations and the last determined best pivot tap location;
• connecting the variable coefficients to said sub-set of optimal locations and replacing the last pivot tap with an mth variable filter tap;
• and scanning the pivot tap through N−m−1 locations remaining and optimising the co-efficient value of the mth variable filter tap until a best location for the pivot tap has been determined as before.