Equalizer co-efficient generation apparatus and method therefor
View Patent ↗Known chip equalizers for Wideband-Code Division Multiple Access (W-CDMA) employ a co-efficient calculator that implements a Minimum Mean Square Error (MMSE) solution to a least squares technique for obtaining equalizer coefficients in response to receipt of a pilot sequence. However, this solution results in an undesirably high processing overhead in downlink receivers operating in a W-CDMA communications system. Consequently, the present invention provides a computationally simpler technique to calculate equalizer coefficients by implementing a minimum-norm solution to the least squares problem.
1. An apparatus for generating a coefficient for an equalizer, the apparatus comprising a receiver and a processing arrangement capable of solving a least squares problem for determining the equalizer coefficient using a received signal corresponding to at least one predetermined symbol sequence, the at least one predetermined symbol sequence and a predetermined spreading code associated with the at least one predetermined symbol sequence, wherein the least squares problem is an underdetermined least squares problem, and the processing arrangement employs a minimum-norm solution to the signal received by the receiver to determine the equalizer coefficient, the minimum-norm solution being:
f =Y H C ( C H YY H C ) −1 p ,
where f is the plurality of equalizer coefficients, (C H YY H C) −1 is an inverse of a correlation matrix, C H is a Hermitian matrix of the predetermined spreading code, and Y is a Toeplitz convolution matrix based upon a vector of received chips, Y , corresponding to the at least one predetermined symbol sequence, P .
2. An apparatus as claimed in claim 1 , wherein the at least one predetermined symbol sequence is a pilot sequence, and the predetermined spreading code is a pilot spreading code.
3. An apparatus as claimed in claim 1 , the processing arrangement comprising:
at least one de-spreader capable of generating a plurality of streams of symbols, each stream being of different delays and corresponding to a correlation matrix of symbols;
a correlator capable of generating correlation data corresponding to a correlation matrix using at least part of the plurality of time-delayed streams of symbols; and
a signal processing arrangement to determine a minimum norm value of the equalizer coefficient; wherein
the correlation data is arranged, when in use, so as to be compatible with the determination of the minimum-norm value.
4. An apparatus as claimed in claim 3 , wherein the correlation data corresponds to correlation between a first set of time-delayed symbols spanning a number of the plurality of streams of symbols and a second set of time-delayed symbols spanning the number of the plurality of streams of symbols.
5. An apparatus as claimed in claim 4 , wherein each symbol of the first set of symbols respectively correspond to a like position within the number of the plurality of streams.
6. An apparatus as claimed in claim 4 , wherein each symbol of the second set of symbols respectively correspond to a like position within the number of the plurality of streams.
7. An apparatus as claimed in claim 3 , wherein the signal processing arrangement is capable of calculating the inverse of the correlation matrix.
8. An apparatus as claimed in claim 7 , wherein the signal processing arrangement is capable of calculating a product of the inverse of the correlation matrix and a predetermined pilot signal.
9. An apparatus as claimed in claim 8 , wherein the signal processing arrangement is capable of calculating a correlation between each of the plurality of streams of symbols and the calculated product of the inverse of the correlation matrix and the predetermined pilot signal, the calculated correlation corresponding to the coefficient for the equalizer.
10. An apparatus as claimed in claim 3 , wherein the correlation data corresponds to a square correlation matrix of dimension between 2 and 4.
11. A spread-spectrum receiver comprising the apparatus for generating a coefficient for an equalizer as claimed in claim 1 .
12. A communications system comprising the spread-spectrum receiver as claimed in claim 11 .
13. An apparatus as claimed in claim 1 wherein the receiver is a third generation Frequency Division Duplex downlink receiver.
14. A method of generating a coefficient of an equalizer of a receiver, the method comprising:
solving a least squares problem for determining the equalizer coefficient using a received signal corresponding to at least one predetermined sequence, the at least one predetermined sequence and a predetermined spreading code associated with the at least one predetermined sequence; and
employing a minimum-norm solution to determine the equalizer coefficient; wherein the least squares problem is an underdetermined least squares problem, and the minimum-norm solution is:
f =Y H C ( C H YY H C ) −1 P ,
where f is the plurality of equalizer coefficients, (C H YY H C) −1 is an inverse of a correlation matrix, C H is a Hermitian matrix of the predetermined spreading code, and Y is a Toeplitz convolution matrix based upon a vector of received chips, Y , corresponding to the at least one predetermined symbol sequence, P .
15. A method as claimed in claim 14 , wherein the at least one predetermined symbol sequence is a pilot sequence, and the predetermined spreading code is a pilot spreading code.
16. A method as claimed in claim 14 , the method further comprising:
generating a plurality of streams of symbols by de-spreading a received pilot signal, each stream being of different delays and corresponding to a correlation matrix of symbols;
generating correlation data corresponding to a correlation matrix using at least part of the plurality of time-delayed streams of symbols; and
determining a minimum-norm value of the equalizer coefficient; wherein
the correlation data is arranged so as to be compatible with the determination of the minimum-norm value.
17. A method as claimed in claim 16 , wherein the correlation data corresponds to correlation between a first set of time-delayed symbols spanning a number of the plurality of streams of symbols and a second set of time-delayed symbols spanning the number of the plurality of streams of symbols.
18. A method as claimed in claim 17 , wherein each symbol of the first set of symbols respectively correspond to a like position within the number of the plurality of streams.
19. A method as claimed in claim 17 , wherein each symbol of the second set of symbols respectively correspond to a like position within the number of the plurality of streams.
20. A method as claimed in claim 16 , further comprising: calculating the inverse of the correlation matrix.
21. A method as claimed in claim 20 , further comprising: calculating a product of the inverse of the correlation matrix and a predetermined pilot signal.
22. A method as claimed in claim 21 , wherein the signal processing arrangement is capable of calculating a correlation between each of the plurality of streams of symbols and the calculated product of the inverse of the correlation matrix and the predetermined pilot signal, the calculated correlation corresponding to the coefficient for the equalizer.
23. A method as claimed in claim 16 , wherein the correlation data corresponds to a square correlation matrix of dimension between 2 and 4.
24. A method as claimed in claim 14 wherein the receiver is a third generation Frequency Division Duplex downlink receiver.