초록 ▼

A novel method and apparatus is provided for enabling the computation of a signal in a certain subspace, its projection that lies outside the subspace, and the orthogonal basis for a given matrix. More particularly, the present invention relates to the use of such a method or apparatus for real-time

A novel method and apparatus is provided for enabling the computation of a signal in a certain subspace, its projection that lies outside the subspace, and the orthogonal basis for a given matrix. More particularly, the present invention relates to the use of such a method or apparatus for real-time hardware applications since the method and apparatus may be utilized without matrix inversions or square root computations.

대표청구항 ▼

1. A method for generating a projection of a received signal y, said received signal comprising H, a signal of a source of interest; S, the signals of all other sources and multi-path versions of the source of interest and composed of vectors s1, s2, s3, . . . , sp; and noise (n); the method compris

1. A method for generating a projection of a received signal y, said received signal comprising H, a signal of a source of interest; S, the signals of all other sources and multi-path versions of the source of interest and composed of vectors s1, s2, s3, . . . , sp; and noise (n); the method comprising the steps of:determining a basis matrix U composed of basis vectors u1, u2, . . . up; storing elements of said basis matrix U; generating a diagonal matrix from stored said elements of the basis matrix U; generating one or more scalars from the diagonal matrix and from the basis vectors of the basis matrix U; and applying the one or more scalars to the received signal to project the signal of the source of interest. 2. The method recited in claim 1, further comprising the step of computing the basis vectors, wherein computing the basis vectors comprises the steps of:A. assigning s1 as a first vector of basis matrix U; B. decomposing s2 into a component which is in said basis matrix U and a component that is not (u2); and C. redefining the basis matrix U to incorporate basis vector u2. 3. The method recited in claim 2, wherein said step of computing the basis vectors further comprises the steps of:repeating steps B and C for each vector of S. 4. The method recited in claim 2, wherein said step of computing the basis vectors further comprises the steps of:comparing ui to a predetermined threshold and if ui is greater than said threshold, adding ui to the basis and repeating steps B and C for each vector of S, else ignoring the ui and continuing to repeat steps B and C. 5. The method recited in claim 2, wherein said step of computing the basis vectors further comprises the steps of:computing 1/σi, where uiTui=σi; and storing ui and 1/σi. 6. The method recited in claim 2, wherein said step of computing the basis vectors further comprises the steps of:computing storing ui and 1/σi, wherein uiTui=σi; and repeating said computing and storing steps if ui is above a predetermine threshold, else ignoring this particular ui. 7. The method recited in claim 1, wherein said step of applying comprises the step of calculating yperp with the following formula: wherein yperp is a projected said received signal y, σi=uiTui, and ui is a basis vector of U.8. The method recited in claim 7, wherein said step of calculating yperp comprises the step of calculating yperp with the following formula: 9. The method recited in claim 8, further comprising the step of determining wherein ys is a projected said signal of the source of interest.10. A method for generating a projection of a received signal y, said received signal comprising H, a spread signal matrix of a source of interest; S, the spread signal matrix of all other sources of interest and composed of vectors s1, s2, s3 . . . , sp; and noise n; the method comprising the steps of:forming an orthogonal basis U of the matrix S, comprising: A. assigning si as a first basis vector u1, B. determining σi, where uiTui=σi, C. storing ui, D. computing of inner products of the si+1 and the u1 through ui vectors, E. multiplying said inner product with a respective scalar 1/σi and thereby creating a first intermediate product, F. scaling each respective basis vector ui by multiplying each respective first intermediate product with each respective basis vector ui, G. obtaining a vector sum from step F, H. subtracting said vector sum from si+1 to obtain the next basis vector ui+1, I. comparing ui+1 to a predetermined value and if equal to or less than said value, discarding the ui+1 and going to step N, J. storing ui+1, K. determining an inner product of uTi+1ui+1, L. determining the reciprocal of step K which is 1/σi+1, M. storing 1/σi+1, N. incrementing i, and O. conducting steps D through N until i=p, where p is the total number of said sources of interest; generating a diagonal matrix from stored 1/σi+1 values; generating one or more scalars from the diagonal matrix and from the basis vectors of the orthogonal basis U; and applying the one or more scalars to the received signal to project the source of interest. 11. The method recited in claim 10, wherein said computing step (D) is conducted in series.12. The method recited in claim 10, wherein said computing step (D) is conducted in parallel.13. The method recited in claim 10, wherein said multiplying step (E) is conducted in series.14. The method recited in claim 10, wherein said multiplying step (E) is conducted in parallel.15. The method recited in claim 10, wherein said scaling step (F) is conducted in series.16. The method recited in claim 10, wherein said scaling step (F) is conducted in parallel.17. The method recited in claim 10, wherein said storing step (C) also stores σi.18. The method recited in claim 10, wherein said storing step (C) also stores 1/σi.19. The method recited in claim 10, wherein said inner product step (K) is conducted in series.20. The method recited in claim 10, wherein said inner product step (K) is conducted in parallel.21. The method recited in claim 10, further comprising the step of determining wherein ys is a projected said source of interest. 22. A method for generating a projection of a received signal y, said received signal comprising H, a spread signal matrix of a source of interest; S, the spread signal matrix of all other sources of interest and composed of vectors s1, s2, s3 . . . , sp; and noise (n); the method comprising the steps of:forming an orthogonal basis U of the matrix S, comprising: A. assigning s1 as a first basis vector u1, B. determining σi, where uiTui=σi, C. storing ui, D. computing of inner products of the si+1 and the u1 through ui vectors, E. multiplying said inner product with a respective scalar 1/σi and thereby creating a first intermediate product, F. scaling each respective basis vector ui by multiplying each respective first intermediate product with each respective basis vector ui, G. serially subtracting said intermediate product from si+1, H. utilizing the result from step G and subtracting the next incoming value of until all the values are processed,I. obtaining the next basis vector ui+1from step H, J. comparing ui+1 to a predetermined value and if equal to or less than said value, discarding ui+1 and going to step O, K. storing ui+1, L. determining an inner product of uTi+1ui+1, M. determining the reciprocal of step K which is 1/σi+1, N. storing 1/σi+1, O. incrementing i, and P. conducting steps D through O until i=p, where p is the total umber of said sources of interest; generating a diagonal matrix from stored 1/σi+1 values; generating one or more scalars from the diagonal matrix and from the basis vectors of the orthogonal basis U; and applying the one or more scalars to the received signal to project the source of interest. 23. The method recited in claim 22, wherein said computing step (D) is conducted in series.24. The method recited in claim 22, wherein said computing step (D) is conducted in parallel.25. The method recited in claim 22, wherein said multiplying step (E) is conducted in series.26. The method recited in claim 22, wherein said multiplying step (E) is conducted in parallel.27. The method recited in claim 22, wherein said scaling step (F) is conducted in series.28. The method recited in claim 22, wherein said scaling step (F) is conducted in parallel.29. The method recited in claim 22, wherein said storing step (C) also stores σi.30. The method recited in claim 22, wherein said storing step (C) also stores 1/σi.31. The method recited in claim 22, wherein said inner product step (L) is conducted in series.32. The method recited in claim 22, wherein said inner product step (L) is conducted in parallel.33. The method recited in claim 22, further comprising the step of determining wherein ys is a projected said source of interest. 34. An apparatus for generating a projection of received signal y, said received signal comprising H, a signal of a source of interest; S, the signals of all other sources and composed of vectors s1, s2, s3 . . . , sp; and noise (n); the apparatus comprising:means for determining a basis vector U; means for storing elements of said basis vector U; and means for generating a diagonal matrix from stored said elements of the basis vector U; means for generating one or more scalars from the diagonal matrix and from the basis vector U; and means for applying the one or more scalars to the received signal to project the signal of the source of interest. 35. An apparatus for generating a projection of a received signal y, said received signal comprising H, a spread signal matrix of a source of interest; S, the spread signal matrix of all other sources of interest and composed of vectors s1, s2, s3 . . . , sp; and noise (n); the apparatus comprising:means for forming an orthogonal basis U of the matrix S, comprising: A. means for assigning s1 as a first basis vector ui, B. means for determining σi, where uiTui=σi, C. means for storing ui, D. means for computing of inner products of the si+1 and the u1 through ui vectors, E. means for multiplying said inner product with a respective scalar 1/σi and thereby creating a first intermediate product, F. means for scaling each respective basis vector ui by multiplying each respective first intermediate product with each respective basis vector ui, G. means for obtaining a vector sum from step F, H. means for subtracting said vector sum from si+1 to obtain the next basis vector ui+1, I. means for comparing ui+1 to a predetermined value and if equal to or less than said value, discarding this ui+1 and going to step N, J. means for storing ui+1, K. means for determining an inner product of uTi+1ui+1, L. means for determining the reciprocal of step K which is 1/σi+1, M. means for storing 1/σi+1, N. means for incrementing i, O. means for conducting steps D through N until i=p, where p is the total number of said sources of interest; means for generating a diagonal matrix from stored 1/σi+1 values; means for generating one or more scalars from the diagonal matrix and from the basis vectors of the orthogonal basis U; and means for applying the one or more scalars to the received signal to project the source of interest. 36. An apparatus for generating a projection from a received signal y, said received signal comprising H, a spread signal matrix of a source of interest; S, the spread signal matrix of all other sources of interest and composed of vectors s1, s2, s3 . . . , sp; and noise (n); the apparatus comprising:means for forming an orthogonal basis U of the matrix S, comprising: A. means for assigning s1 as a first basis vector ui, B. means for determining σi, where uiTui=σi, C. means for storing ui, D. means for computing of inner products of the si+1 and the u1 through ui vectors, E. means for multiplying said inner product with a respective scalar 1/σi and thereby creating a first intermediate product, F. means for scaling each respective basis vector ui by multiplying each respective first intermediate product with each respective basis vector ui, G. means for serially subtracting said intermediate product from si+1, H. means for utilizing the result from step G and subtracting the next incoming value of until all the values are processed,I. means for obtaining the next basis vector ui+1 from step H, J. means for comparing ui+1 to a predetermined value and if equal to or less than said value, going to step O, K. means for storing ui+1, L. means for determining an inner product of uTi+1ui+1, M. means for determining the reciprocal of step K which is 1/σi+1, N. means for storing 1/σi+1, O. means for incrementing i, P. means for conducting steps D through O until i=p, where p is the total number of said sources of interest; means for generating a diagonal matrix from stored 1/σi+1 values; means for generating one or more scalars from the diagonal matrix and from the basis vectors of the orthogonal basis U; and means for applying the one or more scalars to the received signal to project the source of interest. 37. A method for generating a projection of a received signal y, said received signal comprising H, a signal of a source of interest; S, the signals of all other sources and multi-path versions of the source of interest and composed of vectors s1, s2, s3 . . . , sp; and noise (n); the method comprising the steps of:determining a basis matrix U composed of basis vectors u1, u2 . . . , up; storing elements of said basis matrix U; generating a diagonal matrix from stored said elements of the basis matrix U; generating one or more scalars from the diagonal matrix and from the basis vectors of the basis matrix U; applying the one or more scalars to the received signal to project the signal of the source of interest: and determining wherein ys is a projected said signal of the source of interest. 38. An apparatus for generating a projection from a received signal y, said received signal comprising H, a signal of a source of interest; S, the signals of all other sources and composed of vectors s1, s2, s3 . . . , sp; and noise (n); the apparatus comprising:means for determining a basis vector U; means for storing elements of said basis vector U; means for generating a diagonal matrix from stored said elements of the basis vector U; means for generating one or more scalars from the diagonal matrix and from the basis vector U; means for applying the one or more scalars to the received signal to project the signal of the source of interest; and means for determining wherein ys is a projected said signal of the source of interest. 39. A system, comprising:means for generating a first matrix from a received signal, wherein the received signal comprises a plurality of signals; means for generating a second matrix from the first matrix, wherein the second matrix is a substantially orthogonal basis of the first matrix; means for storing values used in generating the second matrix; means for generating a diagonal matrix from stored said values; means for generating one or more scalars from the diagonal matrix and from the second matrix; and means for multiplying the one or more scalars to the received signal to project the received signal substantially orthogonal to said plurality of signals. 40. A method, comprising:generating a first matrix from a received signal, wherein the received signal comprises a plurality of signals; generating a second matrix from the first matrix, wherein the second matrix is a substantially orthogonal basis of the first matrix; storing values used in generating the second matrix; generating a diagonal matrix from stored said values; generating one or more scalars from the diagonal matrix and from the second matrix; and multiplying the one or more scalars to the received signal to project the received signal substantially orthogonal to said plurality of signals.