Application of complex codes to maximize feeder link utilization
View Patent ↗A method of increasing utilization of user link bandwidth for a code division multiple access communications system is disclosed that includes the steps of selecting a set of orthogonal complex codes each having a code length that is greater than a code length of an optimum real code and less than or equal to a number of antenna elements in an antenna array of the feeder link.
1. A method of increasing utilization of feeder link bandwidth for a code division multiple access communications system comprising the steps of:
selecting a set of orthogonal complex codes each having a code length that is greater than a code length of an optimum real code and less than or equal to a number of antenna elements of a feeder link; and
transferring symbols via the feeder link to or from at least one of a corresponding plurality of user terminals wherein the symbols are represented by a corresponding one of the set of orthogonal complex codes.
2. The method of claim 1 wherein the set of orthogonal complex codes is generated from a Kronecker tensor product given by formula:
C L×P =A L {circle around (×)}W p
wherein
C L×P is a matrix of orthogonal complex codes wherein each of the orthogonal complex codes has a code length equal to L×P,
L is a positive integer.
P equals 2 n where n equals a positive integer,
W p is a Walsh code matrix for a code length of P,
A L is a matrix of coefficients a jk wherein j is a row index equal to 1 . . . L, k is a column index equal to 1 . . . L, and
a jk =e j2π(j−1)(k−1)/L .
3. The method of claim 1 wherein the corresponding one of the set of orthogonal complex codes has a code length of 12.
4. The method of claim 1 wherein the number of antenna elements is 12.
5. A code division multiple access communications system comprising:
a base station;
a geo-stationary platform;
a plurality of user terminals; and
at least one feeder link coupled to the plurality of user terminals and to the geo-stationary platform for transferring symbols between the geo-stationary platform and at least one of the plurality of user terminals wherein the symbols are represented by a corresponding one of a set of orthogonal complex codes having a code length that is greater than a code length of an optimum real code and less than or equal to a number of antenna elements in an antenna array of the feeder link.
6. The code division multiple access communications system of claim 5 wherein the set of orthogonal complex codes is generated from a Kronecker tensor product given by:
C L×P =A L {circle around (×)}W p
wherein
C L×P is a matrix of orthogonal complex codes wherein the at least one of the orthogonal complex codes has a code length equal to L×P,
L is a positive integer,
P equals 2 n and n equals a positive integer,
W p is a Walsh code matrix for a code length of p.
A L is a matrix of coefficients a jk , where j is a row index equal to 1 . . . L, k is a column index equal to 1 . . . L, and
a jk =e j2π(j−1)(k−1)/L .
7. The code division multiple access communications system of claim 5 wherein the at least one of the set of orthogonal complex codes has a code length of 12.
8. The code division multiple access communications system of claim 5 wherein the number of antenna elements is 12.
9. A method of increasing utilization of feeder link bandwidth in a code division multiple access communications system comprising the steps of:
selecting a number of antenna elements for an antenna array of a feeder link according to a given antenna array gain and beamwidth; and
selecting a set of orthogonal complex codes each having a code length that is greater than a code length of an optimum real code and less than or equal to the number of antenna elements.
10. The method of claim 9 further comprising the step of transferring symbols across a user link to or from a user terminal wherein the symbols are represented by a corresponding one of the set of orthogonal complex codes.