Method for generating 2D OVSF codes in multicarrier DS-CDMA systems

A wireless communications device comprising:

• a multicarrier direct-sequence code-division multiple-access (MS-DS/CDMA) module for providing MC-DS/CDMA functionality to the wireless device according to a signature sequence;
• and
• an M×N matrix generator for generating a two-dimensional orthogonal variable spreading factor (2D-OVSF) code to serve as the signature sequence, where M relates to the number of available frequency carriers available to the wireless device, N relates to a spreading factor, M=2k,N=2h+α, k is greater than zero, and α is greater than or equal to zero, the M×N matrix generator providing:
• a first set of orthogonal 2×2 matrices
• 10 { A ( 2 × 2 ) ( 1 ) , A ( 2 × 2 ) ( 2 ) } ;
• ⁢
• and
• a second set of orthogonal 2×2 matrices
• 11 { B ( 2 × 2 ) ( 1 ) , B ( 2 × 2 ) ( 2 ) }
• the M×N matrix generator performing the following steps to generate the signature sequence:
• utilizing the first and second 2×2 matrices to generate a progenitor matrix A(1)(2×2α) or A(2)(2×2α) by iterating the relationship:
• A(1)(2×21+β)=[A(1)(2×2β) A(2)2×2β)],
• A(2)(2×21+β)=[A(1)(2×2β) −A(2)(2×2β)].
• utilizing the matrix A(1)(2×2α) or A(2)(2×2α) to generate an M×N matrix by iterating the relationship:
• A(i−1)(O×P)=[B(1)(2×2){circle over (×)}A(i/2)(O/2×P/2)],
• A(i)(O/2×P/2)=[B(2)(2×2){circle over (×)}A(i/2)(O/2×P/2)];
• wherein {circle over (×)} is a Kronecker product.

A wireless communications device comprising:

• a multicarrier direct-sequence code-division multiple-access (MS-DS/CDMA) module for providing MC-DS/CDMA functionality to the wireless device according to a signature sequence;
• and
• a memory for storing a code tree of two-dimensional orthogonal variable spreading factor (2D-OVSF) codes that are capable of serving as the signature sequence, the 2D-OVSF codes each expressible as an M×N matrix A(1)(M×N) in which M relates to the number of available frequency carriers available to the wireless device, N relates to a spreading factor, M=2k, N=2k+α, k is greater than zero, i ranges from one to M, and α is greater than or equal to zero, the 2D-OVSF codes of the code tree being interrelated by:
• 12 A ( 1 ) ⁡ ( 2 × 2 i + 1 ) = [ A ( 1 ) ⁡ ( 2 × 2 i ) ⁢ A ( 2 ) ⁡ ( 2 × 2 i ) ] , A ( 2 ) ⁡ ( 2 × 2 i + 1 ) = [ A ( 1 ) ⁡ ( 2 × 2 i ) - A ( 2 ) ⁡ ( 2 × 2 i ) ] , A ( 0 × P ) ( i - 1 ) = [ B ( 2 × 2 ) ( 1 ) ⊗ A ( 0 / 2 × P / 2 ) ( i / 2 ) ] , and A ( 0 × P ) ( i ) = [ B ( 2 × 2 ) ( 2 ) ⊗ A ( 0 / 2 × P / 2 ) ( i / 2 ) ] ,
• wherein {circle over (×)} is a Kronecker product, A(1)(2×2) is orthogonal to A(2)(2×2), and B(1)(2×2) is orthogonal to B(2)(2×2).

A method for providing a signature sequence to a mobile unit in a multicarrier direct-sequence code-division multiple-access (MS-DS/CDMA) communications system, the method comprising:

• a base station generating an M×N matrix according to a matrix generation method;
• the base station transmitting the M×N matrix to a mobile device;
• and
• the mobile device utilizing the M×N matrix to serve as a signature sequence of the mobile device;
• wherein the matrix generation method comprises:
• providing a first set of orthogonal 2×2 matrices {A(1)(2×2), A(2)(2×2)};
• providing a second set of orthogonal 2×2 matrices {B(1)(2×2), B(2)(2×2)};
• utilizing the first set of 2×2 matrices to generate a pair of progenitor nodes in a code tree that respectively represent matrices A(1)(2×2α) and A(2)(2×2α) by iterating the relationship:
• A(1)(2×21+β)=[A(1)(2×2β) A(2)(2×2β)],
• A(2)(2×21+β)=[A(1)(2×2β) −A(2)(2×2β)];
• and
• utilizing the matrices A(1)(2×2α) and A(2)(2×2α) to generate a child node of one of the progenitor nodes, the child node having the M×N matrix, by iterating the relationship:
• A(i−1)(O×P)=[B(1)(2×2){circle over (×)}A(i/2)(O/2×P/2)],
• A(i)(O×P)=[B(2)(2×2){circle over (×)}A(i/2)(O/2×P/2)];
• wherein {circle over (×)} is a Kronecker product.

A method for providing a signature sequence to a mobile unit in a multicarrier direct-sequence code-division multiple-access (MS-DS/CDMA) communications system, the method comprising:

• a base station generating an M×N matrix according to a matrix generation method;
• the base station transmitting the M×N matrix to a mobile device;
• and
• the mobile device utilizing the M×N matrix to serve as a signature sequence of the mobile device;
• wherein the matrix generation method comprises:
• providing a first set of orthogonal 2×2α matrices A(1)(2×2α) and A(2)(2×2α);
• providing a second set of orthogonal 2×2 matrices {B(1)(2×2), B(2)(2×2)};
• and
• utilizing the matrices A(1)(2×2α) and A(2)(2×2α) to generate the M×N matrix by iterating the relationship:
• A(i−1)(O×P)=[B(1)(2×2){circle over (×)}A(i/2)(O/2×P/2)],
• A(i)(O×P)=[B(2)(2×2){circle over (×)}A(i/2)(O/2×P/2)];
• wherein {circle over (×)} is a Kronecker product.