M. Aguirre’s research while affiliated with The University of Texas at San Antonio and other places

We focus on the application of unit norm tight frames to design code division multiple (CDMA) systems spreading sequences with constant chip magnitude. An algorithm for the design of the overloaded real-valued signature sets with minimum total-squared-correlation equal to the Welch bound equality (WBE) set is presented. By using this algorithm we solved the open problem of existence of complex-valued WBE sequence sets with constant chip magnitude in the case when K=N+1, where K is the number of active users in the system and N is the processing gain. The normalized cross-correlation between any pair of signatures in a set obtained by the proposed algorithm is either 1/(K-1) or -1/(K-1) corresponding to equiangular sequences. The results are derived in the context of synchronous CDMA systems. Numerical examples for K=5 users for real WBE sequences and for K=4,3 users for complex WBE sequences with constant chip magnitude are provided.

We developed an algorithm which allows obtaining a Gram matrix having a particular pattern for crosscorrelations of the signature sequences. When it is used for real numbers, unit tight frame signature sets are obtained, as they are required by 2G or 3G CDMA systems. When this algorithm is used for complex numbers, complex valued signature sets with constant chip magnitude are obtained. The results are derived in the context of synchronous CDMA systems and numerical results are provided to illustrate the mathematical formalism.

An algorithm for the design of the overloaded complex spreading sequence sets on the uplink of multicellular synchronous CDMA systems is introduced. Assuming that in each cell the number of users K is greater than the corresponding processing gain N, the total weighted squared correlation criterion is used as a performance measure. The mathematical formalism is supported with selected numerical examples in the multicellular context.

The matrix model and the total weighted square correlation (TWSC) measure for overloaded uplink multiple cell synchronous DS-CDMA systems in the presence of multipath are introduced. A composite Gram matrix approach is used in order to characterize the generalized WBE (Welch bound equality) sequences in extended multidimensional signal space. We have developed an algorithm that preserves the bandwidth of generalized WBE sequences from each cell in the multidimensional signal space associated with a multicellular system.

A definition of total weighted square correlation (TWSC) for an overloaded multicellular synchronous DS-CDMA system in the presence of multipath on the uplink is introduced. We assume the channel state information is known perfectly both at transmitter and receiver. The optimum solutions for minimizing TWSC are the orthogonal generalized WBE (Welch bound equality) spreading sequences. The design of such sequences in the context of cooperative multibase DS-CDMA systems under the TWSC criterion is presented.