A Game Theoretical Approach of the Total Weighted Squared Correlation in S-CDMA Systems

We characterize the Total Weighted Squared Correlation (TWSC) used in uplink synchronous code division multiple access (S-CDMA) as a payoff function in the context of the game theoretic framework. By using majorization theory we proved that the value of the game for two players is a saddle-point corresponding to the minimum of TWSC. The optimal solution is the Stackelberg equilibrium and is achieved by players choosing the generalized Welch Bound Equality (WBE) sequences as spreading signatures. By deriving the optimum strategy for two players we propose a better method of minimizing TWSC when channel state information is known exactly at both the transmitter and receiver. A comparison of our method in terms of the water filling procedure with the previous methods and the Karystinos-Pados bound is also given.