On the Stackelberg equilibrium of total weighted squared correlation in synchronous DS-CDMA systems: algorithm and numerical results

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. 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 generalized Welch bound equality (WBE) sequences as spreading signatures. We propose an algorithm of minimizing TWSC in the presence of multipath and colored noise when channel state information is known perfectly at both transmitter and receiver. A comparison of our method in terms of BER (bit error rate) and water-filling procedure with the previous known methods is also given.