A sub-optimal soft decision PDA method for binary quadratic programming

Binary quadratic programming (BQP) problems arise frequently in digital communication systems where online solutions are required. The multiuser detection (MUD) problem in code division multiple access (CDMA) communications, studied in the paper, is one such example. Due to the NP-hard nature of the BQP problem arising in MUD, only sub-optimal methods with polynomial complexities can be realistically considered. In the paper, a suboptimal algorithm based on the idea of probabilistic data association (PDA) is proposed. By treating the detection parameters as binary random variables, and by approximating the multi-modal Gaussian mixture by a single Gaussian noise, the PDA method provides near-optimal solution with a computational complexity of O(N³), where N is the problem size. Several other algorithms for the MUD problem are also considered and compared in terms of computational efficiency and the degree of suboptimality