Solving a class of optimum multiuser detection problems with polynomial complexity

We identify a class of optimum multiuser detection problems which can be solved with polynomial complexity in the number of users. The identification is based on transforming a quadratic 0-1 programming problem into an equivalent problem in graph theory. For a synchronous direct sequence code-division multiple access (CDMA) system, the result translates to designing a set of pseudorandom codes with the property that the cross correlation between every pair of codes in the set over one symbol period is nonpositive. We give two sets of codes with good correlation properties that fall within this class. Finally, we derive a bound on the cardinality of a signal set in an n-dimensional space, having the property that the cross correlation between every pair of signals in the set is nonpositive.