Fast optimal and suboptimal any-time algorithms for CDMA multiuser detection based on branch and bound

A fast optimal algorithm based on the branch-and-bound (BBD) method is proposed for the joint detection of binary symbols of K users in a synchronous code-division multiple-access channel with Gaussian noise. Relationships between the proposed algorithms (depth-first BBD and fast BBD) and both the decorrelating decision-feedback (DF) detector and sphere-decoding algorithm are clearly drawn. It turns out that decorrelating DF detector corresponds to a "one-pass" depth-first BBD; sphere decoding is, in fact, a type of depth-first BBD, but one that can be improved considerably via tight upper bounds and user ordering, as in the fast BBD. A fast "any-time" suboptimal algorithm is also available by simply picking the "current-best" solution in the BBD method. Theoretical results are given on the computational complexity and the performance of the "current-best" suboptimal solution.