Multiuser Detection in Overloaded Synchronous CDMA using Modified Probabilistic Data Association

In synchronous CDMA, having more users than the signature length results in a singular correlation matrix. However, with a careful design of the correlations and with the help of the binary feature of user signals, good performance in a slightly overloaded system can still be achieved. However, the singularity of the correlation matrix does make the direct implementation of many multiuser detectors impossible. With the help of successive cancellation, taking inverse of a singular matrix is avoided.