A simple way to compute the minimum distance in multiuser CDMA systems

A simple method to compute the minimum distance Dmin in multiuser code division multiple access (CDMA) systems based on the Cholesky decomposition of the positive-definite symmetric correlation matrix is proposed. Although finding Dmin is known to be NP-hard, this decomposition allows the computation of the minimum distance and the asymptotic efficiency of optimum multiuser detection to be performed very efficiently in almost all cases of practical interest. Numerical results for synchronous CDMA with binary random signature waveforms of length 31 are used to illustrate the method.