In this paper, we develop a new multistage detector to approach the optimal solution of the detection problem in a synchronous code division multiple access (CDMA) system. The transformation modifies the diagonal elements of the Hessian matrix of the quadratic likelihood function and brings the continuous minimum of the transformed function as close to the optimal solution as possible. The computational complexity is essentially linear with the number of users, except that a few computations of a quadratic function are needed.

Although the optimal detection of signals in a K-user CDMA synchronous system has been proved to be NP-hard, some suboptimal methods do exist to approximate the optimal one. The authors develop a new multistage detector using the transformation proposed by Carter (1984) to approach the optimal solution. The transformation modifies the diagonal elements of the hessian matrix of the quadratic function corresponding to the optimal receiver and brings the continuous minimum of the transformed function as closely to the optimal solution as possible. The convergence of the new multistage algorithms is studied. The computational complexity is essentially linear with the number of users except that a few computations of a quadratic function are needed. The numerical results for the detection of synchronous CDMA signals are shown to be very encouraging.>

Two methods are proposed for designing transformation matrices in array processing and spectral analysis: the stochastic method and the p-norm based method. The authors had previously presented the stochastic method for spatial smoothing, but they did not explicitly formulate the problem using the concept of stochastic transformation. The stochastic method can also be used in other applications if the signal statistics are known or can be estimated. The stochastic method enjoys the advantage of being able to utilize a priori signal statistics. The p-norm based method chooses the vector p-norm as the objective function for optimization, and it provides options to satisfy different designing specifications.>