A blind adaptive decorrelating detector for CDMA systems

The decorrelating detector is known to eliminate multiaccess interference when the signature sequences of the users are linearly independent, at the cost of enhancing the Gaussian receiver noise. We present a blind adaptive decorrelating detector which is based on the observation of readily available statistics. The algorithm recursively updates the filter coefficients of a desired user by using the output of the current filter. Due to the randomness of the information bits transmitted and the ambient Gaussian channel noise, the filter coefficients evolve stochastically. We prove the convergence of the filter coefficients to a decorrelating detector in the mean squared error (MSE) sense. We develop lower and upper bounds on the MSE of the receiver filter from the convergence point and show that with a fixed step size sequence, the MSE can be made arbitrarily small by choosing a small enough step size. With a time-varying step size sequence, the MSE converges to zero implying an exact convergence. The proposed algorithm is distributed, in the sense that no information about the interfering users such as their signature sequences or power levels is needed. The algorithm requires the knowledge of only two parameters for the construction of the receiver filter of a desired user: the desired user's signature sequence and the variance of the additive white Gaussian (AWG) receiver noise. This detector, for an asynchronous code division multiple access (CDMA) channel, converges to the one-shot decorrelating detector.