Efficient implementation of linear multiuser detectors for asynchronous CDMA systems by linear interference cancellation

The decorrelating and the linear, minimum mean-squared error (MMSE) detector for asynchronous code-division multiple-access communications are ideally infinite memory-length detectors. Finite memory approximations of these detectors require the inversion of a correlation matrix whose dimension is given by the product of the number of active users and the length of the processing window. With increasing number of active users or increasing length of the processing window, the calculation of the inverse may soon become numerically very expensive. In this paper, we prove that the decorrelating and the linear MMSE detector can both be realized by linear multistage interference cancellation algorithms with ideally an infinite number of stages. It will be: shown that depending on the signal-to-noise ratio, the number of active users, and the choice of the cancellation algorithm, only a few stages are necessary to obtain the same BER performance as with the ideal detectors. The computational costs for one stage of a linear interference cancellation algorithm are essentially given by one matrix-vector multiplication. Thus, the computational complexity can be reduced considerably. Since each stage introduces a time delay equivalent to the bit duration, the number of stages also determines the detection delay. Because a few stages are sufficient, this approach can also be used to obtain receiver structures with low memory consumption and detection delay.