MMSE-based linear parallel interference cancellation in CDMA

We mathematically describe the linear parallel interference canceller (PIC) using matrix algebra. It is shown that the linear PIC, whether conventional or weighted, can be seen as a linear matrix filter applied directly to the received chip-matched filtered signal vector. It is then possible to get an analytical expression for the exact bit error rate and to derive necessary conditions on the eigenvalues of the code correlation matrix and the weighting factors to ensure convergence. The close relationship between the steepest descent method for minimising the mean squared error (MSE) and linear PIC is demonstrated and a modified PIC structure is suggested which converges to the PMMSE detector rather than the decorrelator. Following the principles of the steepest descent method techniques are devised for optimising the choice of weighting factors with respect to the mean squared error. It is shown that only K (the number of users) PIC stages are required for the equivalent matrix filter to be identical to the MMSE filter. For fewer stages, m<K, one unique optimal choice of weighting factors exists which will lead to the minimum achievable MSE at the last stage