Efficient linear equalization for high data rate downlink CDMA signaling

In this paper, we propose an FFT-based linear equalization algorithm for the CDMA downlink. By approximating the correlation matrix with a circulant matrix, which is diagonalized by the DFT matrix, we are able to incorporate the efficient FFT operations and avoid the direct matrix inversion. Furthermore, we show that with the help of Kronecker algebra and the notion of dimension-wise and element-wise FFT, we are able to extend the FFT-based method to cases where multi-channel diversity, such as over-sampling or receive antenna array diversity, is present. Numerical simulations show that the FFT-based algorithm overlaps with the direct matrix inversion method for most of the low to medium SNR range and have a small loss at high SNR.