A method of multi-user detection in a given uplink and downlink time slot in a software-defined receiver which includes filtering and sampling a received signal; forming a block-banded matrix A of the sampled signals; and solving {circumflex over (d)}=T−1y, where T=(AHA), y=AHx. The methods of solving for the matrix T includes a) computing Cholesky factors of the matrix T by approximating using the block-banded property of the matrix T and A; b) Schur decomposition for Cholesky factors of the matrix T and approximating the lower triangular Cholesky factor matrix R using block Toeplitz property of matrix T; or c) Fourier Transformation.