Cholesky Factorization With Symmetric Permutation Applied to Detecting and Precoding Spatially Multiplexed Data Streams

We study computationally efficient spatial multiplexing transmission techniques aiming at high spectral efficiency. Two nonlinear transmission schemes based on the minimum mean-squared error criterion are considered in this paper: a detection scheme also known as V-BLAST and a precoding scheme called Tomlinson-Harashima precoding. The nonlinear techniques are known to be more powerful than simple linear filters, however, a large complexity overhead results. Initial proposals for the nonlinear schemes require the complexity proportional to N⁴ if the number of data streams is denoted by N. We propose to apply Cholesky factorization with symmetric permutation for finding a very simple and efficient algorithm that reduces the complexity by a factor of N. We conclude that the large performance advantage of the nonlinear detection and precoding schemes against their simple linear alternatives can be obtained without complexity overhead