Optimally Conditioned Channel Matrices in Precoding Enabled Non-Terrestrial Networks

This paper explores how the condition number of the channel matrix affects the performance of different precoding techniques in non-terrestrial network (NTN) communications. Precoding is a technique that can improve the signal-to-interference-plus-noise ratio (SINR) and bit error rate (BER) in massive multi-beam systems. However, the performance of precoding depends on the rank and condition number of the channel matrix, which measures how well-conditioned the matrix is for inversion. We compare three precoding techniques: zero-forcing (ZF), minimum mean square error (MMSE), and semi-linear precoding (SLP), and show that their performance degrades as the condition number increases. To mitigate this problem, we propose a user ordering approach that forms optimally conditioned channel matrices by selecting users with orthogonal channel vectors. We demonstrate that this approach improves the SINR and goodput of all the precoding techniques in full-frequency reuse NTN communications.