Bounds on the Maximum SINR of Binary and Quaternary Code Division

In code-division multiplexing, the real/complex-valued sequence (signature) that maximizes the pre-detection signal-to-interference-plus-noise ratio (SINR) at the output of the maximum-SINR filter is simply the minimum-eigenvalue eigenvector of the disturbance autocorrelation matrix. SINR sequence optimization over a finite alphabet, however, is NP-hard in the sequence length. In this paper, we derive new easy to calculate upper and lower bounds on the SINR of the optimal binary and quaternary sequences that can serve as benchmarking tools for any suggested suboptimal designs.