Non-Linear Programming: Maximize SINR for Designing Spreading Sequence

Signal to interference plus noise ratio (SINR) is an important index for wireless communications. This paper shows a method to derive spreading sequences utilized in code division multiple access systems as the solutions of the non-linear programming: maximize SINR. To this end, we consider a frequency-selective wide-sense-stationary uncorrelated-scattering channel and obtain the worst case of SINR. In the course of the evaluation, we derive an expression of SINR, whose main terms consist of periodic correlation terms and odd periodic correlation terms. Also, we show a relation between SINR and mean square correlations. With our expression, we obtain the problem: maximize SINR. Since this problem is not convex, we obtain the relaxed problem with a semidefinite relaxation technique. From this relaxed problem, we obtain the approximated solutions and evaluate the bit error rate for the solutions.