Non-Linear Programming: Maximize SNR for Designing Spreading Sequence - Part I: SNR versus Mean-Square Correlation

Signal to Noise Ratio (SNR) is an important index for wireless communications. In CDMA systems, spreading sequences are utilized. This series of papers show the method to derive spreading sequences as the solutions of the non-linear programming: maximize SNR. In this paper, we consider a frequency-selective wide-sense-stationary uncorrelated-scattering (WSSUS) channel and evaluate the worst case of SNR. Then, we derive the new expression of SNR whose main term consists of the periodic correlation terms and the aperiodic correlation terms. In general, there is a relation between SNR and mean-square correlations, which are indices for performance of spreading sequences. Then, we show the relation between our expression and them. With this expression, we can maximize SNR with the Lagrange multiplier method. In Part II, with this expression, we construct two types optimization problems and evaluate them.