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

TL;DR

This paper derives a new SNR expression for CDMA spreading sequences in frequency-selective channels, linking it to correlation measures, and formulates an optimization problem to maximize SNR using non-linear programming.

Contribution

It introduces a novel SNR expression considering frequency-selective channels and establishes a method to optimize spreading sequences via non-linear programming.

Findings

Derived a new SNR expression involving correlation terms

Established the relation between SNR and mean-square correlations

Proposed an optimization framework to maximize SNR

Abstract

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.