非线性规划：最大化SNR以设计扩频序列-第一部分：SNR与均方相关
Non-Linear Programming: Maximize SNR for Designing Spreading Sequence - Part I: SNR versus Mean-Square Correlation
摘要：
信噪比是无线通信的一个重要指标。在CDMA系统中，使用扩频序列。本系列文章给出了以信噪比最大化为目标的非线性规划的解作为扩频序列的推导方法。在本文中，我们考虑一个频率选择性的广义平稳非相关散射（WSSUS）信道，并评估最坏情况下的SNR。在此基础上，推导出了新的信噪比表达式，其主项由周期相关项和非周期相关项组成。一般来说，SNR和均方相关之间存在关系，均方相关是扩频序列性能的指标。然后，我们展示了我们的表达和他们之间的关系。有了这个表达式，我们可以用拉格朗日乘子法最大化信噪比。在第二部分中，我们利用这个表达式构造了两类优化问题，并对它们进行了评价。
英文摘要：
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.
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