Code design based on dynamical systems theory and its application to digital communications

正交频分复用（OFDM）系统在无线移动的通信中受到了广泛的关注，但其接收机对多普勒效应引起的频偏敏感。本文提出了一种准正交多载波CDMA系统，它不要求子载波间完全正交。在此基础上，我们提出了一种对时间和频率同步误差具有鲁棒性的Gabor-division（GD）CDMA系统。这样的系统具有三个期望的特性：（1）具有负自相关的马尔可夫扩频码可以将多址干扰（MAI）的方差降低9/25。(2)二维码捕获方法同时估计时间和频率偏移。(3)联合使用时域和频域扩频码实现了几乎平坦的频谱。这些特性表明，GD-CDMA系统可以解决多普勒频移带来的问题。锁相环（PLL）电路被广泛应用于接收机中，以保持发射信号和本振的相位同步。提出了一种基于牛顿法的直接估计输入信号频率和相位的新方法。

Orthogonal frequency division multiplexing(OFDM) system has attracted a lot of attention in wireless mobile communications, which has drawback that its receiver is sensitive to frequency offset caused by Doppler effect. We proposed quasi-orthogonal multicarrier CDMA system which does not require complete orthogonality between subcarreiers. Based on this result, we propose a Gabor-division(GD) CDMA system which is robust to time and frequency synchronization errors. Such a system has three desirable properties :(1) Markov spreading codes with negative auto-correlation can reduce the variance of multiple access interference(MAI) by a factor of 9/25.(2) Two dimensional code acquisition method estimates time and frequency offsets simultaneously.(3) Joint use of time and frequency domain spreading codes realizes almost flat spectrum. These properties imply that GD-CDMA system can solve the problem caused by Doppler frequency shift. Phase locked loop(PLL) circuit is widely employed in the receiver to maintain the synchronization of the phase of the transmitted signal and local oscillator. We have proposed a new method based on Newton' s method, which directly gives estimates of frequency and phase of incoming signal.