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

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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.