The Separable Property (SP) condition for time and frequency synchronization compels us to determine phase correction terms in the Gabor Division/Spread Spectrum System (GD/S3). The phase correction technique has led us to design a GD/S3receiver equipped with phase-tuned layers for Mary phase shift keying (MPSK). The resulting signal points of the time domain (TD) and frequency domain (FD) correlator outputs of each layer for M = 16 consist of only three lines, called a main-lobe with a layer-dependent phase angle and sidelobes with phase angle ±2π/16. The two sidelobes suggesting bit errors are removed by using code division multiple target (CDMT), inspired by code division multiple-access (CDMA) philosophy. The simulation result for 16PSK is confirmed.

Delay and Doppler determination of a time-delayed and frequency-shifted signal is one of fundamental problems in communication. The two-parameter estimation is reduced to two one-parameter estimation problems in time- and frequency-domain signals. Motivated by Gabor's communication theory, we proceed further parallelism between time- and frequency-domain signals and solve the two problems individually and cooperatively. Simulation results without prescribed information are reported.

Recently proposed new Time-Domain (TD) synchronization using frequency integration and TD Spread Spectrum (SS) codes has been shown to be robust to frequency offset, that has its dual Frequency-Domain (FD) synchronization using time integration and FD SS codes which is robust to timing offset. Separable Property (SP) is defined for time-frequency synchronization under the condition containing time and frequency deviations to be performed separately and cooperatively. The SP compels us to design phase correction on SS codes and transmitted data.

Non-coherent signal with unknown delay and Doppler is recovered by Gabor division/spread spectrum system. Separable property (SP) condition for time and frequency synchronization leads us to determine delay and Doppler precisely. This paper gives an enlargement of acceptable delay and Doppler region by using multiple codes and their associated receivers simultaneously without increasing computation time. As its application, two-target simultaneous determination is discussed.

Frequency division spread spectrum system (FD/S3) has been recently proposed, which uses frequency domain spreading codes and can allow frequency offsets between users. Motivated by the conventional time-domain code acquisition, we propose a frequency (F)-domain code acquisition method using time (T)-domain integrator, which permits frequency offset, which leads to a new T-domain code acquisition using F-domain integrator. Recently proposed Gabor division (GD)/S3system permits us to use both F- and T-domain code acquisitions separately and cooperatively*.

We propose a Gabor division (GD)-CDMA system which permits time and frequency offsets. Negatively correlated time- and frequency-domain spreading codes have shown to reduce the variances of mutual- and self-interferences. In this paper, we show that such negatively correlated spreading codes have another important property that they flatten the time-frequency energy distributions of signals in GD-CDMA system.

It is believed that the dimension of the signal space with interval T and bandwidth W is 2WT, while we cannot make the out-of-band and out-of-time energies of any waveform zero. We propose a Gaussian pulse shaping for multi-carrier CDMA systems to utilize the time and frequency resources effectively. Gaussian pulses have ICI and ISI; they are not orthogonal. Markovity of spreading codes save the drawback of ICI and ISI. Overlapped Gaussian pulses increase the spectral efficiency.

Slepianpsilas prolate spheroidal wave function (PSWF) is optimum in energy concentration within given frequency bandwidth and time-width. However it is not employed in communications mainly because its inter-symbol interference is unfavorable. We show that introducing Markovian spreading codes makes PSWF be a strong candidate for the chip waveform in CDMA systems. For design tractability, Gaussian waveform is recommended.

Pulse shaping filters are commonly implemented by FIR filters. Motivated by Slepian's philosophy of discrete prolate spheroidal sequences (DPSS), we investigate Welch's lower bound on aperiodic auto- and cross-correlations for oversampled sequences. An oversampled sequence set having minimum cross-correlations in chip-asynchronous CDMA system is provided under a given bandwidth condition.

Performance of chip-asynchronous DS/CDMA system depends on chip waveform as well as spread spectrum (SS) codes. In case of rectangular chip waveform, SS codes generated by a Markov chain were shown to improve bit error rate (BER) performance. However, in commercial CDMA systems, a band-limited root raised cosine (RRC) pulse is used, where the superiority of Markov codes is reduced. RRC pulse fulfills inter-chip interference (ICI)-free condition. In CDMA systems, multiple-access interference (MAI) is of crucial importance. Gaussian pulse used in conjunction with Markovian codes reduces MAI although it does not has the ICI-free property. Computer simulations show that Gaussian pulse with same excess bandwidth energy as the RRC pulse significantly reduces BER.

It is known that spreading codes generated by a Markov chain improve bit error rate performance of direct sequence/code division multiple access (DS/CDMA) systems if the chip pulse is rectangular. Real analysis tells us that a pair of the rectangular and sine functions is one of Fourier transform and its inverse Fourier transform and vice versa. On the other hand, Gaussian pulses have the self-duality property: they have the same expression in both time and frequency domains. Gaussian chip pulses sacrifice inter-symbol interference. However, the use of Markovian codes together with a Gaussian pulse increases the system performance approximately 30% in terms of the number of users

Multiple-access interference (MAI) depends on chip pulse shapes in chip-asynchronous direct sequence/code division multiple access (DS/CDMA) systems. The mean squared MAI averaged over relative time delays is expressed in a quadratic form, where a coefficient matrix is derived from the pulse shapes, while a variable vector consists of aperiodic autocorrelation functions of the signature sequences. This quadratic form gives a lower bound of the mean squared MAI, which is equivalent to the Welch bound if the pulse shape is a delta function. For any continuous pulse shapes, however, the mean squared MAI is shown to be reduced beyond the Welch bound. In case of rectangular pulse, the mean squared MAI is reduced by 13.4%, whereas the reduction ratio is 5.2% for band-limited pulses with excess bandwidth 0.5

Constructing a system capable of functioning without any human support over an extended period is the aim of many engineers. However it is generally considered to be difficult to make decentralized self-organizing autonomous system fault-tolerant. In this paper, we propose to apply the theory of highly structured self-diagnosable systems to this problem. As an example, we apply the theory and recursive procedures method of fault-tolerant system construction to a decentralized self-organizing autonomous robotic system that forms a circle. The result of simulation shows the usefulness of the proposed method. The highly structured self-diagnosable system has an O(|E|)fault-identification algorithm that can diagnose each of the units in the system independently, locally and in any order, where E and |E| mean the set of the directed edges and its cardinality, respectively.

A sequence of binary random variables has found significant applications in modem digital communication systems. For such sequences, several kinds of linear feedback shift register sequences have been proposed. It is, however, well known in probability theory that the Bernoulli shift is a fundamental theoretic model of a sequence of independent identically distributed (i.i.d.) binary random variables. In this paper after reviewing fundamental subjects of chaotic dynamics, in particular a close relationship between information sources and Markov chains, we give the generation method of sequences of i.i.d. binary random variables using chaotic dynamics. Such a generation method is given as a sufficient condition composed of simple symmetric properties for some class of ergodic maps. Furthermore, we give the applications of such sequences: (1) to running-key sequences for stream cipher systems and (2) to a color image communication system through code-division multiple access channels and its extended version, a digital watermarking system. In addition, the performance of spread spectrum codes generated by a Markov chain is theoretically evaluated in asynchronous direct-sequence/code-division multiple access systems.

We have recently shown that a class of ergodic maps with the equidistributivity property (or briefly EDP) can easily produce a sequence of independent and identically distributed (i.i.d.) binary random variables. In this note, it is shown that the Jacobian elliptic Chebyshev rational maps defined here have the EDP and the semi-group property like the Chebyshev polynomial maps. Simple methods are also discussed for generating sequences of i.i.d. random variables based on the Jacobian elliptic Chebyshev rational maps.

Sequences of random numbers generated by a Markov chain have been recently discussed as one of candidates of spreading sequences. We theoretically evaluate distributions of even and odd crosscorrelation values of sequences of binary random variables generated by Markov information sources.

Statistical properties of binary sequences generated by a class of ergodic maps with some symmetric properties are discussed on the basis of an ensemble-average technique. We give a simple sufficient condition for such a class of maps to produce a fair Bernoulli sequence, that is, a sequence of independent and identically distributed (i.i.d.) binary random variables. This condition is expressed in terms of binary function, which is a generalized version of the Rademacher function for the dyadic map.