Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications - the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.

Nonlinear communication channels with capacity above the linear Shannon limit

We prove that, under certain conditions, the capacity of an optical communication channel with in-line, nonlinear filtering (regeneration) elements can be higher than the Shannon capacity for the corresponding linear Gaussian white noise channel. © 2012 Optical Society of America.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Wireless power and data transfer via a common inductive link using frequency division multiplexing

For wireless power transfer (WPT) systems, communication between the primary side and the pickup side is a challenge because of the large air gap and magnetic interferences. A novel method, which integrates bidirectional data communication into a high-power WPT system, is proposed in this paper. The power and data transfer share the same inductive link between coreless coils. Power/data frequency division multiplexing technique is applied, and the power and data are transmitted by employing different frequency carriers and controlled independently. The circuit model of the multiband system is provided to analyze the transmission gain of the communication channel, as well as the power delivery performance. The crosstalk interference between two carriers is discussed. In addition, the signal-to-noise ratios of the channels are also estimated, which gives a guideline for the design of mod/demod circuits. Finally, a 500-W WPT prototype has been built to demonstrate the effectiveness of the proposed WPT system.

Outage-optimal relay strategy under outdated channel state information in decode-and-forward cooperative communication systems

In this study, the authors investigate the outage-optimal relay strategy under outdated channel state information (CSI) in a decode-and-forward cooperative communication system. They first confirm mathematically that minimising the outage probability under outdated CSI is equivalent to minimising the conditional outage probability on the outdated CSI of all the decodable relays' links. They then propose a multiple-relay strategy with optimised transmitting power allocation (MRS-OTPA) that minimises the conditional outage probability. It is shown that this MRS is a generalised relay approach to achieve the outage optimality under outdated CSI. To reduce the complexity, they also propose a MRS with equal transmitting power allocation (MRS-ETPA) that achieves near-optimal outage performance. It is proved that full spatial diversity, which has been achieved under ideal CSI, can still be achieved under outdated CSI through MRS-OTPA and MRS-ETPA. Finally, the outage performance and diversity order of MRS-OTPA and MRS-ETPA are evaluated by simulation.

Finite-size effects and error-free communication in Gaussian channels

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite-size effects are estimated for comparing the results with the bounds set by Shannon. The critical noise level achieved for certain code rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low.

1220km propagation of 40Gbit/s single channel RZ data over dispersion managed standard (non-dispersion shifted) fibre

Error free propagation of a single polarisation optical time division multiplexed 40 Gbit/s dispersion managed pulsed data stream over dispersion (non-shifted) fibre. This distance is twice the previous record at this data rate.

Design and fabrication of fibre Bragg gratings with V-shaped dispersion profile for multi-channel signal processing

We have designed and fabricated a new type of fibre Bragg grating (FBG) with a V-shaped dispersion profile for multi-channel dispersion compensation in communication links.

Typical behavior of relays in communication channels

The typical behavior of the relay-without-delay channel under low-density parity-check coding and its multiple-unit generalization, termed the relay array, is studied using methods of statistical mechanics. A demodulate-and- forward strategy is analytically solved using the replica symmetric ansatz which is exact in the system studied at Nishimori's temperature. In particular, the typical level of improvement in communication performance by relaying messages is shown in the case of a small and a large number of relay units. © 2007 The American Physical Society.

Advanced handover procedure for cellular communication systems

Third Generation cellular communication systems are expected to support mixed cell architecture in which picocells, microcells and macrocells are used to achieve full coverage and increase the spectral capacity. Supporting higher numbers of mobile terminals and the use of smaller cells will result in an increase in the number of handovers, and consequently an increase in the time delays required to perform these handovers. Higher time delays will generate call interruptions and forced terminations, particularly for time sensitive applications like real-time multimedia and data services. Currently in the Global System for Mobile communications (GSM), the handover procedure is initiated and performed by the fixed part of the Public Land Mobile Network (PLMN). The mobile terminal is only capable of detecting candidate base stations suitable for the handover; it is the role of the network to interrogate a candidate base station for a free channel. Handover signalling is exchanged via the fixed network and the time delay required to perform the handover is greatly affected by the levels of teletraffic handled by the network. In this thesis, a new handover strategy is developed to reduce the total time delay for handovers in a microcellular system. The handover signalling is diverted from the fixed network to the air interface to prevent extra delays due to teletraffic congestion, and to allow the mobile terminal to exchange signalling directly with the candidate base station. The new strategy utilises Packet Reservation Multiple Access (PRMA) technique as a mechanism to transfer the control of the handover procedure from the fixed network to the mobile terminal. Simulation results are presented to show a dramatic reduction in the handover delay as compared to those obtained using fixed channel allocation and dynamic channel allocation schemes.

Digital communication networks incorporating mobile data terminals

The use of digital communication systems is increasing very rapidly. This is due to lower system implementation cost compared to analogue transmission and at the same time, the ease with which several types of data sources (data, digitised speech and video, etc.) can be mixed. The emergence of packet broadcast techniques as an efficient type of multiplexing, especially with the use of contention random multiple access protocols, has led to a wide-spread application of these distributed access protocols in local area networks (LANs) and a further extension of them to radio and mobile radio communication applications. In this research, a proposal for a modified version of the distributed access contention protocol which uses the packet broadcast switching technique has been achieved. The carrier sense multiple access with collision avoidance (CSMA/CA) is found to be the most appropriate protocol which has the ability to satisfy equally the operational requirements for local area networks as well as for radio and mobile radio applications. The suggested version of the protocol is designed in a way in which all desirable features of its precedents is maintained. However, all the shortcomings are eliminated and additional features have been added to strengthen its ability to work with radio and mobile radio channels. Operational performance evaluation of the protocol has been carried out for the two types of non-persistent and slotted non-persistent, through mathematical and simulation modelling of the protocol. The results obtained from the two modelling procedures validate the accuracy of both methods, which compares favourably with its precedent protocol CSMA/CD (with collision detection). A further extension of the protocol operation has been suggested to operate with multichannel systems. Two multichannel systems based on the CSMA/CA protocol for medium access are therefore proposed. These are; the dynamic multichannel system, which is based on two types of channel selection, the random choice (RC) and the idle choice (IC), and the sequential multichannel system. The latter has been proposed in order to supress the effect of the hidden terminal, which always represents a major problem with the usage of the contention random multiple access protocols with radio and mobile radio channels. Verification of their operation performance evaluation has been carried out using mathematical modelling for the dynamic system. However, simulation modelling has been chosen for the sequential system. Both systems are found to improve system operation and fault tolerance when compared to single channel operation.

Simulation of optical fibre communication systems influenced by stimulated brillouin scattering

Boyd's SBS model which includes distributed thermal acoustic noise (DTAN) has been enhanced to enable the Stokes-spontaneous density depletion noise (SSDDN) component of the transmitted optical field to be simulated, probably for the first time, as well as the full transmitted field. SSDDN would not be generated from previous SBS models in which a Stokes seed replaces DTAN. SSDDN becomes the dominant form of transmitted SBS noise as model fibre length (MFL) is increased but its optical power spectrum remains independent of MFL. Simulations of the full transmitted field and SSDDN for different MFLs allow prediction of the optical power spectrum, or system performance parameters which depend on this, for typical communication link lengths which are too long for direct simulation. The SBS model has also been innovatively improved by allowing the Brillouin Shift Frequency (BS) to vary over the model fibre length, for the nonuniform fibre model (NFM) mode, or to remain constant, for the uniform fibre model (UFM) mode. The assumption of a Gaussian probability density function (pdf) for the BSF in the NFM has been confirmed by means of an analysis of reported Brillouin amplified power spectral measurements for the simple case of a nominally step-index single-mode pure silica core fibre. The BSF pdf could be modified to match the Brillouin gain spectra of other fibre types if required. For both models, simulated backscattered and output powers as functions of input power agree well with those from a reported experiment for fitting Brillouin gain coefficients close to theoretical. The NFM and UFM Brillouin gain spectra are then very similar from half to full maximum but diverge at lower values. Consequently, NFM and UFM transmitted SBS noise powers inferred for long MFLs differ by 1-2 dB over the input power range of 0.15 dBm. This difference could be significant for AM-VSB CATV links at some channel frequencies. The modelled characteristic of Carrier-to-Noise Ratio (CNR) as a function of input power for a single intensity modulated subcarrier is in good agreement with the characteristic reported for an experiment when either the UFM or NFM is used. The difference between the two modelled characteristics would have been more noticeable for a higher fibre length or a lower subcarrier frequency.

Cryptographic techniques for personal communication systems security

The advent of personal communication systems within the last decade has depended upon the utilization of advanced digital schemes for source and channel coding and for modulation. The inherent digital nature of the communications processing has allowed the convenient incorporation of cryptographic techniques to implement security in these communications systems. There are various security requirements, of both the service provider and the mobile subscriber, which may be provided for in a personal communications system. Such security provisions include the privacy of user data, the authentication of communicating parties, the provision for data integrity, and the provision for both location confidentiality and party anonymity. This thesis is concerned with an investigation of the private-key and public-key cryptographic techniques pertinent to the security requirements of personal communication systems and an analysis of the security provisions of Second-Generation personal communication systems is presented. Particular attention has been paid to the properties of the cryptographic protocols which have been employed in current Second-Generation systems. It has been found that certain security-related protocols implemented in the Second-Generation systems have specific weaknesses. A theoretical evaluation of these protocols has been performed using formal analysis techniques and certain assumptions made during the development of the systems are shown to contribute to the security weaknesses. Various attack scenarios which exploit these protocol weaknesses are presented. The Fiat-Sharmir zero-knowledge cryptosystem is presented as an example of how asymmetric algorithm cryptography may be employed as part of an improved security solution. Various modifications to this cryptosystem have been evaluated and their critical parameters are shown to be capable of being optimized to suit a particular applications. The implementation of such a system using current smart card technology has been evaluated.

Numerical and statistical analysis of long-haul undersea optical communication systems

Firstly, we numerically model a practical 20 Gb/s undersea configuration employing the Return-to-Zero Differential Phase Shift Keying data format. The modelling is completed using the Split-Step Fourier Method to solve the Generalised Nonlinear Schrdinger Equation. We optimise the dispersion map and per-channel launch power of these channels and investigate how the choice of pre/post compensation can influence the performance. After obtaining these optimal configurations, we investigate the Bit Error Rate estimation of these systems and we see that estimation based on Gaussian electrical current systems is appropriate for systems of this type, indicating quasi-linear behaviour. The introduction of narrower pulses due to the deployment of quasi-linear transmission decreases the tolerance to chromatic dispersion and intra-channel nonlinearity. We used tools from Mathematical Statistics to study the behaviour of these channels in order to develop new methods to estimate Bit Error Rate. In the final section, we consider the estimation of Eye Closure Penalty, a popular measure of signal distortion. Using a numerical example and assuming the symmetry of eye closure, we see that we can simply estimate Eye Closure Penalty using Gaussian statistics. We also see that the statistics of the logical ones dominates the statistics of the logical ones dominates the statistics of signal distortion in the case of Return-to-Zero On-Off Keying configurations.

Models and performances of wireless MIMO and cooperative communication systems

Multiple-antenna systems offer significant performance enhancement and will be applied to the next generation broadband wireless communications. This thesis presents the investigations of multiple-antenna systems – multiple-input multiple-output (MIMO) and cooperative communication (CC) – and their performances in more realistic propagation environments than those reported previously. For MIMO systems, the investigations are conducted via theoretical modelling and simulations in a double-scattering environment. The results show that the variations of system performances depend on how scatterer density varies in flat fading channels, and that in frequency-selective fading channels system performances are affected by the length of the coding block as well as scatterer density. In realistic propagation environments, the fading correlation also has an impact on CC systems where the antennas can be further apart than those in MIMO systems. A general stochastic model is applied to studying the effects of fading correlation on the performances of CC systems. This model reflects the asymmetry fact of the wireless channels in a CC system. The results demonstrate the varied effects of fading correlation under different protocols and channel conditions. Performances of CC systems are further studied at the packet level, using both simulations and an experimental testbed. The results obtained have verified various performance trade-offs of the cooperative relaying network (CRN) investigated in different propagation environments. The results suggest that a proper selection of the relaying algorithms and other techniques can meet the requirements of quality of service for different applications.