Outage Capacity for the Optical MIMO Channel

MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. In this paper we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant cross talk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in the transmission may be parameterized by a number of unutilized channels in the fiber. We analyze the system in a dual fashion. First, we evaluate a closed-form expression for the outage probability, which is handy for small matrices. We also apply the asymptotic approach, in particular the Coulomb gas method from statistical mechanics, to obtain closed-form results for the ergodic mutual information, its variance as well as the outage probability for Gaussian input in the limit of large number of cores/modes. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.Comment: Revised version includes more details, proofs and a closed-form expression for the outage probabilit

Applications of Random Matrix Theory in Wireless and Fiber Optical MIMO Channels

Σκοπός αυτής της εργασίας είναι να παρουσιάσει μετρικές όπως η χωρητικότητα διακοπής λειτουργίας και το όριο Gallager για τον χαρακτηρισμό της απόδοσης των ασύρματων και ενσύρματων οπτικών ενσύρματων ΜΙΜΟ καναλιών. Λόγω της αυξημένης πολυπλοκότητας και της υπολογιστικής επιβάρυνσης, αυτές οι μετρικές μπορούν να προσεγγιστούν μόνο μέσω μεθόδων που προκύπτουν από τη θεωρία τυχαίων πινάκων, τη θεωρία μεγάλων αποκλίσεων και τη θεωρία των αντιγράφων. Σε αυτή την εργασία παρέχουμε αναλυτικές εξισώσεις για την προσέγγιση αυτών των μετρικών και αποδεικνύουμε ότι είναι πολύ ακριβείς για τα πραγματικά συστήματα.Aim of this work is to present metrics like Outage Capacity and Gallager Bound for the characterization of the performance of the link of wireless and fiber optica ΜΙΜΟ channels. Due to the increased complexity and computational burden, these metrics can only be approximated through methods stemming from Random Matrix Theory, Large Deviations and Replica Theory. In this work we provide analytic equations for the approximation of these metrics and we show that they are very accurate for real systems

Optical MIMO: Results and analysis

International audience—Spatial Division Multiplexing (SDM) is being in-creasingly applied to optical fiber systems [1]. Thus, SDM is gradually becoming a fundamental part of modern telecommu-nications aiming to provide higher transmission rates that are both error-free and inexpensive. So far, engineers considered packing and operating the many different laser as the biggest problem, but as it seems, the crosstalking phenomenon between the various in-fiber propagating modes creates a great barrier, which needs sophisticated methods to overcome, such as MIMO techniques, which are well known in the wireless field. In this paper, we analyze real data from multimode optical fibers and find that crosstalk seems to be significant. If this is the case, the reception can be problematic without MIMO techniques

Εφαρμογές της θεωρίας μεγάλων τυχαίων πινάκων σε ασύρματα και οπτικά ενσύρματα κανάλια

The main idea of this work stems from the need to provide cost-effective and efficientways of evaluating the performance of modern communication links both fiber opticaland wireless. Therefore, we had to work on different channel models which describe thephysics governing the various connections, by using the assumption of large systemsand hence utilizing the approximations provided by the random matrix theory. It wasshown, however that the analytic expressions which were obtained, are applicable aswell to small-sized systems, thus making our proposed methods especially useful tomodern communication systems.More precisely, for the optical MIMO channel we proved, first of all, the existence ofcrosstalking (Chapter 4) just like in an ordinary wireless system with multiple transmittersand receivers, and further we proposed a method of improving the demodulationprocedure, based on compressed sensing techniques. Therefore, having established thebasic notion that optic fiber links can follow the trend of the wireless ones, namelyincorporate Spatial Division Multiplexing (SDM), we calculated the outage capacityof such a system (Chapter 5) under the assumptions of increased crosstalking andzero loss inside the fiber. Further, we investigated the Gallager bound for the codedfiber optic MIMO link (Chapter 6.2) with fixed power constraints as well as averagepower constraint among all transmitters, and the Sphere-Packing bound. Since, thecalculation of the information capacity of a communication channel, can impose hugecomputational burden, we are obliged to find good enough approximations, which provideus with lower and upper bounds for the corresponding channel capacity. Onceagain, the proposed approximation method follows well the theory. Finally, as concernas the optic fiber channel we investigated a more realistic channel model based on theidea of a chaotic cavity (Chapter 7). Specifically, we modeled the optic fiber MIMOchannel as a chaotic cavity where energy is injected and taken out from leads in theform of particles, and the crosstalking happens in a random way with energy exchangebetween the particles. That way we can address phenomena occurring inside the fibersuch as increased loss, non-linearities and some level of crosstalking.Unlike in the optical domain, the use of random matrix theory methods in thewireless one is a well established practice by numerous of researchers. Hence, in thecontext of this work, we calculated an approximated Gallager bound for the wirelesschannel (Chapter 6.1) in a closed form by using random matrix theory for fixed powerconstraints as well as average power constraint among all transmitters, and the Sphere-Packing bound. That way, we provided a metric of the performance of such a systemwhich although requires minimal computational burden, however it follows well theexpected bounds.Surely, the more we dive into the exciting world of telecommunications with thehelp of random matrix theory, the more questions rise. For example, a more realisticpractical implementation of an optical MIMO system along with a compressed sensingequalization technique is a question for future work, in order to grasp better themechanics of the crosstalking and thus the mechanics also of the optical MIMO. Furthermore,the methodology for the approximation of the Gallager bound can be appliedto include the uplink MU-MIMO and the Amplify-and-Forward channels. Itshould be noted that more general Gaussian channels, which do not have a known jointeigenvalue distribution can be analyzed in similar ways using the replica method.Finally, the newly introduced MIMO fiber optic channel model, although it gives usthe means to analyze the statistics of throughput in the corresponding channel in thepresence of arbitrary level of crosstalk and mode dependent loss, it is however, alsoamenable to extensions, such as dispersion and nonlinear effects.Η βασική ιδέα αυτής της εργασίας πηγάζει από την ανάγκη εύρεσης αποδοτικών και οικονομικών μεθόδων υπολογισμού της απόδοσης των σύγχρονων επικοινωνιακών συνδέσεων, τόσο μέσω οπτικών ινών όσο και ασύρματων. Επομένως, έπρεπε να εργαστούμε σε διαφορετικά μοντέλα καναλιών που περιγράφουν τη φυσική που διέπει τις διάφορες συνδέσεις, χρησιμοποιώντας την θεωρία μεγάλων συστημάτων και επομένως αξιοποιώντας τις προσεγγίσεις που παρέχονται από τη θεωρία τυχαίων πινάκων. Παρόλα αυτά, αποδεικνύεται πως οι αναλυτικές εκφράσεις που αποκτήθηκαν είναι εφαρμόσιμες ακόμα και σε μικρού μεγέθους συστήματα, καθιστώντας έτσι τις προτεινόμενες μεθόδους ιδιαίτερα χρήσιμες στα σύγχρονα συστήματα επικοινωνίας.Πιο συγκεκριμένα, για το οπτικό MIMO κανάλι αποδεικνύουμε πρώτα από όλα την ύπαρξη διομιλίας (Κεφάλαιο 4) ακριβώς όπως σε ένα συνηθισμένο ασύρματο σύστημα με πολλαπλούς πομπούς και δέκτες, και προτείνουμε περαιτέρω μια μέθοδο βελτίωσης της διαδικασίας αποδιαμόρφωσης, βασισμένη σε τεχνικές συμπιεσμένης ανίχνευσης. Επομένως, έχοντας αναπτύξει την βασική ιδέα ότι οι συνδέσεις οπτικών ινών μπορούν να ακολουθήσουν την τάση των ασύρματων αντίστοιχων δικτύων, δηλαδή να ενσωματώσουν πολυπλεξία χώρου, υπολογίζουμε τη χωρητικότητα διακοπής ενός τέτοιου συστήματος (Κεφάλαιο 5) υπό την προϋπόθεση αυξημένης διομιλίας και μηδενικών απωλειών μέσα στην ίνα. Περαιτέρω, ερευνήσαμε το όριο Gallager για το κωδικοποιημένο ΜΙΜΟ κανάλι οπτικών ινών (κεφάλαιο 6.2). Δεδομένου ότι, ο υπολογισμός της χωρητικότητας πληροφορίας ενός καναλιού επικοινωνίας μπορεί να επιβάλει τεράστια υπολογιστική επιβάρυνση, είμαστε υποχρεωμένοι να βρούμε επαρκείς προσεγγίσεις ως προς τα κατώτατα και ανώτερα όρια για την αντίστοιχη χωρητικότητα του καναλιού. Τέλος, όσον αφορά το κανάλι οπτικών ινών, ερευνήσαμε ένα πιο ρεαλιστικό μοντέλο καναλιού βασισμένο στην ιδέα της χαοτικής κοιλότητας (Κεφάλαιο 7). Συγκεκριμένα, μοντελοποιήσαμε το κανάλι MIMO οπτικών ινών ως χαοτική κοιλότητα, όπου η ενέργεια εγχέεται και εξάγεται από την ίνα με τη μορφή σωματιδίων και η διομιλία συμβαίνει τυχαία με την ανταλλαγή ενέργειας μεταξύ των σωματιδίων. Με αυτόν τον τρόπο μπορούμε να αντιμετωπίσουμε φαινόμενα που εμφανίζονται μέσα στην ίνα όπως είναι η αυξημένες απώλειες, η μη γραμμικότητα και ορισμένο επίπεδο διομιλίας.Αντίθετα με τον πεδίο οπτικών επικοινωνιών, η χρήση μεθόδων θεωρίας τυχαίων πινάκων στο αντίστοιχο πεδίο ασύρματων επικοινωνιών, είναι μια καλά εδραιωμένη πρακτική από πολλούς ερευνητές. Ως εκ τούτου, στο πλαίσιο αυτής της εργασίας, υπολογίσαμε ένα προσεγγιστικό όριο Gallager για το ασύρματο ΜΙΜΟ κανάλι (κεφάλαιο 6.1) σε κλειστή μορφή . Έτσι, παρέχουμε μια μετρική της απόδοσης ενός τέτοιου συστήματος η οποία αν και απαιτεί ελάχιστη υπολογιστική επιβάρυνση, ωστόσο ακολουθεί καλά το αναμενόμενα όρια

Outage Capacity for the Optical MIMO Channel

Revised version includes more details, proofs and a closed-form expression for the outage probabilityInternational audienceMIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. In this paper we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant cross talk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in the transmission may be parameterized by a number of unutilized channels in the fiber. We analyze the system in a dual fashion. First, we evaluate a closed-form expression for the outage probability, which is handy for small matrices. We also apply the asymptotic approach, in particular the Coulomb gas method from statistical mechanics, to obtain closed-form results for the ergodic mutual information, its variance as well as the outage probability for Gaussian input in the limit of large number of cores/modes. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels

Natural time analysis of critical phenomena: The case of pre-fracture electromagnetic emissions

Criticality of complex systems reveals itself in various ways. One way to monitor a system at critical state is to analyze its observable manifestations using the recently introduced method of natural time. Pre-fracture electromagnetic (EM) emissions, in agreement to laboratory experiments, have been consistently detected in the MHz band prior to significant earthquakes. It has been proposed that these emissions stem from the fracture of the heterogeneous materials surrounding the strong entities (asperities) distributed along the fault, preventing the relative slipping. It has also been proposed that the fracture of heterogeneous material could be described in analogy to the critical phase transitions in statistical physics. In this work, the natural time analysis is for the first time applied to the pre-fracture MHz EM signals revealing their critical nature. Seismicity and pre-fracture EM emissions should be two sides of the same coin concerning the earthquake generation process. Therefore, we also examine the corresponding foreshock seismic activity, as another manifestation of the same complex system at critical state. We conclude that the foreshock seismicity data present criticality features as well. © 2013 AIP Publishing LLC

Gallager Bound for MIMO Channels: Large-N Asymptotics

The use of multiple antenna arrays in transmission and reception has become an integral part of modern wireless communications. To quantify the performance of such systems, the evaluation of bounds on the error probability of realistic finite length codewords is important. In this paper, we analyze the standard Gallager error bound for both constraints of maximum average power and maximum instantaneous power. Applying techniques from random matrix theory, we obtain analytic expressions of the error exponent when the length of the codeword increases to infinity at a fixed ratio with the antenna array dimensions. Analyzing its behavior at rates close to the ergodic rate, we find that the Gallager error bound becomes asymptotically close to an upper error bound obtained recently by Hoydis et al. 2015. We also obtain an expression for the Gallager exponent in the case when the codelength spans several Rayleigh fading blocks, hence taking into account the situation when the channel varies during each transmission. © 2017 IEEE

Outage capacity for the optical MIMO channel

Multiple-input and multiple-output processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes or multiple cores or both in the fiber. In this paper, we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant crosstalk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in the transmission may be parameterized by a number of unutilized channels in the fiber. We analyze the system in a dual fashion. First, we evaluate a closed-form expression for the outage probability, which is handy for small matrices. We also apply the asymptotic approach, in particular the Coulomb gas method from statistical mechanics, to obtain closed-form results for the ergodic mutual information, its variance as well as the outage probability for Gaussian input in the limit of large number of cores/modes. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels. © 2014 IEEE

Gallager Bound for MIMO Channels: Large- NN Asymptotics

International audienceThe use of multiple antenna arrays in transmission and reception has become an integral part of modern wireless communications. To quantify the performance of such systems, the evaluation of bounds on the error probability of realistic finite length codewords is important. In this paper, we analyze the standard Gallager error bound for both constraints of maximum average power and maximum instantaneous power. Applying techniques from random matrix theory, we obtain analytic expressions of the error exponent when the length of the codeword increases to infinity at a fixed ratio with the antenna array dimensions. Analyzing its behavior at rates close to the ergodic rate, we find that the Gallager error bound becomes asymptotically close to an upper error bound obtained recently by Hoydis et al. 2015. We also obtain an expression for the Gallager exponent in the case when the codelength spans several Rayleigh fading blocks, hence taking into account the situation when the channel varies during each transmission