Fluctuations of an improved population eigenvalue estimator in sample covariance matrix models

This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of available observations is known and comparable in magnitude to the observation dimension. An exact expression as well as an empirical, asymptotically accurate, approximation of the limiting variance is derived. Simulations are performed that corroborate the theoretical claims. A specific application to wireless sensor networks is developed.Comment: 30 p

Signal Processing in Large Systems: a New Paradigm

For a long time, detection and parameter estimation methods for signal processing have relied on asymptotic statistics as the number $n$ of observations of a population grows large comparatively to the population size $N$, i.e. $n/N\to \infty$. Modern technological and societal advances now demand the study of sometimes extremely large populations and simultaneously require fast signal processing due to accelerated system dynamics. This results in not-so-large practical ratios $n/N$, sometimes even smaller than one. A disruptive change in classical signal processing methods has therefore been initiated in the past ten years, mostly spurred by the field of large dimensional random matrix theory. The early works in random matrix theory for signal processing applications are however scarce and highly technical. This tutorial provides an accessible methodological introduction to the modern tools of random matrix theory and to the signal processing methods derived from them, with an emphasis on simple illustrative examples

Fluctuations of an improved population eigenvalue estimator in sample covariance matrix models

30 pp.International audienceThis article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of available observations is known and comparable in magnitude to the observation dimension. An exact expression as well as an empirical, asymptotically accurate, approximation of the limiting variance is derived. Simulations are performed that corroborate the theoretical claims. A specific application to wireless sensor networks is developed

Spectrum sensing and occupancy prediction for cognitive machine-to-machine wireless networks

A thesis submitted to the University of Bedfordshire, in partial fulfil ment of the requirements for the degree of Doctor of Philosophy (PhD)The rapid growth of the Internet of Things (IoT) introduces an additional challenge to the existing spectrum under-utilisation problem as large scale deployments of thousands devices are expected to require wireless connectivity. Dynamic Spectrum Access (DSA) has been proposed as a means of improving the spectrum utilisation of wireless systems. Based on the Cognitive Radio (CR) paradigm, DSA enables unlicensed spectrum users to sense their spectral environment and adapt their operational parameters to opportunistically access any temporally unoccupied bands without causing interference to the primary spectrum users. In the same context, CR inspired Machine-to-Machine (M2M) communications have recently been proposed as a potential solution to the spectrum utilisation problem, which has been driven by the ever increasing number of interconnected devices. M2M communications introduce new challenges for CR in terms of operational environments and design requirements. With spectrum sensing being the key function for CR, this thesis investigates the performance of spectrum sensing and proposes novel sensing approaches and models to address the sensing problem for cognitive M2M deployments. In this thesis, the behaviour of Energy Detection (ED) spectrum sensing for cognitive M2M nodes is modelled using the two-wave with dffi use power fading model. This channel model can describe a variety of realistic fading conditions including worse than Rayleigh scenarios that are expected to occur within the operational environments of cognitive M2M communication systems. The results suggest that ED based spectrum sensing fails to meet the sensing requirements over worse than Rayleigh conditions and consequently requires the signal-to-noise ratio (SNR) to be increased by up to 137%. However, by employing appropriate diversity and node cooperation techniques, the sensing performance can be improved by up to 11.5dB in terms of the required SNR. These results are particularly useful in analysing the eff ects of severe fading in cognitive M2M systems and thus they can be used to design effi cient CR transceivers and to quantify the trade-o s between detection performance and energy e fficiency. A novel predictive spectrum sensing scheme that exploits historical data of past sensing events to predict channel occupancy is proposed and analysed. This approach allows CR terminals to sense only the channels that are predicted to be unoccupied rather than the whole band of interest. Based on this approach, a spectrum occupancy predictor is developed and experimentally validated. The proposed scheme achieves a prediction accuracy of up to 93% which in turn can lead to up to 84% reduction of the spectrum sensing cost. Furthermore, a novel probabilistic model for describing the channel availability in both the vertical and horizontal polarisations is developed. The proposed model is validated based on a measurement campaign for operational scenarios where CR terminals may change their polarisation during their operation. A Gaussian approximation is used to model the empirical channel availability data with more than 95% confi dence bounds. The proposed model can be used as a means of improving spectrum sensing performance by using statistical knowledge on the primary users occupancy pattern

Opportunistic communications in large uncoordinated networks

(English) The increase of wireless devices offering high data rate services limits the coexistence of wireless systems sharing the same resources in a given geographical area because of inter-system interference. Therefore, interference management plays a key role in permitting the coexistence of several heterogeneous communication services. However, classical interference management strategies require lateral information giving rise to the need for inter-system coordination and cooperation, which is not always practical. Opportunistic communications offer a potential solution to the problem of inter-system interference management. The basic principle of opportunistic communications is to efficiently and robustly exploit the resources available in a wireless network and adapt the transmitted signals to the state of the network to avoid inter-system interference. Therefore, opportunistic communications depend on inferring the available network resources that can be safely exploited without inducing interference in coexisting communication nodes. Once the available network resources are identified, the most prominent opportunistic communication techniques consist in designing scenario-adapted precoding/decoding strategies to exploit the so-called null space. Despite this, classical solutions in the literature suffer from two main drawbacks: the lack of robustness to detection errors and the need for intra-system cooperation. This thesis focuses on the design of a null space-based opportunistic communication scheme that addresses the drawbacks exhibited by existing methodologies under the assumption that opportunistic nodes do not cooperate. For this purpose, a generalized detection error model independent of the null-space identification mechanism is introduced that allows the design of solutions that exhibit minimal inter-system interference in the worst case. These solutions respond to a maximum signal-to-interference ratio (SIR) criterion, which is optimal under non-cooperative conditions. The proposed methodology allows the design of a family of orthonormal waveforms that perform a spreading of the modulated symbols within the detected null space, which is key to minimizing the induced interference density. The proposed solutions are invariant within the inferred null space, allowing the removal of the feedback link without giving up coherent waveform detection. In the absence of coordination, the waveform design relies solely on locally sensed network state information, inducing a mismatch between the null spaces identified by the transmitter and receiver that may worsen system performance. Although the proposed solution is robust to this mismatch, the design of enhanced receivers using active subspace detection schemes is also studied. When the total number of network resources increases arbitrarily, the proposed solutions tend to be linear combinations of complex exponentials, providing an interpretation in the frequency domain. This asymptotic behavior allows us to adapt the proposed solution to frequency-selective channels by means of a cyclic prefix and to study an efficient modulation similar to the time division multiplexing scheme but using circulant waveforms. Finally, the impact of the use of multiple antennas in opportunistic null space-based communications is studied. The performed analysis reveals that, in any case, the structure of the antenna clusters affects the opportunistic communication, since the proposed waveform mimics the behavior of a single-antenna transmitter. On the other hand, the number of sensors employed translates into an improvement in terms of SIR.(Català) El creixement incremental dels dispositius sense fils que requereixen serveis d'alta velocitat de dades limita la coexistència de sistemes sense fils que comparteixen els mateixos recursos en una àrea geogràfica donada a causa de la interferència entre sistemes. Conseqüentment, la gestió d'interferència juga un paper fonamental per a facilitar la coexistència de diversos serveis de comunicació heterogenis. No obstant això, les estratègies clàssiques de gestió d'interferència requereixen informació lateral originant la necessitat de coordinació i cooperació entre sistemes, que no sempre és pràctica. Les comunicacions oportunistes ofereixen una solució potencial al problema de la gestió de les interferències entre sistemes. El principi bàsic de les comunicacions oportunistes és explotar de manera eficient i robusta els recursos disponibles en una xarxa sense fils i adaptar els senyals transmesos a l'estat de la xarxa per evitar interferències entre sistemes. Per tant, les comunicacions oportunistes depenen de la inferència dels recursos de xarxa disponibles que poden ser explotats de manera segura sense induir interferència en els nodes de comunicació coexistents. Una vegada que s'han identificat els recursos de xarxa disponibles, les tècniques de comunicació oportunistes més prominents consisteixen en el disseny d'estratègies de precodificació/descodificació adaptades a l'escenari per explotar l'anomenat espai nul. Malgrat això, les solucions clàssiques en la literatura sofreixen dos inconvenients principals: la falta de robustesa als errors de detecció i la necessitat de cooperació intra-sistema. Aquesta tesi tracta el disseny d'un esquema de comunicació oportunista basat en l'espai nul que afronta els inconvenients exposats per les metodologies existents assumint que els nodes oportunistes no cooperen. Per a aquest propòsit, s'introdueix un model generalitzat d'error de detecció independent del mecanisme d'identificació de l'espai nul que permet el disseny de solucions que exhibeixen interferències mínimes entre sistemes en el cas pitjor. Aquestes solucions responen a un criteri de màxima relació de senyal a interferència (SIR), que és òptim en condicions de no cooperació. La metodologia proposada permet dissenyar una família de formes d'ona ortonormals que realitzen un spreading dels símbols modulats dins de l'espai nul detectat, que és clau per minimitzar la densitat d’interferència induïda. Les solucions proposades són invariants dins de l'espai nul inferit, permetent suprimir l'enllaç de retroalimentació i, tot i així, realitzar una detecció coherent de forma d'ona. Sota l’absència de coordinació, el disseny de la forma d'ona es basa únicament en la informació de l'estat de la xarxa detectada localment, induint un desajust entre els espais nuls identificats pel transmissor i receptor que pot empitjorar el rendiment del sistema. Tot i que la solució proposada és robusta a aquest desajust, també s'estudia el disseny de receptors millorats fent ús de tècniques de detecció de subespai actiu. Quan el nombre total de recursos de xarxa augmenta arbitràriament, les solucions proposades tendeixen a ser combinacions lineals d'exponencials complexes, proporcionant una interpretació en el domini freqüencial. Aquest comportament asimptòtic permet adaptar la solució proposada a entorns selectius en freqüència fent ús d'un prefix cíclic i estudiar una modulació eficient derivada de l'esquema de multiplexat per divisió de temps emprant formes d'ona circulant. Finalment, s’estudia l'impacte de l'ús de múltiples antenes en comunicacions oportunistes basades en l'espai nul. L'anàlisi realitzada permet concloure que, en cap cas, l'estructura de les agrupacions d'antenes tenen un impacte sobre la comunicació oportunista, ja que la forma d'ona proposada imita el comportament d'un transmissor mono-antena. D'altra banda, el nombre de sensors emprat es tradueix en una millora en termes de SIR.(Español) El incremento de los dispositivos inalámbricos que ofrecen servicios de alta velocidad de datos limita la coexistencia de sistemas inalámbricos que comparten los mismos recursos en un área geográfica dada a causa de la interferencia inter-sistema. Por tanto, la gestión de interferencia juega un papel fundamental para facilitar la coexistencia de varios servicios de comunicación heterogéneos. Sin embargo, las estrategias clásicas de gestión de interferencia requieren información lateral originando la necesidad de coordinación y cooperación entre sistemas, que no siempre es práctica. Las comunicaciones oportunistas ofrecen una solución potencial al problema de la gestión de las interferencias entre sistemas. El principio básico de las comunicaciones oportunistas es explotar de manera eficiente y robusta los recursos disponibles en una red inalámbricas y adaptar las señales transmitidas al estado de la red para evitar interferencias entre sistemas. Por lo tanto, las comunicaciones oportunistas dependen de la inferencia de los recursos de red disponibles que pueden ser explotados de manera segura sin inducir interferencia en los nodos de comunicación coexistentes. Una vez identificados los recursos disponibles, las técnicas de comunicación oportunistas más prominentes consisten en el diseño de estrategias de precodificación/descodificación adaptadas al escenario para explotar el llamado espacio nulo. A pesar de esto, las soluciones clásicas en la literatura sufren dos inconvenientes principales: la falta de robustez a los errores de detección y la necesidad de cooperación intra-sistema. Esta tesis propone diseñar un esquema de comunicación oportunista basado en el espacio nulo que afronta los inconvenientes expuestos por las metodologías existentes asumiendo que los nodos oportunistas no cooperan. Para este propósito, se introduce un modelo generalizado de error de detección independiente del mecanismo de identificación del espacio nulo que permite el diseño de soluciones que exhiben interferencias mínimas entre sistemas en el caso peor. Estas soluciones responden a un criterio de máxima relación de señal a interferencia (SIR), que es óptimo en condiciones de no cooperación. La metodología propuesta permite diseñar una familia de formas de onda ortonormales que realizan un spreading de los símbolos modulados dentro del espacio nulo detectado, que es clave para minimizar la densidad de interferencia inducida. Las soluciones propuestas son invariantes dentro del espacio nulo inferido, permitiendo suprimir el enlace de retroalimentación sin renunciar a la detección coherente de forma de onda. En ausencia de coordinación, el diseño de la forma de onda se basa únicamente en la información del estado de la red detectada localmente, induciendo un desajuste entre los espacios nulos identificados por el transmisor y receptor que puede empeorar el rendimiento del sistema. A pesar de que la solución propuesta es robusta a este desajuste, también se estudia el diseño de receptores mejorados usando técnicas de detección de subespacio activo. Cuando el número total de recursos de red aumenta arbitrariamente, las soluciones propuestas tienden a ser combinaciones lineales de exponenciales complejas, proporcionando una interpretación en el dominio frecuencial. Este comportamiento asintótico permite adaptar la solución propuesta a canales selectivos en frecuencia mediante un prefijo cíclico y estudiar una modulación eficiente derivada del esquema de multiplexado por división de tiempo empleando formas de onda circulante. Finalmente, se estudia el impacto del uso de múltiples antenas en comunicaciones oportunistas basadas en el espacio nulo. El análisis realizado revela que la estructura de las agrupaciones de antenas no afecta la comunicación oportunista, ya que la forma de onda propuesta imita el comportamiento de un transmisor mono-antena. Por otro lado, el número de sensores empleado se traduce en una mejora en términos de SIR.Postprint (published version

Adaptive Coded Modulation Classification and Spectrum Sensing for Cognitive Radio Systems. Adaptive Coded Modulation Techniques for Cognitive Radio Using Kalman Filter and Interacting Multiple Model Methods

The current and future trends of modern wireless communication systems place heavy demands on fast data transmissions in order to satisfy end users’ requirements anytime, anywhere. Such demands are obvious in recent applications such as smart phones, long term evolution (LTE), 4 & 5 Generations (4G & 5G), and worldwide interoperability for microwave access (WiMAX) platforms, where robust coding and modulations are essential especially in streaming on-line video material, social media and gaming. This eventually resulted in extreme exhaustion imposed on the frequency spectrum as a rare natural resource due to stagnation in current spectrum management policies. Since its advent in the late 1990s, cognitive radio (CR) has been conceived as an enabling technology aiming at the efficient utilisation of frequency spectrum that can lead to potential direct spectrum access (DSA) management. This is mainly attributed to its internal capabilities inherited from the concept of software defined radio (SDR) to sniff its surroundings, learn and adapt its operational parameters accordingly. CR systems (CRs) may commonly comprise one or all of the following core engines that characterise their architectures; namely, adaptive coded modulation (ACM), automatic modulation classification (AMC) and spectrum sensing (SS). Motivated by the above challenges, this programme of research is primarily aimed at the design and development of new paradigms to help improve the adaptability of CRs and thereby achieve the desirable signal processing tasks at the physical layer of the above core engines. Approximate modelling of Rayleigh and finite state Markov channels (FSMC) with a new concept borrowed from econometric studies have been approached. Then insightful channel estimation by using Kalman filter (KF) augmented with interacting multiple model (IMM) has been examined for the purpose of robust adaptability, which is applied for the first time in wireless communication systems. Such new IMM-KF combination has been facilitated in the feedback channel between wireless transmitter and receiver to adjust the transmitted power, by using a water-filling (WF) technique, and constellation pattern and rate in the ACM algorithm. The AMC has also benefited from such IMM-KF integration to boost the performance against conventional parametric estimation methods such as maximum likelihood estimate (MLE) for channel interrogation and the estimated parameters of both inserted into the ML classification algorithm. Expectation-maximisation (EM) has been applied to examine unknown transmitted modulation sequences and channel parameters in tandem. Finally, the non-parametric multitaper method (MTM) has been thoroughly examined for spectrum estimation (SE) and SS, by relying on Neyman-Pearson (NP) detection principle for hypothesis test, to allow licensed primary users (PUs) to coexist with opportunistic unlicensed secondary users (SUs) in the same frequency bands of interest without harmful effects. The performance of the above newly suggested paradigms have been simulated and assessed under various transmission settings and revealed substantial improvements

Compressive Sensing of Multiband Spectrum towards Real-World Wideband Applications.

PhD Theses.Spectrum scarcity is a major challenge in wireless communication systems with their rapid evolutions towards more capacity and bandwidth. The fact that the real-world spectrum, as a nite resource, is sparsely utilized in certain bands spurs the proposal of spectrum sharing. In wideband scenarios, accurate real-time spectrum sensing, as an enabler of spectrum sharing, can become ine cient as it naturally requires the sampling rate of the analog-to-digital conversion to exceed the Nyquist rate, which is resourcecostly and energy-consuming. Compressive sensing techniques have been applied in wideband spectrum sensing to achieve sub-Nyquist-rate sampling of frequency sparse signals to alleviate such burdens. A major challenge of compressive spectrum sensing (CSS) is the complexity of the sparse recovery algorithm. Greedy algorithms achieve sparse recovery with low complexity but the required prior knowledge of the signal sparsity. A practical spectrum sparsity estimation scheme is proposed. Furthermore, the dimension of the sparse recovery problem is proposed to be reduced, which further reduces the complexity and achieves signal denoising that promotes recovery delity. The robust detection of incumbent radio is also a fundamental problem of CSS. To address the energy detection problem in CSS, the spectrum statistics of the recovered signals are investigated and a practical threshold adaption scheme for energy detection is proposed. Moreover, it is of particular interest to seek the challenges and opportunities to implement real-world CSS for systems with large bandwidth. Initial research on the practical issues towards the real-world realization of wideband CSS system based on the multicoset sampler architecture is presented. In all, this thesis provides insights into two critical challenges - low-complexity sparse recovery and robust energy detection - in the general CSS context, while also looks into some particular issues towards the real-world CSS implementation based on the i multicoset sampler

Proceedings, MSVSCC 2011

Proceedings of the 5th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 14, 2011 at VMASC in Suffolk, Virginia. 186 pp

CLT for eigen-inference methods in cognitive radios

This article provides a central limit theorem for a consistent estimator of the population eigenvalues of a class of sample covariance matrices. An exact expression as well as an empirical and asymptotically accurate approximation of the limiting variance is also derived. These results are applied in a cognitive radio context featuring an orthogonal-CDMA primary network and a secondary network whose objective is to maximise the coverage of secondary transmissions under low probability of interference with primary users. Index Terms — CLT, G-estimation, cognitive radios. I

İK2018 17th Internationally Participated Business Congress, 26-28 April 2018, Çeşme, İzmir

Çevrimiçi (XLV, 2055 sayfa )26-28 Nisan 2018 tarihlerinde Çeşme’de düzenlenen, 17. Uluslararası Katılımlı işletmecilik Kongresi’nin İzmir Katip Çelebi Üniversitesi, iktisadi ve idari Bilimler Fakültesi, işletme Bölümü ev sahipliğinde gerçekleştirilmesinden dolayı büyük bir mutluluk ve onur duyduk. Türkiye’de işletmecilik alanında uzun süredir başarıyla gerçekleştirilen ‘İşletmecilik Kongresi’ 17. Oturumunda uluslararası bir nitelik kazandırılarak gerçekleştirilmiştir. Bu vesile ile kongrenin 17. Oturumu ‘Uluslararası Katılımlı İşletmecilik Kongresi’ olarak tanımlanmıştır. Kongrenin bu niteliği kazanmasında katkıları olan herkese teşekkür ederiz. Umut ederiz ki bu kıymetli kongrenin ileriki oturumlarının da bu nitelikte gerçekleşmesidir. 17. Uluslararası İşletmecilik Kongresi’ne akademi, iş dünyası, sivil toplum kuruluşları ve bireysel olarak yaklaşık 700 katılımcı ilgi göstermiştir. Kongrede sunulmak üzere 400’den fazla çalışma tarafımıza ulaşmıştır. Bu çalışmalardan kongrede sunumu yapılan 236 tane tebliğ bu kitapta yer almaktadır. Kongrenin düzenlenmesi sırasında her zaman desteklerini hissettiğimiz Danışma Kurulu değerli üyelerine, bildiri tam metin ve özetlerini dikkatle ve özenle değerlendiren Bilim Kurulu üyelerine ve kongre sponsorlarına çok teşekkür ederiz. Prof.Dr. Hayrettin USUL 17. Uluslararası Katılımlı İşletmecilik Kongresi Dönem Başkan