Multi-user Diversity Systems with Application to Cognitive Radio

abstract: This thesis aims to investigate the capacity and bit error rate (BER) performance of multi-user diversity systems with random number of users and considers its application to cognitive radio systems. Ergodic capacity, normalized capacity, outage capacity, and average bit error rate metrics are studied. It has been found that the randomization of the number of users will reduce the ergodic capacity. A stochastic ordering framework is adopted to order user distributions, for example, Laplace transform ordering. The ergodic capacity under different user distributions will follow their corresponding Laplace transform order. The scaling law of ergodic capacity with mean number of users under Poisson and negative binomial user distributions are studied for large mean number of users and these two random distributions are ordered in Laplace transform ordering sense. The ergodic capacity per user is defined and is shown to increase when the total number of users is randomized, which is the opposite to the case of unnormalized ergodic capacity metric. Outage probability under slow fading is also considered and shown to decrease when the total number of users is randomized. The bit error rate (BER) in a general multi-user diversity system has a completely monotonic derivative, which implies that, according to the Jensen's inequality, the randomization of the total number of users will decrease the average BER performance. The special case of Poisson number of users and Rayleigh fading is studied. Combining with the knowledge of regular variation, the average BER is shown to achieve tightness in the Jensen's inequality. This is followed by the extension to the negative binomial number of users, for which the BER is derived and shown to be decreasing in the number of users. A single primary user cognitive radio system with multi-user diversity at the secondary users is proposed. Comparing to the general multi-user diversity system, there exists an interference constraint between secondary and primary users, which is independent of the secondary users' transmission. The secondary user with high- est transmitted SNR which also satisfies the interference constraint is selected to communicate. The active number of secondary users is a binomial random variable. This is then followed by a derivation of the scaling law of the ergodic capacity with mean number of users and the closed form expression of average BER under this situation. The ergodic capacity under binomial user distribution is shown to outperform the Poisson case. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of different user distributions.Dissertation/ThesisM.S. Electrical Engineering 201

Accessible Capacity of Secondary Users

A new problem formulation is presented for the Gaussian interference channels (GIFC) with two pairs of users, which are distinguished as primary users and secondary users, respectively. The primary users employ a pair of encoder and decoder that were originally designed to satisfy a given error performance requirement under the assumption that no interference exists from other users. In the scenario when the secondary users attempt to access the same medium, we are interested in the maximum transmission rate (defined as {\em accessible capacity}) at which secondary users can communicate reliably without affecting the error performance requirement by the primary users under the constraint that the primary encoder (not the decoder) is kept unchanged. By modeling the primary encoder as a generalized trellis code (GTC), we are then able to treat the secondary link and the cross link from the secondary transmitter to the primary receiver as finite state channels (FSCs). Based on this, upper and lower bounds on the accessible capacity are derived. The impact of the error performance requirement by the primary users on the accessible capacity is analyzed by using the concept of interference margin. In the case of non-trivial interference margin, the secondary message is split into common and private parts and then encoded by superposition coding, which delivers a lower bound on the accessible capacity. For some special cases, these bounds can be computed numerically by using the BCJR algorithm. Numerical results are also provided to gain insight into the impacts of the GTC and the error performance requirement on the accessible capacity.Comment: 42 pages, 12 figures, 2 tables; Submitted to IEEE Transactions on Information Theory on December, 2010, Revised on November, 201

Distributed spectrum leasing via cooperation

“Cognitive radio” networks enable the coexistence of primary (licensed) and secondary (unlicensed) terminals. Conventional frameworks, namely commons and property-rights models, while being promising in certain aspects, appear to have significant drawbacks for implementation of large-scale distributed cognitive radio networks, due to the technological and theoretical limits on the ability of secondary activity to perform effective spectrum sensing and on the stringent constraints on protocols and architectures. To address the problems highlighted above, the framework of distributed spectrum leasing via cross-layer cooperation (DiSC) has been recently proposed as a basic mechanism to guide the design of decentralized cognitive radio networks. According to this framework, each primary terminal can ”lease” a transmission opportunity to a local secondary terminal in exchange for cooperation (relaying) as long as secondary quality-of-service (QoS) requirements are satisfied. The dissertation starts by investigating the performance bounds from an information-theoretical standpoint by focusing on the scenario of a single primary user and multiple secondary users with private messages. Achievable rate regions are derived for discrete memoryless and Gaussian models by considering Decode-and-Forward (DF), with both standard and parity-forwarding techniques, and Compress-and-Forward (CF), along with superposition coding at the secondary nodes. Then a framework is proposed that extends the analysis to multiple primary users and multiple secondary users by leveraging the concept of Generalized Nash Equilibrium. Accordingly, multiple primary users, each owning its own spectral resource, compete for the cooperation of the available secondary users under a shared constraint on all spectrum leasing decisions set by the secondary QoS requirements. A general formulation of the problem is given and solutions are proposed with different signaling requirements among the primary users. The novel idea of interference forwarding as a mechanism to enable DiSC is proposed, whereby primary users lease part of their spectrum to the secondary users if the latter assist by forwarding information about the interference to enable interference mitigation at the primary receivers. Finally, an application of DiSC in multi-tier wireless networks such as femtocells overlaid by macrocells whereby the femtocell base station acts as a relay for the macrocell users is presented. The performance advantages of the proposed application are evaluated by studying the transmission reliability of macro and femto users for a quasi-static fading channel in terms of outage probability and diversity-multiplexing trade-off for uplink and, more briefly, for downlink

Performance analysis of spatially-distributed cooperative networks

PhD ThesisApplications of cooperative communications have attracted considerable attention in academia and industry in the past decade for their potential to exploit network densi cation in meeting the growing demand for data services. However, analytical methods capable of explicitly capturing the impact of the spatial domain on system performance are still rare. The aim of this thesis is to study cooperation between spatially-distributed nodes with the purpose to enhance relevant analytical methods. New approaches to performance analysis of node cooperation and several useful relations are developed in this work in the following three areas. First part of this thesis investigates broadcasting as an important method for TV and network signalling distribution. Cooperative broadcasting (CB) has been generally studied under the assumptions of asymptotically dense or large networks, which rarely hold in practice. In this work, a method to analyse the latency of CB in nite networks is developed using stochastic geometry. New useful relations and inter-node distance distributions are derived, highlighting interesting network characteristics. Second part of this thesis studies relay selection (RS), recognised as a way to reduce overheads arising from cooperative communications. In this thesis, a method for analysing RS is developed based on point processes theory. Presented approach is simpler and more intuitive compared to known methods. This has allowed obtaining exact expressions for outage probability of relay-assisted communication. Additionally, analysis of the sources' contention for relays has revealed that relays can be treated as a scarce resource. Finally, proposed methods are further extended to account for imperfect channel state information (CSI). Practical RS in presence of CSI imperfections remains an active research area, however the aspect of cooperating nodes' spatial distribution remains unexplored. This thesis introduces a novel approach to account for variable levels of CSI accuracy and for the spatial distribution cooperating relays

Studies on Trade-off Between Throughput and Reliability in Wireless Systems

In the first part of the thesis, we study the trade-off between the transmission reliability and data rate in high signal-to-noise ratio regime in ad-hoc wireless networks. Bandwidth allocation plays a significant role in this trade-off, since dividing bandwidth reduces the number of users on each band and consequently decreases the interference level, however it also decreases the data rate. Noting that the interference power is substantially influenced by the network density, this trade-off introduces a measure for appropriate bandwidth allocation among users considering the network density. The diversity-multiplexing trade-off is derived for a one-dimensional regular ad-hoc network. In the second part of the thesis, we study the performance of point-to-point and broadcast systems with partial channel state information at the transmitter in a time-varying environment. First, the capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel state information is perfectly known at the receiver and is fed back to the transmitter at the regular time-intervals. The system capacity is investigated in two cases: i) finite state Markov channel, and ii) additive white Gaussian noise channel with time-correlated fading. In a multiuser scenario, we consider a downlink system in which a single-antenna base station communicates with single antenna users, over a time-correlated fading channel. It is assumed that channel state information is perfectly known at each receiver, while the rate of channel variations and the fading gain at the beginning of each frame are known to the transmitter. The asymptotic throughput of the scheduling that transmits to the user with the maximum signal to noise ratio is examined applying variable code rate and/or variable codeword length signaling. It is shown that by selecting a fixed codeword length for all users, the order of the maximum possible throughput (corresponding to quasi-static fading) is achieved

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

Resource allocation and feedback in wireless multiuser networks

This thesis focuses on the design of algorithms for resource allocation and feedback in wireless multiuser and heterogeneous networks. In particular, three key design challenges expected to have a major impact on future wireless networks are considered: cross-layer scheduling; structured quantization codebook design for MU-MIMO networks with limited feedback; and resource allocation to provide physical layer security. The first design challenge is cross-layer scheduling, where policies are proposed for two network architectures: user scheduling in single-cell multiuser networks aided by a relay; and base station (BS) scheduling in CoMP. These scheduling policies are then analyzed to guarantee satisfaction of three performance metrics: SEP; packet delay; and packet loss probability (PLP) due to buffer overflow. The concept of the τ-achievable PLP region is also introduced to explicitly describe the tradeoff in PLP between different users. The second design challenge is structured quantization codebook design in wireless networks with limited feedback, for both MU-MIMO and CoMP. In the MU-MIMO network, two codebook constructions are proposed, which are based on structured transformations of a base codebook. In the CoMP network, a low-complexity construction is proposed to solve the problem of variable codebook dimensions due to changes in the number of coordinated BSs. The proposed construction is shown to have comparable performance with the standard approach based on a random search, while only requiring linear instead of exponential complexity. The final design challenge is resource allocation for physical layer security in MU-MIMO. To guarantee physical layer security, the achievable secrecy sum-rate is explicitly derived for the regularized channel inversion (RCI) precoder. To improve performance, power allocation and precoder design are jointly optimized using a new algorithm based on convex optimization techniques