The performance of multiple input single output (MISO) broadcast channels is strongly dependent on the availability of channel side information (CSI) at the transmitter. In many practical systems, CSI may be available to the transmitter only in a corrupted and incomplete form. It is natural to assume that the flaws in the CSI are random and can be represented by a probability distribution over the channel. This work is concerned with two key issues concerning MISO broadcast systems with random CSI: performance analysis and system design. First, the impact of noisy channel information on system performance is investigated. A simple model is formulated where the channel is Rayleigh fading, the CSI is corrupted by additive white Gaussian noise and a zero forcing precoder is formed by the noisy CSI. Detailed analysis of the ergodic rate and outage probability of the system is given. Particular attention is given to system behavior at asymptotically high SNR. Next, a method to construct precoders in a manner that accounts for the uncertainty in the channel information is developed. A framework is introduced that allows one to quantify the tradeoff between the risk (due to the CSI randomness) that is associated with a precoder and the resulting transmission rate. Using ideas from modern portfolio theory, the risk-rate problem is modified to a tractable mean-variance optimization problem. Thus, we give a method that allows one to efficiently find a good precoder in the risk-rate sense. The technique is quite general and applies to a wide range of CSI probability distributions.

The performance of multiple input single output (MISO) broadcast channels is strongly dependent on the availability of channel side information (CSI) at the transmitter. In many practical systems, CSI may be available to the transmitter only in a corrupted and incomplete form. It is natural to assume that the flaws in the CSI are random and can be represented by a probability distribution over the channel. This work is concerned with two key issues concerning MISO broadcast systems with random CSI: performance analysis and system design. First, the impact of noisy channel information on system performance is investigated. A simple model is formulated where the channel is Rayleigh fading, the CSI is corrupted by additive white Gaussian noise and a zero forcing precoder is formed by the noisy CSI. Detailed analysis of the ergodic rate and outage probability of the system is given. Particular attention is given to system behavior at asymptotically high SNR. Next, a method to construct precoders in a manner that accounts for the uncertainty in the channel information is developed. A framework is introduced that allows one to quantify the tradeoff between the risk (due to the CSI randomness) that is associated with a precoder and the resulting transmission rate. Using ideas from modern portfolio theory, the risk-rate problem is modified to a tractable mean-variance optimization problem. Thus, we give a method that allows one to efficiently find a good precoder in the risk-rate sense. The technique is quite general and applies to a wide range of CSI probability distributions.

This dissertation deals with the problem of scheduling in wireless MIMO (Multiple-Input Multiple-Output) downlink systems. The focus is on the large-scale systems when the number of subscribers is large. In part one, the problem of user selection in MIMO Broadcast channel is studied. An efficient user selection algorithm is proposed and is shown to achieve the sum-rate capacity of the system asymptotically (in terms of the number of users), while requiring (i)~low-complexity precoding scheme of zero-forcing beam-forming at the base station, (ii)~low amount of feedback from the users to the base station, (iii)~low complexity of search. Part two studies the problem of MIMO broadcast channel with partial Channel State Information (CSI) at the transmitter. The necessary and sufficient conditions for the amount of CSI at the transmitter (which is provided to via feedback links from the receivers) in order to achieve the sum-rate capacity of the system are derived. The analysis is performed in various singnal to noise ratio regimes. In part three, the problem of sum-rate maximization in a broadcast channel with large number of users, when each user has a stringent delay constraint, is studied. In this part, a new definition of fairness, called short-term fairness is introduced. A scheduling algorithm is proposed that achieves: (i) Maximum sum-rate throughput and (ii) Maximum short-term fairness of the system, simultaneously, while satisfying the delay constraint for each individual user with probability one. In part four, the sum-rate capacity of MIMO broadcast channel, when the channels are Rician fading, is derived in various scenarios in terms of the value of the Rician factor and the distribution of the specular components of the channel.

This dissertation deals with the problem of scheduling in wireless MIMO (Multiple-Input Multiple-Output) downlink systems. The focus is on the large-scale systems when the number of subscribers is large. In part one, the problem of user selection in MIMO Broadcast channel is studied. An efficient user selection algorithm is proposed and is shown to achieve the sum-rate capacity of the system asymptotically (in terms of the number of users), while requiring (i)~low-complexity precoding scheme of zero-forcing beam-forming at the base station, (ii)~low amount of feedback from the users to the base station, (iii)~low complexity of search. Part two studies the problem of MIMO broadcast channel with partial Channel State Information (CSI) at the transmitter. The necessary and sufficient conditions for the amount of CSI at the transmitter (which is provided to via feedback links from the receivers) in order to achieve the sum-rate capacity of the system are derived. The analysis is performed in various singnal to noise ratio regimes. In part three, the problem of sum-rate maximization in a broadcast channel with large number of users, when each user has a stringent delay constraint, is studied. In this part, a new definition of fairness, called short-term fairness is introduced. A scheduling algorithm is proposed that achieves: (i) Maximum sum-rate throughput and (ii) Maximum short-term fairness of the system, simultaneously, while satisfying the delay constraint for each individual user with probability one. In part four, the sum-rate capacity of MIMO broadcast channel, when the channels are Rician fading, is derived in various scenarios in terms of the value of the Rician factor and the distribution of the specular components of the channel.

De par la nature ouverte des communications sans-fils, les transmissions sont fortement impactées par divers facteurs limitants: l’interférence (due aux multiples utilisateurs), l’incertitude canal (due à la mobilité des utilisateurs) et la présence d'espions. En théorie de l’information, les « canaux de diffusion » sont un modèle clé des communications cellulaires sans-fils et consistent en une source qui souhaite envoyer deux messages chacun destiné à un utilisateur distinct, les canaux étant modélisés par des lois conditionnelles de probabilité. La gestion d’interférence constitue un point clé des transmissions à travers les canaux à diffusion, car l’augmentation du débit d’un utilisateur résulte inéluctablement en une augmentation de l’interférence à l’autre utilisateur, et elle consiste à fournir les débits maximaux que chacun des utilisateurs peut atteindre avec probabilité d’erreur nulle au décodage. Lorsque l’on couple l’interférence à de l’incertitude canal (lois de probabilités des canaux inconnues à la source), à des transmissions simultanées (plusieurs utilisateurs intéressés par les mêmes messages) ou encore à la présence d’espions (externe aux deux utilisateurs), les techniques existantes de gestion de l’interférence s’avèrent sous-optimales. L’objet de cette thèse a été donc été de développer des techniques de gestion de l’interférence pour les canaux de diffusion avec incertitude canal en se basant sur de nouvelles stratégies de codage, pour les canaux cognitifs à transmission multiples sous plusieurs régimes d’interférences, et enfin pour les canaux de diffusion avec espion où la vraie difficulté résidant dans les preuves d'optimalité. / Due to the open nature of wireless communications, the transmissions on such mediums are subject to many limitations: interference (due to the increasing traffic on the network), channel uncertainty ( due to users’ mobility) and security. The most accurate information theoretic model for cellular wireless communications is the Broadcast Channel that consists of a source transmitting two distinct messages to two receivers through a channel that we model by a conditional probability distribution. Interference Management is the bottleneck of coding for such channels, as increasing the rate of a message results in an increased amount of interference at the opposite receiver. It thus consists in finding the optimal tradeoff between the two messages rates while ensuring zero decoding error probability at both receivers. When interference is coupled with channel uncertainty (channel probability distribution unknown to the source) or with simultaneous transmissions (many users interested in the same message) or even to eavesdropping, the known techniques for interference management appear to be sub-optimal. The purpose then of this thesis was to develop interference mitigation techniques for Broadcast Channels with uncertainty resorting to more involved coding strategies, for the Broadcast Channels with a helper with multiple users under many regimes of interference, and last but not least, for the Wiretap Broadcast CHannel through new outer bounding techniques.

Recent information theoretical results indicate that dirty-paper coding (DPC) achieves the entire capacity region of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). This thesis presents practical code designs for Gaussian BCs based on DPC. To simplify our designs, we assume constraints on the individual rates for each user instead of the customary constraint on transmitter power. The objective therefore is to minimize the transmitter power such that the practical decoders of all users are able to operate at the given rate constraints. The enabling element of our code designs is a practical DPC scheme based on nested turbo codes. We start with Cover's simplest two-user Gaussian BC as a toy example and present a code design that operates 1.44 dB away from the capacity region boundary at the transmission rate of 1 bit per sample per dimension for each user. Then we consider the case of the multiple-input multiple-output BC and develop a practical limit-approaching code design under the assumption that the channel state information is available perfectly at the receivers as well as at the transmitter. The optimal precoding strategy in this case can be derived by invoking duality between the MIMO BC and MIMO multiple access channel (MAC). However, this approach requires transformation of the optimal MAC covariances to their corresponding counterparts in the BC domain. To avoid these computationally complex transformations, we derive a closed-form expression for the optimal precoding matrix for the two-user case and use it to determine the optimal precoding strategy. For more than two users we propose a low-complexity suboptimal strategy, which, for three transmit antennas at the base station and three users (each with a single receive antenna), performs only 0.2 dB worse than the optimal scheme. Our obtained results are only 1.5 dB away from the capacity limit. Moreover simulations indicate that our practical DPC based scheme significantly outperforms the prevalent suboptimal strategies such as time division multiplexing and zero forcing beamforming. The drawback of DPC based designs is the requirement of channel state information at the transmitter. However, if the channel state information can be communicated back to the transmitter effectively, DPC does indeed have a promising future in code designs for MIMO BCs.

Em sistemas MIMO multiusuÃrio, o transmissor pode selecionar um subconjunto de antenas e/ou usuÃrios que tÃm bons canais para maximizar o rendimento do sistema usando vÃrios critÃrios de seleÃÃo. AlÃm disso, os prÃ-codificadores podem proporcionar dimensÃes livres de interferÃncia. O alinhamento de interferÃncia (IA) à baseado no conceito de prÃ-codificaÃÃo e oferece diferentes compromissos entre complexidade e desempenho. A idÃia bÃsica do Alinhamento InterferÃncia consiste em prÃ-codificar os sinais transmitidos de maneira que os mesmos sejam alinhados no receptor, em que eles constituem interferÃncia, enquanto que ao mesmo tempo os separa do sinal desejado. No entanto, a InformaÃÃo do Estado do Canal (CSI) tem sido uma preocupaÃÃo para os pesquisadores porque ela tem um impacto no desempenho de algoritmos de IA. Assim, nos propomos a analisar o desempenho da seleÃÃo de antena e diversidade multiusuÃrio em conjunto, a fim de permitir o IA oportunista usando vÃrios critÃrios com relaÃÃo à perturbaÃÃo da CSI. AnÃlises e simulaÃÃes verificam o comportamento do esquema proposto. / In multiuser MIMO systems, the transmitter can select a subset of antennas and/or users which have good channel conditions to maximize the system throughput using various selection criteria. Furthermore, precoding can provide free interference dimensions. The Interference Alignment (IA) is based on the concept of precoding and it offers different trade-offs between complexity and performance. The basic idea of Interference Alignment consists in precoding the transmitted signals such that they are aligned at the receiver where they constitute interference, while at the same time disjointed from the desired signal. However, the Channel State Information (CSI) has been a concern because it impacts the performance of IA algorithms. Hence, we propose to analyze the performance of antenna selection and multiuser diversity together in order to allow opportunistic IA using several criteria over the disturbance of CSI. Analyses and simulations verify the behavior of the proposed scheme.

A converse method is developed for the source broadcast problem. Specifically, it is shown that the separation architecture is optimal for a variant of the source broadcast problem and the associated source-channel separation theorem can be leveraged, via a reduction argument, to establish a necessary condition for the original problem, which uni es several existing results in the literature. Somewhat surprisingly, this method, albeit based on the source-channel separation theorem, can be used to prove the optimality of non-separation based schemes and determine the performance limits in certain scenarios where the separation architecture is suboptimal. / Thesis / Master of Applied Science (MASc)

Information-theoretic arguments focus on modeling the reliability of information transmission, assuming availability of infinite data at sources, thus ignoring randomness in message generation times at the respective sources. However, in information transport networks, not only is reliable transmission important, but also stability, i.e., finiteness of mean delay in- curred by messages from the time of generation to the time of successful reception. Usually, delay analysis is done separately using queueing-theoretic arguments, whereas reliable information transmission is studied using information theory. In this thesis, we investigate these two important aspects of data communication jointly by suitably combining models from these two fields. In particular, we model scheduled communication of messages , that arrive in a random process, (i) over multiaccess channels, with either independent decoding or joint decoding, and (ii) over degraded broadcast channels. The scheduling policies proposed permit up to a certain maximum number of messages for simultaneous transmission. In the first part of the thesis, we develop a multi-class discrete-time processor-sharing queueing model, and then investigate the stability of this queue. In particular, we model the queue by a discrete-time Markov chain defined on a countable state space, and then establish (i) a sufficient condition for c-regularity of the chain, and hence positive recurrence and finiteness of stationary mean of the function c of the state, and (ii) a sufficient condition for transience of the chain. These stability results form the basis for the conclusions drawn in the thesis. The second part of the thesis is on multiaccess communication with random message arrivals. In the context of independent decoding, we assume that messages can be classified into a fixed number of classes, each of which specifies a combination of received signal power, message length, and target probability of decoding error. Each message is encoded independently and decoded independently. In the context of joint decoding, we assume that messages can be classified into a fixed number of classes, each of which specifies a message length, and for each of which there is a message queue. From each queue, some number of messages are encoded jointly, and received at a signal power corresponding to the queue. The messages are decoded jointly across all queues with a target probability of joint decoding error. For both independent decoding and joint decoding, we derive respective discrete- time multiclass processor-sharing queueing models assuming the corresponding information-theoretic models for the underlying communication process. Then, for both the decoding schemes, we (i) derive respective outer bounds to the stability region of message arrival rate vectors achievable by the class of stationary scheduling policies, (ii) show for any mes- sage arrival rate vector that satisfies the outer bound, that there exists a stationary “state-independent” policy that results in a stable system for the corresponding message arrival process, and (iii) show that the stability region of information arrival rate vectors, in the limit of large message lengths, equals an appropriate information-theoretic capacity region for independent decoding, and equals the information-theoretic capacity region for joint de-coding. For independent decoding, we identify a class of stationary scheduling policies, for which we show that the stability region in the limit of large maximum number of simultane-ous transmissions is independent of the received signal powers, and each of which achieves a spectral efficiency of 1 nat/s/Hz in the limit of large message lengths. In the third and last part of the thesis, we show that the queueing model developed for multiaccess channels with joint decoding can be used to model communication over degraded broadcast channels, with superposition encoding and successive decoding across all queues. We then show respective results (i), (ii), and (iii), stated above.

A Broadcast Channel is a communication path between a single source and two or more receivers or users. The source intends to communicate independent information to the users. A particular case of interest is the Gaussian Broadcast Channel (GBC) where the noise at each user is additive white Gaussian noise (AWGN). The capacity region of GBC is well known and the input to the channel is distributed as Gaussian. The capacity region of another special case of GBC namely Fading Broadcast Channel (FBC)was given in [Li and Goldsmith, 2001]and was shown that superposition of Gaussian codes is optimal for the FBC (treated as a vector degraded Broadcast Channel). The capacity region obtained when the input to the channel is distributed uniformly over a finite alphabet(Constellation)is termed as Constellation Constrained(CC) capacity region [Biglieri 2005]. In this thesis the CC capacity region for two-user GBC and the FBC are obtained. In case of GBC the idea of superposition coding with input from finite alphabet and CC capacity was explored in [Hupert and Bossert, 2007]but with some limitations. When the participating individual signal sets are nearly equal i.e., given total average power constraint P the rate reward α (also the power sharing parameter) is approximately equal to 0.5, we show via simulation that with rotation of one of the signal sets by an appropriate angle the CC capacity region is maximally enlarged. We analytically derive the expression for optimal angle of rotation. In case of FBC a heuristic power allocation procedure called finite-constellation power allocation procedure is provided through which it is shown (via simulation)that the ergodic CC capacity region thus obtained completely subsumes the ergodic CC capacity region obtained by allocating power using the procedure given in[Li and Goldsmith, 2001].It is shown through simulations that rotating one of the signal sets by an optimal angle (obtained by trial and error method)for a given α maximally enlarges the ergodic CC capacity region when finite-constellation power allocation is used. An expression for determining the optimal angle of rotation for the given fading state, is obtained. And the effect of rotation is maximum around the region corresponding to α =0.5. For both GBC and FBC superposition coding is done at the transmitter and successive decoding is carried out at the receivers.