A Rate-Splitting Approach to Fading Channels with Imperfect Channel-State Information

As shown by M\'edard, the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by assuming a Gaussian channel input $X$ with power $P$ and by upper-bounding the conditional entropy $h(X|Y,\hat{H})$ by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating $X$ from $(Y,\hat{H})$. We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input $X$ as the sum of two independent Gaussian variables $X_1$ and $X_2$ and by applying M\'edard's lower bound first to bound the mutual information between $X_1$ and $Y$ while treating $X_2$ as noise, and by applying it a second time to the mutual information between $X_2$ and $Y$ while assuming $X_1$ to be known, we obtain a capacity lower bound that is strictly larger than M\'edard's lower bound. We then generalize this approach to an arbitrary number $L$ of layers, where $X$ is expressed as the sum of $L$ independent Gaussian random variables of respective variances $P_{\ell}$, $\ell = 1,\dotsc,L$ summing up to $P$. Among all such rate-splitting bounds, we determine the supremum over power allocations $P_\ell$ and total number of layers $L$. This supremum is achieved for $L\to\infty$ and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error $H-\hat{H}$ tends to zero as the SNR tends to infinity.Comment: 28 pages, 8 figures, submitted to IEEE Transactions on Information Theory. Revised according to first round of review

Computation Alignment: Capacity Approximation without Noise Accumulation

Consider several source nodes communicating across a wireless network to a destination node with the help of several layers of relay nodes. Recent work by Avestimehr et al. has approximated the capacity of this network up to an additive gap. The communication scheme achieving this capacity approximation is based on compress-and-forward, resulting in noise accumulation as the messages traverse the network. As a consequence, the approximation gap increases linearly with the network depth. This paper develops a computation alignment strategy that can approach the capacity of a class of layered, time-varying wireless relay networks up to an approximation gap that is independent of the network depth. This strategy is based on the compute-and-forward framework, which enables relays to decode deterministic functions of the transmitted messages. Alone, compute-and-forward is insufficient to approach the capacity as it incurs a penalty for approximating the wireless channel with complex-valued coefficients by a channel with integer coefficients. Here, this penalty is circumvented by carefully matching channel realizations across time slots to create integer-valued effective channels that are well-suited to compute-and-forward. Unlike prior constant gap results, the approximation gap obtained in this paper also depends closely on the fading statistics, which are assumed to be i.i.d. Rayleigh.Comment: 36 pages, to appear in IEEE Transactions on Information Theor

Communication rates for fading channels with imperfect channel-state information

The present thesis studies information rates for reliable transmission of information over fading channels in the realistic situation where the receiver has only imperfect channel-state knowledge. Of particular interest are analytical expressions of achievable transmission rates under imperfect and no CSI, that is, lower bounds on the mutual information and on the Shannon capacity. A well-known mutual information lower bound for Gaussian codebooks is obtained when conflating the additive (thermal) noise with the multiplicative noise due to the imperfections of the CSIR into a single effective noise term, and then assuming that this term is independent Gaussian. This so-called worst-case-noise approach allows to derive a strikingly simple and well-known lower bound on the mutual information of the channel. A first part of this thesis proposes a simple way to improve this worst-case-noise bound by means of a rate-splitting approach: by expressing the Gaussian input as a sum of several independent Gaussian inputs, and by assuming that the receiver performs successive decoding of the corresponding information streams, we show how to derive a larger mutual information lower bound. On channels with a single transmit antenna, the optimal allocation of transmit power across the different inputs is found to be approached as the number of inputs (so-called layers) tends to infinity, and the power assigned to each layer tends to zero. This infinite-layering limit gives rise to a mutual information bound expressible as an integral. On channels with multiple transmit antennas, an analogous result is derived. However, since multiple transmit antennas open up more possibilities for spatial multiplexing, the rate-splitting approach gives rise to a whole family of infinite-layering bounds. This family of bounds is closely studied for independent and identically zero-mean Gaussian distributed fading coefficients (so-called i.i.d. Rayleigh fading). Most notably, it is shown that for asymptotically perfect CSIR, any bound from the family is asymptotically tight at high signal-to-noise ratios (SNR). Specifically, this means that the difference between the mutual information and its lower bound tends to zero as the SNR tends to infinity, provided that the CSIR tends to be exact as the SNR tends to infinity. A second part of this thesis proposes a framework for the optimization of a class of utility functions in black-Rayleigh fading multiple-antenna channels with transmit-side antenna correlation, and no CSI at the receiver. A fraction of each fading block is reserved for transmitting a sequence of training symbols, while the remaining time instants are used for transmission of data. The receiver estimates the channel matrix based on the noisy training observation and then decodes the data signal using this channel estimate. For utilities that are symmetric functions of the eigenvalues of the matrix-valued effective SNR (such as, e.g., the worst-case-noise bound), the problems consisting in optimizing the pilot sequence and the linear precoder are cast into convex (or quasi-convex) problems for concave (or quasi-concave) utility functions. We also study an important subproblem of the joint optimization, which consists in computing jointly Pareto-optimal pilot sequences and precoders. By wrapping these optimization procedures into a cyclic iteration, we obtain an algorithm which converges to a local joint optimum for any utility.Aquesta tesi estudia les taxes d'informació per la transmissió fiable d'informació en canals amb esvaïments sota la hipòtesi realista de que el receptor té un coneixement tan sols imperfecte de l'esvaïment aleatori. De particular interès són les expressions analítiques de les taxes de transmissió assolibles amb coneixement imperfecte i sense coneixement de l'estat del canal, és a dir, cotes inferiors de la informació mútua i de la capacitat de Shannon. Una cota inferior de la informació mútua per a codis gaussians ben coneguda s'obté combinant el soroll additiu (tèrmic) amb el terme de soroll multiplicatiu causat per les imperfeccions del coneixement de l'estat del canal en un únic soroll efectiu, i assumint que el soroll és gaussià i independent. Aquesta aproximació del pitjor soroll permet obtenir una expressió molt simple i ben coneguda de la informació mútua del canal. Una primera part d'aquesta tesi proposa un procediment senzill per a millorar aquesta cota associada al pitjor cas mitjançant una estratègia de repartiment de taxa: expressant l'entrada gaussiana del canal com a la suma de diverses entrades gaussianes independents i suposant que el receptor realitza una descodificació seqüencial dels fluxos d'informació, es mostra com obtenir una major cota inferior de la informació mútua del canal. En canals amb una única antena en transmissió, la distribució òptima de potència als diferents fluxos s'obté quan el seu nombre (capes) tendeix a infinit, i la potència associada a cada capa tendeix a zero. El límit associat a un nombre infinit de capes dóna lloc a una expressió integral de la cota de la informació mútua. En canals amb múltiples antenes s'obté un resultat similar. No obstant això, atès que la utilització de múltiples antenes proporciona més possibilitats de multiplexat espacial, el procediment dóna lloc a tota una família de cotes inferiors de la informació mútua associades a una combinació de capes infinita. S'estudia en detall aquesta família de cotes per al cas de coeficients d'esvaïments gaussians de mitjana zero, independents i idènticament distribuïts (conegut com esvaïment i.i.d. Rayleigh). S'obtenen diverses propietats de la família de cotes. És important destacar que per a coneixement asimptòtic perfecte del canal en recepció, qualsevol membre de la família de cotes és asimptòticament ajustat per alta relació senyal a soroll (SNR). En concret, la diferència entre la informació mútua i la seva cota inferior tendeix a zero quan la SNR tendeix a infinit sempre que el coneixement del canal tendeixi a ser exacte a mesura que la SNR tendeix a infinit. Una segona part d'aquesta tesi proposa un marc per a l'optimització d'una classe de funcions d'utilitat en canals amb múltiples antenes i esvaïments Rayleigh per blocs amb correlació en transmissió i sense informació sobre el canal a recepció. Una fracció temporal de cada bloc d'esvaïment es reserva per transmetre una seqüència de símbols d'entrenament mentre que la resta de mostres temporals s'utilitzen per transmetre informació. El receptor estima la matriu del canal partint de la seva observació sorollosa i descodifica la informació mitjançant la seva estimació del canal. Per a una classe de funcions d'utilitat que són funcions simètriques dels autovalors de la SNR matricial efectiva, els problemes consistents en optimitzar la seqüència pilot i el precodificador lineal són transformats en problemes convexos (o quasi-convexos) per a funcions d'utilitat còncaves (o quasi-còncaves). També s'estudia un subproblema important de l'optimització conjunta, que consisteix en el càlcul de les seqüències d'entrenament i dels precodificadors conjuntament Pareto-òptims. Integrant aquests procediments d'optimització en una iteració cíclica, s'obté un algoritme que convergeix a un òptim local conjunt per a qualsevol utilitat quasi-còncav

Topological Interference Management With Transmitter Cooperation

Interference networks with no channel state information at the transmitter except for the knowledge of the connectivity graph have been recently studied under the topological interference management framework. In this paper, we consider a similar problem with topological knowledge but in a distributed broadcast channel setting, i.e., a network where transmitter cooperation is enabled. We show that the topological information can also be exploited in this case to strictly improve the degrees of freedom (DoF) as long as the network is not fully connected, which is a reasonable assumption in practice. Achievability schemes from graph theoretic and interference alignment perspectives are proposed. Together with outer bounds built upon generator sequence, the concept of compound channel settings, and the relation to index coding, we characterize the symmetric DoF for the so-called regular networks with constant number of interfering links, and identify the sufficient and/or necessary conditions for the arbitrary network topologies to achieve a certain amount of symmetric DoF

Transmit precoding and Bayesian detection for cognitive radio networks with limited channel state information

Field of study: Electrical & computer engineering.Dr. Dominic K. C. Ho, Dissertation Supervisor.Includes vita."May 2017."Cognitive radio (CR) represents a recent direction for enabling coexistence among heterogeneous networks. It can be a potential solution for the problem of scarce spectrum available for wireless communication systems. The study here investigates the underlay and interweave paradigms for the coexistence of CR network of secondary users (SUs) with a primary network of primary users (PUs). Under underlay mode, both networks communicates concurrently using the same resources. With interweave, SU is able to communicate as long as (some) PUs are not active. Usually, underlay or interweave employs multiple antennas at SU to use the spectral resources better and manage the interference towards the primary network. Performance of the CR network under either paradigm depends largely on the amount and quality of channel state information (CSI) available about the different communication links. In practical systems, often CSI at SU has uncertainty since it is deviated from the true one or is not known at all. This uncertainty should be accounted when designing the precoding schemes for SU or otherwise the interference impact on primary networks would violate the quality of service (QoS) requirements for PUs. This dissertation considers two cases regarding to the availability of CSI, the first one is when CSI is imperfect and the second is when CSI is completely not known. For the underlay mode, we investigate two manifolds. The first one addresses the problem of maximizing the throughput of a multiple-input multiple-output (MIMO) SU when CSI of the interference link to PU is completely unknown or partially known. We study the achievable rates for SU under two different QoS requirements for the PU: the conventional interference temperature and leakage rate metrics. When CSI is unavailable, we develop an iterative adaptation algorithm that satisfies the QoS constraint through exploiting the side-information in the primary communication network. When CSI is inaccurate, we model the uncertainty deterministically such that the uncertainty error belongs to a convex compact set defined by the Schatten norm. We design the precoder by following the worst case formulation. We further investigate the relation between the unknown and the inaccurate CSI cases when using the interference temperature metric, and reveal that the performance of the latter is not necessarily better than the former. The second manifold assumes there is uncertainty in the SU intended link for communication as well as in the interference link from SU to PU. Similar to the first manifold, we follow the deterministic modelling using Schatten norm for the uncertainty and apply the worst case philosophy. For a given precoder matrix, we find the worst uncertainty error in the set that describes the uncertainty in each link. We further develop an iterative numerical algorithm for the precoder. Simpler solutions for the precoder and the uncertainty errors are derived under some special instances of the Schatten norm and certain requirement of transmission power. For the interweave mode, we assume there is no CSI available at SU and derive a Bayesian detector for the proposed binary hypothesis problem. For the null or noise model, we propose a conjugate prior for the unknown spatial covariance matrix. For the alternative or data model, we propose a new class of improper priors for the covariance matrix. We introduce the fractional Bayes factor (FBF) approach to enhance the detection capability of the Bayes factor. The developed FBF is compared with those using the conjugate priors for both hypotheses and generalized likelihood ratio test (GLRT), and it yields significant improvement.Includes bibliographical references (pages 126-142)

Topological Interference Management with Transmitter Cooperation

Interference networks with no channel state information at the transmitter (CSIT) except for the knowledge of the connectivity graph have been recently studied under the topological interference management (TIM) framework. In this paper, we consider a similar problem with topological knowledge but in a distributed broadcast channel setting, i.e. a network where transmitter cooperation is enabled. We show that the topological information can also be exploited in this case to strictly improve the degrees of freedom (DoF) as long as the network is not fully connected, which is a reasonable assumption in practice. Achievability schemes based on selective graph coloring, interference alignment, and hypergraph covering, are proposed. Together with outer bounds built upon generator sequence, the concept of compound channel settings, and the relation to index coding, we characterize the symmetric DoF for so-called regular networks with constant number of interfering links, and identify the sufficient and/or necessary conditions for the arbitrary network topologies to achieve a certain amount of symmetric DoF.Comment: 46 pages, 10 figures, short version presented at the International Symposium on Information Theory 201

Outage probability formulas for cellular networks (contributions for MIMO, CoMP and time reversal features)

L étude de dimensionnement d un réseau cellulaire est une phase de conception qui doit permettre de déterminer les performances d un système dans une configuration donnée. Elle inclut l étude de couverture et l analyse de trafic. De complexes simulations sont possibles pour connaître les paramètres de performances d un réseau mais seules les études analytiques fournissent des résultats rapides. Par ailleurs, pour faire face à la demande de hauts débits, à la rareté du spectre fréquentiel et à l impossibilité d émettre à de plus fortes puissances, de nouvelles techniques de transmissions sont apparues. Nous sommes ainsi passés d un système classique à une seule antenne à des systèmes à multiple antennes et même à des scénarios de coopération entre stations de base. Dans cette thèse, nous proposons des modèles analytiques pour l étude des performances, notamment en termes de probabilités de coupure, de ces évolutions des réseaux cellulaires. Dans une première phase, nous considérons des systèmes multicellulaires à une antenne émettrice et une antenne réceptrice (SISO). Nous proposons deux méthodes d étude de l impact conjoint de l affaiblissement de parcours, de l effet de masque et des évanouissements rapides. Nous étudions, par la suite, un système à large bande utilisant le retournement temporel comme technique de transmission. Dans une deuxième phase, nous considérons des systèmes multicellulaires à antennes multiple à l émission ou à la réception (MISO/MIMO) implémentant les schémas de diversité Alamouti et de combinaison par rapport maximal (MRC). Ensuite, nous considérons un système multicellulaire multi-utilisateurs à précodage de forçage à zéro (ZFBF).The implementation of cellular systems have aroused issues related to the design of cellular networks termed to as network dimensioning. It includes the coverage estimation and thetraffic analysis. Simple models and methods are required to reduce the time consumption of these two analysis. At the same time, the growing demand for higher data rates constrained by the scarcity of frequency spectrum, and the requirements in terms of power consumption reduction make the telecommunication community think about new transmission techniques moving from the classical single antenna systems to multiple antenna systems and even the newly envisaged cooperative systems. In this thesis, we provide analytical models to assess the performance of these different cellular network evolutions in terms of outage probabilities. In a first study, we consider multicellular single input single output (SISO) systems. First, we propose two accurate methods to study the joint impact of path-loss, shadowing and fast fading. This system has so far been studied either considering the only impact of path-loss and Rayleigh fading, or considering the same channel model as in our case but providing very complex outage probability expressions. Then, we provide an outage probability expression in a wideband communication context implementing the Time Reversal (TR) transmission technique considering the impact of fast fading. In a second study, we focus on multiple antenna systems. We study the performance of a Multiple Input Multiple Output (MIMO) system implementing a transmit and a receivediversity schemes namely the Alamouti code and the Maximum Ratio Combining (MRC).PARIS-Télécom ParisTech (751132302) / SudocSudocFranceF