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In the modern world, the use of Internet based communications has become a daily activity for a big part of the population. In particular, mobile communications are experiencing a relentless growth in the number of users, which has become an issue as they must be allocated in the channels with the limited available time and frequency resources in the physical layer. This is why Non-Orthogonal Multiple Access (NOMA) schemes are being used in 5G mobile communications and are expected to be a key factor in the future 6G communications. Another factor to take into account is the evolution in technologies such as Artificial Intelligence (AI) and Machine Learning (ML) that, as proven in literature, can perform tasks in the telecommunications world. NOMA will play an important role in 6G communications, while AI/ML has proven to play a key role in many layers including the physical layer, to improve the performance. In particular, constellation design to optimize BER vs SNR performance has proven to be feasible via Deep Learning (DL). In this study, we focus on neural design of demappers for an uplink NOMA system, to demonstrate the performance advantages of these systems against classical demapping techniques. The traditional demapping techniques to evaluate are the Successive Interference Cancellation (SIC) and the Joint Demapper. On the other hand, the SICNet demapper , a ML version of the traditional SIC, has been adapted to the uplink NOMA system. The comparison of the performance of all the demappers has been done with BER-EbN0 curves. The results show that the Joint demapper is the most optimal technique in a two-user uplink system. Meanwhile, the SICNet demapper has proven to outperform the SIC demapper in most of the studied scenarios.

In this paper, we explore various multi-agent reinforcement learning (MARL) techniques to design grant-free random access (RA) schemes for low-complexity, low-power battery operated devices in massive machine-type communication (mMTC) wireless networks. We use value decomposition networks (VDN) and QMIX algorithms with parameter sharing (PS) with centralized training and decentralized execution (CTDE) while maintaining scalability. We then compare the policies learned by VDN, QMIX, and deep recurrent Q-network (DRQN) and explore the impact of including the agent identifiers in the observation vector. We show that the MARL-based RA schemes can achieve a better throughput-fairness trade-off between agents without having to condition on the agent identifiers. We also present a novel correlated traffic model, which is more descriptive of mMTC scenarios, and show that the proposed algorithm can easily adapt to traffic non-stationarities, Comment: 15 pages, 10 figures

End-to-end design of communication systems using deep autoencoders (AEs) is gaining attention due to its flexibility and excellent performance. Besides single-user transmission, AE-based design is recently explored in multi-user setup, e.g., for designing constellations for non-orthogonal multiple access (NOMA). In this paper, we further advance the design of AE-based downlink NOMA by introducing weighted loss function in the AE training. By changing the weight coefficients, one can flexibly tune the constellation design to balance error probability of different users, without relying on explicit information about their channel quality. Combined with the SICNet decoder, we demonstrate a significant improvement in achievable levels and flexible control of error probability of different users using the proposed weighted AE-based framework., Comment: 5 pages, 5 figures, to appear at SPAWC 2023

We solve a long-standing open problem about the optimal codebook structure of codes in $n$-dimensional Euclidean space that consist of $n+1$ codewords subject to a codeword energy constraint, in terms of minimizing the average decoding error probability. The conjecture states that optimal codebooks are formed by the $n+1$ vertices of a regular simplex (the $n$-dimensional generalization of a regular tetrahedron) inscribed in the unit sphere. A self-contained proof of this conjecture is provided that hinges on symmetry arguments and leverages a relaxation approach that consists in jointly optimizing the codebook and the decision regions, rather than the codeword locations alone., Comment: 7 pages, submitted for peer review

Routing is a crucial component in the design of Flying Ad-Hoc Networks (FANETs). State of the art routing solutions exploit the position of Unmanned Aerial Vehicles (UAVs) and their mobility information to determine the existence of links between them, but this information is often unreliable, as the topology of FANETs can change quickly and unpredictably. In order to improve the tracking performance, the uncertainty introduced by imperfect measurements and tracking algorithms needs to be accounted for in the routing. Another important element to consider is beamforming, which can reduce interference, but requires accurate channel and position information to work. In this work, we present the Beam Aware Stochastic Multihop Routing for FANETs (BA-SMURF), a Software-Defined Networking (SDN) routing scheme that takes into account the positioning uncertainty and beamforming design to find the most reliable routes in a FANET. Our simulation results show that joint consideration of the beamforming and routing can provide a 5% throughput improvement with respect to the state of the art.

Grant-free random access (RA) techniques are suitable for machine-type communication (MTC) networks but they need to be adaptive to the MTC traffic, which is different from the human-type communication. Conventional RA protocols such as exponential backoff (EB) schemes for slotted-ALOHA suffer from a high number of collisions and they are not directly applicable to the MTC traffic models. In this work, we propose to use multi-agent deep Q-network (DQN) with parameter sharing to find a single policy applied to all machine-type devices (MTDs) in the network to resolve collisions. Moreover, we consider binary broadcast feedback common to all devices to reduce signalling overhead. We compare the performance of our proposed DQN-RA scheme with EB schemes for up to 500 MTDs and show that the proposed scheme outperforms EB policies and provides a better balance between throughput, delay and collision rate, Comment: 6 pages, 7 Figure, accepted in the proceedings of IEEE VTC Spring-2022 Workshops

Random access (RA) schemes are a topic of high interest in machine-type communication (MTC). In RA protocols, backoff techniques such as exponential backoff (EB) are used to stabilize the system to avoid low throughput and excessive delays. However, these backoff techniques show varying performance for different underlying assumptions and analytical models. Therefore, finding a better transmission policy for slotted ALOHA RA is still a challenge. In this paper, we show the potential of deep reinforcement learning (DRL) for RA. We learn a transmission policy that balances between throughput and fairness. The proposed algorithm learns transmission probabilities using previous action and binary feedback signal, and it is adaptive to different traffic arrival rates. Moreover, we propose average age of packet (AoP) as a metric to measure fairness among users. Our results show that the proposed policy outperforms the baseline EB transmission schemes in terms of throughput and fairness., Comment: 6 pages, 9 figures, conference paper accepted in IEEE WCNC'22

Compute-forward is a coding technique that enables receiver(s) in a network to directly decode one or more linear combinations of the transmitted codewords. Initial efforts focused on Gaussian channels and derived achievable rate regions via nested lattice codes and single-user (lattice) decoding as well as sequential (lattice) decoding. Recently, these results have been generalized to discrete memoryless channels via nested linear codes and joint typicality coding, culminating in a simultaneous-decoding rate region for recovering one or more linear combinations from $K$ users. Using a discretization approach, this paper translates this result into a simultaneous-decoding rate region for a wide class of continuous memoryless channels, including the important special case of Gaussian channels. Additionally, this paper derives a single, unified expression for both discrete and continuous rate regions via an algebraic generalization of R\'enyi's information dimension., Comment: 86 pages, 7 figures, submitted to IEEE Transactions of Information Theory

A rate splitting based scheme is proposed to operate a broadcast setting with two antennas at the transmit side and two single-antenna receiving terminals. The transmitter knows the magnitude of the channel coefficients, and it is oblivious to the phase information. Each transmit antenna, with a power constraint, sends a private message and a common message to be decoded by both receivers. An achievable rate region is obtained, which enlarges the capacity region of the vector broadcast channel with vector channel magnitude feedback by means of superposition coding., Comment: \c{opyright} 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with "single-user" or sequential decoding can yield better achievable rates. For instance, the compute-forward problem examines the scenario of recovering $L \le K$ linear combinations of transmitted codewords over a $K$-user multiple-access channel (MAC), and it is well established that linear codebooks can yield higher rates. Here, we develop bounds for simultaneous joint typicality decoding used in conjunction with nested linear codebooks, and apply them to obtain a larger achievable region for compute-forward over a $K$-user discrete memoryless MAC. The key technical challenge is that competing codeword tuples that are linearly dependent on the true codeword tuple introduce statistical dependencies, which requires careful partitioning of the associated error events., Comment: 24 pages, 5 figures, submitted to IEEE Transactions on Information Theory

Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear combinations of colliding packets, whenever the decoding of individual packets fails. The resulting linear combinations are then temporarily stored in the hope of gathering enough linearly independent combinations so as to eventually recover all individual packets through the resolution of a linear system at the end of the contention frame. However, it is unclear which among the numerous linear combinations---whose number grows exponentially with the degree of collision---will have low probability of decoding error. Since no analytical framework exists to determine which combinations are easiest to decode, this makes the case for a machine learning algorithm to assist the receiver in deciding which linear combinations to target. For this purpose, we train neural networks that approximate the error probability for every possible linear combination based on the estimated channel gains and demonstrate the effectiveness of our approach by numerical simulations., Comment: to be presented at SPAWC 2018

We consider a setup in which confidential i.i.d. samples $X_1,\dotsc,X_n$ from an unknown finite-support distribution $\boldsymbol{p}$ are passed through $n$ copies of a discrete privatization channel (a.k.a. mechanism) producing outputs $Y_1,\dotsc,Y_n$. The channel law guarantees a local differential privacy of $\epsilon$. Subject to a prescribed privacy level $\epsilon$, the optimal channel should be designed such that an estimate of the source distribution based on the channel outputs $Y_1,\dotsc,Y_n$ converges as fast as possible to the exact value $\boldsymbol{p}$. For this purpose we study the convergence to zero of three distribution distance metrics: $f$-divergence, mean-squared error and total variation. We derive the respective normalized first-order terms of convergence (as $n\to\infty$), which for a given target privacy $\epsilon$ represent a rule-of-thumb factor by which the sample size must be augmented so as to achieve the same estimation accuracy as that of a non-randomizing channel. We formulate the privacy-fidelity trade-off problem as being that of minimizing said first-order term under a privacy constraint $\epsilon$. We further identify a scalar quantity that captures the essence of this trade-off, and prove bounds and data-processing inequalities on this quantity. For some specific instances of the privacy-fidelity trade-off problem, we derive inner and outer bounds on the optimal trade-off curve., Comment: 47 pages, under revision at JMLR

We present a novel closed-form lower bound on the Gaussian-input mutual information for noncoherent communication (i.e., in which neither transmitter nor receiver are cognizant of the fading state) over a frequency-flat fading channel with additive noise. Our bound yields positive (non-trivial) values even in the most challenging case of zero-mean fast fading, a regime in which the conventional approach of orthogonal time-multiplexed pilots is unavailing and for which, to the best of the author's knowledge, no simple analytical bound is known. Its derivation relies on endowing the transmit signal with a non-zero mean, which can be interpreted as a pilot symbol that is additively superimposed onto the information-bearing Gaussian signal. The optimal fraction of transmit power that one should dedicate to this pilot is computed in closed form and shown to tend to one half at low SNR and to a limit above $2-\sqrt{2} \approx 0.586$ at high SNR. We further show how one can refine the bound for the general case of non-zero mean fading. Finally, we state an extension of our bound to the MIMO setting and apply it to compare superimposed vs. orthogonal pilots on the SISO Rayleigh block fading channel., Comment: 5 pages, submitted to ISWCS 2018

The adoption of aggressive frequency reuse schemes along with interference management techniques has become the leading paradigm in satellite communications to increase the spectral efficiency. In general terms, one cannot rely on precoding techniques in the absence of channel phase information. Nevertheless, the availability of channel magnitude information, makes it possible to explore power-based separation of superimposed signals. In this paper, rate splitting (RS) ideas are exploited, whereby the separation of messages into private and public parts serves to improve the performance of successive cancellation decoding (SCD). Numerical results reveal that in some pertinent system scenarios, the proposed schemes achieve a larger rate region than that of orthogonal schemes that do not exploit the interference and other strategies that either do not allow beam cooperation or do not apply RS., Peer Reviewed, Postprint (published version)

We present a practical strategy that aims to attain rate points on the dominant face of the multiple access channel capacity using a standard low complexity decoder. This technique is built upon recent theoretical developments of Zhu and Gastpar on compute-forward multiple access (CFMA) which achieves the capacity of the multiple access channel using a sequential decoder. We illustrate this strategy with off-the-shelf LDPC codes. In the first stage of decoding, the receiver first recovers a linear combination of the transmitted codewords using the sum-product algorithm (SPA). In the second stage, by using the recovered sum-of-codewords as side information, the receiver recovers one of the two codewords using a modified SPA, ultimately recovering both codewords. The main benefit of recovering the sum-of-codewords instead of the codeword itself is that it allows to attain points on the dominant face of the multiple access channel capacity without the need of rate-splitting or time sharing while maintaining a low complexity in the order of a standard point-to-point decoder. This property is also shown to be crucial for some applications, e.g., interference channels. For all the simulations with single-layer binary codes, our proposed practical strategy is shown to be within \SI{1.7}{\decibel} of the theoretical limits, without explicit optimization on the off-the-self LDPC codes., Comment: 30 pages, 14 figures, submitted to the IEEE Transactions on Wireless Communications

Most performance measures of pilot-assisted multiple-input multiple-output systems are functions of the linear precoder and the pilot sequence. A framework for the optimization of these two parameters is proposed, based on a matrix-valued generalization of the concept of effective signal-to-noise ratio (SNR) introduced in the famous work by Hassibi and Hochwald. Our framework aims to extend the work of Hassibi and Hochwald by allowing for transmit-side fading correlations, and by considering a class of utility functions of said effective SNR matrix, most notably including the well-known capacity lower bound used by Hassibi and Hochwald. We tackle the joint optimization problem by recasting the optimization of the precoder (resp. pilot sequence) subject to a fixed pilot sequence (resp. precoder) into a convex problem. Furthermore, we prove that joint optimality requires that the eigenbases of the precoder and pilot sequence be both aligned along the eigenbasis of the channel correlation matrix. We finally describe how to wrap all studied subproblems into an iteration that converges to a local optimum of the joint optimization., Peer Reviewed, Postprint (author's final draft)

This paper presents a joint typicality framework for encoding and decoding nested linear codes for multi-user networks. This framework provides a new perspective on compute-forward within the context of discrete memoryless networks. In particular, it establishes an achievable rate region for computing the weighted sum of nested linear codewords over a discrete memoryless multiple-access channel (MAC). When specialized to the Gaussian MAC, this rate region recovers and improves upon the lattice-based compute-forward rate region of Nazer and Gastpar, thus providing a unified approach for discrete memoryless and Gaussian networks. Furthermore, this framework can be used to shed light on the joint decoding rate region for compute-forward, which is considered an open problem. Specifically, this work establishes an achievable rate region for simultaneously decoding two linear combinations of nested linear codewords from K senders., Comment: 69 pages, 11 figures, submitted to the IEEE Transactions on Information Theory

In this paper, the operation of a Licensed Shared Access (LSA) system is investigated, considering downlink communication. The system comprises of a Multiple-Input-Single-Output (MISO) incumbent transmitter (TX) - receiver (RX) pair, which offers a spectrum sharing opportunity to a MISO licensee TX-RX pair. Our main contribution is the design of a coordinated transmission scheme, inspired by the underlay Cognitive Radio (CR) approach, with the aim of maximizing the average rate of the licensee, subject to an average rate constraint for the incumbent. In contrast to most prior works on underlay CR, the coordination of the two TXs takes place under a realistic Channel State Information (CSI) scenario, where each TX has sole access to the instantaneous direct channel of its served terminal. Such a CSI knowledge setting brings about a formulation based on the theory of Team Decisions, whereby the TXs aim at optimizing a common objective given the same constraint set, on the basis of individual channel information. Consequently, a novel set of applicable precoding schemes is proposed. Relying on statistical coordination criteria, the two TXs cooperate in the lack of any instantaneous CSI exchange. We verify by simulations that our novel coordinated precoding scheme outperforms the standard underlay CR approach.

As shown by Medard, the capacity of fading channels with imperfect channel-state information (CSI) can be lowerbounded by assuming a Gaussian channel input and by treating the unknown portion of the channel multiplied by the channel input as independent worst-case (Gaussian) noise. Recently, we have demonstrated that this lower bound can be sharpened by a rate-splitting approach: by expressing the channel input as the sum of two independent Gaussian random variables (referred to as layers), say X = X1+X2, and by applying M´edard’s bounding technique to first lower-bound the capacity of the virtual channel from X1 to the channel output Y (while treating X2 as noise), and then lower-bound the capacity of the virtual channel from X2 to Y (while assuming X1 to be known), one obtains a lower bound that is strictly larger than M´edard’s bound. This ratesplitting approach is reminiscent of an approach used by Rimoldi and Urbanke to achieve points on the capacity region of the Gaussian multiple-access channel (MAC). Here we blend these two rate-splitting approaches to derive a novel inner bound on the capacity region of the memoryless fading MAC with imperfect CSI. Generalizing the above rate-splitting approach to more than two layers, we show that, irrespective of how we assign powers to each layer, the supremum of all rate-splitting bounds is approached as the number of layers tends to infinity, and we derive an integral expression for this supremum. We further derive an expression for the vertices of the best inner bound, maximized over the number of layers and over all power assignments., Peer Reviewed, Postprint (published version)

As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input X with power P and by upper-bounding the conditional entropy h(X|Y,H) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from \(Y, 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 X1 and X2 and by applying Médard's lower bound first to bound the mutual information between X1 and Y while treating X2 as noise, and by applying it a second time to the mutual information between X2 and Y while assuming X1 to be known, we obtain a capacity lower bound that is strictly larger than Médard'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 Pl, l = 1, ¿ ,L summing up to P. Among all such rate-splitting bounds, we determine the supremum over power allocations Pl and total number of layers L. This supremum is achieved for L 8 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-H tends to zero as the SNR tends to infinity., Peer Reviewed, Postprint (published version)

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 a, 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 cote, Postprint (published version)

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 reviews

For the vector broadcast channel (BC), the case of erroneous channel state information (CSI) at the receiver is considered. Employing a well established lower bound for the mutual information with Gaussian signaling, a rate balancing problem is formulated where the rates of the different users are maximized under a transmit power constraint, but the rates of the different users have fixed ratios. A duality w.r.t. the signal-to-interference-and-noise ratio (SINR) between the vector BC with erroneous receiver CSI and an appropriately constructed vector multiple access channel (MAC) is established. Based on the observation that an interference function can be defined in the dual vector MAC that is standard, an iterative algorithm can be found for an appropriately formulated quality-of-service (QoS) optimization that is used for solving the balancing problem., Peer Reviewed, Postprint (published version)

Most performance measures of pilot-assisted multiple-input multiple-output (MIMO) systems are functions that depend on both the linear precoding filter and the pilot sequence. A framework for the optimization of these two parameters is proposed, based on a matrix-valued generalization of the concept of effective signal-to-noise ratio (SNR) introduced in a famous work by Hassibi and Hochwald. The framework applies to a wide class of utility functions of said effective SNR matrix, most notably a well-known mutual information expression for Gaussian inputs, an upper bound on the minimum mean-square error (MMSE), as well as approximations thereof. The approach consists in decomposing the joint optimization problem into three subproblems: first, we describe how to reformulate the optimization of the linear precoder subject to a fixed pilot sequence as a convex problem. Second, we do likewise for the optimization of the pilot sequence subject to a fixed precoder. Third, we describe how to generate pairs of precoders and pilot sequences that are Pareto optimal in the sense that they attain the Pareto boundary of the set of feasible effective SNR matrices. By combining these three optimization problems into an iteration, we obtain an algorithm which allows to compute jointly optimal pairs of precoders and pilot sequences with respect to some generic utility function of the effective SNR., Comment: 32 pages, 9 figures, submitted to IEEE Transactions on Information Theory

As shown by Medard (“The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel,” IEEE Trans. Inform. Theory, May 2000), the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by assuming a Gaussian channel input X, and by upper-bounding the conditional entropy h(XY, Ĥ), conditioned on the channel output Y and the CSI Ĥ, by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from (Y, Ĥ). We demonstrate that, by using a rate-splitting approach, this lower bound can be sharpened: we show that by expressing the Gaussian input X as as the sum of two independent Gaussian variables X(1) and X(2), and by applying Medard's lower bound first to analyze the mutual information between X(1) and Y conditioned on Ĥ while treating X(2) as noise, and by applying the lower bound then to analyze the mutual information between X(2) and Y conditioned on (X(1), Ĥ), we obtain a lower bound on the capacity that is larger than Medard's lower bound., Peer Reviewed, Postprint (published version)

We study the maximization of an achievable ergodic rate expression of a multiple-input single-output (MISO) channel where both ends are cognizant of the same erroneous estimate of the current fading state, yet they have complete knowledge of channel statistics. A training procedure estimates each channel state by means of dedicated pilot symbols whose sum energy is fixed, while for data transmission a fixed average energy per channel access (i.e., average power) is available. The optimization consists, on one hand, in finding the optimal beamforming strategy and temporal power control policy, and on the other hand, in optimally constructing the pilot sequence according to the channel's correlation structure., Peer Reviewed, Postprint (published version)

In this paper, we study the balancing of egoistic (maximum-ratio, MR) and altruistic (zero-forcing, ZF) beamforming (BF) in femtocells through simulations. To investigate the achievable gains from operating between the extremes (egoism/altruism) we analyze the performance of beamformers constructed as linear combinations of the MR and ZF beamformers in case of equal gain transmission. We find that significant gains can be achieved if each femto access point (FAP) has knowledge of the preferred MR and ZF beamforming vectors and can choose its strategy accordingly. We also show that the optimality of any such strategy is strongly influenced by the applied criteria (sum rate maximization, fairness etc.)., Peer Reviewed, Postprint (published version)

For single-user, multiple-input multiple-output (MIMO) channels with Rayleigh fading correlated at the transmitter side, and where the receiver only has partial channel knowledge in form of an MMSE channel estimate, we study the joint optimization of the linear precoder and the pilot (training) sequence under the constraint of prescribed transmit power and training energy budgets. Although this joint problem is generally not convex itself, we can show that the two marginal problems of optimizing either the pilot sequence or the precoder when the other variable is fixed, are convex. Furthermore, we characterize the jointly optimal transmit and training directions. Finally, we propose a full characterization of the Pareto efficient joint power loading strategies for the case of two transmit antennas, and illustrate the behavior of the jointly optimal solution., Peer Reviewed, Postprint (published version)

This document looks into coordinated radio resource allocation algorithms in deployments of huge number of femto-access points (FAP) by exploiting the message exchange at control-plane level through the wired ISP backhaul link., This document looks into coordinated radio resource allocation algorithms in deployments of huge number of femto-access points (FAP) by exploiting the message exchange at control-plane level through the wired ISP backhaul link. The algorithms present in this document are based on decentralized cooperative strategies supported by Game Theory. Decentralized resource allocation algorithms based on price exchange have been derived under different criteria: guaranteeing a minimum rate with the minimum power, maximizing the weighted sum-rate of the system, maximizing the opportunistic throughput when there are different source of randomness like random link failures and noise quantization or when the activity of macro-users is not known by FAPs (coordinated channel sensing or modelling the activity). Additionally, a genetic-based resource allocation is investigated, providing centralized and decentralized algorithms, to which the Game Theory solutions are challenged . In all cases, the techniques derived require modifications of the current LTE-A standard which are identified. Finally, some of those algorithms have been evaluated in a realistic corporate scenario elucidating the advantages of coordinated resource allocation techniques proposed., Preprint

For single-user MIMO channels with partial re ceiver CSI, we study the difference between a lower bound and two alternative upper bounds of the mutual information achieved with Gaussian codebooks. These differences are termed bound gaps ¿ and d, respectively. The latter may serve to derive a capacity bound gap. In contrast to previous studies, we assume that the channel estimation error statistics are not given a priori, but depend on the parameters of a training routine, in which a pilot sequence is transmitted, and where the channel realization is linearly estimated. Under these conditions, we successively determine analytic upper and lower bounds on the mutual information bound gap ¿. We further study the asymptotic behavior of said bound gaps for high SNR and a large number of antennas. This allows us to prove, for example, that for MISO channels and a certain class of semicorrelated MIMO channels, when the training and transmit power levels are equal, the capacity is approached to within min(NT, NR) bits by the capacity bounds, where NT and NR stand for the number of transmit and receive antennas, respectively., Peer Reviewed, Postprint (published version)