On the MISO Channel with Feedback: Can Infinitely Massive Antennas Achieve Infinite Capacity?

We consider communication over a multiple-input single-output (MISO) block fading channel in the presence of an independent noiseless feedback link. We assume that the transmitter and receiver have no prior knowledge of the channel state realizations, but the transmitter and receiver can acquire the channel state information (CSIT/CSIR) via downlink training and feedback. For this channel, we show that increasing the number of transmit antennas to infinity will not achieve an infinite capacity, for a finite channel coherence length and a finite input constraint on the second or fourth moment. This insight follows from our new capacity bounds that hold for any linear and nonlinear coding strategies, and any channel training schemes. In addition to the channel capacity bounds, we also provide a characterization on the beamforming gain that is also known as array gain or power gain, at the regime with a large number of antennas.Comment: This work has been submitted to the IEEE Transactions on Information Theory. It was presented in part at ISIT201

Lens antenna arrays: an efficient framework for sparse-aware large-MIMO communications

The recent increase in the demand for higher data transmission rates in wireless communications has entailed many implementation issues that can only be resolved by going through a full paradigm shift. Making use of the millimetric spectrum bands is a very attractive solution to the shortage of radio resources but, to garner all their potential, new techniques must be developed. Most of them are contained in the Massive Multiple Input Multiple Output (M-MIMO) framework: the idea of using very large antenna arrays for cellular communications. In this thesis, we propose the usage of Lens Antenna Arrays (LAA) to avoid the unbearable power and infrastructure costs posed by traditional M-MIMO architectures. This novel communication system exploits the angular-dependent power focusing capabilities of an electromagnetic lens to discern between waves with different angles of arrival and departure, without explicit signal processing. The work presented in this document motivates the use of LAAs in mmWave communications, studies some of their mathematical properties and proposes their application in noncoherent schemes. Numerical results validate the performance of this novel kind of systems and confirm their strengths in both multi-user and block fading settings. LAAs that use noncoherent methods appear to be very suitable for vehicular communications and densely populated cellular networks.En los últimos tiempos, el incremento en la demanda de mayor velocidad de transmisión de datos en redes de comunicación inalámbricas ha conllevado varios problemas de implementación que solo se podrán resolver a través de un cambio total de paradigma. Utilizar bandas milimétricas del espectro es una solución muy atractiva a la escasez de recursos de radio pero, para poder extraer todo su potencial, es necesario desarrollar nuevas técnicas. La mayor parte de éstas pasa por la infraestructura Massive Multiple Input Multiple Output (M-MIMO): la idea de usar matrices de antenas muy grandes para comunicaciones celulares. En esta tesis, proponemos el uso de matrices de antenas con lente, o Lens Antenna Arrays (LAA), para evitar los inasumibles costes energéticos y de instalación propios de las arquitecturas M-MIMO tradicionales. Este novedoso sistema de comunicaciones explota las capacidades de concentración de energía con dependencia angular de las lentes electromagnéticas para distinguir entre ondas con distintas direcciones de llegada y de salida, sin procesado de la señal explícito. El trabajo presentado en este documento motiva el uso de los LAAs en comunicaciones en bandas milimétricas (mmWave), estudia varias propiedades matemáticas y propone su aplicación en esquemas no coherentes. Resultados numéricos validan su ejecución y confirman sus fortalezas en entornos multiusuario y con desvanecimiento en bloque. Los LAAs que utilizan métodos no coherentes parecen ser idóneos para comunicaciones vehiculares y para redes celulares altamente pobladas.En els darrers temps, l'increment en la demanda de major velocitat de transmissió de dades en xarxes de comunicació inalàmbriques ha comportat diversos problemes d'implementació que tan sols es podran resoldre a través d'un canvi total de paradigma. Utilitzar les bandes mil·limètriques de l'espectre és una solució molt atractiva a l'escassetat de recursos de ràdio però, per tal d'extreure'n tot el seu potencial, és necessari desenvolupar noves tècniques. La majoria d'aquestes passa per la infraestructura Massive Multiple Input Multiple Output (M-MIMO): la idea d'utilitzar matrius d'antenes molt grans per a comunicacions cel·lulars. En aquesta tesi, proposem l'ús de matrius d'antenes amb lent, o Lens Antenna Arrays (LAA), per tal d'evitar els inassumibles costos energètics i d'instal·lació propis d'arquitectures M-MIMO tradicionals. Aquest innovador sistema de comunicacions explota les capacitats de concentració d'energia amb dependència angular de les lents electromagnètiques per tal de distingir entre ones amb diferents direccions d'arribada i de sortida, sense processament de senyal explícit. El treball presentat en aquest document motiva l'ús dels LAAs per comunicacions en bandes mil·limètriques (mmWave), n'estudia diverses propietats matemàtiques i proposa la seva aplicació en esquemes no coherents. Resultats numèrics en validen l'execució i confirmen les seves fortaleses en entorns multi-usuari i amb esvaïment en bloc. Els LAAs que utilitzen mètodes no coherents semblen ser idonis per a comunicacions vehiculars i per a xarxes cel·lulars altament poblades

Dynamic Interference Mitigation for Generalized Partially Connected Quasi-static MIMO Interference Channel

Recent works on MIMO interference channels have shown that interference alignment can significantly increase the achievable degrees of freedom (DoF) of the network. However, most of these works have assumed a fully connected interference graph. In this paper, we investigate how the partial connectivity can be exploited to enhance system performance in MIMO interference networks. We propose a novel interference mitigation scheme which introduces constraints for the signal subspaces of the precoders and decorrelators to mitigate "many" interference nulling constraints at a cost of "little" freedoms in precoder and decorrelator design so as to extend the feasibility region of the interference alignment scheme. Our analysis shows that the proposed algorithm can significantly increase system DoF in symmetric partially connected MIMO interference networks. We also compare the performance of the proposed scheme with various baselines and show via simulations that the proposed algorithms could achieve significant gain in the system performance of randomly connected interference networks.Comment: 30 pages, 10 figures, accepted by IEEE Transaction on Signal Processin

Capacity limits of bursty interference channels

Mención Internacional en el título de doctorThis dissertation studies the effects of interference burstiness in the transmission of data in wireless networks. In particular, we investigate the effects of this phenomenon on the largest data rate at which one can communicate with a vanishing small probability of error, i.e., on channel capacity. Specifically, we study the capacity of two different channel models as described in the next sections. Linear deterministic bursty interference channel. First, we consider a two-user linear deterministic bursty interference channel (IC), where the presence or absence of interference is modeled by a block- independent and identically distributed (IID) Bernoulli process that stays constant for a duration of T consecutive symbols (this is sometimes referred to as a coherence block) and then changes independently to a new interference state. We assume that the channel coefficients of the communication and interference links remain constant during the whole message transmission. For this channel, we consider both its quasi-static setup where the interference state remains constant during the whole transmission of the codeword (which corresponds to the case whether the blocklength N is smaller than T) and its ergodic setup where a codeword spans several coherence blocks. For the quasi-static setup, we follow the seminal works by Khude, Prabhakaran and Viswanath and study the largest sum rate of a coding strategy that provides reliable communication at a basic (or worstcase) rate R and allows an increased (opportunistic) rate ΔR in absence of interference. For the ergodic scenario, we study the largest achievable sum rate as commonly considered in the multi-user information theory literature. We study how (noncausal) knowledge of the interference state, referred to as channel state information (CSI), affects the sum capacity. Specifically, for both scenarios, we derive converse and achievability bounds on the sum capacity for (i) local CSI at the receiverside only; (ii) when each transmitter and receiver has local CSI, and (iii) global CSI at all nodes, assuming both that interference states are independent of each other and that they are fully correlated. Our bounds allow us to identify regions and conditions where interference burstiness is beneficial and in which scenarios global CSI improves upon local CSI. Specifically, we show the following: • Exploiting burstiness: For the quasi-static scenario we have shown that in presence of local CSI, burstiness is only beneficial if the interference region is very weak or weak. In contrast, for global CSI, burstiness is beneficial for all interference regions, except the very strong interference region, where the sum capacity corresponds to that of two parallel channels without interference. For the ergodic scenario, we have shown that, under global CSI, burstiness is beneficial for all interference regions and all possible values of p. For local CSI at the receiver-side only, burstiness is beneficial for all values of p and for very weak and weak interference regions. However, for moderate and strong interference regions, burstiness is only of clear benefit if the interference is present at most half of the time. • Exploiting CSI: For the quasi-static scenario, local CSI at the transmitter is not beneficial. This is in stark contrast to the ergodic scenario, where local CSI at the transmitter-side is beneficial. Intuitively, in the ergodic scenario the input distributions depend on the realizations of the interference states. Hence, adapting the input distributions to these realizations increases the sum capacity. In contrast, in the quasi-static case, the worst-case scenario (presence of interference) and the best-case scenario (absence of interference) are treated separately. Hence, there is no difference to the case of having local CSI only at the receiver side. Featuring global CSI at all nodes yields an increased sum rate for both the quasi-static and the ergodic scenarios. The joint treatment of the quasi-static and the ergodic scenarios allows us to thoroughly compare the sum capacities of these two scenarios. While the converse bounds for the quasi-static scenario and local CSI at the receiver-side appeared before in the literature, we present a novel proof based on an information density approach and the Verd´u-Han lemma. This approach does not only allow for rigorous yet clear proofs, it also enables more refined analyses of the probabilities of error that worst-case and opportunistic messages can be decoded correctly. For the converse bounds in the ergodic scenario, we use Fano’s inequality as the standard approach to derive converse bounds in the multi-user information theory literature. Bursty noncoherent wireless networks. The linear deterministic model can be viewed as a rough approximation of a fading channel, which has additive and multiplicative noise. The multiplicative noise is referred to as fading. As we have seen in the previous section, the linear deterministic model provides a rough understanding of the effects of interference burstiness on the capacity of the two-user IC. Now, we extend our analysis to a wireless network with a very large number of users and we do not approximate the fading channel by a linear deterministic model. That is, we consider a memoryless flat-fading channel with an infinite number of interferers. We incorporate interference burstiness by an IID Bernoulli process that stays constant during the whole transmission of the codeword. The channel capacity of wireless networks is often studied under the assumption that the communicating nodes have perfect knowledge of the fading coefficients in the network. However, it is prima-facie unclear whether this perfect knowledge of the channel coefficients can actually be obtained in practical systems. For this reason, we study in this dissertation the channel capacity of a noncoherent model where the nodes do not have perfect knowledge of the fading coefficients. More precisely, we assume that the nodes know only the statistics of the channel coefficients but not their realizations. We further assume that the interference state (modeling interference burstiness) is known non-causally at the receiver-side only. To the best of our knowledge, one of the few works that studies the capacity of noncoherent wireless networks (without considering interference burstiness) is by Lozano, Heath, and Andrews. Inter alia, Lozano et al. show that in the absence of perfect knowledge of the channel coefficients, if the channel inputs are given by the square-root of the transmit power times a power-independent random variable, and if interference is always present (hence, it is non-bursty), then the achievable information rate is bounded in the signal-to-noise ratio (SNR). However, the considered inputs do not necessarily achieve capacity, so one may argue that the information rate is bounded in the SNR because of the suboptimal input distribution. Therefore, in our analysis, we allow the input distribution to change arbitrarily with the SNR. We analyze the asymptotic behavior of the channel capacity in the limit as the SNR tends to infinity. We assume that all nodes (transmitting and interfering) use the same codebook. This implies that each node is transmitting at the same rate, while at the same time it keeps the analysis tractable. We demonstrate that if the nodes do not cooperate and if the variances of the path gains decay exponentially or slower, then the achievable information rate remains bounded in the SNR, even if the input distribution is allowed to change arbitrarily with the transmit power, irrespective of the interference burstiness. Specifically, for this channel, we show the following: • The channel capacity is bounded in the SNR. This suggests that noncoherent wireless networks are extremely power inefficient at high SNR. • Our bound further shows that interference burstiness does not change the behavior of channel capacity. While our upper bound on the channel capacity grows as the channel becomes more bursty, it remains bounded in the SNR. Thus, interference burstiness cannot be exploited to mitigate the power inefficiency at high SNR. Possible strategies that could mitigate the power inefficiency of noncoherent wireless networks and that have not been explored in this thesis are cooperation between users and improved channel estimation strategies. Indeed, coherent wireless networks, in which users have perfect knowledge of the fading coefficients, have a capacity that grows to infinity with the SNR. Furthermore, for such networks, the most efficient transmission strategies, such as interference alignment, rely on cooperation. Our results suggest that these two strategies may be essential to obtain an unbounded capacity in the SNR.Programa Oficial de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Ignacio Santamaría Caballero.- Secretario: David Ramírez García, David.- Vocal: Paul de Kerre

Mitigation techniques through spatial diversity combining and relay-assisted technology in a turbulence impaired and misaligned free space optical channel.

Doctor of Philosophy in Electronic Engineering. University of KwaZulu-Natal, Durban, 2018.In recent times, spectrum resource scarcity in Radio Frequency (RF) systems is one of the biggest and prime issues in the area of wireless communications. Owing to the cost of spectrum, increase in the bandwidth allocation as alternative solution, employed in the recent past, does no longer offer an effective means to fulfilling high demand in higher data rates. Consequently, Free Space Optical (FSO) communication systems has received considerable attention in the research community as an attractive means among other popular solutions to offering high bandwidth and high capacity compared to conventional RF systems. In addition, FSO systems have positive features which include license-free operation, cheap and ease of deployment, immunity to interference, high security, etc. Thus, FSO systems have been favoured in many areas especially, as a viable solution for the last-mile connectivity problem and a potential candidate for heterogeneous wireless backhaul network. With these attractive features, however, FSO systems are weather-dependent wireless channels. Therefore, it is usually susceptible to atmospheric induced turbulence, pointing error and attenuation under adverse weather conditions which impose severe challenges on the system performance and transmission reliability. Thus, before widespread deployment of the system will be possible, promising mitigation techniques need to be found to address these problems. In this thesis, the performance of spatial diversity combining and relay-assisted techniques with Spatial Modulation (SM) as viable mitigating tools to overcome the problem of atmospheric channel impairments along the FSO communication system link is studied. Firstly, the performance analysis of a heterodyne FSO-SM system with different diversity combiners such as Maximum Ratio Combining (MRC), Equal Gain Combining (EGC) and Selection Combining (SC) under the influence of lognormal and Gamma-Gamma atmospheric-induced turbulence fading is presented. A theoretical framework for the system error is provided by deriving the Average Pairwise Error Probability (APEP) expression for each diversity scheme under study and union bounding technique is applied to obtain their Average Bit Error Rate (ABER). Under the influence of Gamma-Gamma turbulence, an APEP expression is obtained through a generalized infinite power series expansion approach and the system performance is further enhanced by convolutional coding technique. Furthermore, the performance of proposed system under the combined effect of misalignment and Gamma-Gamma turbulence fading is also studied using the same mathematical approach. Moreover, the performance analysis of relay-assisted dual-hop heterodyne FSO-SM system with diversity combiners over a Gamma-Gamma atmospheric turbulence channel using Decode-and-Forward (DF) relay and Amplify-and-Forward (AF) relay protocols also is presented. Under DF dual-hop FSO system, power series expansion of the modified Bessel function is used to derive the closed-form expression for the end-to-end APEP expressions for each of the combiners under study over Gamma-Gamma channel, and a tight upper bound on the ABER per hop is given. Thus, the overall end-to-end ABER for the dual-hop FSO system is then evaluated. Under AF dual-hop FSO system, the statistical characteristics of AF relay in terms of Moment Generating Function (MGF), Probability Density Function (PDF) and Cumulative Distribution Function (CDF) are derived for the combined Gamma-Gamma turbulence and/or pointing error distributions channel in terms of Meijer-G function. Based on these expressions, the APEP for each of the under studied combiners is determined and the ABER for the system is given by using union bounding technique. By utilizing the derived ABER expressions, the effective capacity for the considered system is then obtained. Furthermore, the performance of a dual-hop heterodyne FSO-SM asymmetric RF/FSO relaying system with MRC as mitigation tools at the destination is evaluated. The RF link experiences Nakagami-m distribution and FSO link is subjected to Gamma-Gamma distribution with and/or without pointing error. The MGF of the system equivalent SNR is derived using the CDF of the system equivalent SNR. Utilizing the MGF, the APEP for the system is then obtained and the ABER for the system is determined. Finally, owing to the slow nature of the FSO channel, the Block Error Rate (BLER) performance of FSO Subcarrier Intensity Modulation (SIM) system with spatial diversity combiners employing Binary Phase Shift Keying (BPSK) modulation over Gamma-Gamma atmospheric turbulence with and without pointing error is studied. The channel PDF for MRC and EGC by using power series expansion of the modified Bessel function is derived. Through this, the BLER closed-form expressions for the combiners under study are obtained