This dissertation demonstrates how the Weltanschauung found in Álvaro Mutis´s oeuvre is profoundly influenced by a late romantic conscience found in the Latin American posvanguardia generation (1920 – 1940). Melancholy –as late modern affective condition- and fading of the subject –as narrative and aesthetic imaginary- are two central figures in his fictional universe. As a consequence of this, some of the heroes and topics in Mutis’s oeuvre are in dialogue with the main topics of the first literary movement in Hispanic America, Modernism. Some of them are: a religious ambiance in their prose, hedonism, cosmopolitanism, decadentism, Latin American landscape as entropy and a fractured self. There is a narrative logic in the literary corpus analyzed –which one can extend to Mutis’ s oeuvre. The hero, before starting his adventure, begins a psychological phenomenology called “fading of the subject”, which is a symbolic process that affects not only his stability as a hero but also the enterprise to which he is committed; all this thanks to his “melancholic condition”. This emotional process begins by revealing poetic images of internal destruction, amalgamation and death, which the hero transfers to the external world. In some of the texts analyzed this process concludes by producing death and devastation (El Húsar, La muerte del estratega), in others there is an urgent need to a symbolic resignification (Amirbar) that allows the hero to survive and start a new adventure. This “spiritual condition” is something Maqroll - Mutis’ main character- knows well when someone asks him about his precarious physical condition, “The tropical fevers...I have them already!” (Amirbar 491)

Wireless Networks have been the topic of fundamental research in recent years with the aim of achieving reliable and efficient communications. However, due to their complexity, there are still many aspects of such configurations that remain as open problems. The focus of this thesis is to investigate some throughput limits of wireless networks. The network under consideration consists of $n$ source-destination pairs (links) operating in a single-hop fashion. In Chapters 2 and 3, it is assumed that each link can be active and transmit with a constant power P or remain silent. Also, fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. The objective is to choose a set of active links such that the throughput is maximized, where the rate of active links are either unconstrained or constrained. For the unconstrained throughput maximization, by deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading: (i) the maximum throughput scales like $\log n$, (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a threshold-based link activation strategy (TBLAS) is proposed and analyzed. The achieved throughput of TBLAS is by a factor of four larger than what was obtained in previous works with centralized methods and with multihop communications. When the active links are constrained to transmit with a constant rate $\lambda$, an upper bound is derived that shows the number of active links scales at most like $\frac{1}{\lambda} \log n$. It is proved that TBLAS \emph{asymptotically almost surely(a.a.s.)} yields a feasible solution for the constrained throughput maximization problem. This solution, which is suboptimal in general, performs close to the upper bound for small values of $\lambda$. To improve the suboptimal solution, a double-threshold-based link activation strategy (DTBLAS) is proposed and analyzed based on some results from random graph theory. It is demonstrated that DTBLAS performs very close to the optimum. Specifically, DTBLAS is a.a.s. optimum when $\lambda$ approaches $\infty$ or $0$. The optimality results are obtained in an interference-limited regime. However, it is shown that, by proper selection of the algorithm parameters, DTBLAS also allows the network to operate in a noise-limited regime in which the transmission rates can be adjusted by the transmission powers. The price for this flexibility is a decrease in the throughput scaling law by a factor of $\log \log n$. In Chapter 4, the problem of throughput maximization by means of power allocation is considered. It is demonstrated that under individual power constraints, in the optimum solution, the power of at least one link should take its maximum value. Then, for the special case of $n=2$ links, it is shown that the optimum power allocation strategy for throughput maximization is such that either both links use their maximum power or one of them uses its maximum power and the other keeps silent.

This thesis contributes toward understanding fundamental limits of multi-user fading channels and random wireless networks. Specifically, considering different samples of channel gains corresponding to different users/nodes in a multi-user wireless system, the maximum number of channel gains supporting a minimum rate is asymptotically obtained. First, the user capacity of fading multi-user channels with minimum rates is analyzed. Three commonly used fading models, namely, Rayleigh, Rician and Nakagami are considered. For broadcast channels, a power allocation scheme is proposed to maximize the number of active receivers, for each of which, a minimum rate Rmin>0 can be achieved. Under the assumption of independent Rayleigh fading channels for different receivers, as the total number of receivers n goes to infinity, the maximum number of active receivers is shown to be arbitrarily close to ln(P.ln(n))/Rmin with probability approaching one, where P is the total transmit power. The results obtained for Rayleigh fading are extended to the cases of Rician and Nakagami fading models. Under the assumption of independent Rician fading channels for different receivers, as the total number of receivers n goes to infinity, the maximum number of active receivers is shown to be equal to ln(2P.ln(n))/Rmin with probability approaching one. For broadcast channels with Nakagami fading, the maximum number of active receivers is shown to be equal to ln(ω/μ.P.ln(n))/Rmin with probability approaching one, where ω and μ are the Nakagami distribution parameters. A by-product of the results is to also provide a power allocation strategy that maximizes the total throughput subject to the rate constraints. In multiple-access channels, the maximum number of simultaneous active transmitters (i.e. user capacity) is obtained in the many user case in which a minimum rate must be maintained for all active users. The results are presented in the form of scaling laws as the number of transmitters increases. It is shown that for all three fading distributions, the user capacity scales double logarithmically in the number of users and differs only by constants depending on the distributions. We also show that a scheduling policy that maximizes the number of simultaneous active transmitters can be implemented in a distributed fashion. Second, the maximum number of active links supporting a minimum rate is asymptotically obtained in a wireless network with an arbitrary topology. It is assumed that each source-destination pair communicates through a fading channel and destinations receive interference from all other active sources. Two scenarios are considered: 1) Small networks with multi-path fading, 2) Large Random networks with multi-path fading and path loss. In the first case, under the assumption of independent Rayleigh fading channels for different source-destination pairs, it is shown that the optimal number of active links is of the order log(N) with probability approaching one as the total number of nodes, N, tends to infinity. The achievable total throughput also scales logarithmically with the total number of links/nodes in the network. In the second case, a two-dimensional large wireless network is considered and it is assumed that nodes are Poisson distributed with a finite intensity. Under the assumption of independent multi-path fading for different source-destination pairs, it is shown that the optimal number of active links is of the order N with probability approaching one. As a result, the achievable per-node throughput obtained by multi-hop routing scales with Θ(1/√N).

The objective of this diploma work is to investigate a set of Multiple Input Multiple Output (MIMO) channel models compatible with the emerging IEEE 802.11n standard. This diploma work validates also advanced, innovative tools and wireless technologies that are necessary to facilitate wireless applications while maximizing spectral efficiency and throughput. MIMO channel models can be used to evaluate new Wireless Local Area Network (WLAN) proposals based on multiple antenna technologies. The purpose of this thesis is to investigate means of channel models and their implementation in different environments such as: Matlab, C++ and Advanced Design Systems (ADS). The investigation considers also a comparison between the channel models based on theoretical data and parameter setup to the channel models based on statistical characteristics obtained from measured data. Investigation and comparison of a MIMO channel models consider steering channel matrix H, spatial correlation coefficients, power delay profiles, fading characteristics and Doppler power spectrum.

Wireless Networks have been the topic of fundamental research in recent years with the aim of achieving reliable and efficient communications. However, due to their complexity, there are still many aspects of such configurations that remain as open problems. The focus of this thesis is to investigate some throughput limits of wireless networks. The network under consideration consists of $n$ source-destination pairs (links) operating in a single-hop fashion. In Chapters 2 and 3, it is assumed that each link can be active and transmit with a constant power P or remain silent. Also, fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. The objective is to choose a set of active links such that the throughput is maximized, where the rate of active links are either unconstrained or constrained. For the unconstrained throughput maximization, by deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading: (i) the maximum throughput scales like $\log n$, (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a threshold-based link activation strategy (TBLAS) is proposed and analyzed. The achieved throughput of TBLAS is by a factor of four larger than what was obtained in previous works with centralized methods and with multihop communications. When the active links are constrained to transmit with a constant rate $\lambda$, an upper bound is derived that shows the number of active links scales at most like $\frac{1}{\lambda} \log n$. It is proved that TBLAS \emph{asymptotically almost surely(a.a.s.)} yields a feasible solution for the constrained throughput maximization problem. This solution, which is suboptimal in general, performs close to the upper bound for small values of $\lambda$. To improve the suboptimal solution, a double-threshold-based link activation strategy (DTBLAS) is proposed and analyzed based on some results from random graph theory. It is demonstrated that DTBLAS performs very close to the optimum. Specifically, DTBLAS is a.a.s. optimum when $\lambda$ approaches $\infty$ or $0$. The optimality results are obtained in an interference-limited regime. However, it is shown that, by proper selection of the algorithm parameters, DTBLAS also allows the network to operate in a noise-limited regime in which the transmission rates can be adjusted by the transmission powers. The price for this flexibility is a decrease in the throughput scaling law by a factor of $\log \log n$. In Chapter 4, the problem of throughput maximization by means of power allocation is considered. It is demonstrated that under individual power constraints, in the optimum solution, the power of at least one link should take its maximum value. Then, for the special case of $n=2$ links, it is shown that the optimum power allocation strategy for throughput maximization is such that either both links use their maximum power or one of them uses its maximum power and the other keeps silent.

This thesis contributes toward understanding fundamental limits of multi-user fading channels and random wireless networks. Specifically, considering different samples of channel gains corresponding to different users/nodes in a multi-user wireless system, the maximum number of channel gains supporting a minimum rate is asymptotically obtained. First, the user capacity of fading multi-user channels with minimum rates is analyzed. Three commonly used fading models, namely, Rayleigh, Rician and Nakagami are considered. For broadcast channels, a power allocation scheme is proposed to maximize the number of active receivers, for each of which, a minimum rate Rmin>0 can be achieved. Under the assumption of independent Rayleigh fading channels for different receivers, as the total number of receivers n goes to infinity, the maximum number of active receivers is shown to be arbitrarily close to ln(P.ln(n))/Rmin with probability approaching one, where P is the total transmit power. The results obtained for Rayleigh fading are extended to the cases of Rician and Nakagami fading models. Under the assumption of independent Rician fading channels for different receivers, as the total number of receivers n goes to infinity, the maximum number of active receivers is shown to be equal to ln(2P.ln(n))/Rmin with probability approaching one. For broadcast channels with Nakagami fading, the maximum number of active receivers is shown to be equal to ln(ω/μ.P.ln(n))/Rmin with probability approaching one, where ω and μ are the Nakagami distribution parameters. A by-product of the results is to also provide a power allocation strategy that maximizes the total throughput subject to the rate constraints. In multiple-access channels, the maximum number of simultaneous active transmitters (i.e. user capacity) is obtained in the many user case in which a minimum rate must be maintained for all active users. The results are presented in the form of scaling laws as the number of transmitters increases. It is shown that for all three fading distributions, the user capacity scales double logarithmically in the number of users and differs only by constants depending on the distributions. We also show that a scheduling policy that maximizes the number of simultaneous active transmitters can be implemented in a distributed fashion. Second, the maximum number of active links supporting a minimum rate is asymptotically obtained in a wireless network with an arbitrary topology. It is assumed that each source-destination pair communicates through a fading channel and destinations receive interference from all other active sources. Two scenarios are considered: 1) Small networks with multi-path fading, 2) Large Random networks with multi-path fading and path loss. In the first case, under the assumption of independent Rayleigh fading channels for different source-destination pairs, it is shown that the optimal number of active links is of the order log(N) with probability approaching one as the total number of nodes, N, tends to infinity. The achievable total throughput also scales logarithmically with the total number of links/nodes in the network. In the second case, a two-dimensional large wireless network is considered and it is assumed that nodes are Poisson distributed with a finite intensity. Under the assumption of independent multi-path fading for different source-destination pairs, it is shown that the optimal number of active links is of the order N with probability approaching one. As a result, the achievable per-node throughput obtained by multi-hop routing scales with Θ(1/√N).

Recently, the transmission of vector quantization (VQ) over a code-division multiple access (CDMA) channel has received a considerable attention in research community. The complexity of the optimal decoding for VQ in CDMA communications is prohibitive for implementation, especially for systems with a medium or large number of users. A suboptimal approach to VQ decoding over a CDMA channel, disturbed by additive white Gaussian noise (AWGN), was recently developed. Such a suboptimal decoder is built from a soft-output multiuser detector (MUD), a soft bit estimator and the optimal soft VQ decoders of individual users. <p>Due to its lower complexity and good performance, such a decoding scheme is an attractive alternative to the complicated optimal decoder. It is necessary to extend this decoding scheme for a frequency-selective Rayleigh fading CDMA channel, a channel model typically seen in mobile wireless communications. This is precisely the objective of this thesis. <p>Furthermore, the suboptimal decoders are obtained not only for binary phase shift keying (BPSK), but also for M-ary pulse amplitude modulation (M-PAM). This extension offers a flexible trade-off between spectrum efficiency and performance of the systems. In addition, two algorithms based on distance measure and reliability processing are introduced as other alternatives to the suboptimal decoder. <p>Simulation results indicate that the suboptimal decoders studied in this thesis also performs very well over a frequency-selective Rayleigh fading CDMA channel.

A distributed antenna system (DAS) with inter-cell interference (ICI) in composite fading channel, where multipath and shadowing effect simultaneously exist, is considered in this thesis. How to properly choose a set of remote antennas (RAs) to provide spatial diversity as well as enhance the signal quality and transmission rate is the core concept in this work. Some approximation schemes are utilized to derive the closed form of statistical distributions for both the signal to interference ratio (SIR) and outage probability. According to these approximations and the position of mobile station, we can partition the service area into several different cooperative regions. Simulation results show that the derived approximations are very similar to the experiment results.

In this thesis, the problem of data transmission in amplify-and-forward (AF) co- operative system which implemented joint channel estimation and data detection at the destination (receiver) is considered. The nonlinear block code is designed to as- sist the above methodology. The design criterion takes into account the uncertainty of channel parameters at the receiver based on joint channel estimation and data detection algorithm and the simulations will prove that it can achieve full diversity that is offered by multiple relay and frequency-selective fading channel. Using an approximation of the union boun on the error probability as the design criterion, such that it can be simulated as a function for simulated annealing algorithm. The designed codewords are applied to the AF cooperative system. In order to assess the performance of joint estimation and detection fashion, the numerical simulations will be carried out the word error rate (WER) performances illustrate that improve- ment over differnt benchmark schemes can be obtained.

Adaptive modulation and diversity combining represent very important adaptive solutions for future generations of wireless communication systems. Indeed, to improve the performance and the efficiency of these systems, these two techniques recently have been used jointly in new schemes named joint adaptive modulation and diversity combining (JAMDC) schemes. Considering the problem of finding lowcomplexity, bandwidth-efficient, and processing-power efficient transmission schemes for a downlink scenario and capitalizing on some of these recently proposed JAMDC schemes, we propose and analyze three fully joint adaptive modulation, diversity combining, and power control (FJAMDC) schemes. More specifically, the modulation constellation size, the number of combined diversity paths, and the needed power level are determined jointly to achieve the highest spectral efficiency with the lowest possible combining complexity, given the fading channel conditions and the required bit error rate (BER) performance. The performance of these three FJAMDC schemes is analyzed in terms of their spectral efficiency, processing power consumption, and error-rate performance. Selected numerical examples show that these schemes considerably increase the spectral efficiency of the existing JAMDC schemes with a slight increase in the average number of combined paths for the low signal to noise ratio range while maintaining compliance with the BER performance and a low radiated power resulting in a substantial decrease in interference to co-existing systems/users.