Low Complexity Optimization of the Asymptotic Spectral Efficiency in Massive MIMO NOMA

Massive multiple-input multiple-output (MIMO) technology facilitates huge increases in the capacity of wireless channels, while non-orthogonal multiple access (NOMA) addresses the problem of limited resources in traditional orthogonal multiple access (OMA) techniques, promising enhanced spectral efficiency. This work uses asymptotic capacity computation results to reduce the complexity of a power allocation algorithm for small-scale MIMO-NOMA, so that it may be applied for systems with massive MIMO arrays. The proposed method maximizes the sum-capacity of the considered system, subject to power and performance constraints, and demonstrates greater accuracy than alternative approaches despite remaining low-complexity for arbitrarily large antenna arrays

Performance analysis of multi-antenna wireless systems

In this thesis we apply results from multivariate probability, random matrix theory (RMT) and free probability theory (FPT) to analyse the theoretical performance limits of future-generation wireless communication systems which implement multiple-antenna technologies. Motivated by the capacity targets for fifth generation wireless communications, our work focuses on quantifying the performance of these systems in terms of several relevant metrics, including ergodic rate and capacity, secrecy rate and capacity, asymptotic capacity, outage probability, secrecy outage probability and diversity order. Initially, we investigate the secrecy performance of a wirelessly powered, wiretap channel which incorporates a relatively small number of transmit antennas in a multiple-input single-output scenario. We consider two different transmission protocols which utilise physical layer security. Using traditional multivariate probability techniques we compute closed-form expressions for the outage probability and secrecy outage probability of the system under both protocols, based on the statistical properties of the channel. We use these expressions to compute approximations of the connection outage probability, secrecy outage probability and diversity orders in the high signal-to-noise ratio (SNR) regime which enables us to find candidates for the optimal time-switching ratio and power allocation coefficients. We show that it is possible to achieve a positive secrecy throughput, even in the case where the destination is further away from the source than the eavesdropper, for both protocols and compare their relative merits. We then progress to considering small-scale multiple-input multiple-output (MIMO) channels, which can be modelled as random matrices. We consider a relay system that enables communication between a remote source and destination in the presence of an eavesdropper and describe a decode-and-forward (DF) protocol which uses physical layer security techniques. A new result on the joint probability density function of the largest eigenvalues of the channel matrix is derived using results from RMT. The result enables us to compute the legitimate outage probability and diversity order of the proposed protocol and to quantify the effect of increasing the number of relays and antennas of the system. Next, we consider much larger-scale massive MIMO arrays, for which analysis using finite results becomes impractical. First we investigate the ergodic capacity of a massive MIMO, non-orthogonal multiple access system with unlimited numbers of antennas. Employing asymptotic results from RMT, we provide closed-form solutions for the asymptotic capacities of this scenario. This enables us to derive the optimal power allocation coefficients for the system. We demonstrate that our approach has low computational complexity and provides results much closer to optimality when compared with existing, suboptimal methods, particularly for the case where nodes are equipped with very large antenna arrays. Finally, we analyse the ergodic capacity of a single-hop, massive MIMO, multi-relay system having more complex properties, by applying results in FPT. Our method allows for an arbitrary number of relays, arbitrarily large antenna arrays and also asymmetric characteristics between channels, which is a situation that cannot typically be analysed using traditional RMT methods. We compute the asymptotic capacity across the system for the case when the relays employ a DF protocol and no direct link exists between the endpoints. We are able to calculate the overall capacity, to a high degree of accuracy, for systems incorporating channels greater than $128\times 128$ in dimension for which existing methods fail due to excessive computational demands. Finally, the comparative computational complexities of the methods are analysed and we see the advantages of applying the FPT method

Capacity Analysis of Asymmetric Multi-Antenna Relay Systems Using Free Probability Theory

Random matrix theory (RMT) has been used to derive the asymptotic capacity of multiple-input-multiple-output (MIMO) channels by approximating the asymptotic eigenvalue distributions (AEDs) of the associated channel matrices. A novel methodology is introduced which enables the computation of the asymptotic capacity for a generalised system in which two relays cooperate to facilitate communication between two remote devices. It is computationally demanding to calculate this capacity using RMT when nodes are equipped with large-scale antenna arrays, and impossible in the case where asymmetry exists between channels within the system. This is because deriving the capacity across the combined channels from the relays to the receiver involves polynomials in large and non-commutative random matrix variables. This paper uses free probability theory (FPT) as an efficient alternative tool for analysis in these circumstances. The method described can be applied with no additional complexity for arbitrarily large antenna arrays. The minimum SNR required to achieve a given asymptotic capacity is computed and the simulation results verify the accuracy of the FPT approach

The Generation of Badly Approximable Pairs for Communications via Real Interference Alignment

Certain proposed coding schemes require sets of irrational numbers (a1,a2,...,an) which generate linear forms. It is conjectured that the more badly approximable these linear forms, meaning the greater the positive lower bound of qn|q+p1a1+...+pnan| for any choice of integers (q,p1, ..., pn), the better the coding scheme, thus the lower the error rate. In contrast to classical one-dimensional Diophantine approximation theory (n=1), the situation for n>1 is full of unsolved problems, and it is not even known what the worst approximable pair is. The aim of this paper will be to present some purely numerical results which suggest some good candidates for bad pairs, and to demonstrate the performance of these pairs in a transmission protocol. For this we use an algorithm due to Vaughan Clarkson, but the software implementation requires some very delicate treatment of floating-point arithmetic. This results in the first fully-rigorous implementation of an algorithm for finding the sequence of best approximants for a linear form q+p1a1+p2a2, and for the simultaneous rational approximation of two irrationals, and we demonstrate the effect of using such linear forms on the error rate of our coding scheme

Improving Secrecy Performance of a Wirelessly Powered network

This paper considers the secrecy communication of a wirelessly powered network, where an energy constrained legitimate transmitter (Alice) sends message to a legitimate receiver (Bob) with the energy harvested from a dedicated power beacon (PB), while an eavesdropper (Eve) intends to intercept the information. A simple time-switching protocol with a time-switching ratio $\alpha$ is used to supply power for the energy constrained legitimate transmitter. To improve the physical layer security, we firstly propose a protocol that combines maximum ratio transmission (MRT) with zero-forcing (ZF) jamming for the case where Eve is passive in the network, so that Alice only has access to the channel state information (CSI) of Bob. Then we propose a protocol that uses a ZF transmitting strategy to minimize the signal-to-noise ratio (SNR) at Eve for the case where Eve is active in the network, so that Alice only has access to the partial CSI of Eve. Closed-form expressions and simple approximations of the connection outage probability and secrecy outage probability are derived for both protocols. Furthermore, the secrecy throughput as well as the diversity orders achieved by our proposed protocols are characterized and the optimal time-switching ratio $\alpha$ and power allocation coefficient $\beta$ for secrecy throughput maximization are derived in the high SNR regime. Finally, numerical results validate the effectiveness of the proposed schemes

Spatiotemporal analysis of the relative risk of post-infectious versus non-post-infectious hydrocephalus and its relationship with environmental factors

The bacteria, Paenibacillus thiaminolyticus, has been identified as contributing to neonatal sepsis and subsequent post-infectious hydrocephalus (PIH) in Ugandan infants. The absence of infection in mothers suggests that the infants must have been exposed to the bacteria within the first days of life. The spatiotemporal distribution of patients with PIH appears to be inhomogeneous, however the distribution of the bacteria in the environment is currently unknown. Based on an apparent seasonal increase in cases observed by hospital workers when the rains come in, it is hypothesized that the prevalence of the bacteria is related to weather conditions. This work uses data collected over a 20-year period by the CURE Children’s Hospital of Uganda (CCHU) in Mbale on infants with hydrocephalus. The data includes cases of PIH and non-post infectious hydrocephalus (NPIH). By using NPIH as the control population we estimate the relative risk (RR) of PIH. The point pattern data given by the spatiotemporal coordinates of the PIH and NPIH cases are assumed to be realizations of underlying inhomogeneous Poisson point processes. By examining the ratio of their intensities, we can fit a logistic model to the data. Our model identifies areas of elevated RR which can be utilized to inform diagnostics and treatment at point-of-care. We demonstrate increased RR i) spatially: in the area north-west of lake Kyoga throughout the study period and ii) temporally: for the years 2006-2012, across the whole of Uganda. By incorporating information on environmental variables, including rainfall, temperature, and the Standardized Precipitation Evapotranspiration Index, we can explain some of this increased RR. In particular, we find evidence of a significant positive association between RR of PIH and rainfall. This information can be used to predict times, locations, and environmental conditions with increased risk of PIH and to inform preventative measures. The results are being used to instruct further investigation into the distribution of Paenibacillus thiaminolyticus, through soil sampling at relevant locations

Body-composition changes in the Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy (CALERIE)-2 study: A 2-y randomized controlled trial of calorie restriction in nonobese humans

Background: Calorie restriction (CR) retards aging and increases longevity in many animal models. However, it is unclear whether CR can be implemented in humans without adverse effects on body composition.Objective: We evaluated the effect of a 2-y CR regimen on body composition including the influence of sex and body mass index (BMI; in kg/m2) among participants enrolled in CALERIE-2 (Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy), a multicenter, randomized controlled trial.Design: Participants were 218 nonobese (BMI: 21.9-28.0) adults aged 21-51 y who were randomly assigned to 25% CR (CR, n = 143) or ad libitum control (AL, n = 75) in a 2:1 ratio. Measures at baseline and 12 and 24 mo included body weight, waist circumference, fat mass (FM), fat-free mass (FFM), and appendicular mass by dual-energy X-ray absorptiometry; activity-related energy expenditure (AREE) by doubly labeled water; and dietary protein intake by self-report. Values are expressed as means ± SDs.Results: The CR group achieved 11.9% ± 0.7% CR over 2-y and had significant decreases in weight (-7.6 ± 0.3 compared with 0.4 ± 0.5 kg), waist circumference (-6.2 ± 0.4 compared with 0.9 ± 0.5 cm), FM (-5.4 ± 0.3 compared with 0.5 ± 0.4 kg), and FFM (-2.0 ± 0.2 compared with -0.0 ± 0.2 kg) at 24 mo relative to the AL group (all between-group P < 0.001). Moreover, FFM as a percentage of body weight at 24 mo was higher, and percentage of FM was lower in the CR group than in the AL. AREE, but not protein intake, predicted preservation of FFM during CR (P < 0.01). Men in the CR group lost significantly more trunk fat (P = 0.03) and FFM expressed as a percentage of weight loss (P < 0.001) than women in the CR group.Conclusions: Two years of CR had broadly favorable effects on both whole-body and regional adiposity that could facilitate health span in humans. The decrements in FFM were commensurate with the reduced body mass; although men in the CR group lost more FFM than the women did, the percentage of FFM in the men in the CR group was higher than at baseline. CALERIE was registered at clinicaltrials.gov as NCT00427193