Nonnegative Matrix Inequalities and their Application to Nonconvex Power Control Optimization

Maximizing the sum rates in a multiuser Gaussian channel by power control is a nonconvex NP-hard problem that finds engineering application in code division multiple access (CDMA) wireless communication network. In this paper, we extend and apply several fundamental nonnegative matrix inequalities initiated by Friedland and Karlin in a 1975 paper to solve this nonconvex power control optimization problem. Leveraging tools such as the Perron–Frobenius theorem in nonnegative matrix theory, we (1) show that this problem in the power domain can be reformulated as an equivalent convex maximization problem over a closed unbounded convex set in the logarithmic signal-to-interference-noise ratio domain, (2) propose two relaxation techniques that utilize the reformulation problem structure and convexification by Lagrange dual relaxation to compute progressively tight bounds, and (3) propose a global optimization algorithm with ϵ-suboptimality to compute the optimal power control allocation. A byproduct of our analysis is the application of Friedland–Karlin inequalities to inverse problems in nonnegative matrix theory

Maximizing sum rate and minimizing MSE on multiuser downlink: Optimality, fast algorithms and equivalence via max-min SIR

Maximizing the minimum weighted SIR, minimizing the weighted sum MSE and maximizing the weighted sum rate in a multiuser downlink system are three important performance objectives in joint transceiver and power optimization, where all the users have a total power constraint. We show that, through connections with the nonlinear Perron-Frobenius theory, jointly optimizing power and beamformers in the max-min weighted SIR problem can be solved optimally in a distributed fashion. Then, connecting these three performance objectives through the arithmetic-geometric mean inequality and nonnegative matrix theory, we solve the weighted sum MSE minimization and weighted sum rate maximization in the low to moderate interference regimes using fast algorithms

Band-Limited Phase-Only Correlation (Blpoc) Using Fpga For Finger Vein Recognition System

Nowadays, due to the high security and reliable of finger vein pattern, it had become one of the major interests in the biometric research. In the last few years, a number of finger vein recognition algorithms have been proposed. Most of the proposed methods were implemented in software-based on a general-purpose processor, which have limitations on the processing speed, size and power consumption. To overcome these limitations, this thesis presents an architecture for finger vein recognition system based on BLPOC matching method. The BLPOC is a phase-based matching method which have benefits of high accuracy and less affected by image shifted or brightness changed. It involves a high computation process, which is 2D-DFT, therefore, it is necessary to implement on a hardware device such as FPGA. It consists of two types of multiplexer blocks, one DFT block, one CORDIC block, seven types of memory blocks, one subtracter block, one divider block and one comparator block; and is implemented using Verilog HDL and verified using the Altera Cyclone III EP3C120F780 FPGA board. The proposed DFT block had contributed to reduce the area used by 97% of the previously proposed DFT block. A finger vein image database of 204 classes has been used to evaluate the performance of the proposed architecture. Results show that the proposed architecture can process a single matching of two finger vein images in 1.15 ms, which is about nine times faster than the softwarebased implementation, while the accuracy is similar with the software-based implementation. In conclusion, the finger vein recognition system based on BLPOC is successfully implemented on a FPGA board with better processing time as compared with the software-based implementation

Analysis and control of building integrated photovoltaic systems incorporating storage

Imperial Users onl

Optimal Charging of Electric Vehicles in Smart Grid: Characterization and Valley-Filling Algorithms

Electric vehicles (EVs) offer an attractive long-term solution to reduce the dependence on fossil fuel and greenhouse gas emission. However, a fleet of EVs with different EV battery charging rate constraints, that is distributed across a smart power grid network requires a coordinated charging schedule to minimize the power generation and EV charging costs. In this paper, we study a joint optimal power flow (OPF) and EV charging problem that augments the OPF problem with charging EVs over time. While the OPF problem is generally nonconvex and nonsmooth, it is shown recently that the OPF problem can be solved optimally for most practical power networks using its convex dual problem. Building on this zero duality gap result, we study a nested optimization approach to decompose the joint OPF and EV charging problem. We characterize the optimal offline EV charging schedule to be a valley-filling profile, which allows us to develop an optimal offline algorithm with computational complexity that is significantly lower than centralized interior point solvers. Furthermore, we propose a decentralized online algorithm that dynamically tracks the valley-filling profile. Our algorithms are evaluated on the IEEE 14 bus system, and the simulations show that the online algorithm performs almost near optimality ($<1$ relative difference from the offline optimal solution) under different settings.Comment: This paper is temporarily withdrawn in preparation for journal submissio

Joint Beamforming and Power Control in Coordinated Multicell: Max-Min Duality, Effective Network and Large System Transition

This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signal-to-interference-plus-noise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear Perron-Frobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear Perron-Frobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution.Comment: Some typos in the version publised in the IEEE Transactions on Wireless Communications are correcte

Contagion Source Detection in Epidemic and Infodemic Outbreaks: Mathematical Analysis and Network Algorithms

This monograph provides an overview of the mathematical theories and computational algorithm design for contagion source detection in large networks. By leveraging network centrality as a tool for statistical inference, we can accurately identify the source of contagions, trace their spread, and predict future trajectories. This approach provides fundamental insights into surveillance capability and asymptotic behavior of contagion spreading in networks. Mathematical theory and computational algorithms are vital to understanding contagion dynamics, improving surveillance capabilities, and developing effective strategies to prevent the spread of infectious diseases and misinformation.Comment: Suggested Citation: Chee Wei Tan and Pei-Duo Yu (2023), "Contagion Source Detection in Epidemic and Infodemic Outbreaks: Mathematical Analysis and Network Algorithms", Foundations and Trends in Networking: Vol. 13: No. 2-3, pp 107-251. http://dx.doi.org/10.1561/130000006

Factors predictive of the need for renal replacement therapy in critically ill patients with rhabdomyolysis and their outcome

In rhabdomyolysis, the most serious systemic complication is acute kidney injury (AKI), which is associated with the need for renal replacement therapy (RRT) and poor outcome. To identify the factors predictive of the need for RRT in critically ill patients with rhabdomyolysis and their outcome.This was a prospective observational study conducted in the intensive care unit (ICU) of the Hospital Universiti Sains Malaysia over a 1 year period. Consecutive adult patients admitted to the ICU who fulfilled the criteria of rhabdomyolysis at any point during their ICU stay were recruited. Obvious cases of renal failure and pre-existing use of RRT were excluded. Data on factors that are known to predict the need for RRT were recruited. The end point of the study was initiation of RRT during the ICU stay and the outcome. Univariate analysis was performed to identify the factors that were significantly associated with the initiation of RRT. A total of 30 subjects fulfilled the study criteria, of which 4 (13.3%) of them required RRT and 3 (10.0%) death reported. The subject’s APACHE II and SOFA median scores were 9.0 (IQR=14.0) and 3.5 (IQR=6.3), respectively. Majority of the rhabdomyolysis patients 28 (93.3%) were due to trauma. Factors that showed significant association with RRT include SOFA score (P=0.021), peak serum creatine kinase level (P=0.026), peak serum creatinine level (P=0.024), use of sodium bicarbonate (P=0.037), and length of ICU stay (P=0.026). In this study, higher SOFA, peak CK level, peak creatinine level, use of sodium bicarbonate and longer length of stay ICU were the predictive factors leading to initiation of RRT in critically ill patients