arXiv subjects

Christos N. Efrem

Publications and source records attributed to Christos N. Efrem.

14 recordsLinked to original sources

arXiv2026

Learning Asymptotics with Convergence-Rate Guarantees using Linear Least Squares

We introduce a new research area that is called Asymptotics Learning Theory (ALT) and combines optimization with asymptotic analysis. In particular, ALT provides a unified approach for computing unknown constants/parameters in proven asymptotic expansions using optimization theory. In this paper, we focus on a general asymptotic form which includes a broad class of asymptotics. Furthermore, we study two powerful numerical methods, namely, sliding Linear Least Squares (sLLSQ) and sliding Tikhonov Linear Least Squares (sT-LLSQ). For these techniques we rigorously prove asymptotic estimates that lead to sufficient conditions for convergence (to the correct values of unknown parameters) and convergence-rate guarantees. Despite their strengths, both methods have also limitations, e.g., slow convergence---or even, counterintuitively, divergence---in some cases. Moreover, we present fundamental applications in analytic combinatorics, a beautiful field of mathematics that deals with asymptotic enumeration of discrete structures using complex analysis. The proposed techniques complement existing approaches, such as the ratio method and its variants. Numerical examples also verify the theoretical results. Finally, we discuss interesting research directions in ALT.

stat.ML↗

arXiv2025

Joint Power Allocation and Reflecting-Element Activation for Energy Efficiency Maximization in IRS-Aided Communications Under CSI Uncertainty

We study the joint power allocation and reflecting element (RE) activation to maximize the energy efficiency (EE) in communication systems assisted by an intelligent reflecting surface (IRS), taking into account imperfections in channel state information (CSI). The robust optimization problem is mixed integer, i.e., the optimization variables are continuous (transmit power) and discrete (binary states of REs). In order to solve this challenging problem we develop two algorithms. The first one is an alternating optimization (AO) method that attains a suboptimal solution with low complexity, based on the Lambert W function and a dynamic programming (DP) algorithm. The second one is a branch-and-bound (B&B) method that uses AO as its subroutine and is formally guaranteed to achieve a globally optimal solution. Both algorithms do not require any external optimization solver for their implementation. Furthermore, numerical results show that the proposed algorithms outperform the baseline schemes, AO achieves near-optimal performance in most cases, and B&B has low computational complexity on average.

eess.SP↗

arXiv2025

Functional Equations for Generalized Collatz Dynamics Using Integral Representations and Residue Calculus

This paper focuses on a wide class of Collatz-type arithmetic dynamics, and presents a systematic derivation of recursive formulas and functional equations satisfied by the associated generating functions. The main tools belong to complex analysis, including contour-integral representations, residue calculus, and Cauchy's integral formulas. The basic approach is inspired by Egorychev's method, which has been used so far to establish combinatorial identities. Moreover, this work generalizes existing results and extends the methodology to multiple dimensions using several complex variables.

math.DS↗

arXiv2024

Transmit and Receive Antenna Port Selection for Channel Capacity Maximization in Fluid-MIMO Systems

In this letter, we study a discrete optimization problem, namely, the maximization of channel capacity in fluid multiple-input multiple-output (fluid-MIMO) systems through the selection of antenna ports/positions at both the transmitter and the receiver. First, we present a new joint convex relaxation (JCR) problem by using an upper bound on the channel capacity and exploiting the binary nature of optimization variables. Then, we develop and analyze two optimization algorithms with different performance-complexity tradeoffs. The first algorithm is based on JCR and reduced exhaustive search (JCR&RES), while the second on JCR and alternating optimization (JCR&AO).

eess.SP↗

arXiv2024

Recurrence relations for the joint distribution of the sum and maximum of independent random variables

In this paper, the joint distribution of the sum and maximum of independent, not necessarily identically distributed, nonnegative random variables is studied for two cases: i) continuous and ii) discrete random variables. First, a recursive formula of the joint cumulative distribution function (CDF) is derived in both cases. Then, recurrence relations of the joint probability density function (PDF) and the joint probability mass function (PMF) are given in the former and the latter case, respectively. Interestingly, there is a fundamental difference between the joint PDF and PMF. The proofs are simple and mainly based on the following tools from calculus and discrete mathematics: differentiation under the integral sign (also known as Leibniz's integral rule), the law of total probability, and mathematical induction. In addition, this work generalizes previous results in the literature, and finally presents several extensions of the methodology.

math.PR↗

arXiv2024

Robust IRS-Element Activation for Energy Efficiency Optimization in IRS-Assisted Communication Systems With Imperfect CSI

In this paper, we study an intelligent reflecting surface (IRS)-aided communication system with single-antenna transmitter and receiver, under imperfect channel state information (CSI). More specifically, we deal with the robust selection of binary (on/off) states of the IRS elements in order to maximize the worst-case energy efficiency (EE), given a bounded CSI uncertainty, while satisfying a minimum signal-to-noise ratio (SNR). In addition, we consider not only continuous but also discrete IRS phase shifts. First, we derive closed-form expressions of the worst-case SNRs, and then formulate the robust (discrete) optimization problems for each case. In the case of continuous phase shifts, we design a dynamic programming (DP) algorithm that is theoretically guaranteed to achieve the global maximum with polynomial complexity $O(L\,{\log L})$, where $L$ is the number of IRS elements. In the case of discrete phase shifts, we develop a convex-relaxation-based method (CRBM) to obtain a feasible (sub-optimal) solution in polynomial time $O(L^{3.5})$, with a posteriori performance guarantee. Furthermore, numerical simulations provide useful insights and confirm the theoretical results. In particular, the proposed algorithms are several orders of magnitude faster than the exhaustive search when $L$ is large, thus being highly scalable and suitable for practical applications. Moreover, both algorithms outperform a baseline scheme, namely, the activation of all IRS elements.

eess.SP↗

arXiv2023

Global Optimization of Energy Efficiency in IRS-Aided Communication Systems via Robust IRS-Element Activation

In this paper, we study an intelligent reflecting surface (IRS) assisted communication system with single-antenna transmitter and receiver, under imperfect channel state information (CSI). More specifically, we deal with the robust selection of binary (on/off) states of the IRS elements in order to maximize the worst-case energy efficiency (EE), given a bounded CSI uncertainty, while satisfying a minimum signal-to-noise ratio (SNR). The IRS phase shifts are adjusted so as to maximize the ideal SNR (i.e., without CSI error), based only on the estimated channels. First, we derive a closed-form expression of the worst-case SNR, and then formulate the robust (discrete) optimization problem. Moreover, we design and analyze a dynamic programming (DP) algorithm that is theoretically guaranteed to achieve the global maximum with polynomial complexity $O(L \log L)$, where $L$ is the number of IRS elements. Finally, numerical simulations confirm the theoretical results. In particular, the proposed algorithm shows identical performance with the exhaustive search, and significantly outperforms a baseline scheme, namely, the activation of all IRS elements.

eess.SP↗

arXiv2023

Joint IRS Location and Size Optimization in Multi-IRS Aided Two-Way Full-Duplex Communication Systems

Intelligent reflecting surfaces (IRSs) have emerged as a promising wireless technology for the dynamic configuration and control of electromagnetic waves, thus creating a smart (programmable) radio environment. In this context, we study a multi-IRS assisted two-way communication system consisting of two users that employ full-duplex (FD) technology. More specifically, we deal with the joint IRS location and size (i.e., the number of reflecting elements) optimization in order to minimize an upper bound of system outage probability under various constraints: minimum and maximum number of reflecting elements per IRS, maximum number of installed IRSs, maximum total number of reflecting elements (implicit bound on the signaling overhead) as well as maximum total IRS installation cost. First, the problem is formulated as a discrete optimization problem and, then, a theoretical proof of its NP-hardness is given. Moreover, we provide a lower bound on the optimum value by solving a linear-programming relaxation (LPR) problem. Subsequently, we design two polynomial-time algorithms, a deterministic greedy algorithm and a randomized approximation algorithm, based on the LPR solution. The former is a heuristic method that always computes a feasible solution for which (a posteriori) performance guarantee can be provided. The latter achieves an approximate solution, using randomized rounding, with provable (a priori) probabilistic guarantees on the performance. Furthermore, extensive numerical simulations demonstrate the superiority of the proposed algorithms compared to the baseline schemes. Finally, useful conclusions regarding the comparison between FD and conventional half-duplex (HD) systems are also drawn.

cs.IT↗

arXiv2020

Minimizing the Installation Cost of Ground Stations in Satellite Networks: Complexity, Dynamic Programming and Approximation Algorithm

In this letter, we study the optimum selection of ground stations (GSs) in RF/optical satellite networks (SatNets) in order to minimize the overall installation cost under an outage probability requirement, assuming independent weather conditions between sites. First, we show that the optimization problem can be formulated as a binary-linear-programming problem, and then we give a formal proof of its NP-hardness. Furthermore, we design a dynamic-programming algorithm of pseudo-polynomial complexity with global optimization guarantee as well as an efficient (polynomial-time) approximation algorithm with provable performance guarantee on the distance of the achieved objective value from the global optimum. Finally, the performance of the proposed algorithms is verified through numerical simulations.

cs.NI↗

arXiv2020

On the Computation and Approximation of Outage Probability in Satellite Networks with Smart Gateway Diversity

The utilization of extremely high frequency (EHF) bands can achieve very high throughput in satellite networks (SatNets). Nevertheless, the severe rain attenuation at EHF bands imposes strict limitations on the system availability. Smart gateway diversity (SGD) is considered indispensable in order to guarantee the required availability with reasonable cost. In this context, we examine a load-sharing SGD (LS-SGD) architecture, which has been recently proposed in the literature. For this diversity scheme, we define the system outage probability (SOP) using a rigorous probabilistic analysis based on the Poisson binomial distribution (PBD), and taking into consideration the traffic demand as well as the gateway (GW) capacity. Furthermore, we provide several methods for the exact and approximate calculation of SOP. As concerns the exact computation of SOP, a closed-form expression and an efficient algorithm based on a recursive formula are given, both with quadratic worst-case complexity in the number of GWs. Finally, the proposed approximation methods include well-known probability distributions (binomial, Poisson, normal) and a Chernoff bound. According to the numerical results, binomial and Poisson distributions are by far the most accurate approximation methods.

cs.NI↗

arXiv2020

Globally Optimal Selection of Ground Stations in Satellite Systems with Site Diversity

The availability of satellite communication systems is extremely limited by atmospheric impairments, such as rain (for radio frequencies) and cloud coverage (for optical frequencies). A solution to this problem is the site diversity technique, where a network of geographically distributed ground stations (GSs) can ensure, with high probability, that at least one GS is available for connection to the satellite at each time period. However, the installation of redundant GSs induces unnecessary additional costs for the network operator. In this context, we study an optimization problem that minimizes the number of required GSs, subject to availability constraints. First, the problem is transformed into a binary-integer-linear-programming (BILP) problem, which is proven to be NP-hard. Subsequently, we design a branch-and-bound (B&B) algorithm, with global-optimization guarantee, based on the linear-programming (LP) relaxation and a greedy method as well. Finally, numerical results show that the proposed algorithm significantly outperforms state-of-the-art methods, and has low complexity in the average case.

cs.NI↗

arXiv2019

Dynamic Energy-Efficient Power Allocation in Multibeam Satellite Systems

Power consumption is a major limitation in the downlink of multibeam satellite systems, since it has a significant impact on the mass and lifetime of the satellite. In this context, we study a new energy-aware power allocation problem that aims to jointly minimize the unmet system capacity (USC) and total radiated power by means of multi-objective optimization. First, we transform the original nonconvex-nondifferentiable problem into an equivalent nonconvex-differentiable form by introducing auxiliary variables. Subsequently, we design a successive convex approximation (SCA) algorithm in order to attain a stationary point with reasonable complexity. Due to its fast convergence, this algorithm is suitable for dynamic resource allocation in emerging on-board processing technologies. In addition, we formally prove a new result about the complexity of the SCA method, in the general case, that complements the existing literature where the complexity of this method is only numerically analyzed.

cs.NI↗

arXiv2019

Energy Efficiency Optimization: A New Trade-off Between Fairness and Total System Performance

The total energy efficiency (TEE), defined as the ratio between the total data rate and the total power consumption, is considered the most meaningful performance metric in terms of energy efficiency (EE). Nevertheless, it does not depend directly on the EE of each link and its maximization leads to unfairness between the links. On the other hand, the maximization of the minimum EE (MEE), i.e., the minimum of the EEs of all links, guarantees the fairest power allocation, but it does not contain any explicit information about the total system performance. The main trend in current research is to maximize TEE and MEE separately. Unlike previous contributions, this letter presents a general multi-objective approach for EE optimization that takes into account both TEE and MEE at the same time, and thus achieves various trade-off points in the MEE-TEE plane. Due to the nonconvex form of the resulting problem, we propose a low-complexity algorithm leveraging the theory of sequential convex optimization (SCO). Last but not least, we provide a novel theoretical result for the complexity of SCO algorithms.

cs.IT↗

arXiv2019

A Framework for Weighted-Sum Energy Efficiency Maximization in Wireless Networks

Weighted-sum energy efficiency (WSEE) is a key performance metric in heterogeneous networks, where the nodes may have different energy efficiency (EE) requirements. Nevertheless, WSEE maximization is a challenging problem due to its nonconvex sum-of-ratios form. Unlike previous work, this paper presents a systematic approach to WSEE maximization under not only power constraints, but also data rate constraints, using a general SINR expression. In particular, the original problem is transformed into an equivalent form, and then a sequential convex optimization (SCO) algorithm is proposed. This algorithm is theoretically guaranteed to converge for any initial feasible point, and, under suitable constraint qualifications, achieves a Karush-Kuhn-Tucker (KKT) solution. Furthermore, we provide remarkable extensions to the proposed methodology, including systems with multiple resource blocks as well as a more general power consumption model which is not necessarily a convex function of the transmit powers. Finally, numerical analysis reveals that the proposed algorithm exhibits fast convergence, low complexity, and robustness (insensitivity to initial points).

cs.NI↗