Geometric Programming Research Articles

A global interior point method for nonconvex geometric programming

A global interior point method for nonconvex geometric programming

Hierarchical Multiple Access for Spectrum-Energy Opportunistic Ambient Backscatter Wireless Networks

Recently, ambient backscatter communication has become a promising technology to support the low-power and low-cost Internet-of-Things (IoT). However, the nondeterministic and sporadic nature of ambient signals makes it a great challenge when designing multiple access in spectrum opportunistic ambient backscatter wireless networks (AmBWNs). Moreover, the stringent energy supply and ultra-low-cost design of the backscatter transmitter make most multiple access schemes no longer suitable for AmBWNs. To effectively share carrier frequency resources for backscattering, we propose a hierarchical multiple access scheme, which allows beamforming based spatial division multiple access among groups, and non-orthogonal multiple access (NOMA) for multiple users access within a group. Consequently, we formulate a multi-objective optimization problem to balance the sum rate and the fairness by exploiting grouping, beamforming, and reflection coefficients. To solve this problem, we employ the matching theory to tackle the grouping problem and achieve the corresponding beamforming. We then reformulate the non-convex reflection coefficient optimization and solve it with successive convex approximation and geometric programming. Our extensive evaluation results demonstrate that the spectrum and energy efficiency, latency, and fairness can be significantly improved with minimal overhead at the transmitter.

A neurodynamic algorithm for dependent joint chance constrained geometric programs

This research studies the use of copula theory to model dependencies in joint probabilistic constrained geometric programs with dependent rows. The row vectors are assumed to follow an elliptical distribution, and their dependencies are modeled through a Gumbel–Hougaard copula. We use a log transformation to convert the chance-constrained geometric program into a deterministic optimization problem. Then we solve the resulting deterministic program using a dynamical neural network. The stability and convergence of the proposed neural network approach are demonstrated. The primary characteristic of our framework is its ability to solve the dependent joint chance constrained geometric programs without resorting to any convex approximation methods. This feature sets our approach apart from the current state-of-the-art solving techniques. The neurodynamic algorithm is finally applied to solve three geometric optimization problems.

Joint resource allocation and user association for multi-cell integrated sensing and communication systems

The densification of the orthogonal frequency division multiplexing (OFDM) based fifth-generation communication systems, as well as the requirement of integrating sensing and communication functionalities, has promoted the development of integrated-sensing-and-communication (ISAC) dense cellular networks (DCNs). In the OFDM-based ISAC-DCN, multiple base stations simultaneously serve mobile users and sense targets based on the echo of downlink communication signals. In this paper, we establish the interference model in ISAC-DCN for sensing and communication. Focusing on the interference management of the ISAC-DCN, we investigate the multi-dimension resource allocation problem. In particular, we aim to maximize the network utility by jointly optimizing sub-band allocation, user association, and transmission power under the sensing signal-to-interference-plus-noise ratio constraint to be solved iteratively. The mixed-integer optimization problem is decoupled into three sub-problems. Specifically, a greedy genetic sub-band allocation scheme is proposed for sub-band allocation to reduce total interference. We employ the successive convex approximation technique to transform the transmission power control sub-problem and solve it via geometric programming. Simulation results illustrate the trade-off between sensing and communication performances, and show that the proposed algorithm significantly improves the network utility and achieves higher detection probability.

Electrophoretic Molecular Communication with Piecewise Constant Electric Field.

This paper studies a novel electrophoretic molecular communication (EMC) framework utilizing a piecewise constant electric field. EMC is a particular type of molecular communication that exploits electric fields to induce the movement of charged particles to enhance communication performance. Our previous work proposed an EMC framework utilizing a time-varying electric field that exponentially changes; however, the field with such a complicated shape might be challenging to be implemented in practice. Thus, this paper proposes a new EMC approach exploiting a piecewise constant electric field that can be readily implemented via, e.g., an on/off switch method. We formulate two optimization problems to design the electric field based on different objectives: minimizing a mean squared error and minimizing a bit interval. The solutions of each, such as optimal on-off timings and corresponding strengths of the constant electric fields, are obtained through the Lagrange multiplier approach and the geometric programming, respectively. The Monte Carlo simulation results verify that the proposed piecewise constant electric field significantly reduces the bit error rate relative to the constant field benchmark while performing less well, but not significantly, than the exponential field benchmark.

Optimal Epidemics Policy Seeking on Networks-of-Networks Under Malicious Attacks by Geometric Programming

This work deals with the optimal epidemics policy-seeking problem on networks-of-networks (NoN) in the presence of unknown malicious adding-edge attacks. This problem is investigated in a framework of games-of-games (GoG), in which the conflicts between each network policymaker and the attacker are captured by a series of the Stackelberg games, while all network policymakers together compose a Nash game. First, the tolerable maximum attack magnitude is investigated and given implicitly. Then, we prove the existence of the gestalt Nash equilibrium (GNE) under mild attacks bounded by the above magnitude. A Heuristic algorithm based on iterative geometric programming is proposed to seek the GNE of the above GoG, whose asymptotical convergence is verified. Correspondingly, a greedy Heuristic strategy for the malicious attacker to compromise the NoN topology is developed. The practicability and validity of the above theoretical results and algorithms are illustrated via a simulation example.

Resource Allocation for Cell-Free Massive MIMO-Enabled URLLC Downlink Systems

Ultra-Reliable and low-latency communication (URLLC) is a pivotal technique for enabling the wireless control over industrial Internet-of-Things (IIoT) devices. By deploying distributed access points (APs), cell-free massive multiple-input and multiple-output (CF mMIMO) has great potential to provide URLLC services for IIoT devices. In this paper, we investigate CF mMIMO-enabled URLLC in a smart factory. Lower bounds (LBs) of downlink ergodic data rate under finite channel blocklength (FCBL) with imperfect channel state information (CSI) are derived for maximum-ratio transmission (MRT), full-pilot zero-forcing (FZF), and local zero-forcing (LZF) precoding schemes. Meanwhile, the weighted sum rate is maximized by jointly optimizing the pilot power and transmission power based on the derived LBs. Specifically, we first provide the globally optimal solution of the pilot power, and then introduce some approximations to transform the original problems into a series of subproblems, which can be expressed in a geometric programming (GP) form that can be readily solved. Finally, an iterative algorithm is proposed to optimize the power allocation based on various precoding schemes. Simulation results demonstrate that the proposed algorithm is superior to the existing algorithms, and that the quality of URLLC services will benefit by deploying more APs, except for the FZF precoding scheme.

Geometric Programming Approach to Glitch Minimization via Gate Sizing

Geometric Programming Approach to Glitch Minimization via Gate Sizing

Optimal Hovering Height and Power Allocation for UAV-Aided NOMA Covert Communication System

In this letter, we consider an unmanned aerial vehicle (UAV) aided covert communication system in which the UAV provides downlink transmission to the public user and covert user with non-orthogonal multiple access (NOMA). In the considered system, the covert performance can be effectively enhanced by the mobility of the UAV and the transmission from UAV to the public user. Aiming at improving the covert signal-to-noise ratio (SNR), we jointly optimize the hovering height and power allocation of UAV and formulate a signomial programming (SP) problem. To tackle the nonconvex optimization, we develop a successive geometric programming approximation (SGPA) algorithm. The optimal hovering height and power allocation are provided with numerical results and the outperformance of our design is verified.

Nonlinear fuzzy fractional signomial programming problem: A fuzzy geometric programming solution approach

Fuzzy fractional signomial programming problem is a relatively new optimization problem. In real world problems, some variables may vacillate because of various reasons. To tackle these vacillating variables, vagueness is considered in form of fuzzy sets. In this paper, a nonlinear fuzzy fractional signomial programming problem is considered with all its coefficients in objective functions as well as constraints are fuzzy numbers. Two solution approaches are developed based on signomial geometric programming comprising nearest interval approximation with parametric interval valued functions and fuzzy α-cut with min–max approach. To demonstrate the proposed methods, two illustrative numerical examples are solved and the results are comparatively discussed showing its feasibility and effectiveness.

Robust Chance-Constrained Geometric Programming with Application to Demand Risk Mitigation

Robust Chance-Constrained Geometric Programming with Application to Demand Risk Mitigation

Orthogonal-Time-Frequency-Space Signal Design for Integrated Data and Energy Transfer: Benefits From Doppler Offsets

Integrated data and energy transfer (IDET) is an advanced technology for enabling energy sustainability for massively deployed low-power electronic consumption components. However, the existing work of IDET using the orthogonal-frequency-division-multiplexing (OFDM) waveforms is designed for static scenarios, which would be severely affected by the destructive Doppler offset in high-mobility scenarios. Therefore, we proposed an IDET system based on orthogonal-time-frequency-space (OTFS) waveforms with the imperfect channel assumption, which is capable of counteracting the Doppler offset in high-mobility scenarios. At the transmitter, the OTFS-IDET system superimposes the random data signals and deterministic energy signals in the delay-Doppler (DD) domain with optimally designed amplitudes. The receiver optimally splits the received signal in the power domain for achieving the best IDET performance. After formulating a non-convex optimisation problem, it is transformed into a geometric programming (GP) problem through inequality relaxations to obtain the optimal solution. The simulation demonstrates that a higher amount of energy can be harvested when employing our proposed OTFS-IDET waveforms than the conventional OFDM-IDET ones in high mobility scenarios.

Optimal Transmit Power and Channel-Information Bit Allocation With Zeroforcing Beamforming in MIMO-NOMA and MIMO-OMA Downlinks

In downlink, a base station (BS) with multiple transmit antennas applies zeroforcing beamforming to transmit to single-antenna mobile users in a cell. We propose the schemes that optimize transmit power and the number of bits for channel direction information (CDI) for all users to achieve the max-min signal-to-interference plus noise ratio (SINR) fairness. The optimal allocation can be obtained by a geometric program for both non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA). For NOMA, 2 users with highly correlated channels are paired and share the same transmit beamforming. In some small total-CDI rate regimes, we show that NOMA can outperform OMA by as much as 3 dB. The performance gain over OMA increases when the correlation-coefficient threshold for user pairing is set higher. To reduce computational complexity, we propose to allocate transmit power and CDI rate to groups of multiple users instead of individual users. The user grouping scheme is based on K-means over the user SINR. We also propose a progressive filling scheme that performs close to the optimum, but can reduce the computation time by almost 3 orders of magnitude in some numerical examples.

Multi-sinusoidal waveform shaping for integrated data and energy transfer in aging channels

Integrated data and energy transfer (IDET) is capable of simultaneously delivering on-demand data and energy to low-power Internet of Everything (IoE) devices. We propose a multi-carrier IDET transceiver relying on superposition waveforms consisting of multi-sinusoidal signals for wireless energy transfer (WET) and orthogonal-frequency-division-multiplexing (OFDM) signals for wireless data transfer (WDT). The outdated channel state information (CSI) in aging channels is employed by the transmitter to shape IDET waveforms. With the constraints of transmission power and WDT requirement, the amplitudes and phases of the IDET waveform at the transmitter and the power splitter at the receiver are jointly optimised for maximising the average direct-current (DC) among a limited number of transmission frames with the existence of carrier-frequency-offset (CFO). For the amplitude optimisation, the original non-convex problem can be transformed into a reversed geometric programming problem, then it can be effectively solved with existing tools. As for the phase optimisation, the artificial bee colony (ABC) algorithm is invoked in order to deal with the non-convexity. Iteration between the amplitude optimisation and phase optimisation yields our joint design. Numerical results demonstrate the advantage of our joint design for the IDET waveform shaping with the existence of the CFO and the outdated CSI.

On the Mathematical Modeling and Optimization for the Energy Efficiency Performance of CSMA-NOMA Random Access Networks With Channel Inversion

The paradigm of upcoming 5G and beyond is the massive machine type communications (mMTC), where a large number of devices automatically operate wireless communications. Due to their automatic and energy-intensive operations, energy efficiency (EE) becomes crucial, but there is a lack of investigation for EE of random access networks, which is the underlying platform for mMTC. In this paper, we focus on the EE of carrier sense multiple access-based non-orthogonal multiple access (NOMA) random access networks. We first construct mathematical models. Instead of investigating all combinations regarding successful decoding events as in previous works, by pivoting around the decoding process of a specific signal, a hidden pattern of NOMA decoding process is unveiled, which can largely decrease analytical complexity. Then, together with this feature, by adopting Markov chain and Q-function approximation, closed-form formulation for EE is derived. Subsequently, to efficiently solve the complicated non-convex EE maximization problem built via the constructed models, we employ an approach that unifies complementary geometric programming (CGP) and difference of convex programming (DCP) to optimize all the controllable parameters at device side, namely, transmission probability, power, and data rate, with a tightest lower bound strategy to guarantee seamless EE improvement and very fast convergence to local optimal points even in the worst case. Simulation experiments verify the accuracy of mathematical models and efficiency of optimization scheme.

A stochastic geometric programming approach for power allocation in wireless networks

A stochastic geometric programming approach for power allocation in wireless networks

Outage Performance and AoI Minimization of HARQ-IR-RIS Aided IoT Networks

In this paper, reconfigurable intelligent surface (RIS) and hybrid automatic repeat request with incremental redundancy (HARQ-IR) are amalgamated to lower power expenditure, shorten latency and strengthen reliability of the internet of things (IoT) communications. By considering Rician fading channels and multiple RISs, the outage probability of single-input single-output (SISO) HARQ-IR-RIS aided IoT networks is derived in closed-form, with which the asymptotic outage analysis is carried out. The asymptotic results are further extended to single-input multiple-output (SIMO)/multiple-input multiple-output (MIMO) HARQ-IR-RIS aided IoT networks by using random matrix theory. Thereafter, the asymptotic expressions are invoked to reduce the design complexity of the phase shifts, transmit powers, and rate, which aims at minimizing the age of information (AoI) while ensuring the power and outage constraints. Particularly, the optimal phase shifts are firstly determined. The alternating optimization technique is then applied to solve the transmit rate and powers, which are iteratively updated based on majorization-minimization (MM) principle and geometric programming (GP) approximation, respectively. The numerical results consequently corroborate our theoretical analysis. More interestingly, the HARQ-IR-aided scheme with fixed power is found to provide a comparable performance as the proposed scheme with variable power especially for numerous reflecting elements at RIS.

A Finsler Geometrical Programming Approach to the Nonlinear Complementarity Problem of Traffic Equilibrium

We consider a geometrical approach to the optimisation problems motivated by transportation system management. Here, we provide a comprehensive account of geometric programming based on the elementary Finsler geometry in {mathbb {R}}^n. Then, we present a Finslerian dynamical model for the nonlinear complementarity problem of traffic equilibrium that can be applied to a variety of equilibrium problems.

Millimeter Wave and Free-space-optics for Future Dual-connectivity 6DOF Mobile Multi-user VR Streaming

Dual-connectivity streaming is a key enabler of next-generation six Degrees Of Freedom (6DOF) Virtual Reality (VR) scene immersion. Indeed, using conventional sub-6 GHz WiFi only allows to reliably stream a low-quality baseline representation of the VR content, while emerging high-frequency communication technologies allow to stream in parallel a high-quality user viewport-specific enhancement representation that synergistically integrates with the baseline representation to deliver high-quality VR immersion. We investigate holistically as part of an entire future VR streaming system two such candidate emerging technologies, Free Space Optics (FSO) and millimeter-Wave (mmWave), that benefit from a large available spectrum to deliver unprecedented data rates. We analytically characterize the key components of the envisioned dual-connectivity 6DOF VR streaming system that integrates in addition edge computing and scalable 360° video tiling, and we formulate an optimization problem to maximize the immersion fidelity delivered by the system, given the WiFi and mmWave/FSO link rates, and the computing capabilities of the edge server and the users’ VR headsets. This optimization problem is mixed integer programming of high complexity and we formulate a geometric programming framework to compute the optimal solution at low complexity. We carry out simulation experiments to assess the performance of the proposed system using actual 6DOF navigation traces from multiple mobile VR users that we collected. Our results demonstrate that our system considerably advances the traditional state of the art and enables streaming of 8K-120 frames-per-second (fps) 6DOF content at high fidelity.

Linearly-Convergent FISTA Variant for Composite Optimization with Duality

Many large-scale optimization problems can be expressed as composite optimization models. Accelerated first-order methods such as the fast iterative shrinkage–thresholding algorithm (FISTA) have proven effective for numerous large composite models. In this paper, we present a new variation of FISTA, to be called C-FISTA, which obtains global linear convergence for a broader class of composite models than many of the latest FISTA variants. We demonstrate the versatility and effectiveness of C-FISTA through multiple numerical experiments on group Lasso, group logistic regression and geometric programming models. Furthermore, we utilize Fenchel duality to show C-FISTA can solve the dual of a finite sum convex optimization model.