Asymptotic Closed-form Expressions Research Articles

The Terminator: An Integration of Inner and Outer Approximations for Solving Wasserstein Distributionally Robust Chance Constrained Programs via Variable Fixing

We present a novel approach aimed at enhancing the efficacy of solving both regular and distributionally robust chance constrained programs using an empirical reference distribution. In general, these programs can be reformulated as mixed-integer programs (MIPs) by introducing binary variables for each scenario, indicating whether a scenario should be satisfied. Whereas existing methods have focused predominantly on either inner or outer approximations, this paper bridges this gap by studying a scheme that effectively combines these approximations via variable fixing. By checking the restricted outer approximations and comparing them with the inner approximations, we derive optimality cuts that can notably reduce the number of binary variables by effectively setting them to either one or zero. We conduct a theoretical analysis of variable fixing techniques, deriving an asymptotic closed-form expression. This expression quantifies the proportion of binary variables that should be optimally fixed to zero. Our empirical results showcase the advantages of our approach in terms of both computational efficiency and solution quality. Notably, we solve all the tested instances from literature to optimality, signifying the robustness and effectiveness of our proposed approach. History: Accepted by Andrea Lodi/Design & Analysis of Algorithms — Discrete. Funding: This work was supported by Office of Naval Research [N00014-24-1-2066]; Division of Civil, Mechanical and Manufacturing Innovation [2246414]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0299 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0299 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Distributed HAPS-assisted communications in FSO/RF space-air-ground integrated networks

Space-air-ground integrated (SAGI) communication networks have been envisioned as one of the pillars of the next generation communications (6 G). This type of networks are expected to offer fairness and high quality of services in various scenarios where traditional terrestrial communication systems cannot efficiently support due to inherent limitations, e.g., limited coverage areas. In this paper, a distributed transmission scheme is proposed in a SAGI communication network that utilizes free-space-optical (FSO)/radio frequency (RF) links. More specifically, a set of N high altitude platform systems are cooperatively transmit the received signal to the ground station, using the decode-and-forward relaying protocol. For this system, generic analytical expressions for the outage probability (OP) have been derived that take into consideration the impact of turbulence, pointing errors, and atmospheric attenuation (for the FSO links) as well as the impact of composite fading (for the RF links). Moreover, asymptotic closed-form expressions for the OP are also presented, which are used to extract useful insights for the system under consideration. The numerical evaluated results that are illustrated reveal the impact of various system and channel models parameters on the system’s performance. From these results, it is shown that the proposed scheme outperforms a pure FSO-based relaying scheme, which has been used as a benchmark, under different environmental conditions.

Maximizing the Downlink Data Rates in Massive Multiple Input Multiple Output with Frequency Division Duplex Transmission Mode Using Power Allocation Optimization Method with Limited Coherence Time

The expected development of the future generation of wireless communications systems such as 6G aims to achieve an ultrareliable and low-latency communications (URLLCs) while maximizing the data rates. These requirements push research into developing new advanced technologies. To this end, massive multiple input multiple output (MMIMO) is introduced as a promising transmission approach to fulfill these requirements. However, maximizing the downlink-achievable sum rate (DASR) in MMIMO with a frequency division duplex (FDD) transmission mode and limited coherence time (LCT) is very challenging. To address this challenge, this paper proposes a DASR maximization approach using a feasible power allocation optimization method. The proposed approach is based on smartly allocating the total transmit power between the data transmission and training sequence transmission for channel estimation. This can be achieved by allocating more energy to the training signal than the data transmission during the channel estimation process to improve the quality of channel estimation without compromising more training sequence length, thus maximizing the DASR. Additionally, the theory of random matrix approach is exploited to derive an asymptotic closed-form expression for the DASR with a regularized zero-forcing precoder (RZFP), which allows the power optimization process to be achieved without the need for computationally complex Monte Carlo simulations. The results provided in this paper indicate that a considerable enhancement in the DASR performance is achieved using the proposed power allocation method in comparison with the conventional uniform power allocation method.

Reconfigurable Intelligent Surfaces and Capacity Optimization: A Large System Analysis

Reconfigurable Intelligent Surfaces (RISs) have been recently proposed as an enabling technology for programmable wireless environments. In this paper, we present asymptotic closed-form expressions for the mean and variance of the mutual information for a multi-antenna transmitter-receiver pair in the presence of RISs, using statistical physics methods. While nominally valid in the large-system limit, we show that the derived Gaussian approximation for the mutual information can be quite accurate, even for modest-sized antenna arrays and metasurfaces. The above results are particularly useful when fast-fading conditions are present, which renders channel estimation challenging. We find that, when the channel close to an RIS is correlated, for instance due to small angle spread, which is reasonable for wireless systems with increasing carrier frequencies, the communication link benefits significantly from statistical RIS optimization, resulting in gains that are surprisingly higher than the nearly uncorrelated case. Using our novel asymptotic properties of the correlation matrices of the impinging and outgoing signals at the RISs, we can optimize the metasurfaces without brute-force numerical optimization. When the desired reflection from any of the RISs departs significantly from geometrical optics, the metasurfaces can be optimized to provide robust communication links, without significant need for their optimal placement.

STAR-RIS-Enabled Short-Packet NOMA Systems

This paper analyzes the performance of simultaneous transmitting and reflecting (STAR) reconfigurable intelligent surface (RIS)-enabled short-packet non-orthogonal multiple access (NOMA) systems. A mode-switching protocol combined with partition strategies (MSPS) for the STAR-RIS design is proposed to simultaneously serve multiple actuators along with the discrete phase-shift alignment in order to reduce the STAR-RIS implementation costs. Approximate and asymptotic closed-form expressions for the average block error rate (BLER) and achievable rate have been derived to reveal some useful insights, such as the actuators' diversity order, coding gain, the power allocation factor, packet length, and the number of information bits. Numerical results confirm that: i) the considered system achieves better BLER balance among the actuators than classical RIS-based short-packet NOMA systems and higher achievable sum rate than RIS-based short-packet orthogonal multiple access ones; ii) the STAR-RIS with discrete phase shift design using 3-bit quantization achieves near-optimal performance with the continuous phase shift; iii) there is a trade-off between using bit quantizer and the total number of STAR-RIS elements; and iv) the power allocation strategy provides better average sum rate improvement than block-length increasing strategy.

On performance of short-packet ultra-reliable and low-latency communications NOMA MIMO relay networks

This paper proposes and analyzes the performance of a multi-antenna NOMA relay system over the Nakagami-m fading channel, in which the size of signal packets is finite. Based on the application of the Gaussian–Chebyshev quadrature, Riemann integral and incomplete Gamma function, the exact and asymptotic closed-form expressions of the block error rate (BLER), throughput, goodput of the proposed finite block-length multi-antenna NOMA relay system are derived. Moreover, in order to improve the BLER, throughput, and goodput of the proposed system, maximal-ratio combining and maximal-ratio transmission are applied to receivers and transmitters, respectively. The provided analysis and simulation results indicate that the proposed system meets the requirements of ultra-reliable and low-latency communications (URLLC). Especially, the reliability is higher than 99.99%, i.e., the BLER is less than 10−4. The accuracy of analysis results is verified by simulation results. Furthermore, the number of transmission bits and power allocation coefficients are optimized to maximize the throughput, and goodput and minimize the BLER.

Robust Joint Precoding/Combining Design for Multiuser MIMO Systems With Calibration Errors

We consider the downlink of a multiuser system operating in the time-division duplexing mode, for which base station (BS) and users are equipped with multiple antennas, and provide a robust precoding/combining design against imperfect channel state information (CSI) and calibration errors due to hardware mismatch. Towards this end, we first formulate a robust joint precoder and combiner design as a stochastic minimum mean squared error optimization problem. Then, employing an alternating optimization approach, we propose an algorithm to obtain the precoding and combining matrices assuming imperfect CSI and calibration errors at both the BS and the user sides. We also provide asymptotic closed-form expressions for the mean squared error (MSE) and the achievable sum-rate in the massive MIMO regime. The results indicate that while the MSE linearly increases with the calibration errors at the user side, the sum-rate is asymptotically independent of them. Extensive simulation results show that the proposed robust joint precoder/combiner outperforms the existing solutions while having the same order of complexity. Moreover, when the BS sends a quantized version of the combining coefficients to the users, it is observed that the proposed solution is more robust to the quantization errors than the existing algorithms.

Visible Light Communications for Unmanned Aerial Vehicle: Channel Modeling and Experimental Validation

Unmanned aerial vehicles (UAVs) have been widely applied for their high mobility and low cost, and the visible light communication (VLC) aided UAV can combine the flexibility of UAV and the high transmission rate of VLC. However, the VLC links of a UAV are inevitably affected by the jittering effects, which were rarely characterized. In this letter, the channel between a light emitting diode (LED) and a hovering UAV is modeled considering the random orientation error of the UAV. Closed-form expressions are derived for the probability density function (PDF) and the cumulative distribution function (CDF) of the orientation error, which also leads to closed-form asymptotic PDF and CDF expressions of the UAV’s VLC channel gain. Simulation and experimental results are demonstrated to verify the theoretical derivations. The work lays a theoretical foundation for VLC-aided UAVs, providing insightful suggestions for the system design.

Outage and Throughput Analysis of UAV-Assisted NOMA Relay Systems With Indoor and Outdoor Users

Non-orthogonal multiple access (NOMA) and unmanned aerial vehicle (UAV) are two promising technologies for the fifth generation (5G) and beyond networks. On the other hand, the transition environment from outdoor to indoor is an important problem in practical wireless communication. In this paper, we mathematically study a multi-antenna UAV-assisted communication system where a multi-antenna base station (BS) communicates with indoor and outdoor users through a multiantenna UAV using the power-domain NOMA technique. The metric used to evaluate the system performance are outage probability (OP) and throughput of indoor and outdoor users under different communication urban environments. Moreover, the impacts of the UAV's altitude and location and the light-of-sight (LoS) probability on system performance are also considered. We give the exact and asymptotic closed-form OP expressions and then optimize the transmission rate to maximize the throughput of each user and the overall system throughput. Numerical results show that better system performance can be achieved by controlling the altitudes and location of the UAV, selecting an appropriate transmission rate, or equipping BS and UAV with more antennas. Monte-Carlo simulation results are provided to demonstrate the performance of the investigated system and the accuracy of the developed analytical results.

Accurate Asymptotic Characterization of α-κ-μ Shadowed Fading Channel With Application to Secure URLLC

In this paper, we propose a novel characterization method of α-κ-μ shadowed fading channel. For both the single α-κ-μ shadowed random variable (RV) and the sum of independent identically distributed α-κ-μ shadowed RVs, we accurately derive asymptotic closed-form expressions of their probability density functions (PDFs), cumulative distribution functions (CDFs), and moment-generating functions (MGFs) in this method. Moreover, we analyze the secure ultra-reliable and low latency communications (URLLC) in terms of average information leakage (AIL) in the massive multiple-input multiple-output (MIMO) system based on the proposed method. Numerical results of the proposed theory analysis are supported by Monte-Carlo simulations to validate the accuracy of the derivation.

Hybrid Long- and Short-Packet Based NOMA Systems With Joint Power Allocation and Beamforming Design

This paper investigates the performance of non-orthogonal multiple access (NOMA) systems with hybrid long- and short-packet communications, where a cell-center user (CU) demands high quality-of-service while a cell-edge user (CE) faces poor channel quality. Targeting at this problem, we propose an effective power-beamforming scheme by jointly allocating high power to CU and configuring a beamforming vector along with a maximum ratio transmission to CE's direction. The impact of imperfect successive interference cancellation on CE is thoughtfully taken into consideration. Approximate and asymptotic closed-form expressions for the block error rate and effective channel sum capacity are derived. Following that, we further quantify the diversity orders of users to reveal more useful insights into system designs. Numerical results are provided to demonstrate the effectiveness of the proposed power-beamforming scheme and to corroborate the accuracy of the derived theoretical analysis.

Phenomenological analysis of simple ion channel block in large populations of uncoupled cardiomyocytes.

Current understanding of arrhythmia mechanisms and design of anti-arrhythmic drug therapies hinges on the assumption that myocytes from the same region of a single heart have similar, if not identical, action potential waveforms and drug responses. On the contrary, recent experiments reveal significant heterogeneity in uncoupled healthy myocytes both from different hearts as well as from identical regions within a single heart. In this work, a methodology is developed for quantifying the individual electrophysiological properties of large numbers of uncoupled cardiomyocytes under ion channel block in terms of the parameters values of a conceptual fast-slow model of electrical excitability. The approach is applied to a population of nearly 500 rabbit ventricular myocytes for which action potential duration (APD) before and after the application of the drug nifedipine was experimentally measured (Lachaud et al., 2022, Cardiovasc. Res.). To this end, drug action is represented by a multiplicative factor to an effective ion conductance, a closed form asymptotic expression for APD is derived and inverted to determine model parameters as functions of APD and $\varDelta $APD (drug-induced change in APD) for each myocyte. Two free protocol-related quantities are calibrated to experiment using an adaptive-domain procedure based on an original assumption of optimal excitability. The explicit APD expression and the resulting set of model parameter values allow (a) direct evaluation of conditions necessary to maintain fixed APD or $\varDelta $APD, (b) predictions of the proportion of cells remaining excitable after drug application, (c) predictions of stimulus period dependency and (d) predictions of dose-response curves, the latter being in agreement with additional experimental data.

Short-Packet Communications in IoT-Aided Cellular Cooperative Networks With Non-Orthogonal Multiple Access

This paper investigates short-packet communications (SPCs) of a cooperative non-orthogonal multiple access (NOMA) Internet-of-Things (IoT)-based cellular network where an IoT master node acts as: (1) a relay for the cellular system and (2) a source for the IoT system. Accurate and asymptotic closed-form expressions for the average block error rates (BLERs) of cellular user (CU) and IoT user (IU) are derived in the presence of imperfect successive interference cancellation (SIC) and channel state information (CSI). Notably, numerical results show that: (i) IUs' performance is significantly improved by exploitation of NOMA technique and is not dominated by decode-and-forward (DF) or amplify-and-forward (AF) relaying protocol; (ii) CUs' performance may not perform well compared with orthogonal multiple access (OMA)-based systems for both AF and DF protocols; (iii) higher antenna configuration at the cellular transmitter results in a rapid BLER convergence for CU.

Secure MIMO systems with nonlinear energy harvesting using optimal transmit antenna selection over [formula omitted] fading channels

This paper investigates the secrecy performance of multiple-input multiple-output systems with a nonlinear energy harvesting (EH) scheme used at the transmitter to improve energy efficiency and extend the lifetime of energy-constrained systems. Most of the current literature investigates cognitive radio networks with linear EH model. However, in order to realize more realistic scenarios due to hardware constraints, such as the saturation and sensitivity characteristics of the EH components, a nonlinear EH model is examined here and compared with a simpler linear EH scheme. In particular, a practical nonlinear energy harvester model with a source, a destination, an active eavesdropper, and a power beacon is considered under generalized α−μ fading conditions. Here, the eavesdropper can overhear the data transmission messages when the source communicates with the destination using wiretap channels. Furthermore, the source employs all its antennas to combine the radio frequency signals emitted by the power beacon via the maximal ratio combining (MRC) scheme. Moreover, the MRC scheme is used at the destination and eavesdropper to improve the signal’s quality (i.e., at the receiver side). Closed-form expressions for the lower bound and asymptotic security performance are investigated. Next, optimal antenna selection (OAS) scheme and traditional space–time transmission (STT) scheme are compared based on whether the channel state information (CSI) of the wiretap link is available. In addition to deriving the secrecy diversity order and secrecy array gain, asymptotic closed-form analytical expressions for security performance and closed-form analytical expressions for the probability of strictly positive secrecy capacity are also derived for various selection schemes. Finally, numerical results indicate that, compared to the linear EH scheme with just minimal trade-offs, the nonlinear EH scheme represents more realistic and dependable outcomes.

RIS-Assisted Full-Duplex Relay Systems

Reconfigurable intelligent surfaces (RISs) have recently been presented as a revolutionary technique and recognized as one of the candidates for beyond fifth-generation wireless networks. The RIS technology becomes especially attractive due to its capability to operate in a full-duplex (FD) mode, which is able to ideally double the half-duplex radio spectrum efficiency. This article analyzes the performance of an RIS-aided multihop FD relaying system, where an intermediate FD relay is employed to defeat the far-field path-loss effect inherent to RIS communication links. To this end, we analytically derive exact and asymptotic closed-form expressions for the outage probability, average spectral efficiency, and average bit error rate. The RIS-aided system demonstrates effective performance improvement for the proposed network. However, from the results, it is noticed that the increase in the number of RIS units within a certain communication link does not provide linear performance improvement due to the RIS channel's far-field path-loss model. Thus, mixing active FD relaying techniques with passive RIS platforms can be an ideal solution to improve further system performance, such as outage probability, average spectral efficiency, and average bit error rate in RIS-enabled networks.

Rate-Splitting Multiple Access-Enabled Security Analysis in Cognitive Satellite Terrestrial Networks

In this paper, we investigate security and energy efficiency of multicast communication in cognitive satellite terrestrial networks. To achieve high spectrum efficiency and low interference power transmissions in the cognitive terrestrial network, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rate splitting multiple access scheme</i> (RSMA) is employed to prompt the massive access of the secondary users. In particular, we derive analytical and asymptotic closed-form expressions for secrecy outage probability of the satellite terrestrial network with eavesdropping, interfering, and imperfect channel state information. Hence, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">beamforming</i> (BF) scheme based on RSMA for secondary network is proposed to suppress eavesdropping, mitigate interference, and enhance energy efficiency of the proposed system model. Then, we transform non-convex optimization constraints into resoluble problems utilizing Taylor series expansion and successive convex approximation. Finally, simulation results corroborate the above theoretical analysis and highlight the superiority of the designed BF scheme on security and energy efficiency.

Threshold Regions in Frequency Estimation

This article addresses the problem of threshold region characterization of the maximum likelihood (ML) sinusoid frequency estimation. We first study on the exact analytical expression of the probability of detection for the ML mean square error for all the signal-to-noise ranges. Then, we propose a simple asymptotic expression to this ML detection probability and propose a model for the characterization of the variance of the frequency estimation. We also provide asymptotic closed-form expressions to the threshold and the no-information signal-to-noise ratio breakdowns for the ML frequency estimation, respectively. Outcomes of extensive numerical simulations verify our proposed theoretical derivations.

Performance analysis and optimization of energy harvesting cognitive multi-hop relay network over mixed Rayleigh and double-Rayleigh fading channels

In this paper, we investigate the outage performance of an energy harvesting underlay cognitive multi-hop relay network. In the network, energy-constrained secondary network (SN) nodes harvest energy from radio frequency signal of a power beacon (PB) node. The source node transmits information to destination node via multiple intermediate relay nodes by using a time division broadcast protocol, and the hardware impairments of SN nodes’ transceiver are modeled. The outage performance of SN is analyzed and evaluated by accurately approximate and asymptotic closed-form expressions of outage probability (OP) over quasi-static mixed Rayleigh and double-Rayleigh fading channels. Additionally, due to the complexity of OP expression, a chaotic dragonfly algorithm (CDA) is proposed to jointly optimize energy harvesting ratio and PB node’s abscissa, which can achieve OP minimization of SN. Extensive simulations demonstrate the correctness of theoretical analysis and the effectiveness of the proposed CDA.

Security performance analysis for cell-free massive multiple-input multiple-output system with multi-antenna access points deployment in presence of active eavesdropping

This article investigates the influence of multiple-antenna deployment at access points on physical layer security under cell-free massive multiple-input multiple-output systems. To embody the concept of network multiple-input multiple-output, cell-free massive multiple-input multiple-output employs a great deal of geographically distributed access points, which jointly serve multiple users in the same frequency-time resource. Assuming a malicious active eavesdropper having knowledge of instantaneous channel state information, we derive the asymptotic closed-form expression of the achievable secrecy rate, which is used to evaluate network security performance. A distributed power allocation scheme is developed based on channel fading degrees of different users. All of access points distribute a larger proportion of local transmission power to the users with better channel conditions. We verified that the security performance of the multi-antenna access points outperforms that of the single one. Compared to equal power allocation, the proposed power control algorithm can further boost the network security performance.

An Appraisal of Numerical Approaches for a VED Over the Earth or Ocean

The numerical solution of the classical Sommerfeld problem is thoroughly discussed in this work. In particular, the computation of the vertical electric field excited by a vertical electric dipole (VED) is taken as a paradigm to discuss some different approaches that have been proposed in the literature (with some new variations included). A detailed study is carried out on the pros and cons of each method as well as their range of numerical efficiency in terms of frequency, ground losses, height of the dipole, and distance to the observation point. We finally propose a numerical implementation of the steepest descent method as a good overall method in terms of accuracy, computational efficiency, and extended range of validity. Asymptotic closed-form expressions for the far-field region are also provided.