Optimal Power Adaptation Research Articles

A back‐to‐back coordination‐based learning scheme for deceiving reactive jammers in distributed networks

AbstractReactive jammers select jamming strategies according to the users’ responses; thus, conventional anti‐jamming methods such as frequency hopping are inadequate to defeat the jamming attack. In this article, the authors propose a novel uncoupled deception scheme to trap the reactive jammer into attacking a decoy channel in distributed networks. Specifically, the authors design a multi‐functional network utility for every user to mislead the jammer with a minimum energy consumption while achieving the highest network throughput. Based on the network utility, the anti‐jamming problem is formulated as an exact potential game such that the existence of Nash equilibrium can be guaranteed theoretically. The authors further propose a back‐to‐back coordination‐based learning algorithm to reach the optimal channel selection and power adaption in a non‐cooperative way. To alleviate the lack of mutual information exchange, the back‐to‐back coordination mechanism derives all users to deceive the jammer by inferring others’ strategies based on a shared belief. Simulation results show that the proposed algorithm yields higher network throughput and efficiency‐cost ratio compared to the state‐of‐the‐art cooperative schemes.

Optimal Joint Power and Rate Adaptation for Awareness and Congestion Control in Vehicular Networks

To support inter-vehicular applications, vehicles broadcast beacons with information about their state. Congestion may occur when the load on the channel due to beaconing can prevent the transmission of other types of messages. In this paper, we propose a distributed algorithm for optimal joint adaptation of transmit power and beaconing rate for congestion and awareness control. Our approach is based on a network utility formulation of the congestion control problem, which allows us to induce a desired fairness notion and set different priorities for vehicles. We formulate the general problem but, since it is not convex, we assume Rayleigh fading and derive an algorithm, called PRAIOS, that solves the optimization problem in a decentralized way with convergence guarantees. Our results, validated with realistic simulations in both static and dynamic scenarios and compared with other proposals, show that PRAIOS quickly converges to close to optimal allocations, while keeping the maximum beaconing load at the desired level. They also show that it can control the load when the fading is not Rayleigh. Applications can dynamically set their requirements as constraints, that are enforced by the algorithm while complying with the maximum load, which allows seamless integration of operational requirements into the control framework.

Capacity Analysis of Channel Inversion Using Space-Time Block Coding with Transmit Power Control

In this paper, we analyze channel inversion with transmit diversity in terms of capacity and bit error rates in correlated fading. We obtain the Shannon capacity of Rayleigh fading channel under channel inversion using spatially correlated dual branch orthogonal space-time block coding, in comparison with the optimal power and rate adaptation policy, and provide a simple fixed-rate power adaptation policy to invert the Rayleigh fading into additive white Gaussian noise channel, and obtain the bit error rates using binary phase-shift keying modulation with/without channel inversion. It is found that the correlation generally causes a loss in capacity, which becomes more distinct with channel inversion relative to the optimal power and rate adaptation policy, especially when power correlation is greater than 0.5, and hinders otherwise possible full inversion. Transmit power truncation introduces power gain over full inversion, which manifests itself as an increase in capacity and a decrease in bit error probability. This gain increases with decreasing truncation level of the allowed peak transmit power. Inverting with truncation, a gain of about 19 dB in signal-to-noise ratio is obtained over classical single-antenna transmission without inversion. This gain may be further increased by a combination of truncation and correlation levels, as the correlation surprisingly turns to advantage when the normalized permitted peak-power is below 2 dB. However, the gain is normally accompanied by lower throughput or bandwidth expansion for a fixed data rate due to outage.

Capacity analysis of shadowed Beaulieu-Xie fading channels

In this paper, we provide a capacity analysis for the shadowed Beaulieu-Xie (SBX) fading model, under different transmission policies. From this analysis, we derive new expressions for the channel capacity per unit bandwidth considering four adaptive transmission schemes, namely: constant power with optimal rate adaptation (ORA); optimal power and rate adaptation (OPRA); channel inversion with fixed rate (CIFR) and truncated CIFR (TCIFR). We obtain asymptotic expressions for the channel capacity. A unified ergodic capacity analysis is presented for the maximum-ratio combining (MRC), the equal gain combining (EGC) and the selection combining (SC) diversity receivers. We present capacity curves for different parameters that characterize the channel.

Power adaptation for vector parameter estimation according to Fisher information based optimality criteria

The optimal power adaptation problem is investigated for vector parameter estimation according to various Fisher information based optimality criteria. By considering an observation model that involves a linear transformation of the parameter vector and an additive noise component with an arbitrary probability distribution, six different optimal power allocation problems are formulated based on Fisher information based objective functions. Via optimization theoretic approaches, various closed-form solutions are derived for the proposed problems. Also, the results are extended to cases in which nuisance parameters exist in the system model or certain types of nonlinear transformations are applied on the parameter vector. Numerical examples are presented to investigate performance of the proposed power allocation strategies.

On power adaptation schemes in aerial-terrestrial communications

This paper mainly studies the transmission capacity performance of an aerial-terrestrial communication system, in which an unmanned aerial vehicle (S) delivers information bits to a terrestrial receiver (D) by adaptively controlling its transmit power according to the instantaneous channel state information. In this work, three adaptive transmission schemes, i.e., optimal simultaneous power and rate adaptation, optimal rate adaptation with constant transmit power and truncated channel inversion with fixed rate, are considered at S. Closed-form expressions for the ergodic capacity (EC) under these adaptive transmission schemes are derived, while considering the randomness of the location of D. Furthermore, some insights are obtained by deriving asymptotic expressions for the EC. Finally, numerical results are proposed to compare the performance of these considered power adaption methods, as well as to confirm the accuracy of the proposed analytical models.

Capacity and amount of fading analysis for SIMO communications over η–μ and λ–μ fading channels

This study evaluates the performance of single-input multiple-output (SIMO) wireless networks or dual-branch (DB) SIMO scenarios over the η–μ and the λ–μ fading links. First, the probability density functions (PDFs) of the instantaneous signal to noise ratio for a DB SIMO system in the η–μ and the λ–μ fading conditions. Then, the closed-form expressions of the effective rate (ER or effective capacity) for a SIMO network are derived. In addition to this, asymptotic ER expressions for the considered SIMO network are proposed. The analytical capacity expressions with different transmission policies such as optimal rate adaptation with constant transmit power, optimal simultaneous power and rate adaptation, channel inversion with fixed-rate (CIFR), and truncated channel inversion with fixed-rate are obtained for the SIMO network. Furthermore, the capacity expressions with CIFR policy for DB SIMO communications over the η–μ and the λ–μ fading channels are derived by using the proposed PDFs. Finally, the amount of fading expressions for SIMO networks over the η–μ and the λ–μ fading links are proposed by employing the elementary functions. The proposed analytical expressions provide to establish different radio propagation scenarios by adjusting η, λ or μ parameter. To confirm the accuracy of our analysis, the proposed analytical expressions are verified via exact simulations.

Optimal Power Adaptation in Covert Communication With an Uninformed Jammer

Covert communication is achieved if a transmitter (Alice) sends a message to a legitimate receiver (Bob) without being detected by an attentive warden (Willie). Recent work has taken an outage approach that considers an infinite blocklength and analyzes the probability that channel conditions are such that communication is reliable and/or covert. Power adaptation via truncated channel inversion (TCI) has been examined in previous work in an attempt to minimize outage under the covertness constraint. However, the optimality of TCI was not established, and the associated parameters in the TCI scheme were only found numerically. We provide the exact optimal power adaptation schemes under different covertness constraints and with different channel models: 1) when the channel between Willie and an uninformed jammer is AWGN; and 2) when the channel is a Rayleigh fading channel. We also examine the performance improvement of these schemes over standard approaches. This establishes that TCI is optimal in some, but not all, scenarios of interest.

Capacity analysis of free space optical communication system under atmospheric turbulence

In this paper, the analytical channel capacity of the free space optical (FSO) system under weak, moderate and strong turbulence is derived. The FSO channel statistics follows the log-normal distribution under weak turbulence and follows the Gamma–Gamma distribution under moderate and strong turbulence. The three generally used adaptive transmission schemes in FSO communication system are as follows (1) optimal simultaneous power and rate adaptation, (2) optimal rate adaptation with constant transmit power, and (3) truncated channel inversion with a fixed rate. The closed-form approximations for the average ergodic channel capacity for these adaptive transmission schemes under different atmospheric turbulence without any pointing error are derived. Simulation results depict the excellent agreement of the proposed analytical models with the Monte Carlo simulation.

Stabilization of Linear Systems Across a Time-Varying AWGN Fading Channel

This technical note investigates the minimum average transmit power required for mean-square stabilization of a discrete-time linear process across a time-varying additive white Gaussian noise (AWGN) fading channel that is presented between the sensor and the controller. We assume channel state information at both the transmitter and the receiver, and allow the transmit power to vary with the channel state to obtain the minimum required average transmit power via optimal power adaptation. We consider both the case of independent and identically distributed fading and fading subject to a Markov chain. Based on the proposed necessary and sufficient conditions for mean-square stabilization, we show that the minimum average transmit power to ensure stabilizability can be obtained by solving a geometric program.

Hybrid Satellite-Terrestrial Relay Networks With Adaptive Transmission

Hybrid satellite-terrestrial relay network (HSTRN) has been viewed as a flexible and promising solution to be developed with heterogeneous devices and integrated infrastructures for improved coverage and reduced latency. Taking the requirements of overall spectral and power efficiency into account, we consider different adaptive transmission schemes for the hybrid architecture oriented to potential applications in practical scenarios, and obtain the analytical expressions for the achievable channel capacity with respect to different schemes, i.e., optimal power and rate adaptation, and truncated channel inversion and fixed rate. Numerical simulations confirm the validity of the derived theoretical results, and provide useful guidance for emerging applications in HSTRN that are under various fixed/adaptive transmit power or rate requirements.

Exploiting Power Adaptation With Transmit Antenna Selection for Interference-Outage Constrained Underlay Spectrum Sharing

In underlay spectrum sharing, the interference constraint limits transmissions by the secondary transmitter, which concurrently accesses the spectrum, to protect the primary user from excessive interference. Transmit antenna selection enables a secondary user to overcome the limitations imposed by the interference constraint using low-complexity hardware. We develop an optimal and novel joint antenna selection and power adaptation rule that minimizes the average symbol error probability (SEP) of a secondary user that is subject to two practically well-motivated constraints. The first is the less-studied but general interference-outage constraint, which limits the probability that the interference power at the primary receiver exceeds a threshold. The second constraint limits the peak transmit power of the secondary transmitter. We show that the optimal rule for the interference-outage constraint has a novel structure that is markedly different from the rules considered in the literature. We then present an insightful geometric interpretation of its structure. Using this, we also propose a practically amenable and near-optimal variant of the optimal rule called the linear rule, and analyze its performance. Our numerical results show that the optimal rule reduces the average SEP by one to two orders of magnitude compared to the rules in the literature.

Effective Capacity of $L_p$ -Norm Diversity Receivers Over Generalized Fading Channels Under Adaptive Transmission Schemes

This paper presents novel moment generating function (MGF)- and characteristic function (CHF)-based frameworks for the EC performance analysis of a generic L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm diversity combining scheme under adaptive transmission policies. The considered system operates over generalized fading channels, a maximum delay constraint and under various channel state information (CSI) conditions. Depending upon the operational CSI, four policies are studied, namely: i) Constant power with optimal rate adaptation (ORA); ii) Optimal power and rate adaptation (OPRA); iii) Channel inversion with fixed rate (CIFR); and iv) Truncated CIFR (TIFR). The L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm diversity is a generic diversity structure which includes as special cases various well-known diversity schemes, such as equal gain combining (EGC), maximal ratio combining (MRC) and amplify-and-forward (AF) relaying. Under the ORA and OPRA policies, we derive single integral expressions for evaluating the EC of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm diversity reception directly from the MGF or the incomplete MGF of the Signal-to-Noise-Ratio (SNR) at the receiver, respectively. For the EC performance evaluation of the EGC and AF relaying systems operating under the OPRA policy, a CHF-based approach, which is computationally more efficient as compared to the MGF-based approach, is further presented. It is shown that the EC for the CIFR and TIFR policies can be directly evaluated from the MGF or the CHF of the SNR at the receiver, respectively. For the ORA policy, a novel analytical approach for the asymptotic EC performance analysis is also developed and evaluated, revealing how important system operation parameters affect the overall system performance. The mathematical formalism is validated with selected numerical and equivalent simulation performance evaluation results, thus confirming the correctness of the proposed analytical methodology.

Comparison of adaptive algorithms for free space optical transmission in Málaga atmospheric turbulence channel with pointing errors

In this study, the authors investigate average capacity of free space optics communication over Málaga atmospheric turbulence channel with pointing errors and path loss, for intensity modulated/direct detection (IM/DD) and heterodyne detection. Various algorithms which use adaptive transmission with both types of detection are considered, such as: optimal rate adaption (ORA), optimal power and rate adaption (OPRA), channel inversion with fixed rate (CIFR) and truncated channel inversion with fixed rate (TIFR). Analytical closed-form expressions for channel capacities of ORA, OPRA and TIFR adaptive transmission are presented, and the authors prove that CIFR transmission is not feasible in the strict sense for the conditions considered. Obtained analytical results are numerically evaluated and graphically presented for different strengths of atmospheric turbulence (in weak, moderate and strong turbulence regime) for both types of detection (IM/DD and heterodyne), and for considered algorithms of adaptive transmission (ORA, OPRA and TIFR). The authors have developed expressions suitable for approximating high signal-to-noise ratio channel capacity, and they graphically present and compare the asymptotic approximations with the obtained analytical results for different strengths of turbulence for both types of detection. Also, obtained analytical results were confirmed by Monte-Carlo simulations, and graphically compared for different strengths of turbulence regimes.

Asymptotic capacity analysis under different adaptive transmission for TAS/MRC MIMO scheme subject to Weibull fading channels

This paper investigates a unified average channel capacity (ACC) analysis under different adaptive transmission of multiple-input multiple-output (MIMO) system, combining single transmit antenna selection (TAS) and maximal-ratio combining (MRC) receiver operating under independent flat Weibull multipath fading channels (WFCs). Based on a tight approximate probability density function expression of the signal-to-noise ratio (SNR) at the considered receiver output, we derive new accurate closed-form expressions of ACC for TAS/MRC system employing several rate adaptation techniques, namely optimal rate adaptation, optimal simultaneous power and rate adaptation, channel inversion with fixed rate (CIFR), truncated CIFR (TCIFR), and continuous power TCIFR (CTCIFR). Further, asymptotic expressions, in both high and low-SNR regimes, are investigated. The results show high accuracy for significant values of Lt×Lr TAS/MRC system. Indeed, the smaller Lt×Lr, the better the PDF’s accuracy, therefore, the better are the capacities. Numerical outcomes have been assessed by utilizing Mathematica and Matlab Software and corroborated via Monte-Carlo simulations.

Dual-Hop Cooperative Relaying with Beamforming Under Adaptive Transmission in κ–μ Shadowed Fading Environments

In this paper, we analyze the performance of a dual-hop cooperative decode-and-forward (DF) relaying system with beamforming under different adaptive transmission techniques over κ − μ shadowed fading channels. We consider multiple antennas at the source and destination, and communication takes place via a single antenna relay. The published work in the literature emphasized the performance analysis of dual-hop DF relaying systems, in conjunction with different adaptive transmission techniques for classical fading channels. However, in a real scenario, shadowing of the line-of-sight (LoS) signal is caused by complete or partially blockage of the LoS by environmental factors such as trees, buildings, mountains, etc., therefore, transmission links may suffer from fading as well as shadowing, either concurrently or separately. Hence, the κ − μ shadowed fading model was introduced to emulate such general channel conditions. The κ − μ shadowed fading model is a general fading model that can perfectly model the fading and shadowing effects of the wireless channel in a LoS propagation environment, and it includes some classical fading models as special cases, such as κ − μ , Rician, Rician-shadowed, Nakagami- m ^ , One-sided Gaussian, and Rayleigh fading. In this work, we derive the outage probability and average capacity expressions in an analytical form for different adaptive transmission techniques: (1) optimal power and rate adaptation (OPRA); (2) optimal rate adaptation and constant transmit power (ORA); (3) channel inversion with a fixed rate (CIFR); and (4) truncated channel inversion with a fixed rate (TIFR). We evaluate the system performance for different arrangements of antennas and for different fading and shadowing parameters. The obtained analytical expressions are verified through extensive Monte Carlo simulations.

Capacity of dual branch MRC system for correlated imbalanced average SNRs over Nakagami-m fading channels using OPRA scheme

The closed-form expressions of the capacity for dual branch Maximal Ratio Combining (MRC) diversity system with correlated and imbalanced average Signal-to-Noise Ratio (SNRs) over Nakagami-m fading channels are presented. Our approach is based on probability density function to find the mathematical expressions for Optimal Power and Rate Adaptation (OPRA) scheme. Numerically evaluated results are shown and compared with the available capacity results of OPRA scheme in the literature. The effect of different practical constraint i.e. - fade correlation and level of imbalanced in average SNRs on the channel capacity of the systems, is analysed.

Iterative resource efficient power allocation in small cell network

The major considerations in designing wireless networks are spectral efficiency (SE) and energy efficiency (EE). Though it is desirable to enhance both SE and EE, however, a trade-off exists between the two. To deal with this trade-off, a new metric called the resource efficiency (RE) has already been proposed in the literature. With RE as a performance evaluation metric, a balance can be struck between the SE and EE. Resource allocation with RE as an objective has already been proposed in the literature for a conventional cellular network. However, RE for a small cell network (a.k.a. heterogeneous network) has not been investigated yet. Small cells increase the frequency reuse factor, thus significantly enhancing the capacity and coverage of cellular networks. While already being embraced into LTE, the small cell technology will be one of the main features of the 5G cellular networks. In this paper, we investigate the problem of power allocation for a small cell network. An optimization problem is formulated with the objective of maximizing the RE such that maximum power constraint is satisfied. Finally, we propose an iterative heuristic method called the Iterative Resource Efficient Power Allocation (IREPA) algorithm to solve the formulated problem. We compare the performance of the IREPA algorithm with the Gradient Based Optimal Power Adaptation Scheme and the Uniform Power Allocation Scheme. Numerical results demonstrate the effectiveness of the proposed power allocation technique that significantly improves the resource efficiency.

Joint Optimal Mode Switching and Power Adaptation for Nonlinear Energy Harvesting SWIPT System Over Fading Channel

In this paper, the problem of joint mode switching and power adaptation is studied for simultaneous wireless information and power transfer (SWIPT) over a fading channel. The receiver dynamically switches between information decoding (ID) and energy harvesting (EH) modes while the transmitter dynamically adapts the transmit power. Considering the nonlinearity of practical EH circuits, a realistic nonlinear EH model is adopted rather than the idealistic linear EH model. To characterize the ultimate performance tradeoff between ID and EH, an optimization problem is formulated to maximize the average harvested energy under the constraints on the average achievable rate and the average transmit power, which is a nonconvex and combinatorial problem. To solve this problem, first, the optimal power adaptation scheme for the nonlinear EH receiver that operates only in the EH mode is proposed. Using this scheme, the jointly optimal solution for the mode switching and power adaptation is then derived. By comparing the obtained results to the existing results, various useful and interesting insights into the optimized SWIPT system with nonlinear EH are presented. An important insight into the impact of nonlinear EH is that, to exploit the high energy conversion efficiency of the nonlinear circuit, the EH mode has to be selected only in the moderate range of channel gains. Also, in the EH mode, the power has to be adapted to the short-term power threshold only for the moderate channel gains.

Fairness‐adjustable opportunistic relay selection in the power‐constrained cooperative networks with adaptive transmission

The existing literatures have not considered either the fair power consumption in multi-user cooperative networks or the fairness-adjustable relay selection scheme. The authors propose a fairness-adjustable opportunistic relay selection in the multi-user dual-hop decode-and-forward cooperative networks with the optimal simultaneous power and rate adaptation under realistic power constraints, where the selection result is determined by the instantaneous signal-to-noise ratios over the relay links, the power load (PL) of the relays and the weight factor. The weight factor, also behaving as the metric of fairness, is introduced to adjust the bias between the average channel capacity for the relaying user and the fair PL distribution and is obtained by the proposed capacity-fairness bias criterion for the required fairness target. The average channel capacity has been derived approximately for the proposed scheme and the numerical results underscore the significant benefits of jointly exploiting the channel capacity and fairness.