Performance of energy efficient game theoretical-based power control algorithm in a discrete power environment

This paper studies the problem of energy efficiency (EE) maximization via user association, power, and backhaul (BH) flow control in the downlink of millimeter wave BH heterogeneous networks. This problem is mathematically formulated as a mixed-integer non-linear program, which is non-convex. To get a tractable solution, the initial problem is separated into two sub-problems and optimized sequentially. The first is a joint user association and power control sub-problem for the access network (AN) (AN sub-problem). The second is a joint flow and power control sub-problem for the BH network (BH sub-problem). While the BH sub-problem is a convex optimization problem and hence can be efficiently solved, the AN sub-problem assumes the form of a generalized assignment problem, which is known to be NP-hard. To that end, we utilize Lagrangian decomposition to propose two polynomial time solution techniques that obtain a high-quality solution for the AN sub-problem. The first, referred to as Technique A, uses dynamic programming, the subgradient method, and a heuristic. The second, named Technique B, uses the multiplier adjustment method, the sorting algorithm, and a heuristic. Simulation results are used to demonstrate the effectiveness of the proposed energy efficient user association, power, and BH flow control algorithms as compared with benchmark user association schemes that incorporate the BH sub-problem algorithm, in terms of the total AN power, BH power, and overall network (AN plus BH) EE. The computational complexity and practical implementation of the proposed algorithms are discussed.

In this paper, energy efficient power control for the uplink two-tier networks where a macrocell tier with a massive multiple-input multiple-output (MIMO) base station is overlaid with a small cell tier is investigated. We propose a distributed energy efficient power control algorithm which allows each user in the two-tier network taking individual decisions to optimize its own energy efficiency (EE) for the multi-user and multi-cell scenario. The distributed power control algorithm is implemented by decoupling the EE optimization problem into two steps. In the first step, we propose to assign the users on the same resource into the same group and each group can optimize its own EE, respectively. In the second step, multiple power control games based on evolutionary game theory (EGT) are formulated for each group, which allows each user optimizing its own EE. In the EGT-based power control games, each player selects a strategy giving a higher payoff than the average payoff, which can improve the fairness among the users. The proposed algorithm has a linear complexity with respect to the number of subcarriers and the number of cells in comparison with the brute force approach which has an exponential complexity. Simulation results show the remarkable improvements in terms of fairness by using the proposed algorithm.

In this paper, the issue of non-cooperative, energy-efficient power control in a relay-assisted interference channel is considered. The energy efficiency of a given terminal is defined as the ratio between the throughput of that terminal and the consumed power. As far as the computation of the consumed power is concerned, not only the transmit power, but also the power dissipated in terminal's electronic circuitry to operate the device is considered. A non-cooperative power control game is devised, which admits a unique Nash equilibrium, and whose best-response-dynamics is guaranteed to converge to the unique equilibrium. A cooperative power control algorithm is also devised, which is used as a benchmark for the non-cooperative game. Finally, numerical results are provided to show the merits of the proposed algorithms.

Wireless communications systems have transmitter power control as an essential tool for managing radio resources. Decentralized power control is of special interest and may be characterized as a competition among the communication nodes. This indicates the adequacy of the application of noncooperative game theory concepts to the problem. In this work, we formulate a general framework to the distributed power control problem, derive a power control algorithm and use a simple prediction method to improve its performance.

Transmitter power control has proven to be an efficient method to control cochannel interference in cellular PCS, and to increase bandwidth utilization. Power control can also improve channel quality, lower the power consumption, and facilitate network management functions such as mobile removals, hand-off and admission control. Most of the previous studies have assumed that the transmitter power level is controlled in a continuous domain, whereas in digitally power controlled systems, power levels are discrete. In this paper we study the transmitter power control problem using only a finite set of discrete power levels. The optimal discrete power vector is characterized, and a Distributed Discrete Power Control (DDPC) algorithm which converges to it, is presented. The impact of the power level grid on the outage probability is also investigated. A microcellular case study is used to evaluate the outage probabilities of the algorithms.

Distributed power control is an important issue in wireless networks. Recently, due to the bursty nature of data communication, packet switching is used in cellular systems. In addition, majority of previous power control algorithm assume that the transmitter power level can take values in a continuous domain. However, recent trends such as the GSM standard and QUALCOMM's proposal to the IS-95 standard use a finite number of discretized power levels. These motivate the need to investigate solutions for distributed discrete power control for bursty transmission. Therefore, we propose a probabilistic power adaptation algorithm and analyze its theoretical properties along with the numerical behavior for bursty transmission. We approximate the discrete power control iterations by an equivalent ordinary differential equation (ODE) to prove that the proposed stochastic learning power control algorithm converges to a stable Nash equilibrium. Conditions when more than one stable Nash equilibrium may exist are also studied. Experimental results are presented for several cases and the impact of data burstiness on the proposed algorithm is also concerned.

In recent years, besides spectral efficiency (SE), improving energy efficiency (EE) has become a crucial optimization metric in radio resource allocation (RA). This work addresses the joint problem of chunk-level spectral efficient chunk allocation, relay selection, and a subcarrier-level energy-efficient power control algorithm in a multi-user multi-relay orthogonal frequency division multiple access-physical layer network coding (OFDMA-PNC) system. The resulting mixed-integer nonlinear programming (MINLP) problem is NP-hard and computationally intensive. To manage complexity, chunk-level algorithms are used for subcarrier allocation and relay selection. Two MILP solvers and two heuristics handle chunk and relay allocation via Alternating Optimization (AO) method, while power levels are optimized using a convex optimization solver with the Dinkelbach (DKB) algorithm. Simulation results indicate that in a mobile network where user equipment operates at a maximum consumed power of 33.6 dBm, our proposed joint chunk allocation and relay selection method outperforms the heuristic approach, achieving 85% higher SE and a 47% improvement in EE. Additionally, our proposed suboptimal power control algorithm achieves results closely matching the optimal solution obtained using the DKB algorithm, demonstrating its effectiveness in balancing performance and computational efficiency.

Most cellular radio systems provide for the use of transmitter power control to reduce cochannel interference for a given channel allocation. Efficient interference management aims at achieving acceptable carrier-to-interference ratios in all active communication links in the system. Such schemes for the control of cochannel interference are investigated. The effect of adjacent channel interference is neglected. As a performance measure, the interference (outage) probability is used, i.e., the probability that a randomly chosen link is subject to excessive interference. In order to derive upper performance bounds for transmitter power control schemes, algorithms that are optimum in the sense that the interference probability is minimized are suggested. Numerical results indicate that these upper bounds exceed the performance of conventional systems by an order of magnitude regarding interference suppression and by a factor of 3 to 4 regarding the system capacity. The structure of the optimum algorithm shows that efficient power control and dynamic channel assignment algorithms are closely related.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

With the growing concern over energy consumption, green communication is becoming more and more important. Lots of efforts have been put into investigating in energy-efficient wireless systems. Since Fractional Frequency Reuse (FFR) is a widely-used Inter-cell-interference coordination scheme in the OFDMA wireless network, we consider the energy-efficient power control in the FFR system. With demanded user rate constraints, we aim at minimizing the Joule consumed per transmission bit per-cell in the downlink. Based on Dinkelbach's theory, we transform the objective function into a parametric programming problem. By proving the problem is convex, we derive the optimal analytical solution by Karush-Kuhn-Tucker (KKT) conditions, along with an energy-efficient power control algorithm. Numerical results are given to verify our analysis, and demonstrate that the power control algorithm significantly improves the energy efficiency in FFR. The optimal frequency reuse factor is also given when considering the fairness of energy efficiency and power consumption.

In the well-known distributed target-SIR tracking power control algorithm, when the target-SIR requirements are not reachable for all users, all non-supported users (those who do not reach their target SIRs) transmit at their maximum power. Such users inefficiently consume their energies, and introduce unnecessary interference to others, which in turn unnecessarily increases the number of non-supported users. To deal with this, the smallest number of users should be removed due to infeasibility of the system (gradual removal problem). We present a new distributed constrained power control (DCPC) algorithm to address the gradual removal problem. The basic idea is that any transmitting user whose required transmit power for reaching its target-SIR exceeds its maximum power is temporarily removed. Each temporarily removed user resumes its transmission if its required transmit power for reaching its target-SIR goes below a given threshold (lower than its maximum power). This threshold is determined by each removed user in a distributed manner using only local information. We will show that our proposed algorithm has at least one-fixed point (i.e., its convergence can be guaranteed), and at the equilibrium where the algorithm converges, all transmitting users (the users whose transmit powers are greater than zero) reach their target SIRs consuming the minimum aggregate transmit power. Furthermore, in contrast to the existing DCPC algorithms, no user is unnecessarily removed in our proposed scheme, i.e., it is efficient. Our simulation results confirm our analytic developments and show that our scheme outperforms the existing DCPCs in addressing the gradual removal problem, in terms of convergence, outage probability and power consumption.

In this paper, three novel efficient power control algorithms are proposed for V-BLAST system with both total power constraint (TPC) and per-antenna power constraints (PAPC). Through analysis of the Karush-Kuhn-Tucker (KKT) conditions of the optimization problem, we find out that the antennas with the optimal power control can be divided into two sets. The optimal allocated power (OAP) of each antenna in the first set is its per-antenna power constraint, and the OAPs of the antennas in the second set can be obtained easily through a new optimization problem with TPC only. Based on the above analysis, three novel efficient power allocation algorithms are developed, which have much lower computational complexities compared with the existing dual update method. Simulation results are presented to demonstrate the efficiency of the proposed power control schemes.

In this paper, energy efficient power control for small cells underlaying a macro cellular network is investigated. We formulate the power control problem in self-organizing small cell networks as a non-cooperative game, and propose a distributed energy efficient power control scheme, which allows the small base stations (SBSs) to take individual decisions for attaining the Nash equilibrium (NE) with minimum information exchange. Specially, in the non-cooperative power control game, a non-convex optimization problem is formulated for each SBS to maximize their energy efficiency (EE). By exploiting the properties of parameter-free fractional programming and the concept of perspective function, the non-convex optimization problem for each SBS is transformed into an equivalent constrained convex optimization problem. Then, the constrained convex optimization problem is converted into an unconstrained convex optimization problem by exploiting the mixed penalty function method. The inequality constraints are eliminated by introducing the logarithmic barrier functions and the equality constraint is eliminated by introducing the quadratic penalty function. We also theoretically show the existence and the uniqueness of the NE in the non-cooperative power control game. Simulation results show remarkable improvements in terms of EE by using the proposed scheme.

In infrastructure-less sensor networks, efficient usage of energy is very critical because of the limited energy available to the sensor nodes. Among various phenomena that consume energy, radio communication is by far the most demanding one. One of the effective ways to limit unnecessary energy loss is to control the power at which the nodes transmit signals. In this paper, we apply game theory to solve the power control problem in a CDMA-based distributed sensor network. We formulate a noncooperative game under incomplete information and study the existence of Nash equilibrium. With the help of this equilibrium, we devise a distributed algorithm for optimal power control and prove that the system is power stable only if the nodes comply with certain transmit power thresholds. We show that even in a noncooperative scenario, it is in the best interest of the nodes to comply with these thresholds. The power level at which a node should transmit, to maximize its utility, is evaluated. Moreover, we compare the utilities when the nodes are allowed to transmit with discrete and continuous power levels; the performance with discrete levels is upper bounded by the continuous case. We define a distortion metric that gives a quantitative measure of the goodness of having finite power levels and also find those levels that minimize the distortion. Numerical results demonstrate that the proposed algorithm achieves the best possible payoff/utility for the sensor nodes even by consuming less power.

In this paper we study the performance of two Power Control algorithms: the Adaptive Standard Power Control (ASPC) and the Standard Power Control (PCA) algorithms. Simulation of both algorithms is being done under three different network conditions including the case with varying SIR target. In order to achieve robust estimates of the performance we have undertaken Monte-Carlo analysis of 500 runs for each case. These results show that the performance ASPC is be better than PCA under the different network conditions considered in this paper. All simulations are done in MATLAB.

Most of the power control (PC) algorithms assumed that the link gains are fixed, and the power control command can take any value in the real field. These two assumptions are unrealistic in actual communication systems, since link gains are time varying and power control commands must be sent over capacity limited channels. In this paper, we propose a binary feedback power control algorithm (BFPC) for time-varying link gain environments. This algorithm can possibly be implemented as a 1-bit increase/decrease power control command, and we construct a connection between the link gains and the step-size of the proposed algorithm. It is shown that the proposed algorithm drives the CIR to an interval in time-varying link gain environments. Simulation results show that the proposed algorithm is more robust against link gains changes as compared to Foschini and Miljanic's distributed algorithm (FMA) and proportional power control algorithm (PropPC), and the proposed algorithm can be adopted in practical mobile communication systems.