Iterative Water-filling Algorithm Research Articles

Energy-Efficient Power Allocation Maximization for MU-MIMO Multiple Access Channels

We propose an Iterative Water-Filling algorithm for Energy-Efficiency maximization problem of the Multi-User Multiple-Input Multiple-Output Multiple-Access-Channel (MU-MIMO-MAC) system, named as IWF-EE-MIMO. The algorithm can be regarded as two levels of operations. The inner level of IWF-EE-MIMO aims at computing the solution to each user of the family, while other users keeping their previous power allocation, in turn. The outer level of IWF-EE-MIMO aims at determining when to accept a good solution to the considered problem based on the results obtained by the inner level. For our designed algorithms in this paper, WF-EE-MIMO1, as the subordinate algorithm, is only used for the inner level. IWF-EE-MIMO, as the main algorithm, computes the solution to the considered problem. Note that IWF-EE-MIMO includes WF-EE-MIMO1, to avoid confusion. The considered problem is of non-linear fractional semi-definite optimization in complex-valued matrix optimization variables, beyond the range of standard (semi-definite) optimization theory. Thus, the optimality condition of the considered maximization problem needs to be created. Under this creation, for the considered problem, convergence or optimality of IWF-EE-MIMO is obtained with its efficiency.

The Defense Against Jamming Attack in Cognitive Radio Networks: Energy Efficiency Management Perspective

Cognitive Radio Networks (CRN) learning perspective and inherently reconfigurable capability generate a group of novel safety problems. Here, let's analyze the jamming security issue with a smart jammer, which could rapidly study the broadcast power of the users also flexibly regulate their broadcast power towards maximizing the destructive effects. Additionally, the Secondary User (SU) spends energy while switching to next frequency channel, cause degradation of the system performances with respect to energy effectiveness. Here, we explore the use of Stackelberg game to achieve jamming resilient radio transmission and power control strategy of an SU. The optimal power allocation is carried out with the iterative water-filling algorithm (WFA) and Channel Allocation based on Stackelberg Game algorithm (CASG) exhibits the Stackelberg equilibrium and the min-max/max-min best power allocation over the recreation of the various game situations.

A Robust Game-Based Algorithm for Downlink Joint Resource Allocation in Hierarchical OFDMA Femtocell Network System

Femtocell is a promising technology for wireless service networks to facilitate sustainable and efficient services for users. This paper deals with a downlink joint channel assignment and power allocation problem with multiple channels, users, constraints, and uncertainties in the orthogonal frequency division of a multiple-access hierarchical femtocell network system. Specifically, a hierarchical robust Stackelberg game, which aims to achieve robust equilibrium, is first proposed for resource allocation with uncertainties. Then, a low-complexity, low-interference, high-efficiency, and high-performance algorithm is presented to handle the complex robust joint allocation problem. Considering the demand capacity of macro-base stations, an efficient fitness function in conjunction with particle swarm optimization-constriction factor, is utilized to yield the best response in the upper game to satisfy multiple constraints. Meanwhile, an iterative waterfilling algorithm is exploited to achieve the best response of femto-base stations in the lower game. Lastly, a stop protocol is established for two-tier users to accomplish an efficient robust Stackelberg equilibrium. Comparative results demonstrated that the proposed algorithm is superior to the existing game-based algorithms.

Power Allocation for SWIPT in Full-Duplex AF Relay Interference Channels Using Game Theory

A full-duplex, amplify-and-forward multiple relay system employing simultaneous wireless information and power transfer receivers operating in interference channels is studied. Since all links want to maximize their own achievable rate, a power allocation problem under transmit power and energy harvesting constraints is developed. Through alternative optimization, a distributed iterative water-filling algorithm based on game theory with provable convergence is devised. The existence and uniqueness of a Nash equilibrium point are both guaranteed and the convergence of the proposed algorithm is examined using a diagonally strict concavity condition. Numerical results show that the proposed algorithm is convergent and can achieve a higher sum rate than previous schemes.

Reducing Near–Far Problem in a VDSL Network with Modified IWF Algorithm by Using Adaptive Spectral Mask Yielding Improved Data Rate of Near End Users

This paper presents a new technique for reducing the ‘Near–Far’ problem with modified iterative water filling (IWF) algorithm by using the adaptive power spectral mask yielding improved data rate of near end users in a VDSL network. It is shown through graphical results that the proposed technique for spectrum management achieves a significant gain in data rate for ten users VDSL network compared to that of traditional IWF algorithm. However, data rate of the proposed algorithm approaches near to highly complex optimal spectrum balancing (OSB) algorithm. The complexity of the proposed algorithm is same as that of IWF algorithm, which is much lower than that of highly complex OSB algorithm.

Energy-Efficient Precoder Design for Multi-User MIMO Systems With a Full-Duplex Base Station

In this paper, we investigate the downlink (DL) and uplink (UL) precoder design for a multi-user multiple-input multiple-output (MU-MIMO) network consisting of a full-duplex (FD) base station (BS) and multiple users operating in the half-duplex mode. Our goal is to find the precoders that maximize the overall energy efficiency (EE). However, the design problem is intractable to solve due to the fractional optimization formulation. Besides, the self and co-channel interferences also aggravate the design difficulty. To solve the problem, we first apply the UL-DL duality to have the reformulated UL and dual-UL precoder optimization problems. Applying the Dinkelbach’s algorithm, we show that both the UL and dual-UL-precoders can be derived with the proposed iterative water-filling (IWF) algorithm. Finally, the DL precoders are obtained by exploiting the duality property again. Note that the proposed precoders are of closed-form expressions. Simulation results justify the superiority of the proposed scheme over the existing design.

Subcarrier and Power Allocation for the Downlink of Multicarrier NOMA Systems

This paper investigates the joint subcarrier and power allocation problem for the downlink of a multi-carrier non-orthogonal multiple access (MC-NOMA) system. A novel three-step resource allocation framework is designed to deal with the sum rate maximization problem. In Step 1, we relax the problem by assuming that each of the users can use all the subcarriers simultaneously. With this assumption, we prove the convexity of the resultant power control problem and solve it via convex programming tools to get a power vector for each user. In Step 2, we allocate the subcarriers to users by a heuristic greedy manner with the obtained power vectors in Step 1. In Step 3, the proposed power control schemes used in Step 1 are applied once more to further improve the system performance with the obtained subcarrier assignment of Step 2. To solve the maximization problem with fixed subcarrier assignments in both Step 1 and Step 3, a centralized power allocation method based on projected gradient descent algorithm and two distributed power control strategies based, respectively, on pseudo-gradient algorithm and iterative waterfilling algorithm are investigated. Numerical results show that our proposed three-step resource allocation algorithm could achieve comparable sum rate performance to the existing near-optimal solution with much lower computational complexity and outperforms power controlled OMA scheme. Besides, a tradeoff between user fairness and sum rate performance can be achieved via applying different user power constraint strategies in the proposed algorithm.

Joint remote radio heads and baseband units pool resource scheduling for delay-aware traffic in cloud radio access networks

Due to the centralized signal processing and powerful computational ability, cloud radio access networks (C-RAN) is considered as a promising technique to meet the increasing demand of high-data-rate services of the fifth generation wireless communications. This paper investigates the stochastic optimization problem of C-RAN by joint remote radio heads and baseband units pool resource scheduling to achieve the throughput utility maximization. We formulate a problem to maximize the average throughput utility while stabilizing all processing and transmission queues under the power, subcarrier and computational resources constraints. By utilizing Lyapunov optimization technique, the primal problem can be decomposed into four subproblems. Throughput utility maximization, admission control and computational resource allocation subproblems can be solved easily. For the joint power and subcarrier allocation subproblem, we utilize time-sharing and alternating approaches to obtain a feasible solution. By utilizing the results of four subproblems, a joint admission control and resource allocation (JACRA) algorithm is proposed. The simulation results are provided to show that the total average throughput of JACRA algorithm is increased by 4.02% compared with joint Hungarian and iterative waterfilling (JHIW) algorithm, but the total average backlogs of JACRA algorithm are decreased by 7.04% when the control parameter grows from 1 to 10.

SVD-based IWFA for next generation wireless MIMO communication

Abstract Point-to-point MIMO systems without channel state information at the transmitter (No CSIT) and with perfect channel state information at the transmitter (Perfect CSIT) were considered for the application of a novel singular-value-decomposition-based (SVD-based) iterative water-filling algorithm (IWFA). The optimal transmit power was computed for Rayleigh fading-based eigenchannels using an estimated iterative water-filling power allocation algorithm to maximize ergodic capacity. The results obtained with the proposed method showed significant improvements in ergodic capacity compared with the average power allocation method.

Small Cell Cluster-Based Resource Allocation for Wireless Backhaul in Two-Tier Heterogeneous Networks With Massive MIMO

In this paper, we investigate the resource allocation problem in two-tier heterogenous networks (HetNets) with massive MIMO, where two frequency bands, cellular frequency band and millimeter wave frequency band, are used for wireless backhaul links. To coordinate the interference among small cells (SCs), SCs are grouped into multiple SC clusters (SCCs), where SC users are jointly served by SC base stations (BSs) (SBSs) belonging to the same SCC. To eliminate the multi-user and inter-tier interference, we propose a block diagonalization based precoding scheme at macro-BS and each SCC, where the transmit precoding matrix for users is projected onto the null space of interference channels. Following this, we formulate a power allocation optimization problem to maximize the downlink sum rate of the system subject to per-SCC power and users’ quality of service requirements. Since the formulated problem is nonconvex, we transform it into a convex one by appropriate approximation, and a constrained concave convex procedure based iterative algorithm is proposed to obtain the solution. Furthermore, we prove that the obtained solution converges to the local optimum. Meanwhile, according to the structure of the original formulated problem, we divide it into multiple subproblems and propose an optimal iterative water-filling algorithm. Next, we extend the original problem with per-SBS power constraint, which results in that the precoding of each SCC has to be redesigned. On this basis, we propose an iterative water-filling algorithm to obtain the optimal power allocation and precoding. Numerical results are presented to verify the performance of our proposed algorithms.

Interference Coordination via Power Domain Channel Estimation

A novel technique is proposed, which enables each transmitter to acquire global channel state information (CSI) from the sole knowledge of individual received signal power measurements, which makes dedicated feedback or inter-transmitter signaling channels unnecessary. To make this possible, we resort to a completely new technique whose key idea is to exploit the transmit power levels as symbols to embed information and the observed interference as a communication channel the transmitters can use to exchange coordination information. Although the used technique allows any kind of low-rate information to be exchanged among the transmitters, the focus here is to exchange local CSI. The proposed procedure also comprises a phase which allows local CSI to be estimated. Once an estimate of global CSI is acquired by the transmitters, it can be used to optimize any utility function which depends on it. While algorithms, which use the same type of measurements, such as the iterative water-filling algorithm, implement the sequential best-response dynamics (BRD) applied to individual utilities, here, thanks to the availability of global CSI, the BRD can be applied to the sum-utility. Extensive numerical results show that significant gains can be obtained and, this, by requiring no additional online signaling.

Signaling Design of Two-Way MIMO Full-Duplex Channel: Optimality Under Imperfect Transmit Front-End Chain

We derive the optimal signaling for a multiple input multiple output (MIMO) full-duplex (FD) two-way channel under imperfect transmit front-end chains. We characterize two-way rates of the channel by using a game-theoretical approach, where we focus on the Pareto boundary of the achievable rate region and the Nash equilibrium (NE). For a MIMO FD channel, the Pareto boundary achieves the global optimality. However, deriving the Pareto boundary amounts to solving a family of centralized non-convex problems. By introducing auxiliary variables, we decouple and convert the Pareto boundary into a family of convex problems, which enables us to obtain the Pareto boundary with low computational complexity. In a MISO FD two-way channel, we further present a closed-form expression for the Pareto-optimal signaling. In our numerical examples, we quantify gains in the achievable rates of the Pareto-optimal signaling over the zero-forcing beamforming and NE. For a distributed MIMO FD channel, we establish the existence of NE and present a condition for the uniqueness of NE. We then propose an iterative water-filling algorithm, which is capable of reaching the NE. Through simulations, the threshold of the self-interference level is found below which the FD NE outperforms the half-duplex TDMA.

A Robust Distributed Power Control Algorithm for Minimum Interference to Primary Users in Underlay Cognitive Radio Networks

<p class="Abstract"><span lang="EN-US">A robust distributed optimal power control (RDPC) scheme under worst case condition is proposed to make primary users (PUs) receive minimum interference generated from all secondary users (SUs) in underlay cognitive radio networks (CRNs). The strategy considers the transmit power of each SU below the maximum allowable power of the devices and interference plus noise ratio (SINR) of each SU under the minimum threshold. Simulation illustrate thatthe RDPC can lead SUs to reduce the interference to PUs, and simultaneously the better meet quality of service (QoS) requirement of SUs in comparison with the distributed power control algorithm (DPC) and the traditional iterative water filling algorithm (IWFA) in time-varying channel environment.</span></p>

An Improved Iterative Water Filling Algorithm in Multiuser DSL Environment

In digital subscriber line system, crosstalk is created among a bundle of twisted copper pairs due to the effect of an electromagnetic coupling. In very high bit rate digital subscriber line system, higher frequencies are used for data transmission. At these higher frequencies crosstalk seriously affects the system performance. The crosstalk from the near end users in upstream data transmission at higher frequency band significantly declines the bit rate of far end users. In order to resolve this `Near-Far' problem the effective spectrum management techniques are used. Iterative water-filling (IWF) is one of the spectrum management techniques in which power from all subcarriers of near end user are reduced in order to remove crosstalk at far end user. IWF algorithm has low complexity but due to inefficient use of bandwidth it does not give optimal result. In this paper a modified IWF algorithm is proposed in which power from only those subcarriers of near end user are reduced which has a worst effect on bit rates of far end users. The power back off from these subcarriers is done by reducing power spectral masks at these subcarriers. The simulation results of the proposed algorithm give significant performance advantage in terms of data rate over the traditional IWF algorithm. These results approach near to the performance of highly complex optimal spectrum management algorithms while maintaining the complexity as that of traditional IWF algorithm.

A dynamic spectrum management algorithm in VDSL systems

A modified iterative water-filling algorithm is proposed in which power from only those subcarriers of the near end user are reduced, which has the worst effect on bit rates of far end users. The power back off from these subcarriers is done by reducing power spectral masks at respective subcarriers. The results after simulating the proposed algorithm give significant performance advantages in terms of data rate over the traditional iterative water-filling algorithm. These results approach the performance of highly complex optimal spectrum management algorithms while maintaining the complexity of the traditional iterative water-filling algorithm.

Optimized Joint Power and Resource Allocation for Coordinated Multi-point Transmission for Multi-user LTE-Advanced Systems

Recent research has shown that coordinated multi-point (CoMP) transmission can provide significant gains in terms of the overall throughput of cellular systems. The main purpose of this paper is to enhance the overall cell throughput and to optimize the power consumption in LTE-Advanced systems using CoMP. In particular, we present joint resource allocation, precoding and power allocation (PA) algorithms based on the signal-to-leakage-plus-noise-ratio (SLNR) for the CoMP downlink. The proposed resource allocation and precoding algorithm selects the user equipment that can efficiently share the same resource block in the same cell without degrading the overall throughput by using the SLNR metric. This sharing is possible due to the existence of multiple transmitters within a cell in a CoMP setting. Additionally, we propose a set of PA algorithms that significantly improve the overall throughput and reduce the power consumption. The PA algorithms are based on solving a set of constrained convex optimization problems using the log-barrier penalty function approach based on the Newton method. We evaluate the proposed PA algorithms by comparing them to the iterative water-filling (IWF) algorithm. Performance evaluation results show that the proposed SLNR-based PA algorithms provide considerable performance gains in terms of the overall system throughput and are also shown to have even less power consumption compared to the IWF.

Linear Precoding Game for MIMO MAC With Dynamic Access Point Selection

This paper examines a non-cooperative game in precoding design for MIMO multiple-access channels with dynamic access point (AP) selection. This game is first shown to be a potential game, where the potential function is the sum rate achieved by successive interference cancellation. Due to the mixed-integer nature of the optimization variable, it is challenging to directly characterize the maximum of the potential function, which are closely related to the Nash equilibrium (NE) of the game. Instead, we establish the existence and achievability of the maximum through non-decreasing and upperbounded properties of the potential function as a direct result of our proposed update scheme. A distributed algorithm is designed where each player selfishly optimizes its AP selection and linear precoding strategy in a sequential manner. Convergence is a by-product of the established properties of the potential function which are materialized by an iterative waterfilling algorithm. Numerical results show that the algorithm is able to reach fast convergence and provides a system sum rate nearing that of the optimal centralized solution.

Distributed algorithms for sum rate maximization in multi-cell downlink OFDMA with opportunistic DF relaying

This paper considers a multi-cell orthogonal frequency division multiple access (OFDMA) downlink system with several decode-and-forward (DF) relay stations (RSs) aiding the base station (BS) transmissions. The problem considered is the maximization of the system sum rate with a total power constraint in each cell. An iterative semi-distributed resource allocation (RA) algorithm is first proposed to optimize mode selection (decision whether relaying should be used or not and which relay), subcarrier assignment (MSSA), and power allocation (PA), alternatively. During the MSSA stage, the problem is decoupled into subproblems which can be solved distributively in linear time. During the PA stage, an algorithm based on single condensation and Lagrange duality (SCLD) is designed to optimize PA with the tentative MSSA results. The convergence of the SCLD-based RA algorithm is theoretically guaranteed and an local optimum is reached after convergence. To solve the formulated problem autonomously, a modified iterative water-filling (IWF) algorithm is further proposed. Specifically, each cell autonomously optimizes its own sum rate with the estimated power values of the received interferences from the other cells. An optimum algorithm is proposed to solve the local RA problem in each cell. Through numerical experiments, the convergence of the two proposed algorithms as well as their benefits compared with a centralized algorithm (CA) are illustrated.

Distributed allocation of subcarrier, power and bit‐level in multicell orthogonal frequency‐division multiple‐access networks

The downlink of multicell orthogonal frequency-division multiple-access (OFDMA) networks is studied, and the adaptive allocation of spectrum, power and rate is addressed. The authors consider networks with adaptive frequency reuse and discrete-level rates. Initially, the joint allocation problem is formulated as a centralised non-linear mixed-integer program (MIP), which is computationally intractable to solve optimally for practical problem sizes. Then, the capability of the receivers is exploited to estimate the subcarrier channel gains and the joint allocation problem is accordingly decomposed into subproblems, each of which is solved by a different base station with linear complexity. In the proposed iterative algorithm, the base stations perform rate and receiver allocation per subcarrier, with concurrent iterations. A filtering method is introduced to further decrease the algorithm complexity. Furthermore, for benchmarking purposes, the authors transform the original non-linear MIP to a linear MIP and find the optimal solution by means of standard branch-and-cut solvers. The merit of the proposed algorithm is demonstrated with numerical comparisons of its performance against the solutions of the linear MIP and the iterative waterfilling algorithm.

A Refined Convergence Condition for Iterative Waterfilling Algorithm

In a multi-user spectrum optimization problem, iterative waterfilling is normally used as a distributed power allocation algorithm. In this letter, we derive a new sufficient condition for its convergence, which is more relaxed than previous conditions. Our result strengthens the fact that the convergence of iterative waterfilling is dependent on signal-to-noise ratio (SNR), and that convergence is much easier in the low SNR regime.