Water-filling Problem Research Articles

Rate-Constrained Noise Reduction in Wireless Acoustic Sensor Networks

Wireless acoustic sensor networks (WASNs) can be used for centralized multi-microphone noise reduction, where the processing is done in a fusion center (FC). To perform the noise reduction, the data needs to be transmitted to the FC. Considering the limited battery life of the devices in a WASN, the total data rate at which the FC can communicate with the different network devices should be constrained. In this article, we propose a rate-constrained multi-microphone noise reduction algorithm, which jointly finds the best rate allocation and estimation weights for the microphones across all frequencies. The optimal linear estimators are found to be the quantized Wiener filters, and the rates are the solutions to a filter-dependent reverse water-filling problem. The performance of the proposed framework is evaluated using simulations in terms of mean square error and predicted speech intelligibility. The results show that the proposed method is very close in performance to that of the existing optimal method based on discrete optimization. However, the proposed approach can do this at a much lower complexity, while the existing optimal reference method needs a non-tractable exhaustive search to find the best rate allocation across microphones.

Quicker solution for interference reduction in wireless networks

In this study, a closed-form solution is presented for the constrained water-filling problem (CWFP) where in powers allocated to the user resources maximise the user's capacity under an interference constraint and a total power constraint. Total power constraint in CWFP is to save the energy in wireless network. To solve CWFP, erstwhile algorithms compute powers for all the resources iteratively. Unlike existing algorithms, the proposed method calculates the number of resources that gets positive (or non-zero) powers using the concepts of traditional water-filling problem. Later, powers are allocated to the resolved resources (that gets positive powers) alone using the closed-form solution, which reduces the number of computations. It can be discerned that the computational complexity of the given solution is of the order of , where is the total number of resources; which is remarkably lower than that of the prior algorithms specified by an order of .

Optimizing power allocation in wireless networks: Are the implicit constraints really redundant?

The widely considered power constraints on optimizing power allocation in wireless networks, e.g., non-negative individual power and limited sum of all the individual power, imply the constraints where each individual power is not greater than the limited sum. However, the related implicit constraints are generally regarded as redundant for algorithm design in most current studies. In this paper, we explore the question “Are the implicit constraints really redundant?” in the optimization of power allocation especially when using iterative methods (e.g., subgradient method) that have slow convergence speeds. Using the water-filling problem as an illustration, we first derive the structural properties of the optimal solutions based on Karush–Kuhn–Tucker conditions. Then we propose a non-iterative closed-form optimal method and use iterative methods (i.e., bisection method and subgradient method) to solve the problem. Our theoretical analysis shows that the implicit constraints are not redundant, and particularly, their consideration can effectively speed up the convergence of the subgradient method and reduce its sensitivity to the chosen step size. Numerical results for the water-filling problem and another existing power allocation problem demonstrate the effectiveness of considering the implicit constraints.

Fast Computation of Generalized Waterfilling Problems

In this letter, we present a novel method of solving the Generalized Waterfilling problem (GWFP) using equivalence with a waterfilling problem (WFP) which has a closed form solution. Consequentially, a class of WFPs with only one-step called `1-step' WFP is used to derive a low complexity algorithm which has the smallest worst case complexity reported. The proposed algorithm is verified by simulations.

A Generalized Water-Filling Algorithm with Linear Complexity and Finite Convergence Time

This letter presents an algorithm with linear complexity and finite convergence time for solving the generalized water-filling (WF) problem. The WF problem is generalized by using a weighted-sum-rate, weighted-sum-power, and peak power constraints. The proposed algorithm solves the optimization problems with concave (power and rate) or quasi-concave (energy-efficiency) objective functions. Additionally, it can simultaneously use maximum-power and minimum-rate constraints and give a priority to one of the constraints in the event they generate an infeasible region. Through this generalization, the algorithm can be applied to many WF-based methods proposed in the literature. Moreover, this letter shows multiple ways to further reduce the computational complexity and, via simulation, illustrates the effectiveness of the proposed algorithm.

Downlink Resource Allocation for Next Generation Wireless Networks with Inter-Cell Interference

This paper presents a novel downlink resource allocation scheme for OFDMA-based next generation wireless networks subject to inter-cell interference (ICI). The scheme consists of radio resource and power allocations, which are implemented separately. Low-complexity heuristic algorithms are first proposed to achieve the radio resource allocation, where graph-based framework and fine physical resource block (PRB) assignment are performed to mitigate major ICI and hence improve the network performance. Given the solution of radio resource allocation, a novel distributed power allocation is then performed to optimize the performance of cell-edge users under the condition that desirable performance for cell-center users must be maintained. The power optimization is formulated as an iterative barrier-constrained water-filling problem and solved by using the Lagrange method. Simulation results indicate that our proposed scheme can achieve significantly balanced performance improvement between cell-edge and cell-center users in multi-cell networks compared with other schemes, and therefore realize the goal of future wireless networks in terms of providing high performance to anyone from anywhere.

Closed form solutions for water-filling problems in optimization and game frameworks

We study power control in optimization and game frameworks. In the optimization framework there is a single decision maker who assigns network resources and in the game framework users share the network resources according to Nash equilibrium. The solution of these problems is based on so-called water-filling technique, which in turn uses bisection method for solution of non-linear equations for Lagrange multipliers. Here we provide a closed form solution to the water-filling problem, which allows us to solve it in a finite number of operations. Also, we produce a closed form solution for the Nash equilibrium in symmetric Gaussian interference game with an arbitrary number of users. Even though the game is symmetric, there is an intrinsic hierarchical structure induced by the quantity of the resources available to the users. We use this hierarchical structure to perform a successive reduction of the game. In addition to its mathematical beauty, the explicit solution allows one to study limiting cases when the crosstalk coefficient is either small or large. We provide an alternative simple proof of the convergence of the Iterative Water Filling Algorithm. Furthermore, it turns out that the convergence of Iterative Water Filling Algorithm slows down when the crosstalk coefficient is large. Using the closed form solution, we can avoid this problem. Finally, we compare the non-cooperative approach with the cooperative approach and show that the non-cooperative approach results in a more fair resource distribution.

Capacity calculations for rapidly fading communications channels

Communication over rapidly changing channels such as the underwater acoustic channel has been an active research area, as well as an engineering challenge, for more than three decades. This paper derives an upper bound for the Shannon channel capacity-cost function for a class of randomly time-varying channels under an average power constraint. The channels considered can be characterized by a series of uncorrelated parallel diversity channels with Gaussian-distributed random gain and additive white Gaussian noise parameters. The resulting expression for the single-channel case clearly shows that such channels have finite capacity even when the source power is unconstrained. Extensions are made to the multiple-diversity-channel case with a modified water-filling problem resulting.