Iterative Waterfilling Research Articles

Downlink Transmission Scheme for Wireless MIMO Broadcast Channels with Multiuser Diversity

Sum power iterative water-filling (SPIWF) algorithm provides sum-rate-optimal transmission scheme for wireless multiple-input multiple-output (MIMO) broadcast channels (BC), whereas it suffers from its high complexity. In this paper, we propose a new transmission scheme based on a novel block zero-forcing dirty paper coding (Block ZF-DPC) strategy and multiuser-diversity-achieving user selection procedure. The Block ZF-DPC can be considered as an extension of existing ZF-DPC into MIMO BCs. Two user selection algorithms having linear increasing complexity with the number of users have been proposed. One aims at maximizing the achievable sum rate directly and the other is based on Gram-Schmidt Orthogonalization (GSO) and Frobenius norm. The proposed scheme is shown to achieve a sum rate close to the sum capacity of MIMO BC and obtain optimal multiplexing and multiuser diversity gain. In addition, we also show that both selection algorithms achieve a significant part of the sum rate of the optimal greedy selection algorithm at low computation expenditure.

Asynchronous Iterative Water-Filling for Gaussian Frequency-Selective Interference Channels

This paper considers the maximization of information rates for the Gaussian frequency-selective interference channel, subject to power and spectral mask constraints on each link. To derive decentralized solutions that do not require any cooperation among the users, the optimization problem is formulated as a static noncooperative game of complete information. To achieve the so-called Nash equilibria of the game, we propose a new distributed algorithm called asynchronous iterative water-filling algorithm. In this algorithm, the users update their power spectral density (PSD) in a completely distributed and asynchronous way: some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference. The proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water-filling algorithms, e.g., sequential and simultaneous versions. The main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the (unique) Nash equilibrium of the game.

Performance Analysis of Fixed-Margin Iterative Water-Filling for ADSL2+ and VDSL Mixed System

Crosstalk is a major issue in modern ADSL and VDSL systems. Static spectrum management (SSM), the traditional way to guarantee spectrum compatibility, employs spectral masks which can be overly restrictive and result in poor performance. In this paper, fixed margin iterative water-filling algorithm is investigated in downstream VDSL and ADSL2+ scenario when they are in the same binder. The algorithm can minimize the transmission power and at the same time the overall high-quality service is guaranteed for all the users of the same binder. Simulation results show that ADSL2+ can realize performance gains of up to 80% compared with SSM techniques or ADSL.

Distributed resource allocation for rate-constrained users in multi-cell OFDMA networks

This letter addresses resource allocation in multi-cell OFDMA networks. It describes a heuristic for distributed sum power minimization under target data rate requirements. The proposed method establishes a set of target SINR per user and subcarrier, determined to reach the target data rate of each user, while avoiding power divergence situations. Power control can then be performed independently over each subcarrier. Compared to iterative water-filling, this method proves to be very efficient at any load in terms of resource consumption and users' rejection.

Price-Based Spectrum Management in Cognitive Radio Networks

Cognitive radios (CRs) have a great potential to improve spectrum utilization by enabling users to access the spectrum dynamically without disturbing licensed primary radios (PRs). A key challenge in operating these radios as a network is how to implement an efficient medium access control (MAC) mechanism that can adaptively and efficiently allocate transmission powers and spectrum among CRs according to the surrounding environment. Most existing works address this issue via suboptimal heuristic approaches or centralized solutions. In this paper, we propose a novel joint power/channel allocation scheme that improves the performance through a distributed pricing approach. In this scheme, the spectrum allocation problem is modeled as a noncooperative game, with each CR pair acting as a player. A price-based iterative water-filling (PIWF) algorithm is proposed, which enables CR users to reach a good Nash equilibrium (NE). This PIWF algorithm can be implemented distributively with CRs repeatedly negotiating their best transmission powers and spectrum. Simulation results show that the social optimality of the NE solution is dramatically improved through pricing. Depending on the different orders according to which CRs take actions, we study sequential and parallel versions of the PIWF algorithm. We show that the parallel version converges faster than the sequential version. We then propose a corresponding MAC protocol to implement our resource management schemes. The proposed MAC allows multiple CR pairs to be first involved in an admission phase, then iteratively negotiate their transmission powers and spectrum via control-packet exchanges. Following the negotiation phase, CRs proceed concurrently with their data transmissions. Simulations are used to study the performance of our protocol and demonstrate its effectiveness in terms of improving the overall network throughput and reducing the average power consumption.

Capacity Optimizing Power Allocation in Interference Channels

The interference channel is an essential model in both wireline and wireless communication systems. This article addresses transmit power allocation in interference channels with total transmit power constraint. The optimum power allocation maximizing the sum rate in two user interference channels can be derived analytically. However, the non-convexity of the optimization problem makes it prohibitively complex to obtain the optimum solution either analytically or numerically in general K user scenarios. After reviewing several conventional suboptimum power allocation schemes including equal power allocation, greedy power allocation and waterfilling power allocation, an iterative waterfilling algorithm is proposed and discussed. The performance of various power allocation schemes is evaluated through simulations, which suggests that the proposed iterative waterfilling outperforms other suboptimum power allocation schemes in certain scenarios.

Sum Capacity of One-Sided Parallel Gaussian Interference Channels

The sum capacity of the one-sided parallel Gaussian interference channel is shown to be a concave function of user powers. Exploiting the inherent structure of the problem, we construct a numerical algorithm to compute it. Two suboptimal schemes are compared with the capacity-achieving scheme. One of the suboptimal schemes, namely iterative waterfilling, yields close-to-capacity performance when the cross link gain is small.

The Capacity Region of Frequency-Selective Gaussian Interference Channels Under Strong Interference

This paper presents the capacity region of frequency-selective Gaussian interference channels under the condition of strong interference, assuming an average power constraint per user. First, a frequency-selective Gaussian interference channel is modeled as a set of independent parallel memoryless Gaussian interference channels. Using nonfrequency selective results, the capacity region of frequency-selective Gaussian interference channels under strong interference is expressed mathematically. Exploiting structures inherent in the problem, a dual problem is constructed for each independent memoryless channel, in which both mathematical and numerical analysis are performed. Furthermore, three suboptimal methods are compared to the capacity-achieving coding and power allocation scheme. Iterative waterfilling, a suboptimal scheme, provides close-to-optimum performance and has a distributed coding and power allocation scheme, which are attractive in practice.

Convergence of Iterative Waterfilling Algorithm for Gaussian Interference Channels

Iterative waterfilling power allocation algorithm for Gaussian interference channels is investigated. The system is formulated as a non-cooperative game. Based on the measured interference powers, the users maximize their own throughput by iteratively adjusting their power allocations. The Nash equilib- rium in this game is a fixed point of such iterative algorithm. Both synchronous and asynchronous power update are considered. Some sufficient conditions under which the algorithm converges to the Nash equilibrium are derived.

Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems Based on Game Theory—Part II: Algorithms

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this two-part paper, we address the problem of finding the optimal precoding/multiplexing scheme for a set of noncooperative links sharing the same physical resources, e.g., time and bandwidth. We consider two alternative optimization problems: P.1) the maximization of mutual information on each link, given constraints on the transmit power and spectral mask; and P.2) the maximization of the transmission rate on each link, using finite-order constellations, under the same constraints as in P.1, plus a constraint on the maximum average error probability on each link. Aiming at finding decentralized strategies, we adopted as optimality criterion the achievement of a Nash equilibrium and thus we formulated both problems P.1 and P.2 as strategic noncooperative (matrix-valued) games. In Part I of this two-part paper, after deriving the optimal structure of the linear transceivers for both games, we provided a unified set of sufficient conditions that guarantee the uniqueness of the Nash equilibrium. In this Part II of the paper, we focus on the achievement of the equilibrium and propose alternative distributed iterative algorithms that solve both games. Specifically, the new proposed algorithms are the following: 1) the <emphasis emphasistype="italic">sequential</emphasis> and <emphasis emphasistype="italic">simultaneous</emphasis> iterative waterfilling-based algorithms, incorporating spectral mask constraints and 2) the <emphasis emphasistype="italic">sequential</emphasis> and <emphasis emphasistype="italic">simultaneous</emphasis> gradient-projection-based algorithms, establishing an interesting link with variational inequality problems. Our main contribution is to provide sufficient conditions for the <emphasis emphasistype="italic">global</emphasis> convergence of all the proposed algorithms which, although derived under stronger constraints, incorporating for example spectral mask constraints, have a broader validity than the convergence conditions known in the current literature for the sequential iterative waterfilling algorithm. </para>

Generalization of Hybrid Time Divisioning for Power Allocation in DMT-Based DSL Systems

We propose an algorithm that seeks to generalize the recently proposed hybrid time divisioning scheme. It tries to make optimal groupings amongst all the (user, subchannel) pairs by deciding which users should transmit alone in a subchannel and which users should transmit along with each other in order to yield substantial data rate increments. This time divisioning based modification can be applied over any resource allocation scheme (e.g multi user discrete bit loading, iterative waterfilling, optimal spectrum balancing) which involves simultaneous transmission of all the users.

Optimization-Theoretic Analysis of Stability-Optimal Transmission Policy for Multiple-Antenna Multiple-Access Channel

The philosophy of scheduler design in modern wireless data networks exposes the tendency towards layer-spanning optimization (cross-layer design). An important particular goal of joint design of the physical and (data) link layer appears to be the achievement of the entire stability region of the network. In this work, we provide the optimization-theoretic analysis of the corresponding policy, referred to as stability-optimal policy, in the multiple-antenna multiple-access channel. We characterize some useful features of the policy. In particular, we state the conditions for optimality of link subset transmission and expose essential differences to the established scheduling approaches, such as sum-rate maximization. This further allows for the statement of necessary and sufficient conditions for the overall stability optimality of successive interference cancellation order. Finally, we present the approach of splitting of the multilink stability problem into the set of single-link optimization problems. We propose a corresponding iterative optimization method, which is an extension of the known concept of iterative waterfilling from

Selective Iterative Waterfilling for Digital Subscriber Lines

This paper presents a high-performance, low-complexity, quasi-distributed dynamic spectrum management (DSM) algorithm suitable for DSL systems. We analytically demonstrate that the rate degradation of the distributed iterative waterfilling (IW) algorithm in near-far scenarios is caused by the insufficient utilization of all available frequency and power resources due to its nature of noncooperative game theoretic formulation. Inspired by this observation, we propose the selective IW (SIW) algorithm that can considerably alleviate the performance degradation of IW by applying IW selectively to different groups of users over different frequency bands so that all the available resources can be fully utilized. For N users, the proposed SIW algorithm needs at most N times the complexity of the IW algorithm, and is much simpler than the centralized optimal spectrum balancing (OSB), while it can offer a rate performance much better than that of the IW and close to the maximum possible rate region computed by the OSB in realistic near-far DSL scenarios. Furthermore, its predominantly distributed structure makes it suitable for DSL implementation.

Low-Complexity Iterative Algorithm for Finding the MIMO-OFDM Broadcast Channel Sum Capacity

A novel low-complexity and provably convergent algorithm is proposed to find the sum capacity for vector Gaussian broadcast channels. Unlike the recently proposed sum-power constraint iterative waterfilling (SPC-IWF) algorithms, it has lower complexity and requires no additional precautions to ensure the convergence. We have proved analytically the convergence with probability one, and the computer simulations show that the proposed algorithm converges faster than the earlier variants of SPC-IWF algorithms. We formulate the problem in the context of a multiple-input multiple-output orthogonal frequency-division multiplexing system and discuss the simplifications provided by the block-diagonal channel structure

Achieving the Capacity Region Boundary of Fading CDMA Channels via Generalized Iterative Waterfilling

We characterize the optimum power control policies that achieve arbitrary rate tuples on the boundary of the capacity region of a power controlled, code division multiple access (CDMA) system in a fading channel with perfect channel state information (CSI). We propose a generalized waterfilling approach, and provide an iterative algorithm that solves for the optimum power allocation policy, for a given arbitrary rate tuple on the boundary of the capacity region. We then investigate the effects of limited feedback on the capacity region, and demonstrate that a good power control policy may require only a very low rate feedback

Optimal multiuser spectrum balancing for digital subscriber lines

Crosstalk is a major issue in modern digital subscriber line (DSL) systems such as ADSL and VDSL. Static spectrum management, which is the traditional way of ensuring spectral compatibility, employs spectral masks that can be overly conservative and lead to poor performance. This paper presents a centralized algorithm for optimal spectrum balancing in DSL. The algorithm uses the dual decomposition method to optimize spectra in an efficient and computationally tractable way. The algorithm shows significant performance gains over existing dynamics spectrum management (DSM) techniques, e.g., in one of the cases studied, the proposed centralized algorithm leads to a factor-of-four increase in data rate over the distributed DSM algorithm iterative waterfilling.

Analysis of Iterative Waterfilling Algorithm for Multiuser Power Control in Digital Subscriber Lines

We present an equivalent linear complementarity problem (LCP) formulation of the noncooperative Nash game resulting from the DSL power control problem. Based on this LCP reformulation, we establish the linear convergence of the popular distributed iterative waterfilling algorithm (IWFA) for arbitrary symmetric interference environment and for certain asymmetric channel conditions with any number of users. In the case of symmetric interference crosstalk coefficients, we show that the users of IWFA in fact, unknowingly but willingly, cooperate to minimize a common quadratic cost function whose gradient measures the received signal power from all users. This is surprising since the DSL users in the IWFA have no intention to cooperate as each maximizes its own rate to reach a Nash equilibrium. In the case of asymmetric coefficients, the convergence of the IWFA is due to a contraction property of the iterates. In addition, the LCP reformulation enables us to solve the DSL power control problem under no restrictions on the interference coefficients using existing LCP algorithms, for example, Lemke's method. Indeed, we use the latter method to benchmark the empirical performance of IWFA in the presence of strong crosstalk interference.

Spectrally Compatible Iterative Water Filling

Until now static spectrum management has ensured that DSL lines in the same cable are spectrally compatible under worst-case crosstalk conditions. Recently dynamic spectrum management (DSM) has been proposed aiming at an increased capacity utilization by adaptation of the transmit spectra of DSL lines to the actual crosstalk interference. In this paper, a new DSM method for downstream ADSL is derived from the well-known iterative water-filling (IWF) algorithm. The amount of boosting of this new DSM method is limited, such that it is spectrally compatible with ADSL. Hence it is referred to as spectrally compatible iterative water filling (SC-IWF). This paper focuses on the performance gains of SC-IWF. This method is an autonomous DSM method (DSM level 1) and it will be investigated together with two other DSM level-1 algorithms, under various noise conditions, namely, iterative water-filling algorithm, and flat power back-off (flat PBO).

A hybrid time divisioning scheme for power allocation in DMT-based DSL systems

We propose an iterative waterfilling based multiuser Hybrid Time Divisioning (HTD) scheme for power allocation in DMT based DSL systems. The problem of finding the (user,subchannel) pairs which should transmit alone and the pairs which should transmit along with other users, so as to result in the maximum aggregate data rate achievable using time divisioning, has been considered. The proposed scheme Is a low complexity, sub-optimal solution to this problem. Results show that the HTD scheme can achieve better data rates than Iterative Waterfilling a well as Multiuser Discrete Bit Loading scheme (for high coupling coefficient values) with comparatively lesser complexity

ADSL Transceivers Applying DSM and Their Nonstationary Noise Robustness

Dynamic spectrum management (DSM) comprises a new set of techniques for multiuser power allocation and/or detection in digital subscriber line (DSL) networks. At the Alcatel Research and Innovation Labs, we have recently developed a DSM test bed, which allows the performance of DSM algorithms to be evaluated in practice. With this test bed, we have evaluated the performance of a DSM level-1 algorithm known as iterative water-filling in an ADSL scenario. This paper describes the results of, on the one hand, the performance gains achieved with iterative water-filling, and, on the other hand, the nonstationary noise robustness of DSM-enabled ADSL modems. It will be shown that DSM trades off nonstationary noise robustness for performance improvements. A new bit swap procedure is then introduced to increase the noise robustness when applying DSM.