Power Control with Quantized Feedback in Wireless Networks: Stability Analysis of Foschini-Miljanic Algorithm

We present a brief account of three problems in wireless networks. First, on the problem of scalability, we show that under a certain model of interference, a network with n nodes can only provide a per-node throughput of order square-root of n bits/sec. However, an experimental investigation with IEEE 802.11 technology yielded the considerably worse power law of n raised to -1.68. We then present a new media access control protocol for ad hoc networks, called SEEDEX. It attempts to make reservations without explicitly doing so for each and every packet. Nodes use random schedule, and can inform each other about their schedules merely by exchanging the seeds of their pseudo random number generators. Last we turn to the problem of power control in ad hoc networks. We present a new protocol called COMPOW, which is designed to find the lowest power level at which the entire network is connected. We provide the theoretical justification for it, and a solution of the architectural issues involved. Using a notion of parallel modularity at the network layer, this protocol provides a joint solution for both the routing and power control problems. It has been implemented in the Linux kernel.

This invited paper outlines some recent results on the max-min SIR balancing problem in wireless networks in which power control and beamforming are the only mechanisms for resource allocation and interference management. In addition, we describe several potential extensions and improvements to existing algorithmic solutions, as well as prove the convergence of a distributed algorithm for joint power control and receive beamforming to a global optimum of the max-min SIR balancing problem. Finally we briefly discuss a possibility of how to incorporate the optimization of transmit beamformers.

The problem of mean square bounded-input bounded-output(BIBO) stability is investigated for a class of discrete-time stochastic control systems with time delays and non-linear perturbations. In this paper, a special point δ in the time delay's variation interval is introduced, and the variation interval is divided into two subintervals. Then, by defining a special Lyapunov-Krasovskii functional and checking its variation in the two subintervals, respectively, some novel delay-dependent stability criteria for the discrete-time stochastic control systems are derived. These conditions are expressed in the forms of linear matrix inequalities(LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Meanwhile, this paper provides a new method for studying discrete-time stochastic mean square BIBO stability. Finally, a numerical example is given to illustrate the validity of the main results.

In previous publications, the authors presented novel techniques for the design and realization of Bode-type variable-amplitude digital equalizers. The frequency response of the resulting variable-amplitude digital equalizers can be varied from that of an arbitrary shaping transfer function to its inverse by varying the value of a single variable digital multiplier. This paper is concerned with the development of an exact bounded-input bounded-output (BIBO) stability condition for general-order Bode-type variable-amplitude digital equalizers. The salient feature of the resulting BIBO stability condition is that it guarantees the stability of the Bode-type variable-amplitude digital equalizers over an entire range of values for the constituent variable digital multiplier. Moreover, this BIBO stability condition can simply be evaluated by examining the shaping transfer function associated with the variable-amplitude digital equalizer proper.

A distributed priority-based power and admission control algorithm is presented to address the priority-based gradual removal problem in cellular wireless networks. We assume that there exist two classes of priority for users (high-priority users versus low-priority users) and minimal number of low-priority users should be gradually removed, subject to the constraint that all high-priority users are supported with their target signal-to-interference-plus-noise ratios (SINRs) which is assumed feasible. In our proposed algorithm, each high-priority user rigidly tracks its target-SINR by employing the conventional target-SINR tracking power control algorithm, and each transmitting low-priority user tracks its target-SINR as long as its required transmit power is below a threshold, otherwise it temporarily removes itself. Each removed low-priority user resumes its transmission if the required transmit power to reach its target-SINR goes below a given threshold which is different from the former. Of these two thresholds, whose values are analytically obtained, the former is provided by the base station and the latter is obtained in a distributed manner as a function of the former. We show that the distributed power-update function corresponding to our proposed algorithm has at least one fixed-point which is not unique in general. The convergence point, where our proposed algorithm potentially converges to, depends on initial transmit power levels of users. We also show that our proposed algorithm, at each of its fixed-points, not only provides all high-priority users with their (feasible) target-SINRs but also guarantees that no low-priority user is erroneously removed (i.e., no additional low priority user can be supported along with currently supported users). Furthermore, for the special case of tracking a common target-SINR by all low-priority users, we show that our proposed algorithm minimizes the outage-ratio of low-priority users subject to zero-outage-ratio of high-priority users. Simulation results confirm our analytical developments and show that our proposed priority-based power and admission control algorithm solves the priority-based gradual removal problem efficiently.

Since the work of Goodman, a pressing problem of research in multidimensional systems and circuits has been the study of nonessential singularities of the second type and testing for the bounded-input, bounded-output (BIBO) stability in the presence of those singularities. In this paper, the stability behavior of two-variable (2-V) analog functions in the presence of singularities of the second kind is studied. As the double bilinear transformation gives a unique mapping relationship between analog and digital biplanes, this study is aimed at contributing to the design of 2-D recursive filters based on 2-V analog circuit theory. Also, the relationship between the Hurwitz nature of the denominator of a 2-V function and BIBO stability is discussed.

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.

Delay-dependent BIBO stability analysis of switched uncertain neutral systems

Throughput is an important performance consideration for multihop wireless networks. In this paper, we study the joint link scheduling and power control problem, focusing on maximizing the network throughput. We formulate the maximum throughput link scheduling with power control (MATH-SPC) problem, and present a mixed integer linear programming (MILP) formulation to provide optimal solutions. However, simply maximizing the throughput leads to a severe bias on bandwidth allocation among all links. In order to enhance both throughput and fairness, we define a new parameter, the demand satisfaction factor (DSF), to characterize the fairness of bandwidth allocation. We formulate the maximum throughput fair link scheduling with power control (MATA-SPC) problem and present an MILP formulation for this problem. We also present an effective polynomial time heuristic algorithm, namely, the serial LP rounding (SLPR) heuristic. Our numerical results show that bandwidth can be fairly allocated among all links/flows by solving our MATA-SPC formulation or using our heuristic algorithm at the cost of a minor reduction of network throughput

It has been shown that power control is an efficient approacn to achieve me quality of service (QoS) requirement in wireless networks. In this letter, we present a utility function that denotes the QoS and energy efficiency of each wireless terminal. We propose a framework of power control based on the game theory for the QoS of wireless mesh networks (WMNs). In this framework, all players do their best to maximize their own utility. Furthermore, we present a Nash Equilibrium (NE) point of the power control game. We prove that the equilibrium is inefficient, and we propose a distributed power control algorithm that improves the total utility with respect to the NE point. Finally, the proposed framework is evaluated by a numerical experiment, the results of which show the rationality of our system model and the efficiency of our power control algorithm.

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.

Multicast routing in wireless networks that possess the wireless multicast advantage could significantly reduce the power and energy consumption. However, this kind of multicast routing that only addresses the transmission radius coverage might not be able to meet the bandwidth requirement of the users. As a result, additional transmissions are required to incur more energy consumption and carbon dioxide emissions that make existing algorithms not applicable to bandwidth constrained applications. In this paper, for the first time, we address the bandwidth aware minimum power multicast routing problem in wireless networks where the objective function is to minimize the total power consumption subject to the users’ bandwidth requirements. This problem is a challenging cross-layer design problem that requires seamless and sophisticated integrated design in the network layer (multicast routing) and physical layer (bandwidth-aware wireless transmission and power control). We first formulate this problem as a mixed integer linear programming problem and then propose a Lagrangian relaxation based algorithm to solve this problem. Numerical results demonstrate that the proposed approach is a sound green networking algorithm that outperforms the existing power efficient multicast routing approaches under all tested cases, especially in large bandwidth request, fine radius granularity, large group size and sparse network.

This paper addresses the problem of power control in ad hoc networks supporting multicast traffic. First, we present a distributed algorithm which, given the set of multicast transmitters and their corresponding receivers, provides an optimal solution to the power control problem, if there is any. The transmit power levels obtained by solving the optimization problem minimize the network power expenditure while meeting the requirements of the SNR at the receivers. Whenever no optimal solution can be found for the given set multicast transmitters, we introduce a joint scheduling and power control algorithm, which eliminates the strong interferers thus allowing the other transmitters to solve the power control problem. The algorithm can be implemented in a distributed manner; however, it provides a sub-optimal solution since it is based on local information. Simulation results show that the obtained solution is close to the global optimum, when it exists. When there is no optimal solution, the proposed algorithm tries to maximize the number of successful multicast transmission.

In modern digital subscriber line (DSL) systems where multiple users coexist in the same frequency band, multiuser power control is an effective technique for reducing crosstalk interference and improving total system throughput. This paper considers the rate and power control problem in a frequency selective interference channel. The objective of the rate and power control is to maximize the achievable rate region, given an average power constraint for each user. We analyse the performance of both the distributed and centralized multiuser power control algorithms for very high bit rate digital subscriber lines (VDSL) and suggest a multiuser centralized power control algorithm which when applied to the VDSL upstream transmission enlarges the data rate region

Recently, the authors developed a new synthesis technique for the design of higher-order Bode-type variable-amplitude (VA) wave-digital (WD) equalizers. The salient feature of the resulting VA WD equalizers is that they permit the continuous variation of the WD equalizer transfer function from a shaping transfer function to its inverse by changing the value of a single variable digital multiplier only. The proposed design technique was based on the WD realization of the corresponding positive-real analog prototype shaping impedance function, and on the realization of the equalizer transfer function as the reflectance of the shaping impedance function with respect to the constituent variable digital multiplier. This paper is concerned with an investigation of the bounded-input bounded-output (BIBO) stability of general-order VA WD equalizers. It is shown that the resulting conditions are both necessary and sufficient for the BIBO stability of the VA WD equalizers for the entire range of values for the variable digital multiplier. These conditions can be checked in a straightforward fashion in terms of the characteristics of the shaping transfer function alone. An application example is given to illustrate the main results.