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The Power of Non-Uniform Wireless Power

Profile image of Magnus M. HalldorssonMagnus M. Halldorsson

2012

Abstract

We prove optimal bounds for inductive independence, implying a number of algorithmic applications. An algorithm is provided that achieves --- due to existing lower bounds --- capacity that is asymptotically best possible using oblivious power assignments. Improved approximation algorithms are provided for a number of problems for oblivious power and for power control, including distributed scheduling, connectivity, secondary spectrum auctions, and dynamic packet scheduling.

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A fundamental problem for wireless ad hoc networks is the assignment of suitable transmission powers to the wireless devices such that the resulting communication graph is connected. The goal is to minimize the total transmit power in order to maximize the lifetime of the network. Our aim is a probabilistic analysis of this power assignment problem. We prove complete convergence for arbitrary combinations of the dimension d and the distance-power gradient p. Furthermore, we prove that the expected approximation ratio of the simple spanning tree heuristic is strictly less than its worst-case ratio of 2. Our main technical novelties are twofold: First, we find a way to deal with the unbounded degree that the communication network induced by the optimal power assignment can have. Minimum spanning trees and traveling salesman tours, for which strong concentration results are known in Euclidean space, have bounded degree, which is heavily exploited in their analysis. Second, we apply a recent generalization of Azuma-Hoeffding's inequality to prove complete convergence for the case p ≥ d for both power assignments and minimum spanning trees (MSTs). As far as we are aware, complete convergence for p > d has not been proved yet for any Euclidean functional.

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Distributed power control algorithms for wireless networks
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Power control has been shown to be an effective way to increase capacity in wireless systems. In previous work on power control, it has been assumed that power levels can be assigned from a continuous range. In practice, however, power levels are assigned from a discrete set. In this work, we consider the minimization of the total power transmitted over given discrete sets of available power levels subject to maintaining an acceptable signal quality for each mobile. We have developed distributed iterative algorithms for solving a more general version of this integer programming problem, which is of independent interest, and have shown that they find the optimal solution in a finite number of iterations which is polynomial in the number of power levels and the number of mobiles

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In the opportunistic power control algorithm (OPC), designed in [1], , each user tries to keep the product of its transmit power and its experienced effective interference to a constant, called the target signal-interference product (SIP). This increases the transmit power when the channel is good and reduces it when the channel is poor (opportunism). It has been shown that the OPC always converges to a fixed point irrespective of whether the power is constrained (where there is no upper bound on transmit power) or unconstrained (where an upper bound on transmit power is taken into account). It has also been shown via simulation that the throughput achieved by the unconstrained OPC is significant (as compared to other existing distributed schemes), and is an increasing function of the target-SIP set by users, in the sense that a higher target-SIP results in a higher throughput. In this paper, we show that in contrast to the unconstrained OPC, when the constrained OPC is applied, not only the throughput is not necessarily increased as the target-SIPs increase, but it may even decrease if some users set their target-SIPs at high values. Furthermore, we propose a heuristic solution to determine the target-SIPs by users in a distributed manner. Our simulation results show that the throughput achieved by our distributed setting of the target-SIPs very closely approaches the maximum achievable throughput by the constrained OPC, and is very close to the global optimum value.

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Dynamic Power Allocation Under Arbitrary Varying Channels - The Multi-User Case
Niv Buchbinder

2010 Proceedings IEEE INFOCOM, 2010

We consider the power control problem in a timeslotted wireless channel, shared by a finite number of mobiles that transmit to a common base station. The channel between each mobile and the base station is time varying, and the system objective is to maximize the overall data throughput. It is assumed that each transmitter has a limited power budget, to be sequentially divided during the lifetime of the battery. We deviate from the classic work in this area, by considering a realistic scenario where the channel quality of each mobile changes arbitrarily from one transmission to the other.

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A bargaining approach to power control in networks of autonomous wireless entities
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2010

Abstract Interference is a fundamental problem in wireless networks, even in sparse topologies. Power Control (PC) is a powerful tool for mitigating it, however how to apply it to achieve the desired results is not obvious and satisfying the goals of all entities is not always possible.

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Distributed power control for time varying wireless networks: Optimality and convergence
Peter Glynn

2003

This paper presents a new distributed power control algorithm for ad-hoc wireless networks in random channel environments. Previous work in this area has focused on distributed power control for ad-hoc networks with fixed channels. We show that the algorithms resulting from such formulations do not accurately capture the dynamics of a time-varying channel. The performance of the network, in terms of power consumption and generated interference, can be severely degraded when a power control algorithm designed for a deterministic channel is applied to a random channel. In particular, some well-known strong optimality results for such algorithms no longer hold. In order to address these problems we propose a new criterion for power optimality in ad-hoc wireless networks. We then show that the optimal power allocation for this new criterion can be found through an appropriate stochastic approximation algorithm. Ultimately, the iterations of the stochastic approximation algorithm can be decoupled to form an optimal fully distributed on-line power control algorithm for ad-hoc wireless networks with time-varying channels.

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Wireless scheduling with power control
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ACM Transactions on Algorithms, 2012

We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signal-to-interference-plus-noise (SINR) constraints.

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The Power of Oblivious Wireless Power
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SIAM Journal on Computing, 2017

We study a fundamental measure for wireless interference in the SINR model known as (weighted) inductive independence. This measure characterizes the effectiveness of using oblivious power-when the power used by a transmitter only depends on the distance to the receiver-as a mechanism for improving wireless capacity. We prove optimal bounds for inductive independence, implying a number of algorithmic applications. An algorithm is provided that achieves capacity that is-due to existing lower bounds-asymptotically best possible using oblivious power assignments. Improved approximation algorithms are provided for a number of problems involving both oblivious power and arbitrary power control, including connectivity, secondary spectrum auctions, and dynamic packet scheduling. We also show that the price of oblivious power-the relative increase in capacity possible when using unconstrained power control-is only doubly logarithmic in the maximum link length.

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The Price of Local Power Control in Wireless Scheduling
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We first show that the known algorithms fail to obtain sub-logarithmic bounds; that is, their approximation ratio are $\tilde\Omega(\log \max(\Delta,n))$, where $n$ is the number of links, $\Delta$ is the ratio of the maximum and minimum link lengths, and $\tilde\Omega$ hides doubly-logarithmic factors. We then present the first $O(\log{\log\Delta})$-approximation algorithm, which is known to be best possible (in terms of $\Delta$) for oblivious power schemes. We achieve this by representing interference by a conflict graph, which allows the application of graph-theoretic results for a variety of related problems, including the weighted capacity problem. We explore further the contours of approximability, and find the choice of power assignment matters; that not all metric spaces are equal; and that the presence of weak links makes the problem harder. Combined, our result resolve the price of oblivious power for wireless scheduling, or the value of allowing unfettered power control.

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Wireless Capacity with Oblivious Power in General Metrics
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The capacity of a wireless network is the maximum possible amount of simultaneous communication, taking interference into account. Formally, we treat the following problem. Given is a set of links, each a sender-receiver pair located in a metric space, and an assignment of power to the senders. We seek a maximum subset of links that are feasible in the SINR model: namely, the signal received on each link should be larger than the sum of the interferences from the other links. We give a constant-factor approximation that holds for any length-monotone, sub-linear power assignment and any distance metric.

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On the Power of Uniform Power: Capacity of Wireless Networks with Bounded Resources
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The throughput capacity of arbitrary wireless networks under the physical Signal to Interference Plus Noise Ratio (SINR) model has received much attention in recent years. In this paper, we investigate the question of how much the worst-case performance of uniform and non-uniform power assignments differ under constraints such as a bound on the area where nodes are distributed or restrictions on the maximum power available. We determine the maximum factor by which a non-uniform power assignment can outperform the uniform case in the SINR model. More precisely, we prove that in one-dimensional settings the capacity of a non-uniform assignment exceeds a uniform assignment by at most a factor of O(log Lmax) when the length of the network is Lmax. In two-dimensional settings, the uniform assignment is at most a factor of O(log Pmax) worse than the non-uniform assignment if the maximum power is Pmax. We provide algorithms that reach this capacity in both cases. Due to lower bound examples in previous work, these results are tight in the sense that there are networks where the lack of power control causes a performance loss in the order of these factors. As a consequence, engineers and researchers may prefer the uniform model due to its simplicity if this degree of performance deterioration is acceptable.

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