Extending Wireless Algorithm Design to Arbitrary Environments via Metricity ∗ Helga Gudmundsdottir School of Computer Science, CRESS Reykjavik University, Iceland helgag10@ru.is Eyjólfur I. Ásgeirsson School of Science and Engineering, ICE-TCS Reykjavik University, Iceland eyjo@ru.is Marijke H. L. Bodlaender School of Computer Science, ICE-TCS Reykjavik University, Iceland marijke12@ru.is Joseph T. Foley School of Science and Engineering Reykjavik University, Iceland foley@ru.is Magnús M. Halldórsson School of Computer Science, ICE-TCS Reykjavik University, Iceland mmh@ru.is Ymir Vigfusson School of Computer Science, ICE-TCS, CRESS Reykjavik University, Iceland ymir@ru.is ABSTRACT Efficient spectrum use in wireless sensor networks through spatial reuse requires effective models of packet reception at the physi- cal layer in the presence of interference. Despite recent progress in analytic and simulations research into worst-case behavior from interference effects, these efforts generally assume geometric path loss and isotropic transmission, assumptions which have not been borne out in experiments. Our paper aims to provide a methodology for grounding theoreti- cal results into wireless interference in experimental reality. We de- velop a new framework for wireless algorithms in which distance- based path loss is replaced by an arbitrary gain matrix, typically ob- tained by measurements of received signal strength (RSS). We ex- perimentally evaluate the framework in two indoors testbeds with 20 and 60 motes, and confirm superior predictive performance in packet reception rate for a gain matrix model over a geometric distance-based model. At the heart of our approach is a new parameter ζ called metricity which indicates how close the gain matrix is to a distance metric, effectively measuring the complexity of the environment. A pow- erful theoretical feature of this parameter is that all known SINR scheduling algorithms that work in general metric spaces carry over to arbitrary gain matrices and achieve equivalent performance guar- antees in terms of ζ as previously obtained in terms of the path loss constant. Our experiments confirm the sensitivity of ζ to the nature of the environment. Finally, we show analytically and empirically how multiple channels can be leveraged to improve metricity and thereby performance. We believe our contributions will facilitate experimental validation for recent advances in algorithms for phys- ical wireless interference models. ∗ Supported by grant-of-excellence no. 120032011 from the Ice- landic Research Fund. 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INTRODUCTION There is mounting demand for tomorrow’s wireless networks to provide higher performance while lowering costs. A central chal- lenge in meeting this demand is to improve the utilization of the wireless spectrum to enable simultaneous communications at the same radio frequency. To accommodate research into efficient use of wireless channels, for instance through spatial reuse, we require practical models of signal propagation behavior and reception at the physical layer in the presence of wireless interference. Early models of worst-case wireless communication under inter- ference were graph-based, most commonly based on distances. In comparison, physical models, or SINR (signal to interference and noise ratio) models, capture two important features of reality: sig- nal strength decays as it travels (rather than being a binary prop- erty) and interference accumulates (rather than being a pairwise relation). Analytic work on SINR – introduced by Gupta and Kumar [14] in an average-case setting and Moscibroda and Wattenhofer [26] in worst-case – has generally assumed geometric path loss, referred to here as the GEO- SINR model: signals decay as a fixed polynomial of the distance traveled. While free space exhibits geometric decay, the reality for real- world wireless environments is more complex. When located above an empty plane, a signal bounces off the ground, resulting in com- plicated patterns of superpositions known as multi-path fading. Most real scenarios are more complex, with walls and obstructions. In particular, cityscape and indoor environments are notoriously hard to model. Moreover, the simple range-based models often make further assumptions into geometric path loss that do not concord with experiments, such as smooth and isotropic polynomial de- crease in the signal strength. In fact, quoting recent meta-analysis [3], “link quality is not correlated with distance.”