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Robust allocation of RF device capacity for distributed spectrum functions

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Abstract

Real-time awareness of radio spectrum use across frequency, geography and time is crucial to effective communications and information gathering in congested airway environments, yet acquiring this awareness presents a challenging sensing and data integration problem. A recent proposal has argued that real-time generation of spectrum usage maps might be possible through the use of existing radios in the area of interest, by exploiting their sensing capacity when they are not otherwise being used. In this paper, we assume this approach and consider the task allocation problem that it presents. We focus specifically on the development of a network-level middleware for task management, that assigns resources to prospective mapping applications based on a distributed model of device availability, and allows mapping applications (and other related RF applications) to specify what is required without worrying about how it will be accomplished. A distributed, auction-based framework is specified for task assignment and coordination, and instantiated with a family of minimum set cover algorithms for addressing “coverage” tasks. An experimental analysis is performed to investigate and quantify two types of performance benefits: (1) the basic advantage gained by exploiting knowledge of device availability, and (2) the additional advantage gained by adding redundancy in subregions where the probability of availability of assigned devices is low. To assess the effectiveness of our minimum set cover algorithms, we compute optimal solutions to a static version of the real-time coverage problem and compare performance of the algorithms to these upper bound solutions.

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Notes

  1. In fact, our larger effort within the DARPA RadioMap program is aimed at the development this middleware.

  2. The reader is referred to our related work [5] for details on how this is accomplished in the highly constrained and uncertain environment where RadioMap is targeted to operate.

  3. Specification of techniques for obtaining these models is beyond the scope of this paper, but we believe that this is a tractable problem. Within a given node, periods of availability and unavailability can be estimated by periodically measuring the activity of the RF resources, calculating a time windowed average of activity level at some temporal granularity, and normalizing the resulting values for interpretation as a probability of availability over each window. Simple clustering of adjacent windows based on similarity could then be applied to produce a more task-oriented usage profile over time. It is reasonable to assume that construction and management of such availability profiles over the immediate past can be accomplished in real-time, and if RF activity patterns exhibit any degree of continuity, this basic model should enable reliable prediction of near-term future availability. However, the opportunity also exists to improve estimation of availability by discovering and exploiting knowledge of the actual activity patterns associated with the node’s primary mission. For example, a particular device may exhibit infrequent activity during certain periods of the day (e.g., over lunch hour). If additional feature data (e.g., time of day) is collected and integrated with availability profile data, then machine learning techniques such as [8] are immediately relevant to extracting such patterns to enhance the node’s availability model. As a first step, pattern extraction could be formulated as an offline learning process, with the resulting patterns then used to bias real-time prediction of the node’s future availability.

  4. In this experimental study, we reason geometrically using rectangles rather than circles to simplify the implementation.

  5. In all experiments presented in this paper, we make this assumption. Although it is a simplification of the general model of availability defined in Sect. 4.1, characteristics of the Radiomap domain suggest that this simple model of node availability is a reasonable basic assumption. RF scans are carried out by custom hardware and are typically of relatively short time durations of the order of 1–50 ms. Primary mission activity is most often dictated by time constants associated with human controlled activities, such as voice communication, data communication, and persistent RF emissions for disrupting such voice and data communication. These are typically of the order of seconds to 100’s of seconds. Given the extreme time scale differences associated with these activity patterns, a single, time-windowed average availability value that reflects the most recent RF activity associated with the primary mission should provide a good estimate of availability for much shorter duration RF scan tasks in the near future. Some error could creep in if the time instant of availability sampling happens to occur towards the end of the primary mission activity—we estimate this error to be 5–0.1 % overall, given the time differential in activities indicated above. On the other hand, there are also circumstances where a more fine-grained model of availability as a discrete probability distribution can make sense. If the node has visibility of a ”primary mission plan” (or has extracted predictable primary mission usage patterns from historical data), then it has more precise knowledge of when it will and will not be available. Furthermore, some nodes may employ communication waveforms in which the primary mission activity is further scheduled according to some known activity schedule (e.g., time division multiple access or TDMA [9]).

  6. Here we assume that requests are weighted by submission time, which determines the order in which task assignments are made.

  7. Of course, there are other sources of task failure as well, but for our purposes here we assume that they are abstracted into \(Prob_{avail}\).

  8. For simplicity, we represent probability of availability as a single value over time horizon, as was assumed in the experiments in Sects. 4 and 5. Note, however, that the formulation can be easily extended to a discrete distribution that varies over time.

  9. In our implementation bounding overlapping rectangles are computed and used to minimize space requirements.

  10. Larger problem sizes were also tried but these instances could not be reliably solved by our MILP implementation within the time limit set.

  11. Here and below, percentage of optimal is computed as \(\frac{CoverageScore(Alg)}{ CoverageScore(MILP)} \times 100\), where Alg is the heuristic task allocation procedure.

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Acknowledgments

This material is based upon work partially supported by DARPA under the RadioMap program, Contract No. FA8750-13-C-0014. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government. The authors would like to thank Jayanth Mogali for his help in formulating and implementing the upper bound MILP solution used to analyze the performance of our heuristic solution in Sect. 6.

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Authors and Affiliations

  1. The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Stephen F. Smith & Zachary B. Rubinstein

  2. Applied Communication Sciences, Basking Ridge, NJ, USA

    David Shur

  3. DOD Advanced Research Projects Agency, Arlington, VA, USA

    John Chapin

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  1. Stephen F. Smith
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Correspondence to Stephen F. Smith.

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Smith, S.F., Rubinstein, Z.B., Shur, D. et al. Robust allocation of RF device capacity for distributed spectrum functions. Auton Agent Multi-Agent Syst 31, 469–492 (2017). https://doi.org/10.1007/s10458-016-9329-5

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