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An urn occupancy approach for cognitive radio networks in DTVB white spaces

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Abstract

The paradigm of cognitive radio recently received considerable interest to address the so called ‘spectrum scarcity’ problem. In the USA, the Federal Communications Commission issued the regulatory for the use of cognitive radio in the TV white space spectrum. The primary objective is the design of cognitive devices able to combine the use of spectrum sensing and GEO-location information with the concept of the cognitive control channel to manage the cognitive devices. The recent standard ECMA-392 defines physical layer techniques and medium access control protocols to enable a cognitive network managed in a fully distributed fashion.

In this work, we pursue the design of an efficient medium access control protocol for the cognitive control channel to flexibly and reliably exchange messages inside the cognitive radio network. In particular, we explore how the cognitive devices can raise their awareness of spectrum vacancies of spectrum vacancies by means of sensing when the distributed beaconing defined by ECMA-392 is used.

Our main contributions are the following: (1) we propose a proprietary medium access control protocol based on the Standard ECMA-392; (2) we model the behavior of the cognitive radio network by means of an innovative urn model approach, (3) we investigate the access of the cognitive devices to the frequency channels with and without spoofing attacks and (4) we investigate the ability of the cognitive devices to identify frequency holes accounting for perfect and imperfect spectrum sensing, as well as we study the network throughput.

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Notes

  1. In a real system adjacent channels might be weakly correlated.

  2. In this work we do not explicitly tackle the hidden terminal problem but we instead partially address this aspect by means of a non-ideal sensing.

  3. In principle a similar type of problem could be formulated when the spoofers provide correct or incorrect sensing in a random fashion.

  4. Physical Layer Convergence Protocol.

  5. This situation can well describe the cases in which the information obtained from the DB is either outdated or incomplete.

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Acknowledgements

This research was supported, in part, by the European Commission Marie Curie International Outgoing Fellowship under Grant 2010-27292.

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Authors and Affiliations

  1. Joint Research Center (JRC), Via Enrico Fermi 2749, Ispra, Italy

    Leonardo Goratti, Gianmarco Baldini & Alberto Rabbachin

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  1. Leonardo Goratti
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  2. Gianmarco Baldini
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  3. Alberto Rabbachin
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Correspondence to Leonardo Goratti.

Appendix: The saddle point approximation

Appendix: The saddle point approximation

The method of the steepest descendant is a method used to approximate the probability density function (pdf) of some statistic, when it exists, starting from the known characteristic function of the statistic itself. This method, also referred to as the saddle point approximation, provides an accuracy of the approximated pdf that is O(k −1) and moreover it allows to approximate particularly well the tails of a distribution. A pioneering work on this method is provided in [32] considering the ensemble of k independent random variables with known mean. In this and other studies, parameters m and k are supposed roughly proportional as they tend to grow to the infinity.

In this paper, we are interested in determining the coefficient of a term having the following general form: e mz f(z). Consequently, a suitable extension to the work developed in [32] is provided by [34]. The latter studies the case in which the rates of growth of the function f(z) and m are decoupled. Therefore, this paper provides an adaptation to the saddle point approximation that better suits the purpose of our study. Since the provision of detailed derivations of the saddle point approximation is out of the scope of our paper, we use the method provided in [31] (which relies on [34]) to derive the coefficient of interest. However, the interested reader is remanded to the above cited papers for a more in-depth explanation.

$$\begin{aligned} \bigl[z^k\bigr]\big\{e^{(m-a)z}f(z) \big\} =&\frac{e^{(m-a) \alpha}f(\alpha)}{\alpha^{k+1}\sqrt{2\pi \varPhi(\alpha)}}\biggl(1+ \frac{\epsilon^2 +2\epsilon}{2k} \\ &{} - \frac{1}{12k} +o\biggl(\frac{1}{k} \biggr) \biggr), \end{aligned}$$
(33)

where α=k/m, ϵ=1+aα−δf(α), δf(z)=zf′(z)/f(z) and Φ(α)=f′′(α)/f(α)−(f′/f)2(α)+(k+1)/α 2. In our study we consider only the first term of the development shown in (33).

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Goratti, L., Baldini, G. & Rabbachin, A. An urn occupancy approach for cognitive radio networks in DTVB white spaces. Telecommun Syst 56, 229–244 (2014). https://doi.org/10.1007/s11235-013-9832-9

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