Virgiliorodriguez.info

Inattentive cognitive radios: Cognition with Communication Networks (ComNets) Research Group Abstract—A “true” cognitive radio is a sophisticated A cognitive radio was originally envisioned as a devise that is aware of, can adapt to, and even learn sophisticated devise capable of becoming aware of, from its environment. To do so, such device would need adapting to, and even learning from its environment, to perform many complex (parallel) tasks in minuscule to achieve the most efficient possible operation amounts of time, and within tight size, weight, heat, and [2][3]. In order to accomplish that, such device energy limitations. In any sophisticated computing system,communication and computation limit each other. Here would need to perform many complex (parallel) we discuss a formal model that abstract an information- tasks in minuscule amounts of time, and within processing limited rational entity (human or not) seeking extremely tight size, weight, heat, and energy lim- to maximise a performance function that depends on both itations. In a “true” cognitive radio, as in any so- an action under its control, and and an exogenous input.
phisticated computing system, communication and The entity finds and optimal probabilistic response such computation limit each other [1, P.4]. Thus, the that the Shannon-theoretic mutual information betweeninput and output does not exceed an information capacity list of factors constraining the device’s operation constraint. The possible application to secondary dynamic must also include limited information processing spectrum access receives special attention, but the frame- work is of interest whenever the practical limits on acognitive radio information processing capacity cannot be The problem of information processing con- neglected. Rather than proposing a particular algorithm straints affects other rational entities, including hu- and showing numerical results, our aims are to (i) in-troduce an important practical problem affecting “true” man beings. For instance, in an economic environ- cognitive radios, (ii) introduce a body of existing scientific ment, a rational consumer or investor may have at its literature not widely known in engineering, and (iii) discuss disposal much more information that it can “digest” potential applications of this literature to cognitive radio on time to make a critical decision. This includes not only information available by subscription from “ex-pert” sources, but also freely available information obtainable from news broadcasts, popular media, or from government sources. New telecommuni- cation technologies such as the world-wide web and social networking websites have increased the availability of both paid and free information. Thus, a rational investor or consumer need to find “sub- limited. These become intertwined. . . ”[1, optimal” strategies that yield choices under limited information-processing capability in finite time.
Below we focus on an approach to the prob- V. Rodriguez is now with the Signal & System Theory Group at the Universität Paderborn, in Germany.
lem of rational decision-making under information- processing constraints proposed in [4]∗. It consists and I(X, Y ) denotes mutual information, defined as of a formal model that abstract a rational entity (human or machine) that seeks to maximise a per- formance function that depends on both an action under its control, and and an exogenous input.
The entity finds and optimal probabilistic response such that the mutual information between inputand output does not exceed a Shannon-theoretic Above, f can be interpreted as an algorithm – or a physical device — that takes input x and We focus on the “tracking” performance function.
probabilistically produces and output y. One wants Here “tracking” simply means that the performance to design f to maximise the expected value of function is monotonic in the absolute value of U , while obeying(1d), which can be interpreted as the difference between the value of the exogenous an “information processing” constraint. To produce signal and the entity’s choice, thus, the entity want y from x in given time, an information carrying its choice to “track” (that is, to stay near) the signal (or “data”) must travel at a maximum rate value of the external signal. A simple example is C. The “optimal” f must not require or imply a (x−y)2 with x the exogenous and y the endogenous mutual information between X and Y that exceeds variable. A function such as this can — as discussed the information that can actually be delivered in the below — be of interest in two communication scenarios: jamming, and secondary radio-spectrum A probabilistic response is common in another mathematical model: Game Theory [6], [7]. Cer- We continue by introducing and discussing the tain games are known to have a “mixed strategy” formal Shannon-theoretic model from [4]. Then we equilibrium in which it is optimal for one or more discuss briefly common dynamic-spectrum access players to randomly choose among available actions scenarios, and describe how ideas from the model according to a probability distribution over those can be useful in these scenarios. Finally, we provide actions that satisfy some optimality condition(s); that is, the player derives an optimal probabilitydistribution that produces the player’s response.
The solution to problem (1) also answers the following information-theoretic question: Among all communication channels ofcertain capacity, C, which one is optimalgiven a performance function, U (x, y) of the channel’s input x and its output y? To immediately develop some intuition on prob- lem (1), let x be associated with the energy sensed by a receiver coming from its desired transmitter over a period of interest. Then, U (x, y) = −(x − X and gY are the probability density func- tions (pdf) associated with an information source, ky)2 could be of interest to a nearby “jammer”, with y denoting its energy output over the same period, and k an appropriate constant. Solving (1) with this U will yield an f such that, on average, the transmitter and the jammer’s signals reach thevictim receiver with similar strength, which would be most disruptive to the victim. Below we shall The author of [4], Prof. Christopher A. Sims, is co-recipient of the 2011 Nobel Prize in Economic Science [5].
see that a nearby secondary user, in a dynamic spectrum access scenario, can behave constructively search for radio spectrum bands that are temporarily by following a strategy that is similar but “opposite” unused ( “spectrum holes”), an utilise such bands as 1) First-order optimising conditions: It can be 1) The “spectrum interweave” scenario: In a shown that at any (x, y) such that both f (x, y) > 0 common dynamic spectrum access (DSA) scenario and gX(x) > 0, the first-order optimising conditions (“spectrum interweave”), a secondary user with a stream of data to transmit periodically senses cer-tain communication channels and only uses those expected to be unused by primary users in the with µ(x) and λ ≥ 0 Lagrange-multipliers asso- 2) Major challenges for instantaneous sensing ciated with, respectively, (1b) (the source marginal based approaches: However, even with an ex- tremely accurate sensing system, the “hidden termi- 2) General solution form: For λ > 0, and with nal problem” remains a major challenge. Further- more, the possibility that a primary user starts ac-cessing a channel — or, conversely, stops using it — immediately after the sensing operation has ended could never be ruled out. Thus, recent work has The desired conditional pdf is f (y\x) — not proposed secondary channel-usage policies based on f (x\y) — because gX is given, and f (x, y) = f (y\x)gX(x). Nevertheless, (2b) provides valuable 3) Statistical approach to secondary DSA: Be- cause of the challenges of relying solely on instan- 3) Particular solution forms: (2b) reveals that a taneous sensing information for secondary spectrum quadratic U (e. g., (x − y)2) will yield a conditional access, several recent proposals seek secondary ac- f (x\y) with the “Gaussian” form, irrespective of cess strategies based on statistics obtained from his- torical information about the primary user’s channel Furthermore, as λ approaches zero; that is, as access. For instance, [10] focuses on a wireless LAN capacity becomes very large, the conditional proba- scenario — in which the hidden terminal node is not bility density ordinate becomes very large. Since the an issue — and utilises empirical information to total area under the density must equal one, a very predict idle periods between bursty transmissions.
large “peak” implies that all the probability mass On a non-contiguous OFDM scenario, [11] pro- must be allocated about a single point. Thus, when poses portfolio theory [12], for a secondary user capacity is very large, the optimal relation between to determine on the basis of historical information inputs and outputs (that is, the underlying algorithm) on which channels to “invest” communication re- sources. Then, [13] amends [11]’s scheme to also For given input x1, the optimal deterministic y is, consider the interest of the primary user, while[14] of course, the one that maximises φ(y) := U (x1, y).
C. Information-capacity limited secondary access As conceptualised by [2], and discussed by [3], As mentioned before in the discussion of the a cognitive radio terminal is aware of, can adapt to, jammer scenario, one can view the secondary user and even learn from its environment, to achieve the as the jammer’s antithesis. Thus, we can also apply most efficient possible operation. However, most of the framework introduced in section II to obtain a the literature has focused in a much narrower con- statistical secondary user access strategy. Specifi- cept of “spectrum agile” radios[8]. These radios can cally, we can find a solution to problem (1) which the secondary user can utilise to randomly (but opti- considering its information processing limitations.
mally) choose a transmission power. Of course, we We have presented, motivated, and interpreted a must specify an appropriate performance function, formal information-theoretic framework from [4], U , along with the exogenous parameters gX and C.
which is relevant to this scenario, and shown gen- 1) Single-channel scenario: If the radio is mon- eral solution forms. Hundreds of publications have itoring a single channel. The input x can be asso- followed [4] nearly all devoted to macroeconomic ciated with the energy sensed by a common energy issues, reporting analysis, numerical results and detector, which at least in the simplest case follows empirical data. It seems sensible to examine this a χ2 distribution[15]. The quadratic performance vast literature, to identify those results that are, function U (x, y) = (kx − y)2, with k a suitable after suitable adaptation, potentially most useful to If the secondary radio determines its energy usage The ideal cognitive radios seem far from practical by following the output of the optimal channel realisation, and most of the scientific literature has implied by f , it will tend to emit a high power focused on “spectrum agile” radios that can find when the input energy reading is low, and a low “spectrum holes” for secondary dynamic spectrum power when sensed energy is high. Notice that if the access. Thus, we have also considered the possible primary receiver uses successive interference can- application of ideas from this framework to the cellation, high interference (relative to the desired signal strength) is also favourable.
However, just as the “true” cognitive radio is Above model can be improved, by defining x as much more than a mere “spectrum agile” radio, the (predicted) actual energy that would be sensed the issues discussed herein reach much farther than if the sensing was done during channel usage (to its application to the mundane “spectrum holes” account for the fact that the primary user can en- scenario. The central issue is that a “true” cognitive ter/exit the channel after the sensing has just ended.
radio will “encounter both a computation limit and a In this case, the pdf of x would be a function of that communication limit”[1, P.4]. Thus, as this radio is of the output of the energy sensor, which would be asked to perform ever more sophisticated (parallel) tasks within minuscule amounts of time, and within 2) Multiple secondary channels: If the secondary the ever present size, weight, heat, and perhaps most user has a “long queue” of data to transmit, then importantly, energy limitations, it must consider its it can use as many secondary channels as it can information processing limits when devising opti- find. Thus, it can apply the previous analysis on a channel by channel basis, to transfer as much data The previously discussed model does provide an as possible. However, some consideration must be insight that may serve as a guiding principle for given to the power constraint, which must be shared designers of “true” cognitive radios: This radio will often find itself overwhelmed by the sheer amount The secondary user sorts the target channels by of information it needs to process in order to make channel state, and determines the energy to be used an “optimal” decision in minuscule time. Rather in each channel sequentially, starting with the best than finding the “true” (deterministic) optimum, the channel. Thus, after choosing the power to be used radio must content itself with making a decision at on the best channel (as discussed above), the radio random. At random, yes, but not haphazardly (as by updates its power budget, and then choose the power choosing uniformly over the set of actions). Rather, for the second-best channel (as discussed above), a decision judiciously random, through an optimised and again update its power budget, and so on, until probabilistic rule. This rule yields decisions that on average optimise the desired performance function,while utilising not more information than what the radio can actually process in the available decision We have focused on a scenario in which a cog- nitive radio must make an optimal choice while [1] T. M. Cover and J. A. Thomas, Elements of Information Theory.
John Wiley & Sons, Inc., 2nd ed., 2006.
[2] J. Mitola, III and G. Q. Maguire, Jr., “Cognitive radio: making software radios more personal,” IEEE Personal Comm., vol. 6,pp. 13–18, Aug 1999.
[3] S. Haykin, “Cognitive radio: Brain-empowered wireless com- munications,” IEEE J. on Selected Areas in Comm., vol. 23,pp. 201–20, Feb. 2005.
[4] C. A. Sims, “Implications of rational inattention,” Journal of Monetary Economics, vol. 50, no. 3, pp. 665 – 690, 2003.
Economic Sciences 2011.” Press release, October 2011.
Available: http://www.nobelprize.org/nobel_prizes/economics/laureates/2011/press.html.
[6] J. V. Neumann and O. Morgenstern, Theory of games and eco- nomic behavior. Princeton Univ. Press, 3rd ed., 1953. Available:http://www.archive.org/details/theoryofgamesand030098mbp.
[7] J. Nash, “Non-cooperative games,” The Annals of Mathematics, vol. 54, no. 2, pp. pp. 286–295, 1951. Available: http://www.
princeton.edu/mudd/news/faq/topics/nash_annmat54.pdf.
[8] S. Mangold, Z. Zhong, K. Challapali, and C.-T. Chou, “Spec- trum agile radio: radio resource measurements for opportunisticspectrum usage,” in Global Telecommunications Conference,IEEE, vol. 6, pp. 3467 – 3471 Vol.6, nov.-3 dec. 2004.
[9] A. Goldsmith, S. Jafar, I. Maric, and S. Srinivasa, “Breaking spectrum gridlock with cognitive radios: An information the-oretic perspective,” Proceedings of the IEEE, vol. 97, pp. 894–914, may 2009.
[10] S. Geirhofer, L. Tong, and B. Sadler, “Dynamic spectrum access in the time domain: Modeling and exploiting white space,”Communications Magazine, IEEE, vol. 45, pp. 66 –72, may2007.
[11] J. Mwangoka, K. Ben Letaief, and Z. Cao, “Robust end-to-end QoS maintenance in non-contiguous OFDM based cognitiveradios,” in Communications, IEEE International Conference on,pp. 2905–2909, May 2008.
[12] H. Markowitz, “Portfolio selection,” The Journal of Finance, [13] T. Wysocki and A. Jamalipour, “Portfolio selection based power allocation in OFDM cognitive radio networks,” in Signal Pro-cessing and Communication Systems, Inter. Conf. on, pp. 1–7,Sept. 2009.
[14] Z. Hasan, G. Bansal, E. Hossain, and V. Bhargava, “Energy- efficient power allocation in OFDM-based cognitive radio sys-tems: A risk-return model,” Wireless Communications, IEEETransactions on, vol. 8, pp. 6078 –6088, december 2009.
[15] H. Urkowitz, “Energy detection of unknown deterministic sig- nals,” Proceedings of the IEEE, vol. 55, pp. 523 – 531, april1967.

Source: http://www.virgiliorodriguez.info/papers/dsa_cog_inatt_rodriguez12.pdf