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Pricing of Cognitive Radio Rights to Maintain the Risk-Reward of Primary User Spectrum

Investment

Tadeusz Wysocki and Abbas JamalipourSchool of Electrical and Information EngineeringThe University of Sydney, NSW 2006, Australia

IEEE Symposium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN) 2010

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Outline

• Introduction• Rational Investor Model• Floor Price of Cognitive Radio Rights• Simulation and Analysis• Conclusion• Comment

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I. Introduction

• Radio spectrum is a scarce resource. • Often suffers from the problem of inefficient use. • Promising solutions: – Cognitive Radio

• Opportunistic access• Or spectrum sharing

– Radio Spectrum Markets• The spectrum is efficiently allocated to those require it

most. – Combination of the above two

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I. Introduction: related work (1/3)

• Cognitive Radio– Spectrum sensing [11]– Power control [12][13]– MAC design [14]

[11] W Lee, I Akyildiz, “Optimal Sensing Framework for Cognitive Radio Networks,” IEEE Transactions On Wireless Comm, vol 7, no 10, pp 3845-3857, Oct 2008.[12] X Kang, Y Liang, A Nallanathan, H Garg, R Zhang, “Optimal Power Allocation for Fading Channels in Cognitive Radio Networks: Ergodic Capacity and Outage Capacity,” IEEE Transactions On WirelessComm, vol 8, no 2, pp 940-950, Feb 2009.[13] X Kang, R Zhang, Y Liang, H Garg, “Optimal Power Allocation for Cognitive Radio under Primary Outage Loss Constraint,” IEEE ICC 2009, Dresden, Germany, Jun 2009.[14] C Cormio, K Chowdhury, “A Survey of MAC Protocols for Cognitive Radio Networks,” Ad Hoc Networks, Elsevier, Feb 2009.

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I. Introduction: related work (2/3)

• Spectrum Markets– A price based spectrum allocation scheme,

determined by end user utility [2]– An analysis of price dynamics in a competitive

spectrum market [3]– Trading of spectrum between Pus [4]– A broker based spectrum management scheme [8]– Secondary market [9]

[2] J Acharya, R Yates, “A Price Based Dynamic Spectrum Allocation Scheme,” Asilomar Conference on Signals, Systems, and Computers 2007, Monterey, California, Nov 2007.[3] Y Xing, R Chandramouli, C Corderio, “Price Dynamics in Competitive Agile Spectrum Access Markets,” IEEE Journal on Selected Areas in Comm, vol 25, no 3, pp 613-621, Apr 2007.[4] C Chin, S Olafsson, B Virginas, G Owusu, “Trading Strategies in Radio Spectrum Management”, 3rd International Symposium on Wireless Pervasive Computing, ISWPC 2008, pp 680-684, Santorini, Greece, May 2008.[8] M Buddhikot, K Ryan, “Spectrum Management in Coordinated Dynamic Spectrum Access Based Cellular Networks,” IEEE DySPAN 2005, Baltimore, USA, Nov 2008.[9] FCC, “Promoting Efficient Use of Spectrum through Elimination of Barriers to the Development of Secondary Markets”, Report no 04-167, Sept 2004.

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I. Introduction: related work (3/3)

• Combination– A dynamic game-theoretic approach to determine

the optimal price for Cognitive Radio access to PU licensed spectrum [5]

– Extended from [5], 3 different pricing models are considered: market-equilibrium, competitive, and cooperative [6]

– The market-equilibrium pricing model is further analyzed [7]

[5] D Niyato, E Hossain, “Optimal Price Competition for Spectrum Sharing in Cognitive Radio: A Dynamic Game-Theoretic Approach,” IEEE GLOBECOM’07, pp 4625-4629, Washington DC, USA, Nov 2007.[6] D Niyato, E Hossain, “Market-Equilibrium, Competitive and Cooperative Pricing for Spectrum Sharing in Cognitive Radio Networks: Analysis and Comparison,” IEEE Transactions on Wireless Comm, vol 7, no 11, pp 4273-4283, Nov 2008[7] D Niyato, E Hossain, “Spectrum Trading in Cognitive Radio Networks: A Market-Equilibrium-Based Approach,” IEEE Wireless Communications, vol 15, no 6, pp 71-80, Dec 2008.

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I. Introduction: contribution

• We view the PU spectrum license as an investment.

• And we use the Sharpe Ratio as a measure. • Based on the above, the compensation SU

should pay is found. • Through simulation, we see that it is possible

that the compensation is less than the lost revenue.

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II. Rational Investor Model

• Goal: propose a measure (Sharpe Ratio) that a rational investor concerns most.

• We know that – expected return and variance of return are two

frequently used characteristics of assets and portfolios of assets,

– and rational investors are generally risk-averse. • Rational, risk-averse investors tend to prefer the

strategy with the higher Sharpe Ratio.

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II. Rational Investor Model: Formulation of Sharpe Ratio

• The Sharpe Ratio encapsulates the mentioned two measures with respect to a reference asset (risk-free asset).

• The Sharpe Ratio of an asset or portfolio with return r is:

– E(r): expected return – σ(r): variance of return– rf: risk-free rate

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II. Rational Investor Model: Assumptions

• The Primary User (PU) is risk-averse. • The PU’s investments (spectrum asset,

Φspectrum) consist only of: – spectrum licenses, – associated wireless infrastructure.

• The PU’s holding of other investment types (except risk-free asset) are small.

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II. Rational Investor Model: PU’s Sharpe Ratio (1/2)

• The PU’s return on the spectrum asset is:

– n(τ): the number of ongoing calls during period τ. – R: the revenue earned per period of each ongoing

call. – K: the price of the spectrum assets.

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II. Rational Investor Model: PU’s Sharpe Ratio (2/2)

• The Sharpe Ratio of the per-period spectrum asset return is:

– where

• We can then analyze the effects of CR SU(secondary user) activity on the mean and variance of the return on Φspectrum.

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III. Floor Price of Cognitive Radio Rights

• The presence of CR SUs will affect E(rspectrum) and σ2(rspectrum).

• And the Sharpe Ratio with CR SU activity may decrease.

• Therefore SU should compensate PU. • Goal: find the floor price SU should pay to PU

such that the Sharpe Ratio is maintained.

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III. Floor Price of Cognitive Radio Rights: modified Sharpe Ratio

• Let βM and βV be the factors affecting the above two.

• Then the mean and variance of the return with CR SU activity are:

• And the Sharpe Ratio with CR SU activity is:

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III. Floor Price of Cognitive Radio Rights: Sharpe Ratio changes (1/2)

• Results in [11] ~ [14] suggests that with CR SU activity, E(n) will decrease, that is, βM < 1.

• However, βV depends on: – the statistical characteristics of the PU traffic and– the effect of CR activity on PU call dropping.

• Thus the Sharpe Ratio may decrease.

[11] W Lee, I Akyildiz, “Optimal Sensing Framework for Cognitive Radio Networks,” IEEE Transactions On Wireless Comm, vol 7, no 10, pp 3845-3857, Oct 2008.[12] X Kang, Y Liang, A Nallanathan, H Garg, R Zhang, “Optimal Power Allocation for Fading Channels in Cognitive Radio Networks: Ergodic Capacity and Outage Capacity,” IEEE Transactions On WirelessComm, vol 8, no 2, pp 940-950, Feb 2009.[13] X Kang, R Zhang, Y Liang, H Garg, “Optimal Power Allocation for Cognitive Radio under Primary Outage Loss Constraint,” IEEE ICC 2009, Dresden, Germany, Jun 2009.[14] C Cormio, K Chowdhury, “A Survey of MAC Protocols for Cognitive Radio Networks,” Ad Hoc Networks, Elsevier, Feb 2009.

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III. Floor Price of Cognitive Radio Rights: Sharpe Ratio changes (2/2)

• Fig 1 illustrates the change of the Sharpe Ratio. The points on the same line have the value of Sharpe Ratio

Sharpe Ratio decreases

SU should compensate PU to maintain Sharpe Ratio

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III. Floor Price of Cognitive Radio Rights: the SU compensates the PU

• If a PU finds the degradation of the Sharpe Ratio, the SU needs to compensate the PU.

• Let the SU pays a coupon c to the PU• Then the Sharpe Ratio becomes:

• Recall the original Sharpe Ratio

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III. Floor Price of Cognitive Radio Rights: the SU compensates the PU

• Equate (3) and (10) and solve for c:

• Substituting:

• we obtain:

• Note: the actual amount that will be paid is cK.

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IV. Simulation and Analysis

• Goal: – Define the example PU and SU communication

system– Simulate– Analyze the effect of CR SU activity and the

proposed valuation method

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IV. Simulation and Analysis: System Model (1/3)

• We model the PU as a single mobile provider– Call arrival: a stationary Poisson process with rate

λ per timeslot. – Call duration: stationary exponentially distributed

with mean μ timeslots• Without any CR SU activity, the offered load

during each timeslot is ρ = λ/μ.

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IV. Simulation and Analysis: System Model (2/3)

• The mobile system is modeled as an M/G/C loss system for simplicity.

• The PDF of the number of simultaneously active calls is independent of the service distribution G and is given by [22]: (!)

[22] R Wolff, Stochastic Modelling and the Theory of Queues, Prentice Hall 1989.

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IV. Simulation and Analysis: System Model (3/3)

• The CR SU network is located in the same region as the PU mobile cell (Fig 3)

• We assume that PU QoS degradation is manifest by call dropping– The probability of each active call being dropped is

Pdrop in each timeslot.

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IV. Simulation and Analysis: the mean and variance of the return (1/2)

• Without CR SU activity, the number of active calls in each timeslot is given by:

• If the call capacity C is large compared to ρ, (17) can be approximated by:

• Therefore, n in each timeslot is approximately Poisson distributed with E(n) = σ2(n) = ρ.

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IV. Simulation and Analysis: the mean and variance of the return (2/2)

• Thus the mean and variance of the return and the Sharpe Ratio are:

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IV. Simulation and Analysis: effect of Pdrop (1/7)

• Setting– Average arrival rate λ = 17 calls/min (0.283

calls/sec)– Average call duration μ = 3 min (180 sec) (1/μ ?) – Pdrop = {0, 0.001, 0.002, …, 0.01}– Capacity C = 150 voice channels

• The simulation was carried out for 86400 time-steps (1 day), and repeated 20 times

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IV. Simulation and Analysis: effect of Pdrop (2/7)

• Note: the distribution of active calls remains Poisson– Apply the Chi-Squared Goodness-of-Fit test – Graphically comparison (Fig 6)

The sample CDF fits the poisson CDF with sample mean for all Pdrop.

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IV. Simulation and Analysis: effect of Pdrop (3/7)

• And from table 1, the factor βM, βV are approximately equal.

Average of βM, βV

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IV. Simulation and Analysis: effect of Pdrop (4/7)

• Thus the Sharpe Ratio with CR SU activity would locate on the parabola A in Fig 7

Sharpe Ratio moves down as Pdrop increasesThe coupon

payment is less than the reduction in the mean return

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IV. Simulation and Analysis: effect of Pdrop (5/7)

• Setting for calculating the coupon payment and the Sharpe Ratio– R = $0.005/call/sec– K = $40 million– rf = 5% annualized (1.5855*10-7% per second)

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IV. Simulation and Analysis: effect of Pdrop (6/7)

• Comparison of mean return

Mean return decreases with CR SU activity.

Coupon payment increases as Pdrop increases.

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IV. Simulation and Analysis: effect of Pdrop (7/7)

• Comparison of the Sharpe RatioApproximately the same. (?)The difference may be from the error of calculation.

Sharpe Ratio decreases since the CR SU activity.

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V. Conclusion• The QoS degradation of PU since the SU activity may

cause PU feel unhappy. • This paper finds the amount SU should pay to PU based

on maintaining the PU’s Sharpe Ratio. • Through the simulation we see that

– the variance of return may decrease with SU participating, – and the coupon payment may be less than the reduction of

the mean return. • This approach could be used in conjunction with existing

market and auction based proposals for pricing CR rights.

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VI. Comment

• 這篇比較像是從財務管理或是投資學的角度切入，特別與無風險資產比較的話可以確定是否要投資。• Sharpe Ratio在一定程度上跟 utility function很像，只是前者與資產報酬率有關而後者跟滿意程度有關。• 但前者又比較適用在已經獲得 license，確定投資的金額的情況；未獲得 license之前不曉得該怎麼使用 Sharpe Ratio代替 utility function。