An Auction-based Approach for Spectrum Leasing in ... - IEEE Xplore

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Abstract—Using the spectrum intelligently have widely been investigated in the past years. Recently, spectrum leasing has been proposed as a powerful ...

2011 Wireless Advanced

An Auction-based Approach for Spectrum Leasing in Cognitive Radio Networks Seyed Mahdi Mousavi Toroujeni, Seyed Mohammad-Sajad Sadough and Seyed Ali Ghorashi Cognitive Telecommunication Research Group, Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Shahid Beheshti University G. C., Evin 1983963113, Tehran, IRAN. Email: [email protected], {s sadough, a ghorashi}@sbu.ac.ir Abstract—Using the spectrum intelligently have widely been investigated in the past years. Recently, spectrum leasing has been proposed as a powerful technique for spectrum management in communication networks. In this paper, we propose an auction-based joint spectrum leasing and relay-based cooperative communication for OFDM systems. In this scenario, the primary user leases its resources to a secondary user as a remuneration for its cooperation. An iterative auction-based spectrum leasing scheme between the primary and secondary networks is assumed in this process. The amount of resources that have to be leased to the secondary users and the process of selecting the best relay for this purpose are also investigated. Numerical results show that the primary network can achieve a higher data rate by this cooperation compared to the case where no cooperation is exploited. Besides, secondary users can increase their quality of service via this cooperation process.

I. INTRODUCTION Cognitive radio has been proposed as a way for utilizing the spectrum more efficiently by sharing the spectrum dynamically [1]. In cognitive radio, the user who has the license for a specific part of the spectrum (primary user) shares its spectrum with unlicensed users (secondary users). Several researchers have investigated the implementation challenges of cognitive radio. Spectrum leasing is a technique for spectrum sharing in which the primary user leases a part of its spectrum to some secondary users in exchange of a specific reward. Some studies on different issues in spectrum leasing can be found in [2] and [3]. In [2], the authors considered a single carrier cognitive system in which the primary user leases its spectrum to some cooperative ad hoc relays by optimizing the time allocated for the leasing process. In [3], a spectrum leasing scenario for OFDM-based cognitive networks composed of some ad hoc relays is studied in which the primary knows all the information in the network and solves the problem of spectrum leasing based on this information. In this paper, a cooperative communication joint with spectrum leasing is considered for orthogonal frequencydivision multiplexing (OFDM) systems in an auction framework. In our considered scenario, the primary transmits its data to destination by means of a relay and leases a part of its resources (in both time and frequency) to a cooperative relay for its own communication as a reward of cooperation with the primary network. By doing so, the primary shares its

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spectrum with the secondary cooperative relay and increases the achievable data rates for its link. Besides, the secondary relay can increase its quality of service by using the leased resources for its own communications. In the past years, many researchers focused on auctionbased [4] solutions for spectrum sharing in cognitive networks which is known to be a reliable and suitable solution for spectrum vendors to share or sell their resources. In [5], a vickrey auction is considered for a spectrum owner to share different parts of its spectrum between multiple secondary spectrum buyers. In our considered model, the well-known English auction [4] between the primary and the secondary relays is proposed for an OFDM network in which the primary (auctioneer) wishes to share a part of its spectrum in a fraction of time with the relays (bidders). The relays offer the power they can allocate for the primary signal retransmission as the bid. In the English auction, the bidder who has the highest bid wins the auction. In an iterative process the primary and the secondary relays change their actions and after some iterations, the primary makes the final decision and selects the best secondary relays such that the cooperation process provides higher achievable rates. The rest of this paper is organized as follows. The considered model and our main assumptions are explained in Section II. Mathematical derivations and analysis of the proposed spectrum leasing are presented in Section III. Simulation results are gathered in Section IV and finally, Section V concludes the paper. II. S YSTEM M ODEL AND M AIN A SSUMPTIONS We consider a cognitive network composed of a primary transmitter (source), s, and a primary receiver (destination), d, at a distance L, and N pairs of secondary transmittersreceivers which the secondary transmitters can operate as relays. The primary selects one relay for cooperation. In this network, each secondary transmitter which is located at the middle part of the network, has a single receiver placed at a random location as shown in Fig. 1. In the sequel, we denote the i-th relay as ri . The channel model is assumed to be frequency selective with slow time variations within a block of OFDM symbols.

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Fig. 1. Considered model composed of a primary source and destination and N pairs of secondary users (here N = 4). Fig. 2.

Moreover, it is assumed that all the users do not know the instantaneous channel coefficients but the expected values of the channel gains. In our model, only the path-loss is considered in which the channel gains for different links depend on the distance between the receiver and the transmitter. For instance, the channel gain between a transmitter, say a and a receiver b is E[|ha,b |2 ] = l21 a,b where la,b is the distance between a and b (we show the distance between the i-th relay and its respective receiver by li,i ). To perform spectrum leasing, the primary network divides each OFDM frame into two main parts. The first part which contains Ns − α OFDM symbols is dedicated for primary transmission and the rest α symbols are allocated to the secondary relay transmission. In the second part, the secondary relay uses a number of γ subcarriers for source-signal retransmission toward the primary destination and the remained M − γ subcarriers are used for its intra-link communication to its respective receiver (see Fig. 2). Based on the amount of the leased resources from the primary (time and frequency), the secondary relays allocate different powers for primary signal retransmission. Each secondary relay, by knowing the distance to its respective receiver and by defining a utility function (which shows each relay’s benefit in the cooperation process), tries to select the best power to maximize its utility function and to offer this power to the primary user. After listening to different offers coming from the relays, the primary user selects the best relay for cooperation. Then, the source announces the amount of resources for leasing to all secondary users and the secondary users update their relaying power based on the new amount of leased resources in order to maximize their revenue and this iterative process continues until all the users do not change their action, considerably. At this time, as shown in Fig. 1, the primary user sends its data indirectly to its destination by the help of the selected relay. In the next section, we formulate these spectrum leasing interactions.

Time and frequency allocation for different transmissions.

III. P ROBLEM F ORMULATION AND S PECTRUM L EASING A NALYSIS If we consider the time average of the channel gains instead of instantaneous channel gains, the achievable rate for primary link transmission, s-to-d, in a frame of OFDM with Ns symbols and M subcarriers, can be written as:    ρs L12 Rs,d = M log2 1 + (1) N0 where ρs = Ps /M is the power of each subcarrier and Ps is the total power which the source allocates to an OFDM symbol. If the source leases α symbols to the relay and sends its data to its respective destination by means of one relay, the rate for the primary link in the case of cooperation, by utilizing a decode and forward (DF) scheme is: Rcoop = min {(Ns − α)Rs,r , αRr,d }

(2)

where Rs,r is the rate achieved in the s-to-r link with M subcarriers. Since, the instantaneous channel gain is unknown and the relays are in a same location, this rate can be written as: ⎛

⎞ Rs,r

ρs ⎜ = M log2 ⎝1 +

1 L/2

N0

2

⎟ ⎠.

(3)

For a fair comparison, it is assumed that the total allocated power for transmission by the primary user in the direct link transmission (without any cooperation from the secondary users) and the cooperative transmission are equal. This means that if the allocated power for transmitting Ns OFDM symbols by the primary user is Ns Ps , by leasing α symbols to the secondary relay, the power for each OFDM symbol is Ns Ps . Ps (α) = N s −α By utilizing a space-time cooperative diversity scheme [6] in relays for decoding the source signal and forwarding it to

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the destination in γ subcarriers, Rr,d , defined as the rate in r-to-d link is given by:   ρi . (4) Rr,d = γ log2 1 + N0 (L/2)2 Consequently, the achievable rates for each relay to its respective receiver link in the remained M − γ subcarriers can be written as:   ρi (5) Rri = (M − γ) log2 1 + 2 li,i N0 The utility function for secondary relays which shows the benefit of cooperation is defined as: ui = αωi Rri − αPri

(6)

where ωi is the worth of the spectrum for secondary users i. It can be shown that the utility function for the secondary users are concave and the optimum power (bid) for each secondary relay to consume in the cooperation process with respect to a fix value of γ is given by:  2 if ui > 0 ωi C(M − γ) − N0 M li,i Pri = (7) 0 else where C = (ln 2)−1 . Each secondary user selects the optimum power for cooperation with the primary based on (7). This power may change in an iterative negotiation. After gathering the secondary offers, the source tries to maximize its rate by solving the following maximization problem: subject to :

max Rcoop ˆ α ˆ .ˆ γ = M (Ns − α)

(8) (9)

where the condition arises from the proposed cooperative model in which the transmitted symbols for s-to-r should be equal to the number of subcarriers in the r-to-d link. Therefore, the condition can be rewritten as: M . (10) α ˆ = Ns M + γˆ Equation (2) for the i-th relays can be rewritten as: Rcoop = min {A, B} where

(11)

A = Ns M

  γ (M + γ)Ps log2 1 + M +γ γM N0 (L/2)2

(12)

B = Ns M

  γ Pri log2 1 + . M +γ M N0 (L/2)2

(13)

and

Expressions A and B inside min {A, B} determine the maximum achievable rate for the primary link. The primary first suggest the value of γ to the secondary relays and the secondary relays announce their desirable power for consuming in the cooperation process.

Since the selected powers from the relays affect the final achievable rate of the primary user, the primary changes the value of γ by using the following formula: ΔPri (14) Δt where β is the updating rate for γ and Δt is the time interval between two decisions of the relays. The obtained γ should be bounded in the interval [0, M ]. Equation (14) shows that If the relays decrease their powers, since the rate in r-to-d decreases, it is better for the primary to decrease the number of allocated subcarriers for cooperative transmission, γ, and consequently, to increase the time of its transmission, Ns − α. In other words, increasing or decreasing γ has a direct relation with increasing or decreasing the power of relays. Based on each relay’s bid and (14), a different γi can be determined. The primary user calculates its final achievable rate in (11) by the help of (12) and (13) and determines the best relay for cooperation. The γ related to the best relay is assumed as the new γ and announced to all the relays. The secondary users update their power based on (7) to reach their best answer. This iterative process continues until it converges. Note that if the calculated final amount of the primary rate becomes less than the rate of direct link transmission, the primary can refuse the cooperation and send its data directly to the destination. γˆi = γi + β

IV. S IMULATION R ESULTS Throughout the simulations, a cognitive network is considered in which the distance between the source and the destination is assumed to be normalized to 1. The considered network is composed of 4 pairs of secondary users. The power allocated to a primary OFDM symbol is normalized to Ps = 1. ω is set to 3 for all users and the updating rates are set to 0.1 (β = 0.1). Δt which is the time interval is set to unit and the channel model is considered to be Rayleigh. For simulation, the total amount of the primary spectrum (bandwidth) is normalized to 1. Also, the length of an OFDM block is normalized to 1 time unit. i.e., a one by one block of resources in an OFDM modulation is assumed to be share between the users. γ is initialized to 1/2 of the total bandwidth. By using the initial value for γ, the secondary relays offer their power to the primary. Based on (14), the primary calculates the desired value of γ and announces it to the secondary relays and the iterative approach continues until convergence. The initial value of allocated power by the secondary relays are set to Pri = 1. The auction is finished if the variations of γ in two consecutive steps be less than a predefined threshold (here 0.001). The result are obtained by Monte Carlo simulation method. Figure 3 shows the final value of γ and α, allocated in this leasing process. For a network with the considered parameters, the final value can be reached after about 10 iterations. It can be seen that 0.58 of bandwidth and 0.64 of time slots in a block of OFDM resources must be leased to the winner secondary relay. The final achievable rate of the primary depends on

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0.68 γ α

0.64 0.62 0.6 0.58 0.56

2

1.8 1.6

1.4

0.54 1.2

0.52 0.5

1

2

3

Fig. 3.

4

5 6 7 Number of Iterations

8

9

1

10

The leasing parameters γ and α.

1.15 1.1 1.05 1 0.95

1

2

3

4

5

6

7

8

9

4

5 6 7 Number of Iterations

8

9

10

ACKNOWLEDGMENTS

10

Number of Iterations

Fig. 4.

3

In this paper, we proposed an auction-based mechanism between the primary and secondary users for spectrum leasing joint with a cooperative communication in an OFDM-based network composed of one primary user and some secondary users. Secondary transmitters act as relays for the primary signal retransmission and try to gain their highest benefit in the cooperation process. An iterative updating algorithm is suggested for the primary network to find the amount of leased spectrum and also for the secondary users to find the optimum power for primary signal retransmission. The proposed cooperation scheme may serve in a cognitive network in which the primary network aims at increasing the reliability of its link.

1.2

0.9

2

V. C ONCLUSION

With Cooperation Without Cooperation

1.25

1

Fig. 5. The power of the secondary relays. The relay with the highest power is selected for the cooperation.

1.3

The Primary Final Rate

1st Relay 2nd Relay 3rd Relay 4th Relay

2.2

The Relays Powers

The Values of Leasing Parameters

0.66

This work is supported by Iranian Education and Research Institute for Information and Communication Technology (ERICT) under the grant number 500/8974.

The final Achievable rate for the primary.

R EFERENCES the power level which the secondary relays wish to consume. The location of the relays receiver has an important role in determining this power. From (7) we conclude that the relay which is closer to its respective receiver consumes a higher level of power to reach its highest profit. The achievable rates for the primary user in this cooperation process is depicted in Fig. 4. This amount is compared with the case where there is no cooperation between the users in this network. We can see that the cooperation has more benefits for the primary user, compared to the direct transmission case. Figure 5 shows the power of relays in different iterations. This power depends on the profit of each secondary relay in the leasing process. In this figure, the third relay is the winner. Note that the total power of the the primary user in both cooperative and non-cooperative communications is 1.

[1] J. Mitola, “Cognitive radio: an integrated agent architecture for software defined radio,” Ph.D. dissertation, Royal Institute of Technology (KTH), Stockholm, Sweden, 2000. [2] O. Simeone, I. Stanojev, S. Savazzi, Y. Bar-Ness, U. Spagnolini, and R. Pickholtz, “Spectrum leasing to cooperating secondary ad hoc networks,” IEEE Journal on Selected Areas in Communications, vol. 26, no. 1, pp. 1–11, January 2008. [3] S. M. M. Toroujeni, S. M. S. Sadough, and S. A. Ghorashi, “Timefrequency spectrum leasing for ofdm-based dynamic spectrum sharing systems,” IEEE 6th Conference on Wireless Advanced (WiAD), June 2010. [4] V. Krishna, Auction Theory. London, U.K.: Academic, 2002. [5] X. Wang, Z. Li, P. Xu, Y. Xu, X. Gao, and H. Chen, “Spectrum sharing in cognitive radio networksan auction-based approach,” IEEE Trans. on System, Man and Cybernetics– Part B: Cybernetics, vol. 40, no. 3, pp. 2651–2660, June 2010. [6] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. on Information Theory, vol. 50, no. 12, pp. 3062–3080, December 2004.

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