Power Control for Time-Varying Cognitive RadioNetworks

Ruifeng Duan∗, Mohammed Elmusrati∗, Riku Jantti†, and Reino Virrankoski∗∗Telecommunication Engineering Group

University of Vaasa, 65101, Vaasa, FinlandEmail: firstname.lastname@uwasa.fi

†Department of Communications and Networking (Comnet)Aalto University, FIN-00076 Aalto, Finland

Email: riku.jantti@tkk.fi

Abstract—In this paper we propose a new power controlscheme for cognitive radios, Distributed Power Control Algo-rithm for Cognitive Radios (DPCACR). As we know that ina cognitive system, the secondary users (SU) either transmitin an opportunistic way or coexist with the primary users totransmit simultaneously under the constraints that will not harmto the primary users. Previously, the interference temperaturewas announced to limit the transmit power of SUs. However, in2007 the FCC has abandoned the concept which is not workable.In this paper, we consider the elastic transmission scenario forsecondary system. The cognitive networks using code-divisionmultiple access (CDMA) technology to transmit simultaneouslywith primary users in the same spectral band.

I. INTRODUCTION

The electromagnetic radio spectrum is a precious naturalresource, which is regulated by the government agencies.Current wireless systems are characterized by command-and-control structure of frequency allocation. The Federal Com-munications Commission’s (FCC) frequency allocation chartindicates overlapping allocations over all of the frequencybands. However, the recent studies by the FCC’s SpectrumPolicy Task Force showed that large portions of the licensedbands remain unused for as much as 90% of the time [1].In order to utilize these spectrum ’white spaces’, the FCChas issued a Notice of Proposed Rule Making [2] advancingCognitive Radio (CR) technology as a candidate to implementopportunistic spectrum sharing. Coined by Mitola [3] and thenpromoted by FCC, Cognitive Radio technologies have thepotential to provide a number of benefits that would result inincreased access to spectrum and also make new and improvedcommunication services available to the public [4], [5].

There are two spectrum sharing methodologies defined inliterature, overlay and underlay [6], [5], [7]. In an overlayspectrum sharing approach, the secondary users access thenetwork when the spectrum holes appear [4], which meansthat secondary users can not use the spectrum while primarysystem is working. Accurate spectrum sensing needs to beperformed to avoid possible collision with primary users [8].Consequently the interference caused by the secondary usersto the primary system is minimized. In an underlay case, thesecondary users are allowed to transmit when the interferenceto the primary is kept at a reasonable level. This means that

the simultaneous transmission is possible in this scenario. Inthis paper we discuss the simultaneous transmission approach.

Power control scheme is an efficient approach to managethe interference problem, which have been extensively studiedfor CDMA networks. However, many new challenges exist onpower control of cognitive radio networks. In [9], a schemebased on outage probability of primary systems was proposed,where the outage probability can be broadcasted to SUs whowant to transmit before starting the communication. [10]proposed an efficient power control scheme based on the built-in fuzzy power controller, where the SU is able to dynamicallyadjust its transmission power in response to the changinginterference level caused by the SUs to the PUs. In [11],an optimal power control problem is modeled as a concaveminimization problem, where the authors investigate the opti-mal power control with and without interference temperatureconstraints base on Shannon capacity. However, in [10], [11]no SU is allowed to transmit before receiving authorizationfrom the manager, thus heavy signaling is really possible. In[12], power control for Cognitive Radio Ad Hoc Networkswas studied, where the genie-aided distributed power controlscheme maximizes the energy efficiency of SUs and guaran-tees the QoS of both PUs and SUs. First, the transmissionpower of each SU is determined by the distributed powercontrol algorithm. Then if the interference level caused byall opportunistic communications is so high that the PU isviolated, a genie placed near by the PU informs the SUs. In[13], an fully distributed power control algorithm is presentedwithout an additional process for CR networks. Specifically,the constraint for the sum of the interference induced by allSUs in the network is replaced by new one which limits theindividual transmission power. Since each SU determines itstransmission power within the range of the limit to protectthe PU, the additional process required in previous works isunnecessary. The authors show that the proposed scheme neverexceed the interference temperature limit of the PU. However,the authors only consider the path loss model as the one thatthe transmission power only attenuates with distance.

In this paper we propose a new power control schemefor cognitive radios, Distributed Power Control Algorithm forCognitive Radios (DPCACR). The cognitive networks using

2010 17th International Conference on Telecommunications

978-1-4244-5247-7/09/$26.00 ©2009 IEEE 133

Fig. 1. System Model

Fig. 2. Channel Model

code-division multiple access (CDMA) technology to transmitsimultaneously with primary users in the same spectral band.The secondary users utilize the part information of feedbackchannel of the primary system. This part is related to thepower control command, which is sent by the PR to the PT.Our paper’s contributions are as following: the time-varyingwireless channel model is considered; the primary user isprotected based on the part of feedback information of primarysystem. The rest of this paper is organized as follows. Thesystem model is proposed in Section II. The power controlalgorithms are described in Section III. Section IV shows thenumerical studies. The last section concludes our paper.

II. SYSTEM MODEL

Given a primary system with a coverage radius Rp and asecondary system with a coverage radius Rs (see Figure 1).Without losing generality we assume that the primary receiver(PR) is located in the center of the circular region with radiusRp, and the primary transmitter (PT) is located uniformly inthe primary region with a minimum distance R0 from thePR. Also, we assume that a CR receiver (SR) is uniformlylocated in the same area as primary transmitter does, and aCR transmitter (ST) is located uniformly in the region withradius Rs where the CR receiver is centered. The minimumdistance between the CR pair is also assumed to be R0.

We assume that the primary system utilizes closed powercontrol to adjust its transmission power with the power updat-ing step size 1dB, for instance, the classic Foschini-Miljanicpower control algorithm [14]. We assume that the secondaryuser can decode part of the feedback channel of the primary

system. This part is related to the power control command,which is sent by the PR to the PT. In addition, the transmissionpower of all users is constrained by Pmax. Moreover, weassume that each SR has a register with a capacity of C formemorizing the update feedback commands of the primarysystem.

A. Channel Model

While the CR system designer can determine the transmitpower, it is the propagation channel that determines how muchof that power arrives as interference to primary and otherCR users [6]. We assume the link gains vary during thepower control process in accordance with shadow fading andmultipath fading. Let Gij(t) be the time-varying channel gainat a particular time instant t from transmitter j to receiver i,i, j ∈ (p, s), where p, s means primary user and secondaryuser respectively.

Let dij(t) be the distance between j and i at time t, αbe the path loss exponent, Sij(t) be the dB attenuation due toshadow fading which is usually modeled as a Gaussian randomvariable with zero mean and standard deviation σ, and Mij(t)be the multipath fading, which follows exponential distributionfor Rayleigh fading. Mij has mean value 1 in linear scale.And for convenience, Sij(t) and Mij(t) are measured to beindependent of the distance.

Thus, the continuous time model for the link gain matrix isgiven below :

Gij(t) =10−Sij(t)/10 ·Mij(t)

dαij(t)(1)

B. Shadowing Fading

According to Gudmundson [15], S(dB) follows an expo-nential spatial correlation. Assume that a user moves at speedv. The spacial correlation is given by

R(S(t), S(t+ T )) = σ2εvT/DD = σ2ρ (2)

where σ2 is the variance of S which is usually in the ragebetween 3 and 10dB, T is sample interval of the receivedsignal, D is the reference distance, εD is the correlationbetween two points separated by distance D, and ρ = ε

vT/DD is

the correlation coefficient. For typical suburban propagation at900MHz, it has been experimentally verified by Gudmundsonthat σ ≈ 7.5dB with a spatial correlation of approximately0.82 at a distance of 100m; for typical microcellular propa-gation at 1700MHz, σ = 4.3dB with a spatial correlation of0.3 at a distance of 10m [15], [16]. In this paper, let T be theduration of one slot for power adjustment. Then Sij(dB) canbe represented in a discrete-time way by the following modelbased on a Gauss-Markov process [17], [18]

S(k + 1) = ρS(k) +√

1− ρ2W (k) (3)

where ρ is the correlation coefficient and W (k) has a normaldistribution with mean zero and variance σ2.

134

C. Multipath Fading

In this paper we assume the case that there is no line-of-sightpath between the transmitter and receiver. This small-scalefading is described with accuracy statistically by Rayleigh dis-tribution. That is, the received signal envelope R is Rayleigh-distributed with the probability density function (PDF) of

fR(r) =r

σ2exp(

−r2

2σ2), r ≥ 0 (4)

The power fading is modeled by Exponential distributionwith the mean of large-scale fading caused by path loss andshadowing. It follows the PDF of

fP (p) =1

2σ2exp(

−p2σ2

), p ≥ 0 (5)

D. Composite Fading

According to the continuous time model in Equation (1), thediscrete time model for the link gain matrix is given below :

Gij(k) =10−Sij(k)/10 ·Mij(k)

dαij(6)

In this paper, we assume that the distance will not changeso much during the simulation, which means that the path losswill be constant and only the shadowing and multipath fadingare considered to be time variant. In addition, flat fading isassumed in this paper.

III. POWER CONTROL FOR CR SYSTEMS

In this section we discuss centralized and distributed powercontrol schemes for the system given in previous section,where there are one pair of primary users and one pair ofsecondary users.

A. Centralized Power Control for CR System

In this section, we study the centralized power controlalgorithm for CR system. The SINR value at the primaryreceiver Γp(k) could be represented as [19],

Γp(k) =Pp(k)Gpp(k)

Ps(k)Gps(k) +Np≥ ΓTp (7)

where Gpp is the channel gain between PT and PR, Pp is thetransmission power of PT, Ps is the transmitter power of ST,Gps is the channel gain between PR and ST, Np is the additivenoise at PR, and ΓTp is the target SINR of PR.

To make the received SINR of the primary user as high aspossible, the optimum solution is to switch off all secondarytransmitters. Since we are seeking for any opportunity for co-existence with primary users, this switching-off approach isnot attractive. To maximize the SINR for the secondary users,the transmission power follows

Ps(k) =Pp(k)Gpp(k)

ΓTpGps(k)− NpGps(k)

(8)

Fig. 3. Distributed Power Control Flow Chart for CR System

B. Distributed Power Control for CR System

In this section, we propose our new power control schemefor CR system. The secondary transmitter updates its trans-mission power according to the feedback commands of theprimary system which are sent from primary receiver to itstransmitter.

The received SINR of the secondary receiver at time slot kis

Γs(k) =Ps(k)Gss(k)

Pp(k)Gsp(k) +N(9)

The transmission power at next time slot, (k + 1)th ,of thesecondary transmission power is given by (all are in dB scale)

Ps(k + 1) =

min{Ps(k) + step, Pmaxs }, R < 0max{Ps(k)− step, Pmins }, R > 0Ps(k), others

(10)

where R is the mean value of the register during the pastseveral time slots, Pmaxs is the maximum transmission powerof secondary users, and Pmins is the minimum transmissionpower of secondary users. Ps(k) is the transmission power ofsecondary transmitter at time slot k, Gss is the channel powergain of the secondary pair, and Gsp is the channel power gainfrom the primary transmitter to secondary receiver.

Figure 3 shows the logic how the algorithm works. If theaverage of the past C power control commands of the primarysystem is positive, which means that the primary transmitterincreased its transmission power in average during past C timeslots, the secondary transmitter will decrease its transmissionpower in next time slot. When the average is negative, thesecondary transmitter will increase its transmission power.Otherwise, the secondary transmitter will maintain its trans-mission power in next time slot.

IV. NUMERICAL STUDIES

In this section we present numerical results for the dis-tributed power control scheme proposed in previous sections.The default parameters used in our simulation are Rp = 500m,R0 = 20m, Rs = 100m, carrier frequency fc = 1700 MHz,

135

Fig. 4. Channel Gains: primary transmitter to primary receiver (gpp), primarytransmitter to secondary receiver (gsp), secondary transmitter to primaryreceiver (gps), secondary transmitter to secondary receiver (gss)

Fig. 5. SINR of optimal and proposed schemes for primary and secondarysystems, where the secondary system has a 5-bit register for recording thepower update commands of primary system (C=5)

the speed of users moving v = 3.6 km/h. For shadowingfading, the parameters are σ = 6dB, the correlation distanceD = 10m and the corresponding spacial shadow correlationηD = 0.3. Also, the register of a secondary user has a 5-bitmemory, which means it could store 5 previous commandsissued by the primary receiver to primary transmitter. In addi-tion, the locations of primary transmitter and secondary usersare generated randomly according to uniform distribution. Thereceiver thermal noise is −120dBw at all receivers. The targetSINR of primary user is 10dB with a 3dB margin to mitigatethe fading to some degree. The multipath fading is generatedusing Zheng and Xiao algorithm [20].

Figure 4 shows the four time-varying channels in dB, whichare primary transmitter to primary receiver (gpp), primarytransmitter to secondary receiver (gsp), secondary transmitterto primary receiver (gps), and secondary transmitter to sec-ondary receiver (gss).

Figure 5 and 6 show the SINRs and transmission power ofprimary and secondary systems, where the secondary system

Fig. 6. Transmission Power of optimal and proposed schemes for primaryand secondary systems, where the secondary system has a 5-bit register forrecording the power update commands of primary system (C=5)

Fig. 7. SINR of optimal and proposed schemes for primary and secondarysystems, where the secondary system has a 1-bit register for recording thepower update commands of primary system (C=1)

Fig. 8. Transmission Power of optimal and proposed schemes for primaryand secondary systems, where the secondary system has a 1-bit register forrecording the power update commands of primary system (C=1)

has a register with a capacity of 5 bits (C=5). This means thatthe secondary system update its transmission power based on

136

the 5 previous commands of primary system. Also illustratethe optimal transmission power and achieved SINR underthe condition, for comparison, that the PU transmitter usesthe same transmission power for both optimal and distributedcases. We can see that because of deep fading the secondarytransmitter has to switch off (23rd slot). However, the primarysystem can not achieve its target.

Figure 7 and 8 show the SINRs and transmission power ofprimary and secondary system, where the secondary systemhas a register with a capacity of 1 bit (C=1). This means thatthe secondary system update its transmission power based onthe previous command of primary system. In order to comparethe performance, in this case we use the same parametersas in C=5 case. Comparing this case with previous case(C=5), we could find that in this case the convergence speedof transmission power of primary transmitter is faster thanprevious case. However, the SINR of primary system is worsethan C=5 case while the deep fading happens to the primarylink. This is because in C=5 case the speed of reducing thetransmission power of secondary transmitter is faster than C=1case, which is also shown in Figure 6 and 8. Here we alsoillustrate corresponding the optimal transmission power andachieved SINR.

Let us take look at Figure 5 and 7. We could see thatthe SINR and transmission power of PU converge slightlyslower in C=5 case than in C=1 case after the deep fading.This is because the SU responds slower to the change ofthe transmission power of primary user while C=5. However,from Figure 6 and 6 we can see that in C=1 case the PU hasa higher possibility to transmit using maximum transmissionpower because of the deep fading.

V. CONCLUSION

In this paper, we proposed a new algorithm for spectrumshared Cognitive network based on part of the feedbackchannel of the primary system. This part is related to thepower control command, which is sent by the PR to the PT.In Section IV, we simulate the centralized (optimal) scenariowhere the same transmission power of primary system andthe same channel are used, and distributed algorithms, wherethe channels suffer path loss, shadowing and Rayleigh fading,and also compare the distributed algorithm to centralizedone. The results show that the secondary system can workwith primary system simultaneously with slightly harm to theprimary system. Also, we could apply cross-layer optimizingschemes together with the proposed algorithms to optimize thesystem further. For example, the secondary user could switchoff itself when it can not achieve its target SINR in order toreduce the interference to primary system.

REFERENCES

[1] FCC, “Spectrum policy task force report,” Federal CommunicationsCommission, Online Tech. Rep. 02-135, November 2002. [Online].Available: http://hraunfoss.fcc.gov/edocs public/attachmatch/DOC-228542A1.pdf

[2] ——, “Notice of proposed rule making and order,” Federal Communi-cations Commission, Tech. Rep. ET Docket No. 03-322., Dec. 2003.

[3] J. Mitola, “Cognitive radio: an integrated agent architecture for softwaredefined radio,” Ph.D. dissertation, Computer Communication SystemLaboratory, Department of Teleinformatics, Royal Institute of Technol-ogy (KTH), May 2000.

[4] S. Haykin, “Cognitive radio: brain-empowered wireless communica-tions,” IEEE Journal on Selected Areas in Communications, vol. 23,no. 2, pp. 201–220, 2005.

[5] I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, “Nextgeneration/dynamic spectrum access/cognitive radio wireless networks:a survey,” Comput. Netw., vol. 50, no. 13, pp. 2127–2159, 2006.

[6] A. F. Molisch, L. J. Greenstein, and M. Shafi, “Propagation issues forcognitive radio,” Proceedings of the IEEE, vol. 97, no. 5, pp. 787–804,May 2009.

[7] Q. Zhao and B. Sadler, “A survey of dynamic spectrum access: Sig-nal processing, networking, and regulatory policy,” Signal ProcessingMagazine, IEEE, vol. 24, no. 3, pp. 79–89, May 2007.

[8] L. B. Le and E. Hossain, “Resource allocation for spectrum underlay incognitive radio networks,” Wireless Communications, IEEE Transactionson, vol. 7, no. 12, pp. 5306–5315, December 2008.

[9] B. Zayen, M. Haddad, A. Hayar, and G. E. ien, “Binary powerallocation for cognitive radio networks with centralized and distributeduser selection strategies,” Physical Communication, vol. 1, no. 3, pp.183 – 193, 2008.

[10] H.-S. Le and Q. Liang, “An efficient power control scheme for cog-nitive radios,” Wireless Communications and Networking Conference,2007.WCNC 2007. IEEE, pp. 2559–2563, March 2007.

[11] W. Wang, T. Peng, and W. Wang, “Optimal power control under in-terference temperature constraints in cognitive radio network,” WirelessCommunications and Networking Conference, 2007.WCNC 2007. IEEE,pp. 116–120, March 2007.

[12] L. Qian, X. Li, J. Attia, and Z. Gajic, “Power control for cognitiveradio ad hoc networks,” in Local and Metropolitan Area Networks, 2007.LANMAN 2007. 15th IEEE Workshop on, June 2007, pp. 7–12.

[13] S. Im, H. Jeon, and H. Lee, “Autonomous distributed power control forcognitive radio networks,” Vehicular Technology Conference, 2008. VTC2008-Fall. IEEE 68th, pp. 1–5, Sept. 2008.

[14] G. Foschini and Z. Miljanic, “A simple distributed autonomous powercontrol algorithm and its convergence,” Vehicular Technology, IEEETransactions on, vol. 42, no. 4, pp. 641–646, Nov 1993.

[15] M. Gudmundson, “Correlation model for shadow fading in mobile radiosystems,” Electronics Letters, vol. 27, no. 23, pp. 2145–2146, Nov. 1991.

[16] G. L. Stuber, Principles of mobile communication, 2nd ed. Norwell,MA, USA: Kluwer Academic Publishers, 2001.

[17] B. Liang and Z. Haas, “Predictive distance-based mobility managementfor pcs networks,” in INFOCOM ’99. Eighteenth Annual Joint Confer-ence of the IEEE Computer and Communications Societies. Proceedings.IEEE, vol. 3, Mar 1999, pp. 1377–1384 vol.3.

[18] H. Zhang, C. S. Chen, and W. S. Wong, “Distributed power control fortime varying systems: performance and convergence analysis,” VehicularTechnology, IEEE Transactions on, vol. 54, no. 5, pp. 1896–1904, Sept.2005.

[19] J. Zander and S.-L. Kim, Radio Resource Management for WirelessNetworks. Norwood, MA, USA: Artech House, Inc., 2001.

[20] Y. Zheng and C. Xiao, “Improved models for the generation of multi-ple uncorrelated rayleigh fading waveforms,” Communications Letters,IEEE, vol. 6, no. 6, pp. 256–258, Jun 2002.

137