SECONDARY TRANSMISSION POWER OF COGNITIVE RADIOS FOR DYNAMIC SPECTRUM ACCESS

Transcription

1 SECONDARY TRANSMISSION POWER OF COGNITIVE RADIOS FOR DYNAMIC SPECTRUM ACCESS Xiaohua Li 1 1 Department of ECE State University of New York at Binghamton Binghamton, NY 139, USA {xli,jhwu1}@binghamton.eu Jinying Chen, Juite Hwu 1 Department of Communication Engineering College of Information Engineering Chengu University of technology Chengu 6159, CHINA chjy@cut.eu.cn ABSTRACT In this paper, we analyze the allowable transmission power of cognitive raios when use as seconary users in a ynamic spectrum access network. Close-form upper an lower bouns are erive, while accurate solutions to transmission power are available through numerical evaluation. The transmission power epens on the istance between primary an seconary transmitters as well as the number of ranomly istribute primary receivers. The results show that at the cost of a small SINR reunancy of primary users, cognitive raios can use a significant level of transmission power in certain conitions. Inex Terms cognitive raio, ynamic spectrum access, transmission power, signal to interference an noise ratio SINR 1. INTRODUCTION Cognitive raio CR has attracte great attention recently as a potential way of realizing ynamic spectrum access DSA. CR-base DSA can help resolve the shortage problem of the overly crowe wireless communication spectrums [1]. It has been fining many practical applications, such as using the TV ban for seconary spectrum access, or in certain military applications for both spectrum efficiency an security. In DSA networks, there are various ways to support seconary spectrum access. One of the ways is for seconary users to utilize the spectrum hole which the primary users o not use uring some time perio an in some place. Another way is to allow the seconary users to utilize the same spectrum at the same time an the same place with the primary users. In orer to mitigate the interference to primary users, seconary transmitters may use an unerlay approach Li was partly supporte by US AFRL uner a subcontract to Grant FA Chen was partly supporte by the Grant # 6BAC13B4-3 from the 11-5 Scientific Projects of China. for spectrum access, such as the ultra-wieban UWB transmission. An alternative approach is overlay, in which seconary transmitters can have larger transmission power. In this case, in orer to limit the interference to the primary users, the seconary transmitters either scheule their transmission power so that their interference to primary users is limite to an acceptable level [], or exploit special coing techniques such as irty paper coing so that they can use a portion of the transmission power to help the primary users while the rest of the power to transmit their own information [3]. In this paper, we focus on an approach similar to [] where seconary spectrum access is allowable as long as the interference to primary users is within a certain threshol. We will analyze the signal-to-interference-an-noise-ratiosinr an fin the seconary transmitters allowable transmission power. In contrast to [] which stuies fixe users both number an location, we erive the average transmission power by consiering uniformly istribute primary receivers in the network. Some preliminary results along this line has been reporte in [4], but without the close-form bouns being erive. The organization of this paper is as follows. In Section, we give the system moel. Then in Section 3, we analyze the transmission power by a geometric metho for a single seconary transmitter. Simulations are conucte in Section 4. Conclusions are then given in Section 5.. DSA SYSTEM MODEL We consier a cellular-like system, where in a cell there is a base station that communicates with multiple mobile users. We enote the base station as primary transmitter T an the mobile users as primary receivers. In aition, there is a seconary transmitter enote as T1 an the corresponing seconary receivers. Both the number an the positions of the primary receivers are unknown to the seconary users. We put the base station T in the center of a cell with raius r,

2 an let the istance between T an T1 be. We assume there are M primary receivers that are uniformly istribute insie the cell. The seconary transmitter T1 may transmit at the same time an the same frequency as the primary user T. The transmission power of T1 shoul be etermine appropriately so that all the primary receivers can still work. In other wors, while seconary transmission egraes the primary receivers SINR, such a egraation shoul be smaller than certain threshol. For this purpose, the primary system shoul have been esigne with certain reunancy in SINR, i.e., the worst case SINR of the primary receivers is larger than the minimum require SINR Γ when there is no seconary spectrum access. Let the reunancy be escribe by a factor Γ. In case of without seconary transmission, primary receivers have SINR no less than KP r α Γ + Γ, 1 N where P is the transmission power of the base station T, N is the AWGN noise power at the receiver which we assume ientical for all the receivers, the parameter α is the path-loss exponent, an K is the constant that inclues all other propagation effects such as antenna gains an carrier wavelength. In case of seconary spectrum access, we just nee to assure the SINR γ of any primary receiver to satisfy γ Γ. 3. SECONDARY TRANSMISSION POWER If there are primary receivers close to T1, then the transmission power of T1 has to be small in orer to avoi introucing excessive interference. The transmission power of T1 epens on the position of the primary receivers. Consiering the ranom istribution of primary receivers an the fact that T1 oes not have etaile information about the locations of the primary receivers, we evaluate the expecte transmission power of T1 in this section Upper boun of seconary transmission power To erive the upper boun of the seconary transmission power, let us consier first the case that all the primary receivers are locate outsie of a circle of raius x aroun T. We can moel the cummulative istribution of this case as M F 1 x = 1 πx A πr A, 3 where x x r an A = πx. Note that the parameters x an A are use in orer to inclue the general case where the primary receivers have a istance at least x away from the primary transmitter T. This istance may be ue to the far-fiel effect of antenna transmissions, or ue to some other r R3 R R T x Fig. 1. A cell with a primary transmitter T an all the primary receivers being outsie of the circle with raius x. T1 is the seconary transmitter. The primary receiver R has the highest SINR, which is exploite to erive the upper boun of T1 s transmission power. reasons. Then the probability ensity that there are some primary receivers with istance x to T but no primary receivers closer to T than x is f 1 x = F 1x x T1 = πmx M 1 πr A 1 πx A πr A. 4 Note that the negative sign in 4 is to guarantee a positive ensity. Proposition 1. If the minimum istance between T an primary receivers is x, then the transmission power of T1 satisfies P 1 x x + α P x α N. 5 Γ K The equality is achieve when the SINR Γ is actually achieve by some primary receivers. Outline of Proof. To save space, we only outline the proof. Details will be reporte elsewhere. We can prove 5 by consiering the two circles in Fig. 1, where the bigger one is the circle of T with raius r whereas the smaller one is the circle with raius x. We can show that if there is a primary receiver R lies in the intersection of the small circle an the line T-T1, then R has the highest SINR among all the primary receivers. The transmission power of T1 erive from this SINR is an upper boun of the seconary transmission power. R s SINR is KP x α γ R x = KP 1 xx + α + N, from which 5 can be obtaine. The upper boun of the expecte seconary transmission power can then be erive from 5. When evaluating of average power, however, it might be better to use its ecibel value. Therefore, we change 5 first into [ P 1 xb = 1 log 1 x + α P Γ x α N ]. 6 K

3 where P 1 xb enotes the upper boun for this special case. The upper boun of the expecte seconary transmission power is then evaluate as P 1 B = r P 1 xbf 1 xx 7 From 7, we can evaluate P 1 B numerically. Nevertheless, to analyze the connections between the transmission power an the transmission parameters, a close-form solution is more esirable. In orer to erive close-form solution to 7, we have to take some simplifications. First, we let x =,soa =. Then, we consier only the noiseless case with N =. After some teious but straight-forwar integration euction, we have P 1,N= B = P r α 1 log 1 +5[ψM +1 ψ1] log1 e α Γ [ πmγmr 1 +1 Γ M + 3 F 1, 1,M + 3, r r ] M +1 F 1 1, 1,M +, r. 8 Note that Γ, F 1 an ψ enote Gamma function, Hypergeometric function, an PolyGamma function, respectively. From 8, we can reaily see that the seconary transmission power increases when the ratio /r becomes large, or the number of primary receivers M reuces. A big path-loss exponent α is helpful for seconary spectrum access. 3.. Lower boun of seconary transmission power The evaluation of the lower boun of seconary transmission power nees to take a ifferent approach. In contrast to the approach in Section 3.1, we consier the scenario that all the primary receivers are away from T1 with a istance x. Such a scenario gives a circle of raius x centere aroun T1, as shown in Fig.. Depening on the position of T1, the range of x is ifferent. Specifically, if r, i.e., T1 is within the primary cell, then x x r +. Otherwise, if >r, then the vali range of x is max{x, r } x + r. The cummulative istribution of the case that there are no primary receivers in the circle of T1 epens on the area Ax of the cross section of the two circles in Fig.. Specifically, the cummulative istribution can be foun as F x = 1 Ax A M πr A, 9 where max{x, r } x +r. If the raius x is small so that x x r, as shown in Fig. 1a, then the area of the cross section is Ax =πx, x r. 1 R3 T T a R x R b T1 x R3 R Fig.. Circles of primary transmitter T an seconary transmitter T1. a For x r, primary receiver R has the smallest SINR. b For r <x r +, primary receivers R an have the same smallest SINR. Such smallest SINR are use to erive the lower boun of the seconary transmission power. Otherwise, if the raius x is larger so that r <x r +, as shown in Fig. 1b, then the area of the intersection is Ax =x η+r φ r sinφ, r x r +, 11 where η =cos 1 + x r x T1 R r, φ =cos 1 + x r 1 For the case of >r, it can be easily verifie that the area is Ax = r. x [φ sinφ] + [η sinη], 13 where r x + r. Consiering that F x in 9 is a ecreasing function of x, probability ensity function of x shoul be f x = F x x. 14 Proposition. Let all primary receivers lie outsie of the circle of T1 with raius x, an the noise power be negligibly small i.e., N KP 1 xr + α. If r, the

4 seconary transmission power satisfies P 1 x [ x α P Γ + x α N K x α P Γ r α N K If >r, then ], if x x r, if r x r P 1 x x α P r α N Γ K 16 if max{x, r } x r +. The equality can be achieve in some special primary receiver istributions. Outline of Proof. Consiering first the two circles in Fig. a, where the bigger one is the circle of T with raius r while the smaller one is the circle of T1 with raius x, we can show that the primary receiver R has the lowest SINR, base on which we can rive the first equation in 15. The other part of 15 can be prove similarly by consiering Fig. b, an so oes 16. Note that although we have in 15-16, they are erive from the primary users with the lowest SINR. Therefore, we can efine the lower boun of P 1 x as P 1 x which equals to the right han sie of 15 an 16. The meaning of lower boun is that the seconary transmission power can always be larger than this lower boun without causing interference problem. Obviously, the seconary transmission power can be smaller than this value as well, in which case it just means the seconary transmitter oes not fully utilize the transmission capacity. The lower boun of the expecte transmission power of the seconary transmitter T1 can thus be obtaine by evaluating the expectation of P 1 x over the probability ensity f x, P 1 B = 1 log 1 [P 1 x]f xx. 17 If the istance of a seconary transmitter T1 to a primary transmitter T is known, then the lower boun of the average transmission power of T1 can be etermine from 17 numerically. The close-from solution to 17 is even more ifficult to erive than the upper boun case, mainly because the ensity function is nontrivial. Again, we have to aopt some approximations. First, the lower boun is usually extremely small when <r, i.e., when T1 lies within the cell. Therefore, we consier only the r case for close-form solutions. Next, to eal with the major problem of the non-trivial ensity function, we approximate the cummulative istribution function F x by F x = 1 x + r M 4r, r x + r, 18 which means we reuce the cross section area to a circle with raius x + r /. Note that we have also let x =. The ensity function can thus be approximate as f x = M r x + r 1 x + r M r With the above simplifications, the lower boun of the seconary transmission power is approximate as +r P x α P 1 B 1 log 1 f r Γ r α xx. If we consier the special case that T1 is near the cell bounary, i.e., /r 1, then we can reuce into α P P 1,/r 1B 1 log 1 5[ψM+1 ψ1] log Γ 1 e α. 1 In this case, 1 shows that the seconary transmission power reuces with the number of primary receivers when the seconary transmitter is near cell bounary. To evaluate in more general case, we can further apply an approximation logx r + x/x r + + log r, where log is natural logarithm. Then we can reuce into α P r P 1 B 1 log 1 + 1αr r log1 Γ [ M πγm ΓM+ 3 F 1 1, 3,M + 3, 4r r ] 4r M+1 r 4r F 1 1,,M +, r. On the other han, if we use the approximation logx r + x/ r +log r instea, then we can get a relatively looser but more succinct approximation as P 1 B 1 log P r α 1αr 1 Γ + M πγm α r log1 ΓM+ 3 3 Both an 3 inicate that the lower boun of expecte seconary transmission power is an increasing function of /r. Especially, if M is large enough, then the lower boun increases with log 1 /r 1 α. 4. SIMULATIONS In this section, we compare numerically the bouns an the exact values of the seconary transmission power. We assume the transmission power of T be 1 watts, the AWGN noise power be N =5 1 1 watts. The gains of the transmission antenna an the receiving antenna are all 1. We have effective primary transmission range r 1 meters. We set the

5 Power Ratio P 1 /P 1 Primary Rx Upper boun Upper boun approx Average Lower boun Lower boun approx Transmitter istance ratio /r Power Ratio P 1 /P /r = Upper boun Upper boun approx Average Lower boun Lower boun approx Number of Primary Receivers M Fig. 3. Seconary transmission power as functions of primary/seconary transmitters istance ratio. Fig. 4. Seconary transmission power as functions of number of primary receivers. path loss exponent as α =3to simulate an urban cellular raio environment. Γ =B is the primary receiver s SINR requirement in case of without seconary transmissions. An SINR reunancy of 3 B is simulate. For the bouns of the seconary transmission power, we irectly evaluate both the integration equations an the closeform solutions. The latter is inicate as approx in simulation figures. For the exact values of the seconary transmission power, which are enote as average in the simulation figures, we use Monte-Carlo simulations, where in each run we ranomly generate M primary receivers, an then calculate the transmission power base on the assumption that the seconary transmitter T1 knows all their positions. In Fig. 3, we can see that the bouns evaluate from numerical integrations are very close to the bouns calculate from close-form expressions. In aition, the exact values in general lie between the upper bouns an the lower bouns. In Fig. 4, we can see that the exact values of the seconary transmission power are close to upper boun when M is small, an are close to the lower boun when M becomes large. In aition, the close-form expressions again fit tightly to the numerical integrations. 6. REFERENCES [1] Q. Zhao an B. M. Saler, A survey of ynamic spectrum access, IEEE Singal Processing Mag., vol. 4, no. 3, pp , May 7. [] M. Gastpar, On capacity uner receive an spatial spectrum-sharing constraints, IEEE Trans. Info. Theory, vol. 53, no., pp , Feb. 7. [3] N. Devroye, P. Mitran an V. Tarokh, Achievable rates in cognitive raio channels, IEEE Trans. Info. Theory, vol. 5, no. 5, pp , May 6. [4] X. Li, J. Hwu an N. Fan, Transmission power an capacity of seconary users in a ynamic spectrum access network, IEEE Military Communications Conference MILCOM 7, Orlano, FL, Oct. 9-31, CONCLUSIONS In this paper, we analyze the allowable transmission power of cognitive raios when use for seconary spectrum access purpose. Transmission power of a single seconary cognitive raios are erive in the form of integration equations, an close-form solutions are obtaine uner certain simplifications. Simulations are conucte to show their effectiveness.