Non-Intrusive Cognitive Radio Networks based on Smart Antenna Technology

Transcription

1 Non-Intrusive Cognitive Radio Networks based on Smart Antenna Technology Senhua Huang, Zhi Ding, and Xin Liu University of California Davis Davis, CA 95616, USA Abstract Cognitive radio has recently been identified as a potential relief to spectrum scarcity by improving temporal spectral efficiency. We investigate a flexible non-intrusive cognitive radio network based on smart antenna technologies. The proposed scheme exploits transmit beamforming to enable better spectral sharing between primary users and cognitive (secondary) users. As proposed, the cognitive transmitter equipped with antenna array forms transmit beamforming to keep the interference to primary receiver below a given threshold. By also adopting smart antennas at primary transmitters, we can significantly boost the successful transmission probability of cognitive users; thereby improving the spectrum utilization efficiency of the wireless communication networks. 1 I. INTRODUCTION The rapid growth of wireless technologies and applications has made radio spectrum an increasingly scarce commodity. The need for higher spectral efficiency has attracted extensive research interests. At the same time, according to measurement results reported [1], [2], a large proportion of the licensed spectrum remain mostly unused or under-utilized, indicating that the current spectral shortage may be partially relieved by a more flexible user access rather than the presently rigid and static spectral allocation. Cognitive radio, as a promising technology, may lead to better spectral efficiency by permitting opportunistic access of licensed bands by cognitive users when the primary licensees are inactive [3], [4], [5]. We have witnessed a surge of recent activities on cognitive radio research. In [6], a sensing-based opportunistic channel access scheme was proposed. In [7], a cognitive approach based on dynamic spectrum management was proposed to access the available spectrum in an opportunistic manner. In [8], cognitive technology is used to enable wide area networks to share the available void frequency spectrum. In [9] and [1], cognitive transmitters are modeled as decision makers that utilize game theory to optimally control their activities. In most existing proposals (e.g., [6], [7], [8], [9], [1]), the cognitive transmitter (CT) cannot access the spectrum simultaneously with the primary transmitter (). In [11], the authors proposed a technique similar to the Gel fan-pinsker coding to enable simultaneous transmission by CT and. The disadvantage of this scheme, however, is that CT must detect the signal before implementing the interference-mitigating 1 This work is supported in part by the National Science Foundation Grant CNS and Grant CNS coding techniques. This approach would not succeed unless the CT is equipped with reliable primary signal detectors. In this paper, we propose a more flexible opportunistic spectrum access scheme based on spatial diversity and smart antenna technology. The proposed non-intrusive cognitive scheme exploits the spatial void and thus can further improve the spectral efficiency. Our goal is to jointly integrate the advantages of cognitive radio and multiple antenna diversity. Our basic idea is that, when CT has multiple antennas, it can construct its transmission beam pattern such that its interference to the primary receiver () is either minimized or constrained. Combined with transmission power control, the effective interference to can be limited below a predefined power threshold. Meanwhile, depending on the relative location of the cognitive receiver (CR) and the, interference from to CR can be very small in a large area known as the decodable zone. Therefore, CT and can transmit to their respective receivers with high enough SINR with high probability when CRs are in the decodable zone. We organize this paper as follows. We present our system model and describe the problem formulation of the proposed cognitive radio system in Section II. We describe, in Section III, an optimal transmit beamforming algorithm that guarantees the spectrum access of cognitive radio to be non-intrusive to primary users while maximizing the achievable signal to interference and noise ratio (SINR) at the CR. In Section IV, we use performance analysis and numerical results to demonstrate the benefit of our proposed scheme. Section V summarizes our work. II. SYSTEM MODEL AND OBLEM DESCRIION We consider a scenario in which two wireless links are deployed to coexist in a geographical region: one primary communication link and one (secondary) cognitive communication link. The primary users are the rightful radio spectrum licensees, while the cognitive users may have access to the primary s spectrum under the condition of non-intrusion. The entire setup is illustrated in Fig. 1 in which the primary transmitter () is located at (x,y ) while the cognitive transmitter (CT) is located at (x 1,y 1 ). They use the same spectral band. We further assume that and CT are not co-located, with a separation distance of D = (x x 1 ) 2 +(y y 1 ) 2. The primary receiver () is randomly distributed within the circle

2 existence of CR and will not adapt its transmission behavior. Hence, the implementation of our cognitive radio must limit its interference to the. In other words, as a condition for the cognitive users to access the primary s spectrum, the CT must guarantee that its interference to the is limited by a predefined threshold. We use subscript () p and () c to denote the primary user and cognitive user, respectively. The received signals at and CR can be written, respectively, as Fig. 1. Cognitive Radio System Scheme with Smart Antenna Technology of radius D. This means that the CT is deployed at the edge of the primary network. Such a case is reasonable. Often, there is a spatial variation in the activities of the, i.e., in some regions, there is a low probability of presence. We deploy the CR in one such circular region. The CRs can be randomly distributed in this circular region centered at (x 1,y 1 ) with a (small) radius d. Here, we use d pp, d pc, d cp and d cc to denote the distance between and, and CR, CT and, CT and CR respectively, as shown in Fig. 1. Clearly, because of the constraint on its interference to the, the cognitive system cannot be arbitrarily deployed. Our goal is to determine the region where cognitive radio can be deployed using smart antennas. To better utilize the limited spectrum, cognitive transmitter is equipped with multiple antennas. It can therefore exploit smart antenna technologies such as beamforming to curb its interference to the primary receivers. Here, we assume that the antennas used by cognitive transmitter forms a 2-D uniform circular array (UCA) with M antenna elements. For simplicity, only azimuth angles are considered in the propagation geometry. Assuming a relative narrow-band transmission, the antenna manifold vector of the UCA can be written as: v(ζ) = v 1 (ζ) v 2 (ζ). v M (ζ) = e j2π(r/λ)cos(ζ φ1) e j2π(r/λ)cos(ζ φ2). e j2π(r/λ)cos(ζ φm ), (1) where R is the array radius, λ is the carrier wavelength, φ i = 2π M i, i =1,,M is the angle of the antenna elements with respect to the horizontal reference line, and ζ is the direction of transmission beam. As shown in Fig. 1, the direction of with respect to and CT are denoted by θ pp and θ cp, respectively. The direction of CR with respect to and CT are characterized by θ pc and θ cc, respectively. In this work, we only consider the path loss in the largescale wireless channel model and denote the path loss factor as α. In addition, we focus on the downlink only and thus assume that there is only one antenna at CR and. In the non-intrusive network, the is not concerned about the y p = h pp s p + h cp s c + n p (2) y c = h cc s c + h pc s p + n c where s p and s c are the source signals for and CR, respectively, while n p and n c represent noises at the and the CR that are white with the same power spectrum N. Let w i,i = p, c be an M 1 transmit beamforming vector. The corresponding beamforming gain in the direction of θ becomes G i (θ) =wi H v i(θ). (3) Thus, channel gain for each pair of transmitter and receiver can be expressed as h ij = d α ij wh i v i (θ ij )=d α ij G i(θ), i, j = p, c. (4) Hence, the signal to interference and noise ratio (SINR) at primary receiver SINR p and at the cognitive receiver SINR c can be expressed as: P p d α pp G p (θ pp ) 2 SINR p = N + P c d α cp G c (θ cp ), 2 P c d α cc SINR c = G c(θ cc ) 2 (5) N + P p d α pc G p (θ pc ). 2 Here P p and P c denote the transmitted powers of and CT, respectively, subject to the maximum power constraint. III. NON-INTRUSIVE OIMAL BEAMFORMING Because the cognitive system is non-intrusive, the primary transmission dose not need adjustment. We consider two fixed transmission strategies at the : one that uses omnidirectional antenna, the other that adopts the following transmit beamforming algorithm: min w p max G p(θ pi ), θ pi [θ pp Δθ,θ pp+δθ] subject to G p (θ pp ) =1 where Δθ is the designed half-power beamwidth of the transmit beamforming of. The second strategy is a beamforming algorithm that minimizes the transmission gain outside a narrow beamwidth while maintaining a unit gain in the direction. This beamforming algorithm for is reasonable, since it can reduce inter-cell interference for the primary system. Obviously, the omni-directional case sets a tighter bound on the performance of CR because the interference is greater than the case when the uses transmit beamforming. The CT, however, has to guarantee that its interference to the primary receiver is below a limit or a threshold I, in order to gain access and remain non-intrusive. Thus, the (6)

3 cognitive radio must be aware of the approximate location of the primary receiver. This knowledge may be acquired in various ways. Firstly, it can be obtained through database. For instance, the primary users may be static computer stations with fixed locations. Secondly, several cognitive users can estimate the distance and angle of arrival of by monitoring the uplink communication between primary users. Thirdly, this information can be obtained by deploying a number of measurement devices in coverage area. Normally, the location information of is not accurate due to the estimation error and possible scatters around the. Hence, the CT must limit the worst case interference on the under the threshold I. Here, we consider the uncertainty on the angle information of θ cp only, and use Δφ to denote this angle ambiguity. The distance is known accurately. The information of CR s location can be obtained by feedback channel and measurement in the uplink channel of cognitive users. Given the (approximate) location or angle, the optimal CT beamforming can be optimized via max SINR c w c subject to P c d α cp G c(θ cp ) 2 I G c (θ cc ) =1 G c (θ cj ) 1/2,θ cj [θ cc Δθ, θ cc +Δθ] P c P max, where P c d α cp G c(θ cp ) 2 I is the interference constraint on the CT, G c (θ cj ) 1/2 is a constraint on the sidelobe leakage of the CT antenna beam, and the maximum transmission power of the CT P max is determined by d cc and SNR requirement of the CR γ c as P max = γ c N d α cc. For given w c, we define g c = max G c(θ), (8) θ cp Δφ θ θ cp+δφ which indicates the worst interference gain to the. As a result, we have the interference constraint on the CT as: P c d α cp gc 2 I (9) From (5), because the can not be required (due to nonintrusiveness) to minimize G p (θ pc ) 2, we have to increase P c to increase SINR c. However, when P c increases, the interference on the will increase. Thus, the performance of SINR c is tightly related to g c, and we rewrite the optimization problem (7) as follows: min w c max θ cp Δφ θ ci θ cp+δφ G c (θ ci ) subject to G c (θ cc ) =1 G c (θ cj ) 1/2, θ cj [θ cc Δθ, θ cc +Δθ]. (7) (1) As shown in [12], (6) and (1) are convex optimization problems and thus can be solved very efficiently using algorithms such as interior point methods. Also notice that, when θ cc [θ cp Δφ, θ cp +Δφ], wehaveg c =1. After determining the optimal beamforming vector w c for CT, the CT s transmission power can be written as P c = min {I g c 2 d α cp,γ cn d α cc } (11) Consequently, the SINR at and CR can be written as SINR p P pd α pp = γ p N + I 1+c (d cp /d cc ) α g c 2 SINR c = min {c 1+γ p (d pp /d pc ) α G p (θ pc ) 2, P max d α cc N + P p d α pc G p (θ cp ) } (12) 2 (d cp /d cc ) α g c 2 = min {c 1+γ p (d pp /d pc ) α G p (θ pc ) 2, γ c 1+γ p (d pp /d pc ) α G p (θ cp ) 2 } where c = I /N denotes the ratio of endurable interference at to the noise power, and γ p = P p d α pp /N is the SNR of the. Obviously, the larger the I, the greater the SINR c, while the smaller the SINR p. Thus, I can be regarded as a tradeoff parameter balancing the performance of primary users and cognitive users. We provide an example beam-pattern of CT in Fig. 2. It shows that, the beamforming gain in the direction of the can be made very small. The performance of the cognitive beamforming algorithm (1) is also numerically evaluated to yield the results of Figures 3(a) 3(b). The relationship between angle ambiguity and g c is shown in Fig. 3(a). We observe that g c increases when Δφ increases, as expected. Fig. 3(b) demonstrates the relationship between the angle separation Δθ c = θ cc θ cp and g c,givenδφ =1 o. G s (θ ci ) in db Beamforming Pattern of Cognitive Tx Cognitive Rx Primary Rx θ ci Fig. 2. An example of CT s beamforming pattern IV. PERFORMANCE ANALYSIS AND NUMERICAL RESULTS To characterize the performance of the new cognitive radio system equipped with smart antennas, we study the probability distribution of Pr{SINR c T }. First, we note that the distances and the angles are independent random variables in our model. From (6) and (1), the solution to the beamforming problem is determined by the angles information and constraints, i.e., θ cp, θ cc, θ pp, θ cc, Δφ and half-power beamwidth Δθ.

4 1 2 Using the relationship of D d cc <d pc <D+ d cc, we can obtain an upper/lower bound of this probability P + T and P T, respectively, as g c (db) M = 16 Δ θ = 15 o θ cc = 6 o θ cp = 1 o Δ φ P T = Pr{dα cc g2 c +( d cc ) α γ p d α pp D d g2 c dα cpc cc T } = Pr{gc 2 (d2 cc + γ pd α d α cc pp (D d cc ) α ) dα cp c T } = ds d α cc } S :{(d cc,θ cc):gc 2(d2 cc +γpdα pp (D dcc) α ) dα cp c T (15) Fig. 3. g c (db) (a) Angle Ambiguity Versus g c M = 16 Δ φ = 1 o θ cc = 6 o Δ θ = 15 o Δ θ c (b) Angle Separation Versus g c Relationship between Angle Ambiguity, Angle Separation and g c When uses omni-directional antenna, we have g p =1. Thus, we can obtain a lower bound on the performance of SINR c. Additionally, if there is no power constraint on CT, i.e., P max =, we can obtain an upper bound on SINR c. Consequently, SINR c = c (d cp/d cc ) α gc 2 1+γ p (d pp /d pc ) α. (13) We consider two different cases: one for the scenario with a fixed location primary receiver, and one for the scenario with a fixed cognitive receiver. A. Fixed Location Primary Receiver Fixing the location of also fix parameters d pp, d cp, and θ cp. Then, because g c = f(θ cc θ cp ) becomes a function of only θ cc, SINR c becomes a function of only d cc, θ cc and d pc, Note that d cc and θ cc are independent and uniformly distributed random variables with d cc U(d min,d max ) and θ cc U(, 2π) (U denotes uniform distribution). Here, we set d max = D and d min =1m, which justifies the largescale wireless channel model. The probability can be further expanded into P T = Pr{c (d cp/d cc ) α gc 2 1+γ p (d pp /d pc ) α T } = Pr{d α ccgc 2 +( d cc ) α g d cγ 2 p d α pp dα cp c (14) pc T }. P + T = Pr{dα ccgc 2 d cc +( ) α γ p d α D + d ppgc 2 d2 cp c cc T } = Pr{gc(d 2 2 cc + γ p d α d α cc pp (D + d cc ) α ) dα cpc T } = ds. d α cc } S + :{(d cc,θ cc):gc 2(d2 cc +γpdα pp (D+dcc) α ) dα cp c T (16) Notice that P T and P + T are monotonically increasing functions of d cc, because their first order derivative is greater than for <d cc <D. This means that for a given θ cc,ifwehave (d,θ cc ) in S and S +, then any (d cc,θ cc ) with d cc <d will also be in S and S +. If we define the decodable zone of CR as S := ds, S:(d cc,θ cc):sinr c T then the integration regions S in (15) and S + (16) are actually the lower and upper bounds on the decodable zone, respectively. In fact, for every θ cc and consequently g c,we have a lower bound and an upper bound on d as solutions to the following equations with constraint <d <D: d α lb + γ p d α ub + γ p d α pp (D d lb )α d lb d α pp (D + d ub )α d ub α = dα cpc Tgc 2 α = dα cp c Tgc 2. (17) To illustrate how tight the bounds are, Monte-Carlo simulations are used to generate the decodable zone of CR. We set γ c =1,and γ p =1. Interference threshold to the from CT is fixed at I =.1N, thus we have SINR p =9.1. The path loss factor is set as α =2. When the uses omni-directional antenna, we obtain the decodable zones for T =6dB, shown as shaded regions in Fig. 4 with γ c =1dB and γ c =2dB respectively. The units of the two axes are meters. The lower/upper bound S and S + are also shown in Fig. 4 as bold lines for comparison purpose. From Fig. 4, we see that when the maximum transmission power is very large, the bounds we obtain in (17) are very tight. The difference of shaded areas between Fig. 4(a) and 4(b) can be regarded as power-limited area. In this area, the interference from the is the main constraint of the SINR c performance. When the uses transmit beamforming with weight vector calculated from (6), the decodable zones of CR

5 45 45 γc = 1dB 4 γc = 1dB CT S (a) Decodable zone of CR with γc = 1dB c γ = 2dB CT c S with γc = 1dB and γc = 2dB are shown in Fig. 5(a) and Fig. 5(b). We see that, when the uses transmit beamforming, the decodable zones of CR increases dramatically. This results from the fact that the interference from the is greatly reduced if the uses smart antenna technique to steer its main-lobe to the direction of the. Therefore the SINR c will increase without increasing the maximum transmission power of the CT. B. Fixed Location Cognitive Receiver By fixing the location of CR, probability ρ(d cc, θcc ) = P r{sinrc T } describes the performance SINR c of the given CR with the randomly located at the region centered at the. ρ(dcc, θcc ) can also be regarded as the probability of certain CR falling into the decodable zone and achieve successful transmission. In different location of CR, the probability P r{sinrc T } is different. The total improvement on spectral efficiency ρ can thus be expressed as ρ(dcc, θcc ) da 5 (Tx BF) S (b) Decodable Zone of CR with γc = 2dB Decodable Zone of CR when uses omni-directional antenna A:{dcc [dmin,dmax ],θcc [,2π)} 5 (b) Decodable zone of CR with γc = 2dB ρ = 1 45 γ = 2dB 4 Fig (Tx BF) S+ (a) Decodable Zone of CR with γc = 1dB 45 CT 35 (18) Since dpc, dcc and θcc are fixed, SINRc is a function of d cp, θcp and dpp. However, since g c = f (θcp ) in the expression (13) is a function of θ cp, which depends on both of θ pp and dpp, we are unable to separate g c2 from dpp. Instead, MonteCarlo method is used to determine the P r{sinr c T }. Regions in which CR satisfies P r{sinrc T } > p are marked by dots in Fig. 6 and Fig. 7 for γ c = 1dB and γc = 15dB, respectively. If we deploy the CRs in the shaded regions, at least ρ = p ShadedArea T otalarea in spectral efficiency Fig. 5. Decodable Zone of CR when uses transmit beamforming can be achieved. From simulations, we show that, 13.45%, 42.48%, 4.63%, and 45.15% increases in spectrum efficiency can be achieved as shown in Figures 6(a), 6(b), 7(a) and 7(b), respectively. From Fig. 6 and Fig. 7, we observe that, SINR c is most limited by the interference from the. Thus, when the uses transmit beamforming technique, the interference from the to the CR is reduced and thus the shaded region expands significantly. Another way to increase the shaded region is to relax the transmission power constraint of the CT, which can be also observed from the simulation results. Notice that, even when we increase the transmission power of the CT, the interference to the is still limited to I. Therefore, by applying smart antenna techniques, we can achieve a tradeoff between the implementation complexity/power and the wireless spectrum. From the presented performance analysis and numerical results, we can see that the proposed cognitive radio network based on smart antenna technology (transmit beamforming) enables cognitive users to have access to the primary users spectrum simultaneously with the primary users. The size of decodable zone of CR relative to the entire coverage area of the CT represents the improvement on spectrum efficiency. Cognitive receivers that are out of the decodable zone should switch to another spectral band or wait until the primary communication link ceases transmission or migrates away. In conjunction with sensing-based opportunistic spectrum access schemes and frequency hand-over techniques, the proposed approach can significantly enhance the spectral efficiency by

6 γ = 1dB c p = γ = 15dB c p = (Tx BF) (Tx BF) (a) uses transmit beamforming (a) uses transmit beamforming γ = 1dB c p = γ = 15dB c p = (b) uses omni-directional antenna (b) uses omni-directional antenna Fig. 7. Regions of CR with Pr{SINR c T } >pfor γ c =15dB Fig. 6. Regions of CR with Pr{SINR c T } >pfor γ c =1dB utilizing both spatial and temporal spectral vacancy. V. CONCLUSION In this paper, we presented a cognitive radio system based on smart antenna technologies to achieve non-intrusiveness to primary licensees. This system allows simultaneous operation of primary users and cognitive users while suppressing the interference generated by the cognitive radios to the primary users under a tolerable limit. We improved the overall spectral efficiency by positioning the cognitive system in areas that have low or no primary activity. We also determined the decodable zones for cognitive radio based on different transmitter power constraints and verified the tightness of a lower/upper bound of the decodable zone. Future works may include the investigation of transmission strategies and performance analysis to (small scale) timevarying fading channels, and consideration of inaccuracy on distance information. The deployment of multiple antennas in systems where multiple cognitive nodes coexist is also of interest. Another possible direction is to develop efficient hybrid MAC layer protocol to jointly exploiting the spectral vacancy in both the spatial and temporal domains. [3] FCC, Facilitating opportunities for flexible, efficient, and reliable spectrum use employing cognitive radio technologies, notice of proposed rule making and order, et docket no , December 23. [4] M. Marcus, Real time spectrum markets and interruptible spectrum: new concepts of spectrum use enabled by cognitive radio, in First IEEE International Symposium on Dynamic Spectrum Access Networks, DySPAN 25, 25, pp [5] S. Haykin, Cognitive radio: brain-empowered wireless communications, IEEE Journal on Selected Areas in Communications, vol. 23, no. 2, pp , 25, [6] X. Liu and S. Shankar, Sensing-based opportunistic channel access, in ACM MONET, vol. 11, 26. [7] D. Carbric, S. M. Mishra, D. Willkomm, R. Brodersen, and A. Wolisz, A cognitive radio approach for usage of virtual unlicensed spectrum, in 14th IST Mobile and Wireless Communications Summit, 25. [8] W. Krenik and A. Batra, Cognitive radio techniques for wide area networks, in 42nd Design Automation Conference, 25. Proceedings, 25, pp [9] N. Nie and C. Comaniciu, Adaptive channel allocation spectrum etiquette for cognitive radio networks, in IEEE DySPAN, 25. [1] J. Huang, R. Berry, and M. Honig, Auction-based spectrum sharing, to appear in ACM/Kluwer Journal of Mobile Networks and Applications special issue on WiOpt 4., 25. [11] N. Devroye, P. Mitran, and V. Tarokh, Achievable rates in cognitive radio channels, IEEE Transactions on Information Theory, vol. 52, no. 5, pp , 26. [12] H. Lebret and S. Boyd, Antenna array pattern synthesis via convex optimization, IEEE Transactions on Signal Processing[see also IEEE Transactions on Acoustics, Speech, and Signal Processing], vol. 45, no. 3, pp , 1997, X. REFERENCES [1] FCC, Spectrum policy task force report. et docket no , November 22. [2] J. Yang, Spatial channel characterization for cognitive radios, MS Thesis, UC Berkeley, 24.