This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings Optimal Sensing and Power Allocation Strategy for an Efficient Cognitive Radio System Stergios Stotas and Arumugam Nallanathan Department of Electronic Engineering, King’s College London, London, WC2R 2LS, U.K. Email: stergios.stotas@kcl.ac.uk, nallanathan@ieee.org Abstract— Cognitive radio has attracted a lot of attention recently as an effective method of alleviating the spectrum scarcity problem in wireless communications. However, the constraints imposed on cognitive radio networks as secondary networks restrict their achievable throughput and highlight the importance of efficient spectrum sensing and power allocation. In this paper, we focus on maximizing the ergodic throughput of the opportunistic spectrum access cognitive radio system proposed in [1] under both average transmit and interference power constraints. More specifically, we propose an algorithm that obtains the optimal power allocation strategy and target detection probability, which under the imposed average interference power constraint becomes an additional optimization variable in the ergodic throughput maximization of the cognitive radio system. Finally, we provide simulation results and discuss the effects of the power allocation and target detection probability on the achievable ergodic throughput of the cognitive radio system. I. I NTRODUCTION Cognitive radio is an emerging technology that aims for efficient spectrum usage by allowing unlicensed (secondary) users to access licensed frequency bands, under the condition of protecting the quality of service (QoS) of the licensed (primary) users [2]. Two main spectrum access approaches have been proposed for cognitive radio so far: (i) Opportunistic spectrum access (OSA) [3], according to which the secondary users can access a frequency band only when it is detected to be idle, and (ii) Spectrum sharing (SS) [4], according to which the secondary users coexist with the primary users under the condition of protecting the QoS of the primary network. The frame structure of the opportunistic spectrum access cognitive radio systems studied so far consists of a sensing slot (during which data transmission is prohibited) and a data transmission slot, as depicted in Fig. 2. Therefore, an inherent tradeoff exists in this frame structure between the duration of spectrum sensing and data transmission (hence the throughput of the cognitive radio system), which was studied in [5] under a single target detection probability constraint. In [1], the authors proposed a method to overcome this sensingthroughput tradeoff by introducing a novel cognitive radio system that is able to perform spectrum sensing and data transmission at the same time. It was shown in [1] that the proposed cognitive radio system is able to achieve higher average throughput compared to conventional opportunistic spectrum access cognitive radio systems under a high target detection probability constraint for the protection of the primary users. In this paper, we study the problem of maximizing the ergodic throughput of the cognitive radio system proposed  SU-Rx  g  SU-Tx  h PU-Rx  Fig. 1. System model. Frame n Frame n+1 Sensing Data Transmission Sensing IJ T-IJ IJ Data Transmission T-IJ Fig. 2. Frame structure of conventional opportunistic spectrum access cognitive radio networks. in [1] under both average transmit and interference power constraints. More specifically, we focus on determining the optimal power allocation strategy for the proposed cognitive radio system, as well as the optimal target detection probability, which under the imposed average interference power constraint becomes an additional optimization variable. The effect of the target detection probability on the system’s ergodic throughput can be better seen in the simulation results in Section IV. Finally, we propose an algorithm that acquires the optimal target detection probability and power allocation strategy that maximizes the ergodic throughput of the proposed cognitive radio system and present simulation results. The rest of the paper is organized as follows. In Section II, we present the system model and provide an overview of the cognitive radio system proposed in [1]. In Section III, we study the problem of maximizing the ergodic throughput of the proposed cognitive radio system under both average transmit and interference power constraints and propose an algorithm that acquires the optimal target detection probability and power allocation strategy for the proposed cognitive radio system. In Section IV, we present and discuss the simulation results. Finally, the conclusions are drawn in Section V. + Notations: E {·} denotes the expectation operation, [x] denotes max (0, x), P denotes power and P probability. 978-1-61284-231-8/11/$26.00 ©2011 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings  Decoder II. P ROPOSED COGNITIVE RADIO SYSTEM We consider the cognitive radio system presented in Fig. 1. Let g and h denote the instantaneous channel power gain from the secondary transmitter (SU-Tx) to the secondary receiver (SU-Rx) and the primary receiver (PU-Rx), respectively. The channels g and h are assumed to be ergodic, stationary and known at the secondary transmitter as in [6], [7], whereas the noise is assumed to be circularly symmetric complex Gaussian (CSCG) with zero mean and variance σn2 , namely CN (0, σn2 ). In the following, we present an overview of the cognitive radio system proposed in [1], as well as the employed receiver and frame structure. y Spectrum Sensing Fig. 3. The cognitive radio system proposed in [1] operates as follows. In the beginning, an initial spectrum sensing is performed to determine the status (active/idle) of a frequency band. When the frequency band is detected to be idle, the secondary transmitter accesses it for the duration of a frame and transmits information to the secondary receiver. The latter decodes the signal from the secondary transmitter, strips it away from the received signal and uses the remaining signal for spectrum sensing, in order to determine the action of the cognitive radio system in the next frame. At the end of the frame, if the presence of primary users is detected, namely if the primary users started transmission after the initial spectrum sensing was performed, data transmission will be ceased, in order to protect the primary users from harmful interference. In the opposite case, the secondary users will access the frequency band again in the next frame. Finally, the process is repeated. B. Receiver and frame structure The receiver structure of the cognitive radio system proposed in [1] is presented in Fig. 3. The received signal at the secondary receiver is given by y = θxp + xs + n, (1) where θ denotes the actual status of the frequency band (θ = 1 if the band is active and θ = 0 otherwise), xp and xs represent the received signal from the primary users and the secondary transmitter, respectively, and finally n denotes the noise. The received signal y is initially passed through the decoder, as depicted in Fig. 3, where the signal from the secondary transmitter is obtained. In the following, the signal from the secondary transmitter is canceled out from the aggregate received signal y and the remaining signal, i.e. ỹ = θxp + n, (2) is used to perform spectrum sensing. This is the same signal that the secondary receiver would receive if the secondary transmitter had ceased data transmission, which is the way that was proposed to perform spectrum sensing in [5]. Here, instead of using a limited amount of time τ , almost the whole duration of the frame T can be used for spectrum sensing. This Sensing decision Receiver structure of the cognitive radio system proposed in [1].   Frame n Frame n+1 Data transmission / Spectrum sensing Data transmission / Spectrum sensing  T Fig. 4. A. System overview Information from secondary user T Frame structure of the cognitive radio system proposed in [1]. way we can perform spectrum sensing and data transmission at the same time and therefore maximize the duration of both. Finally, the frame structure of the cognitive radio system proposed in [1] is presented in Fig. 4 and consists of a single slot during which both spectrum sensing and data transmission are performed at the same time using the receiver structure presented in Fig. 3. The advantages of the proposed cognitive radio system can be found in detail in [1]. III. O PTIMAL POWER ALLOCATION STRATEGY FOR THE PROPOSED COGNITIVE RADIO SYSTEM In this section, we study the problem of determining the optimal power allocation strategy that maximizes the ergodic throughput of the proposed cognitive radio system. We consider the energy detection scheme [5], [8] here as a method for spectrum sensing, in order to determine the status (active/idle) of the frequency band. The detection and false alarm probability under the energy detection scheme are given by    ǫ T fs , (3) −γ−1 Pd = Q σn2 2γ + 1   Pf a (Pd ) = Q 2γ + 1Q−1 (Pd ) + T fs γ , (4) respectively [5]. Here, ǫ denotes the decision threshold of the energy detector, γ the received signal-to-noise ratio (SNR) from the primary user at the secondary detector, T denotes the frame duration and finally fs represents the sampling frequency. For a given target detection probability Pd = P̂d , the decision threshold ǫ is given by   2γ + 1 −1 ǫ = σn2 Q (P̂d ) + γ + 1 . (5) T fs Following the approach in [4], [9], the instantaneous transmission rate of the cognitive radio system when the frequency . However, band is idle (H0 ) is given by r0 = log2 1 + gP 2 σn considering the fact that perfect spectrum sensing may not be achievable in practice due to the limitations of spectrum sensing techniques and the nature of wireless communications that included phenomena such as shadowing and fading, we consider the more realistic scenario of imperfect spectrum This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings sensing, where the actual status of the primary users might be falsely detected. Therefore, we additionally consider in this paper the case that the frequency band is falsely detected to be transidle, when in fact it is active (H1 ). The instantaneous  mission rate in this case is given by r1 = log2 1 + σ2gP , 2 n +σp 2 where σp denotes the received power from the primary users. In order to keep the long-term power budget and effectively protect the primary users from harmful interference, we consider similar to [6], [10], [11] an average (over all different fading states) transmit and interference power constraint that can be formulated as follows Eg,h {P (H0 ) (1 − Pf a (Pd )) P +P (H1 ) (1 − Pd ) P } ≤ Pav , Eg,h {P (H1 ) (1 − Pd ) hP } ≤ Γ, (6) (7) respectively. Here, Pav denotes the maximum average transmit power of the secondary users and Γ the maximum average interference power that is tolerable by the primary users. As a result, the optimization problem that maximizes the ergodic throughput of the proposed opportunistic spectrum access cognitive radio system under both average transmit and interference power constraints can be formulated as follows maximize C(P, Pd ) = Eg,h {P (H0 ) (1 − Pf a (Pd )) · {P,Pd }     gP gP log2 1 + 2 + P (H1 ) (1 − Pd ) log2 1 + 2 σn σn + σp2 (8) subject to : (6), (7), P ≥ 0, 0 ≤ Pd ≤ 1. By considering an average interference power constraint similar to spectrum sharing cognitive radio networks [7], the detection probability Pd becomes an optimization variable in the problem of maximizing the ergodic throughput of the proposed cognitive radio system. The dependance of the ergodic throughput on the detection probability Pd can be better observed in the simulation results in Section IV. Now returning to the optimization problem (8), it can be seen that it is convex with respect to the transmit power P , but not with respect to the probability of detection Pd due to the dependance of the false alarm probability Pf a on the detection probability Pd [12]. Therefore, the optimal detection probability can not be obtained using convex optimization techniques, but taking into consideration that the detection probability lies in the interval [0, 1], it can be easily obtained using one-dimensional exhaustive search. As a result, we will focus in the following on finding the optimal power allocation strategy that maximizes the ergodic throughput of the proposed opportunistic spectrum access cognitive radio system for a target detection probability Pd = P̄d . By writing the Lagrangian L (P, λ, µ) with respect to the transmit power P for a target detection probability Pd = P̄d , the Lagrange dual optimization problem can be formulated as minimize λ≥0, µ≥0 g (λ, µ) , (9) where g (λ, µ) denotes the Lagrange dual function that is given by g (λ, µ) = supP L (P, λ, µ). It can be seen from (8) that the primal optimization problem with respect to the transmit power P is convex with linear inequality constraints and that Slater’s condition holds [12]. Therefore, the difference between the optimal value of the objective function of the primal and dual optimization problem (namely the optimal duality gap) is zero, which guarantees [12] that the primal optimization problem (8) with respect to the transmit power P can be equivalently solved by the dual optimization problem (9). We therefore focus on solving the Lagrange dual optimization problem (9). In order to calculate the Lagrange dual function g (λ, µ), we need to find the supremum of the Lagrangian L (P, λ, µ) with respect to the transmit power P . By applying the KarushKuhn-Tucker (KKT) conditions [12], the optimal power allocation P for given Lagrange multipliers λ and µ is given by √ + A+ ∆ , (10) P = 2 where A and ∆ are given at the top of the following page by + the equations (11) and (12), respectively, whereas [x] denotes max (0, x). In order to determine the optimal power allocation strategy, the optimal values of the Lagrangian multipliers λ and µ that minimize the Lagrange dual function g(λ, µ) need to be found. The ellipsoid method [13] is used here to find the optimal solution, which requires the subgradient of the dual function g(λ, µ). The latter is given by the following proposition. Proposition 1: The subgradient of the Lagrange dual function  g(λ, µ)  is [D, E], where  D is givenby D =Pav − Eg,h P (H0 ) 1 − Pf a (P̄d ) P +P (H1 ) 1 − P̄d P  and E is given by E = Γ − Eg,h P (H1 ) 1 − P̄d hP , where λ ≥ 0, µ ≥ 0, and P denotes the optimal power allocation for fixed λ, µ. Proof : The proof is omitted here due to lack of space.  The algorithm that acquires the optimal target detection probability and power allocation strategy for the proposed opportunistic spectrum access cognitive radio system is presented in the following table. Algorithm: Optimal detection probability and power allocation for the proposed opportunistic spectrum access cognitive radio system. ◮ For P̄d = 0 : 1 1) Initialize λ, µ. 2) Repeat: - calculate P using (10)-(12); - update λ, µ using the ellipsoid method; 3) Until λ, µ converge. ◮ End. ◮ Optimal detection probability   and power allocation: P̄dopt = arg max C P̄d , P and Popt = {P }P̄d =P̄ opt d This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings       2σ 2 + σp2 log2 (e) P (H0 ) 1 − Pf a P̄d + P (H1 ) 1 − P̄d     − n    . A=  g λ P (H0 ) 1 − Pf a P̄d + P (H1 ) 1 − P̄d + µP (H1 ) 1 − P̄d h 4 ∆ = A2 − g  (11)         log2 (e)[P (H0 ) 1 − Pf a P̄d (σn2 + σp2 ) + P (H1 ) 1 − P̄d σn2 ] σn2 σn2 + σp2        . −  g λ P (H0 ) 1 − Pf a P̄d + P (H1 ) 1 − P̄d + µP (H1 ) 1 − P̄d h (12) P =15 dB av 4.5 4.5 P =5 dB av 4 Pav=10 dB 4 av 3.5 Ergodic throughput (bits/sec/Hz) Ergodic throughput (bits/sec/Hz) P =15 dB Pav=20 dB 3 2.5 2 1.5 3.5 3 2.5 2 Pd=0.01% 1.5 P =50% d P =75% d 1 P =99.99% d 1 0.5 0.5 0 5 10 15 SU−Tx to PU−Rx channel attenuation (dB) 20 Fig. 5. Ergodic throughput of the proposed cognitive radio system versus the additional channel power gain attenuation for different values of average transmit power Pav and target detection probability P̄d = 90%. IV. S IMULATION R ESULTS In this section, we presented the simulation results for the proposed opportunistic spectrum access cognitive radio system using the energy detection scheme as a spectrum sensing technique. The frame duration is set to T = 100 ms, the probability that the frequency band is idle is considered to be P (H0 ) = 0.6, whereas the bandwidth and the sampling frequency fs are assumed to be 6 MHz. The channels g and h are assumed to follow the Rayleigh fading model and more specifically, they are the squared norms of independent CSCG random variables that are distributed as CN (0, 1) and CN (0, 10), respectively. The average tolerable interference power at the primary receiver is considered to be Γ = 1 and the received SNR from the primary user is considered to be γ = −20 dB. As in [6], an additional channel power gain attenuation is considered here for the channel h between the secondary transmitter and the primary receiver, where an attenuation of 10 dB for example, means that E {h} = 1. In Fig. 5, the ergodic throughput of the proposed cognitive radio system is presented versus the additional channel power gain attenuation between the secondary transmitter (SU-Tx) and the primary receiver (PU-Rx) for different values of the average transmit power Pav of the secondary user and for a target detection probability P̄d = 90%. It can be clearly seen that for all values of the average transmit power Pav , the achievable ergodic throughput increases as the channel 0 0 5 10 15 SU−Tx to PU−Rx channel attenuation (dB) 20 Fig. 6. Ergodic throughput of the proposed cognitive radio system versus the additional channel power gain attenuation for different values of detection probability P̄d and average transmit power Pav = 15 dB. power gain attenuation between the secondary transmitter and the primary receiver obtains higher values. This can be easily explained by the fact that as the channel power gain attenuation increases, the average interference power constraint allows the use of higher transmit power P , which leads to an increased achievable ergodic throughput for the cognitive radio system. Furthermore, it can be seen for all values of the average transmit power Pav that the achievable ergodic throughput reaches a maximum value that is imposed by the average transmit power constraint, whereas the point that this maximum is achieved depends on the value of the average transmit power Pav . This point is reached for higher values of channel power gain attenuation as the average transmit power Pav increases, which is due to the increased transmit power that is available to the secondary users on the one hand, in combination with the imposed average interference power constraint on the other. In Fig. 6, the ergodic throughput of the proposed cognitive radio system is presented versus the additional channel power gain attenuation between the secondary transmitter and the primary receiver for different values of detection probability P̄d and for an average transmit power of the secondary user equal to Pav = 15 dB. In this figure, an interesting result can be observed regarding the achievable ergodic throughput of the cognitive radio system. Beyond a certain value of the channel power gain attenuation between the secondary transmitter and the primary receiver, the initially imposed high target detection This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings V. C ONCLUSIONS In this paper, we studied the problem of maximizing the ergodic throughput of the opportunistic spectrum access cognitive radio system proposed in [1] under average transmit and interference power constraints and proposed an algorithm that acquires the optimal target detection probability and power allocation strategy that maximize the achievable ergodic throughput of the proposed opportunistic spectrum access cognitive radio system. Moreover, we provided simulation results that demonstrate the effect of the target detection probability and power allocation strategy on the ergodic throughput of the proposed cognitive radio system and which indicate that after a certain value of channel power gain attenuation between the secondary transmitter and the primary receiver, a high value of target detection probability has a negative effect on the achievable ergodic throughput of the cognitive radio system and that a low value of target detection probability provides better P =20 dB av 6 5 Ergodic throughput (bits/sec/Hz) probability P̄d = 99.99% not only does not provide better protection for the primary users, but it also has a negative effect on the achievable ergodic throughput of the secondary system. It can be clearly seen from Fig. 6 that lower values of target detection probability P̄d lead to higher achievable ergodic throughput for the cognitive radio system, whereas the optimal value of the target detection probability appears to be P̄d ≃ 0. This interesting result can be explained by the fact that after a certain value of channel power gain attenuation, the average transmit power constraint becomes the dominant constraint on the optimal power allocation process, as opposed to the average interference power constraint that was dominant before. As a result, a lower target detection probability P̄d while satisfying the average interference power constraint on the one hand, leads to a lower false alarm probability Pf a (P̄d ) on the other. This in return leads to higher allocated transmit power P for the secondary users (as seen from the average transmit power constraint (6)) and therefore to higher ergodic throughput for the cognitive radio system. Finally, in Fig. 7, the ergodic throughput of the proposed cognitive radio system is presented versus the additional channel power gain attenuation between the secondary transmitter and the primary receiver for different values of detection probability P̄d and for a higher (compared to Fig. 6) average transmit power equal to Pav = 20 dB. Comparing Fig. 6 and Fig. 7, an interesting observation can be made: the value of the channel power gain attenuation after which the average transmit power constraint becomes dominant is larger as the average transmit power Pav increases. This can be explained by the fact that for higher values of average transmit power Pav , the average interference power constraint becomes dominant in higher values of channel power gain attenuation due to the increased transmit power P that is available to the secondary users, but should be restricted by the average interference power constraint for the protection of the quality of service (QoS) of primary users. 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