Spectrum Sensing and Data Transmission Tradeoff in Cognitive Radio Networks

Transcription

1 Spectrum Sensing Data Transmission Tradeoff in Cognitive Radio Networks Yulong Zou Yu-Dong Yao Electrical Computer Engineering Department Stevens Institute of Technology, Hoboken 73, USA Yulong.Zou, Baoyu Zheng Institute of Signal Processing Transmission Nanjing Univ. of Posts & Telecomm., Nanjing, China Abstract In cognitive radio networks, a cognitive source node typically requires two essential phases to complete a cognitive transmission process: the phase of spectrum sensing with a certain time duration to detect a spectrum hole (thus also referred to as spectrum hole detection phase the phase of data transmission through the detected spectrum hole. In this paper, we focus on the analysis of cognitive transmissions by jointly considering the two phases. An exact closed-form expression of an overall outage probability that accounts for both the probability of no spectrum hole detected the probability of a channel outage is derived for cognitive transmissions. Based on the derived overall outage probability, we investigate the spectrum hole utilization efficiency, which is used to quantify the percentage of spectrum holes utilized by the cognitive source for its successful data transmission. Numerical results show that there is a tradeoff in determining the time durations for hole detection data transmission phases in order to maximize the spectrum hole utilization efficiency. Index Terms Cognitive radio, spectrum sensing, tradeoff, cognitive transmission, outage probability. I. INTRODUCTION Cognitive radio [], [], [3] is emerging as a promising technology to improve the utilization efficiency of wireless spectrum resources. In cognitive radio networks, a cognitive source node typically requires two essential phases to complete its transmission to the destination: a spectrum sensing phase, in which the cognitive source attempts to detect a spectrum hole with a certain time duration (referred to as spectrum sensing overhead, a data transmission phase, in which data is transmitted to the destination through the detected spectrum hole. The two phases have been studied individually in terms of different detection [4] - [8] or different transmission [9] - [4] techniques. It is important to notice that the spectrum hole detection data transmission phases can not be designed optimized in isolation since they could affect each other [5], [6]. For example, an available spectrum hole would get wasted if the cognitive source has not detected the hole within a certain time duration. This decreases the spectrum hole utilization efficiency. While increasing the time duration of the hole detection phase improves the detection probability of spectrum holes, it comes at the expense of a reduction in transmission performance since less time is now available for the data transmission. Presently, very little research has been conducted to investigate the two phases as a whole. In [5], a sensing-throughput tradeoff has been explored for cognitive radio networks, where the research focus is on the maximization of secondary throughput (of cognitive users under the constraint of primary user protection. Paper [5] derives a closed-form expression of the probability of false alarm of the primary-user-presence under a target detection probability by considering the energy detection method over additive white Gaussian noise (AWGN channels. The main contributions of this paper are described as follows. First, unlike the separate analysis of the spectrum hole detection data transmission phases [5] - [4], we jointly consider the two parts to examine the impact of the spectrum sensing overhead on the overall system performance. Second, we derive an exact closed-form expression of the overall outage probability, which accounts for both the probability of no spectrum hole detected the probability of a channel outage, for cognitive transmissions, differing from [5] where sensingthroughput tradeoff results are obtained based on computer simulations. Third, using the derived overall outage probability, the spectrum hole utilization efficiency is investigated to evaluate the percentage of spectrum holes utilized by the cognitive source for its successful data transmissions. The remainder of this paper is organized as follows. Section II describes the system model of cognitive transmission that considers both the hole detection the data transmission phases, followed by the performance analysis in Section III, where closed-form expressions of the overall outage probability spectrum hole utilization efficiency are derived over Rayleigh fading channels. In Section IV, we conduct numerical evaluations to show the system performance of cognitive transmission. Finally, we make some concluding remarks in Section V. II. SYSTEM MODEL Consider a cognitive radio network where a cognitive source (CS is sending data to a cognitive destination (CD over a spectrum hole unoccupied by a primary user (PU, as shown in Fig. (a. Specifically, if CS detects an idle licensed frequency channel (that is not occupied currently by PU, it will use this channel for its data transmission (secondary data transmission; otherwise, CS will continue detecting the licensed frequency b to seek an available transmission opportunity. From Fig., one can see that the whole cognitive transmission

2 coverage boundary of PU CS primary network PU detection transmission time slot (k (a (b CD cognitive radio network Hole detection Data transmission - Fig.. (a Coexistence of a primary wireless network a cognitive radio network; (b The allocation of time durations: Hole detection versus data transmission process is divided into two phases: hole detection of the licensed b data transmission from CS to CD. The allocation of time durations between the two phases is depicted in Fig. (b, where the detection phase the transmission phase occupy α -α fractions, respectively, of one time slot, α is referred to as spectrum sensing overhead that can be varied to optimize the system performance. In addition, we assume that the primary traffic status does not change during one time slot. In Fig. (a, each transmission link between any two nodes is modeled as a Rayleigh fading channel, moreover, the fading channel is considered as constant during one time slot. The additive white Gaussian noise (AWGN at the receivers has the power spectral density N. The transmit power of PU CS are P p P s, respectively. For notational convenience, let H p (k denote, for time slot k, whether or not the licensed b is occupied by PU, i.e, H p (k =H represents the b being unoccupied by PU, otherwise, H p (k = H. Note that throughout this paper, we use a Bernoulli distribution with parameter P a (the probability of the licensed b being available for CS to model the rom variable H p (k, i.e., Pr (H p (k =H = P a Pr (H p (k =H = P a. Thus, the signal detected by CS from PU can be expressed as y s (k =h ps (k P p θ(k, + n s (k ( where h ps (k is the fading coefficient of the channel from PU to CS at time slot k, n s (k is AWGN with zero mean the power spectral density N, θ(k, is defined as ; Hp (k =H θ(k, = x p (k, ; H p (k =H where x p (k, is the transmission signal of PU during the first phase (namely hole detection phase of time slot k. Based on Eq. (, CS will make a decision Ĥs(k on whether the licensed b is occupied by PU. Specifically, Ĥ s (k =H considers that the b is available for secondary transmissions; Ĥ s (k = H considers the b is unavailable. Therefore, the signal received at CD from CS can be written as y d (k =h sd (k P s β(k+h pd (k P p θ(k, + n d (k ( where h sd (k h pd (k are the fading coefficients of the channel from CS to CD that from PU to CD, respectively. In addition, β(k θ(k, are defined as follows, xs (k; Ĥ β(k = s (k =H ; Ĥ s (k =H ; Hp (k =H θ(k, = x p (k, ; H p (k =H where x s (k x p (k, are the transmission signals of CS at time slot k that of PU at the second phase of time slot k, respectively. Notice that the variances of the fading coefficients h sd (k, h ps (k h pd (k are sd, ps pd, respectively. III. OUTAGE ANALYSIS OF COGNITIVE TRANSMISSION OVER RAYLEIGH FADING CHANNELS In this section, we analyze the overall outage probability of the cognitive transmission to examine the impact of the spectrum sensing overhead on system performance. As is known [7], [], [3], an outage event is considered to occur when the channel capacity falls below a required data rate R. Therefore, following Eq. (, it can be shown that the outage probability of the cognitive transmission is given by Eq. (3 at the top of the following page, where the coefficient α in the front of log( is due to the fact that only α fraction of a time slot is utilized for the CS s data transmission phase. Considering total probability law, Eq. (3 can be exped as Eq. (4, which can be rewritten as P out =PaPd Pr h sd (k < Λ h sd (k h pd (k γ p Λ < Λ +( PaPf Pr + Pa( Pd+( Pa( Pf where Λ = R/( α γ s, γ s = P s /N, γ p = P p /N, P a = Pr(H p (k = H is the probability that there is a spectrum hole, P d = Pr(Ĥs(k = H H p (k = H Pr(Ĥs(k = H H p (k = H are defined as the probability of correct detection of spectrum hole the probability of false detection of spectrum hole, respectively. It is noted that throughout this paper, the energy detector [5], [8] is used to evaluate the detection performance of the spectrum hole detection process. Using the results of Appendix A, we obtain P out =PaPd[ exp( Λ ] (5 +( PaP f [ pd γ pλ+ exp( Λ (6 ] + Pa( Pd+( Pa( P f

3 ( h sd (k P s β(k P out =Pr ( α log + h pd (k P p θ(k, <R + N (3 P out =Pr(Ĥs(k =H,H p (k =H Pr ( α log +Pr(Ĥs(k =H,H p (k =H Pr ( α log (+ h sd (k γ s +Pr(Ĥs(k =H,H p (k =H Pr( α log ( <R +Pr(Ĥs(k =H,H p (k =H Pr( α log ( <R ( <R + h sd(k γ s h pd (k γ p + <R (4 where the probability of correct detection of spectrum hole P d is conditioned on the probability of false detection of spectrum hole P f as given below [ ln( Pd ]( P d ; psαγ p = Γ( P d ( Γ( P d ps αγp ; others (7 where Γ = /( psαγ p γ p = P p /N. As can be observed from Eq. (6, the derived closed-from expression of outage probability accounts for both the probability of no available channel detected in the spectrum hole detection phase the probability of channel outage occurred in the subsequent data transmission phase, thus we call it overall outage probability. Notice that the primary user would be interfered by the cognitive user when the false detection occurs at CS. Therefore, the false detection probability P f shall be set to a required threshold (that is usually smaller than. by the cognitive system to guarantee the QoS (Quality of Service of the primary user. Throughout this paper, we will use. to conduct the numerical evaluations. Following Eq. (6 letting γ s +, we are able to obtain the floor of the overall outage probability P out,floor = Pa( Pd+( Pa( P f (8 Eq. (8 can also be explained as follows. Once CS detects a spectrum hole (no matter it is a correct or a false detection in the first phase, a channel outage would not occur in the subsequent data transmission phase due to γ s +. Thus, when γ s +, the outage occurs only when CS does not detect a hole no matter whether the hole really exists or not, implying P out,floor =Pr(H p (k =H Pr(H s (k =H H p (k =H +Pr(H p (k =H Pr(H s (k =H H p (k =H =Pa( Pd+( Pa( P f which is same as Eq. (8. Besides, with perfect spectrum hole detection, a cognitive source would start its data transmission only when the spectrum b is not occupied by the primary user, thus a lower bound on the overall outage probability of cognitive transmissions can be given by P out,bound = P a (9 where P a = Pr(H p (k = H is the probability that the licensed b is not occupied by the primary user. In order to show the effectiveness or efficiency of the cognitive transmissions, we define an efficiency indicator η, called spectrum hole utilization efficiency, as given below η =( P out /P a ( which is used to evaluate the percentage of the available spectrum holes that are utilized by CS for its successful data transmitted. Combining Eq. (6 Eq. (7, one can see that the overall outage probability of the cognitive transmission is the function of P a, P d, P f,r, ps, pd, sd,γ s,γ p,α, where the data rate R may often be set by the system in accordance with the QoS requirement the network environment, the spectrum sensing overhead α is a parameter that can be adapted to optimize the system performance. To obtain a general expression for an optimal α opt as a function of the other parameters is very complicated infeasible. Nevertheless, for any given parameter set P a, P d, P f,r, ps, pd, sd,γ s,γ p, an optimal value of α can be determined through numerical computation. IV. NUMERICAL RESULTS AND ANALYSIS In this section, we present numerical results of the overall outage probability the spectrum hole utilization efficiency to show the system performance of cognitive transmissions. Fig. plots Eq. (6 as a function of the transmit SNR at CS γ s for different spectrum sensing overhead values. The corresponding outage probability floors for the three cases (i.e., α =., α =.4 α =.8 the lower bound on outage probability are plotted using Eq. (8 Eq. (9, respectively. As shown in Fig., the curves of the overall outage probability converge to the corresponding floors in high γ s regions. The occurrence of outage floor is due to the fact that when the transmit SNR γ s is very high, the overall outage probability is dominated by the probability of no spectrum hole detected that is independent from γ s. Besides, the floors observed are reduced with the increase of the overhead α, which is resulted from the improvement of the detection probability of spectrum holes as the overhead α increases. In Fig. 3, we further show the spectrum hole utilization efficiency by plotting Eq. ( as a function of the transmit

4 Overall outage probability Lower bound on outage probability α=. α=.4 α= Transmit SNR at CS (γ s Spectrum hole utilization efficiency R=.4 b/s/hz R=.8 b/s/hz R=. b/s/hz Spectrum sensing overhead (α Fig.. Overall outage probability versus the transmit SNR at CS γ s for different values of the spectrum sensing overhead α with P a =.6,., R =.4 b/s/hz, γ p =5dB ps = sd = pd =. Fig. 4. Spectrum hole utilization efficiency versus the spectrum sensing overhead α for different values of the data rate R with P a =.6,., γ s =db, γ p =5dB ps = sd = pd =. Spectrum hole utilization efficiency α=.8 α=.4 α= Transmit SNR at CS (γ s Fig. 3. Spectrum hole utilization efficiency versus the transmit SNR at CS γ s for different values of the spectrum sensing overhead α with P a =.6,., R =.4 b/s/hz, γ p =5dB ps = = pd =. SNR, γ s, at CS. One can see from Fig. 3 that in high SNR regions, the spectrum hole utilization efficiency is improved with the increase of the spectrum sensing overhead α. Thisis because that the spectrum hole utilization efficiency at high γ s values mainly depends on the detection probability of spectrum holes since the channel outage probability is very low for large γ s. Moreover, increasing overhead α results in the improvement of detection probability, which leads to a higher spectrum hole utilization efficiency. However, in lower transmit SNR γ s regions, the relationship between the utilization efficiency the spectrum sensing overhead is not simply increasing or decreasing as depicted in Fig. 3. There can exist an optimal spectrum sensing overhead α opt to maximize the utilization efficiency, which is illustrated in the following. Fig. 4 illustrates the spectrum hole utilization efficiency versus the spectrum sensing overhead α for different values of the data rate, where the three performance curves plotted correspond to R =.4 b/s/hz, R =.8 b/s/hz R =. b/s/hz, respectively. All the curves plotted in Fig. 4 demonstrate that, given the parameter set P a, P f,r, ps, pd, sd,γ s,γ p, there always exists an optimal spectrum sensing overhead α opt, i.e., a maximum utilization efficiency can be achieved through a tradeoff in determining the time durations for the hole detection the data transmission phases. It is noted that for any given parameter set, an optimal spectrum sensing overhead α opt can be determined by maximizing the utilization efficiency as given by Eq. (. V. CONCLUSION Cognitive radio has been proposed as an effective means to promote the utilization of valuable wireless spectrum resources. In this paper, we have presented a comprehensive analysis for the cognitive transmission, where a cognitive source first detects the available spectrum holes through spectrum sensing then transmits its data over the detected holes. Exact closed-form expressions of the overall outage probability the spectrum hole utilization efficiency for the cognitive transmission have been obtained to show the impact of spectrum sensing overhead on the system performance. Numerical results have shown that maximum spectrum hole utilization efficiency can be achieved through a tradeoff between the hole detection the data transmission phases. APPENDIX A DERIVATION OF EQ. (6AND EQ. (7 Notice that RVs h sd (k h pd (k follow the exponential distribution with parameters, respectively, pd

5 are independent from each other. Thus, the probability integrals given in Eq. (5 can be calculated as Pr h sd (k < Λ = exp( Λ (A. Pr h sd (k h pd (k γ p Λ < Λ = Ω = pd γ pλ+ exp( x pd exp( y pd dxdy exp( Λ (A. where Ω = (x, y x yγ p Λ < Λ. Substituting Eq. (A. Eq. (A. into Eq. (5 gives P out =PaPd[ exp( Λ ] +( PaP f [ pd γ pλ+ exp( Λ (A.3 ] + Pa( Pd+( Pa( P f This is Eq. (6. Considering an energy detector following Eq. (, the probability of correct detection P d the probability of false detection P f can be calculated as P d =Pr(Ĥs(k =H H p (k =H =Pr n s (k (A.4 <δ Pr(Ĥs(k =H H p (k =H =Pr αp p h ps (k + n s (k (A.5 <δ where δ is the energy threshold that is usually determined by the false detection probability, moreover, the parameter α in the second equation of Eq. (A.5 is due to the fact that the detection phase only occupies a fraction α of one whole time slot, resulting in that the energy of the received primary signal is αp p h ps (k. Note that the rom variables (RVs, x = n s (k y = h ps (k, follow the exponential distribution with parameters N, respectively. Hence, from Eq. ps (A.4 Eq. (A.5, we further obtain P d = δ exp( x dx = exp( δ N N N x+αp py<δ (A.6 exp( x N N ps exp( y ps dxdy exp( δ ; N N psαγ p = ( + δ = Γexp( δ N ( Γ exp( ps δ αpp ; others (A.7 where Γ=/( psαγ p γ p = P p /N. Combining Eq. (A.6 Eq. (A.7, we obtain [ ln( Pd ]( P d ; psαγ p = Γ( P d ( Γ( P d ps αγp ; others (A.8 This is Eq. (7. REFERENCES [] J. Mitola G. Q. Maguire, Cognitive radio: Making software radios more personal, IEEE Personal Communications,vol.6,pp.3-8,999. [] S. Haykin, Cognitive radio: Brain-empowered wireless communications, IEEE Journal on Selected Areas in Communications, vol. 3, no., pp. -, 5. [3] F. Akyildiz, W. Y. Lee, M. C. Vuran, S. Mohanty, NeXt generation/dynamic spectrum access/cognitive radio wireless networks: A survey, Computer Networks, vol. 5, pp. 7-59, 6. [4] J. Ma, Y. G. Li, B. H. Juang, Signal processing in cognitive radio, Proceeding of the IEEE, vol. 97, no. 5, pp , 9. [5] H. Urkowitz, Energy detection of unknown deterministic signals, Proceeding of the IEEE, vol. 55, no. 4, pp , 967. [6] P. D. Sutton, K. E. Nolan, L. E. Doyle, Cyclostationary signatures in practical cognitive radio applications, IEEE Journal on Selected Areas in Communications, vol. 6, no., pp. 3-4, 8. [7] A. Ghasemi E. S. Sousa, Collaborative spectrum sensing for opportunistic access in fading environment, in Proc. IEEE DYSPAN, pp. 3-36, 5. [8] G. Ganesan Y. G. Li, Cooperative spectrum sensing in cognitive radio, Part I: Two user networks, IEEE Transactions on Wireless Communications, vol. 6, no. 6, pp. 4-3, 7. [9] R. W. Pabst B. H. Shultz, et al., Relay-based deployment concepts for wireless mobile broadb radio, IEEE Communications Magazine, vol. 4, no. 9, pp. 8-89, Sep. 4. [] A. J. Paulraj, D. A. Gore, R. U. Nabar, H. Bolcskei, An overview of MIMO communications - A key to gigabit wireless, Proceedings of the IEEE, vol. 9, no., pp. 98-8, Feb. 4. [] J. N. Laneman G. W. Wornell, Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks, IEEE Transactions on Information Theory, vol. 49, no., pp , Oct. 3. [] A. Nosratinia T. E. Hunter, Cooperative communication in wireless networks, IEEE Communications Magazine, vol. 4, no., pp.74-8, 4. [3] Y. Zou, B. Zheng, J. Zhu, Outage analysis of opportunistic cooperation over Rayleigh fading channels, IEEE Transactions on Wireless Communications, vol. 8, no. 6, pp , Jun. 9. [4] Y. Zou, B. Zheng, W. P. Zhu, An opportunistic cooperation scheme its BER analysis, IEEE Transactions on Wireless Communications, vol. 8, no. 9, pp , Sep. 9. [5] Y.-C. Liang, Y. Zeng, E. Peh, A. T. Hoang, Sensing-throughput tradeoff for cognitive radio networks, IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp , April 8. [6] Y. Zou, Y.-D. Yao, B. Zheng, Outage probability analysis of cognitive transmissions: Impact of spectrum sensing overhead, IEEE Transactions on Wireless Communications, under nd round review,. [7] C. E. Shannon, A mathmatical theroy of communication, Bell System Technical Journal, vol. 7, pp , 948. [8] J. Zhu, Y. Zou, B. Zheng, Cooperative detection for primary user in cognitive radio networks, EURASIP Journal on Wireless Communications Networking, vol. 9, Article ID 673, pages, 9. doi:.55/9/673.