Prediction Based Cognitive Spectrum Access 1

Transcription

1 Prediction Based Cognitive Spectrum Access 1 Boris Oklander Department of Electrical Engineering Technion Israel Institute of Technology Haifa, Israel oklander@tx.technion.ac.il Moshe Sidi Department of Electrical Engineering Technion Israel Institute of Technology Haifa, Israel moshe@ee.technion.ac.il Abstract A prediction-based spectrum access for cognitive radio (CR) is considered. In a typical scenario, CR accesses the communication channels as a secondary user (SU), under the requirement for collisions avoidance with the primary users (PU). In order to meet this requirement, CR frequently senses the communication channels and estimates their availability. Generally, sensing and transmission processes are mutually exclusive, which turns the sensing time into an overhead. Therefore, CR has a strong incentive to predict the future availability of the channels. Consequently, by sensing less, CR is able to increase the proportion of time allocated for the transmissions. We propose a novel analytical model of CR which consists of communication processes and cognitive components. The communication processes include packet arrivals, queueing and transmissions, while the cognitive components include sensing, estimation, multi-step ahead prediction of the channels' states and a component of decisionmaking. The prediction based policies show a significant improvement in the performance measures of throughput and delay compared to the reactive behavior. Keywords-cognitive radio networks; state estimation; prediction; queueing analysis; transient analysis I. INTRODUCTION Cognitive radios are expected to operate in dynamic environments characterized by varying availability of communication recourses. As many studies have shown, the intensity at which the licensed spectrum bands are accessed by the primary users (PU) varies in time and space [1],[2]. CR technology proposes to exploit the underutilized spectrum by opportunistically accessing the channels that are temporally unoccupied by PUs. This involves sensing of the channels for identification of transmission opportunities and minimization of the interference with PUs by leaving the channel immediately after a PU was detected. In order to provide stable communication sessions over dynamic communication environment, CR relies on its cognitive capabilities. These capabilities allow CR to allocate its resources dynamically and to make decisions that would improve its performance. In the decision-making phase, CR applies some policy to decide on the course of action. The decision includes choice of the channels for access and optimization of the sensing-transmission trade-off which arises when in-band sensing and transmission are mutually exclusive. The cognition might also include 1 This research has been partially supported by the CorNet consortium funded by the chief scientist in the Israeli Ministry of Industry, Trade and Labor /12/$ IEEE learning phase, in which CR exploits the collected data as well as operational experience to adopt it models of the environment and to improve its decision-making functionality. Throughput, delay, packet loss and power consumption are common performance measures of wireless communication systems. However, when CR is considered, there much more measures of interest arising in the face of the new "cognitive" dimension added to the radios. These "cognitive" measures include spectrum utilization efficiency, interference to PU's and other more abstract measures such as situation awareness, adaptation, decision making and planning capabilities, which are still waiting for their rigorous definitions. For a more detailed discussion on this important issue the reader is referred to [3]. In this work we study the advanced capability of CR to predict the future access patterns of PUs. The predictionbased proactive spectrum access allows CR to achieve better performance as compared to a reactive CR. In reactive mode of operation, there is an inherent delay between the time a change in the environment occurs and the time CR detects this change and acts correspondingly. The delayed responsiveness of CR results in unavoidable disruptions to the PUs and decreased spectrum utilization. This is especially true for wideband communication systems where the time-consuming sensing turns into a significant overhead [4]. The prediction based cognitive spectrum access provides a solution to these problems. The contribution to the research of CR presented in this paper is threefold: We propose a novel multi-step ahead prediction method which provides an analytical tool for planning in a stochastic environment. In addition, we analytically demonstrate how this method is coupled with the sensing process, and effectively improves CR s capability of estimating current state of the communication channels. Finally, we embed the proposed prediction method into CR s analytical model and evaluate its performance. Our study shows that the prediction utilization achieves better performance, compared to the reactive operation mode. There is a substantial number of works that study the reactive operation of CR in presence of the PUs [5] - [8]. A group of studies focuses on the predictive functionality of CR. A predictive model for dynamic spectrum access based

2 on the collected channel usage history is proposed in [9]. Hidden Markov model is used in [10] to forecast the times intervals during which PUs are idle. In [11], a binary time series for the spectrum availability indication and prediction is proposed. In [12], a "voluntary" spectrum access scheme is proposed to minimize SU disruption periods. In [13], a dynamic spectrum access scheme that utilizes the error of prediction of the channel usage is considered. In [14], an experimental cognitive radio test bed for sensing and predicting the white spaces of WLAN transmissions is presented. However, none of these works presented the analysis of the prediction on CR s performance. Collision avoidance and spectrum utilization are important performance measures of CR [3]. The advantage of predictability allows CR to improve its collision avoidance capability by holding-off transmissions before PU accesses the channel. Additionally, CR increases its spectrum utilization by predicting transmission opportunities and consequently shortening the time it takes to detect an available channel for secondary access. Furthermore, from comparison of CR s performance at various system loads, we gain important insights regarding the queueing behavior of CR packets, which has a great impact on the average waiting times of the packets as well as on system stability. II. COGNITIVE RADIO MODEL Operation of CR is characterized by cognitive and communication processes. In our model the communication processes of CR include arrivals and transmissions of the packets. Generally, due to the dynamic availability of the channels, CR cannot transmit all the packets immediately upon their arrivals. Therefore the arriving packets queue in a buffer till an appropriate opportunity for spectrum access is found. This situation implies a strong dependence of CR s transmissions, and hence its performance, on the cognitive processes. The cognitive processes are naturally divided into two groups. The first group is responsible for the perception of the current environment state. CR maintains its perception of the environment through sensing and estimating the availability of the channels. The importance of the perception is twofold. Firstly, it facilitates the detection of the transmission opportunities. Secondly, it helps to minimize the CR s interference with PUs. The second group of cognitive processes is responsible for the decision making and dynamic resources allocation. As already stated, the in-band sensing and transmission are mutually exclusive. This gives a rise to the well known transmission-sampling trade-off [15], which is actually a resource allocation problem. By increasing the sensing rate, CR is able to keep a better track of the channels state at the expense of the lower transmission rate and vice-versa. Interference with PUs is harmful to CR s transmissions, which gives CR a strong incentive to properly allocate its resources. Given the estimation of the currently available channels, CR makes decision regarding the spectrum access. CR decides whether or not to access channels that are estimated as available but have high probability of being accessed by PUs in a short time. Prediction of the future access patterns of PUs enables CR s capability to operate in a proactive manner. There is an inherent delay from the moment a PU starts its transmissions till the moment it has been detected by CR. The PU detection delay depends on the sampling rate and on the quality of the estimation method employed by CR. Long delays increase the interference with PUs and consequently decrease spectrum availability for CR access due to PU retransmissions. In the proactive operation mode, CR makes decisions based on sampling and prediction. Therefore, CR decreases interference by abandoning channels with high probability of PU appearance, before it was detected. Additionally, accurate predictions allow CR to reduce the sampling rate while preserving the level of perception. Having this capability, CR is able to improve its performance by increasing the transmission rate. In the following subsections, we model the environment s dynamics, CR s perception module, decision making and transmission processes. Next, these models are unified under the entire system framework which used later for the performance evaluation of CR. A. Environment Model A wireless communication system consisting of M channels is considered. Every channel alternates between ON and OFF states. The ON state corresponds to the time interval T ON during which a channel is used by PUs while the OFF state represents the time interval when the PUs are idle. As many studies propose [20][21], the dynamics of the channel availability is modeled by a continuous time Markov chain, imposing exponential distribution of the intervals T ON and T OFF with parameters α and β, respectively. Consequently, the number of channels available for SU access S t (S t S={0,1,,M}) at time t is a continuous time Markov chain (CTMC) with transition rates q ij given by (see Fig. 1 (a)): ( M j) α, j = i+ 1,0 i< M qij = jβ, j = i 1,0< i M 0, else In the above, we have assumed that the channels are statistically independent. Removing this restriction results in a more complex structure of S t. However, the analytical tractability of the proposed model is preserved. B. Perception Model The environment state S t is unknown to CR and therefore CR should estimate it. We assume that CR knows the environment model, for example it can be learned from the history of CR s interaction with the environment. CR senses the environment and uses the collected data to obtain the estimation Ŝ t of the state S t. Further, we distinguish between reactive and proactive operation modes. (1)

3 1) Reactive Mode In the reactive mode, Ŝ t updates occur at time instants t k, k {0,1,2 }. The notations of Ŝ k and S k describe the values of Ŝ t and S t at time t k. At each instant t k, S k is sampled and its value becomes visible to CR. Therefore, at this moment, the estimation Ŝ k is updated to be the true value of S k and remains unchanged till the next update instant t k+1, which is a Zero-Order Hold (ZOH) update method (see Fig. 1 (b)), denoted by Ŝ t ZOH : (a) (b) Figure 1. (a) CTMC of the environment process. (b) CTMC of the Z t={s t,ŝ t} process for M=3. Sˆ = Sˆ, t t < t + (2) ZOH t tk k k 1 We assume that the length of the interval (t k,t k+1 ) is exponentially distributed with rate δ t. Note that the estimation process alternates between correct and wrong estimations since after any update instant t k, at some time in the interval (t k,t k+1 ), the environment s state might change while the estimation will be updated only at t k+1. CR is capable of controlling its performance by adaptively changing the sample rate according to the current estimation Ŝ t. In fact, sensing is useful only for detection of the environment s state transitions. Therefore, when Ŝ t represents a rapidly changing state, it might be reasonable for CR to increase the sensing rate in order to detect the upcoming state transition. On the other hand, when the estimation represents a slowly changing state, CR might decrease the sensing rate for the sake of higher transmission rate that will increase the throughput. Denote by Z t ={S t,ŝ t } a compound process that represents the mutual evolvement of the environment dynamics and the ZOH estimation. Note, that by construction Z t is a continuous time Markov chain (CTMC) (see Fig. 1 (b)). Since the environment dynamics is independent of the estimation process Ŝ t, the horizontal transitions in Z t are actually the replications of the environment process S t. The vertical transitions describe the updates of the estimator Ŝ t toward the correct value of S t. The states for which S t =Ŝ t act as absorbers in accordance with the ZOH estimation method. Once the process enters such a state, the vertical transitions stop until the environment state changes. 2) Proactive Mode In the proactive mode, CR generates estimations Ŝ t PR by merging prediction-based and sensing-based estimations. At each update instant t k, the estimation Ŝ t is updated to be the true value of S t. Therefore, from Markov property of S t, given the last update Ŝ t at time t k, the future states of S t for t>t k are independent of the previous updates. Hence the proactive estimator is given by: Sˆ = arg max Pr( S = j Sˆ ), t t< t + PR t j S t tk k k 1 From the Markov chains theory, the structure of the underlying CTMC S t is captured by the rate-matrix Q, also called infinitesimal generator: Q={q ij }, i,j S, where q ij are given in (1), with a change for i=j, q ii = i j q ij. In order to calculate the estimator Ŝ PR t in (3), the transient distribution of S t is required. Let p ij (t)=pr{s t =j S 0 =i}, i,j S, be the transition probabilities, and let P(t)={p ij (t)} be the matrix of these probabilities. Since S t is an irreducible homogeneous Markov process with finite state-space S, by applying Kolmogorov s forward equations [19], one can show that the transition matrix is given by: n Qt ( Qt ) P () t = e = (4) n! n= 0 Let 1(j) be raw vector of length S with all but j th element equal 0 with the j th element equals 1. Then, given the last sample-based update Ŝ t at time t k, during the interval [t k,t k+1 ) we have: (5) ( ) 1 ˆPR S arg max ( ˆ t = 1 St ) P t t, k k tk t < t k + j S It can be seen from (5) that Ŝ t PR and Ŝ t ZOH equal at the sample-based update times t k. In contrast to ZOH estimation, the transients embedded in P(t) assume the possibility of multiple transitions of S t between two successive samplebased updates. Therefore, the proactive scheme introduces the flexibility of a multi-step ahead prediction. The ideas of the reactive and proactive estimation methods are demonstrated in the following example. Suppose we are given some CTMC S t on a finite statespace S={1,2,3}, and its rate matrix Q is given by: (3)

4 2 1 1 Q = First we would like to demonstrate the proactive estimation for S t. Suppose at time t 0 =0, we got a samplebased estimation Ŝ 0 ZOH S, and this is the only sample-based update time in this scenario. We are interested in calculating Ŝ t PR by using (4) and (5) for the time interval 0 t 1. The result of the numerical calculations appears in Fig. 2. It can be seen that for all values of Ŝ 0 ZOH S, at time t=0, the proactive estimator coincides with Ŝ 0 ZOH with probability 1. As time advances, it can be seen that the probabilities converge to the stationary distribution π=[0.45,0.36,0.19] obtained from (6). During the time interval [0,1], a transient in the probability distribution occurs in a non-monotonic way and the estimator switches accordingly to (5). In case of Ŝ 0 ZOH =3 the estimator switches twice, without new updates from the sensing process, in a proactive way that reflects the most probable dynamics of the underlying CTMC S t. (6) D. Transmission Process The arrivals generated by CR are modeled as a Poisson process with rate λ [bit/sec]. The service time is exponentially distributed with rate μ t [bit/sec], which varies in time. The value of μ t depends on the number of accessed channels C t, the proportion of the bandwidth allocated for transmission θ t, the actual number of the available channels S t and the penalty for interfering with PU. The combination of these factors results in following expression: θctμ Ct St μt = 0 Ct> St E. CR Process Having defined the components of the environment dynamics, the cognitive and the transmission processes, we couple them into unified model. We define {X t,s t,ŝ t } to be the process of the entire system for which at time t there are X t (X t {0,1,2, }) queued packets in CR s buffer. This process forms a three dimensional CTMC, exact structure and analysis of which were studied in [16],[17]. Similar guidelines are used here to compare the performance of the prediction-based and the reactive operation modes. Additionally, we would like to compare prediction-based CR performance against the performance of ultimate CR which represents SU who has all the information regarding the environment state at any time instant. In other words, for such CR for all times t, S t =Ŝ t, and the compound process {X t,s t,ŝ t } can be replaced by {X t,s t }.This process forms a two dimensional continuous time Markov chain (CTMC) illustrated in Fig. 3, which is homogeneous, irreducible and stationary. Note that the columns of the CTMC in Fig.3, which are referred to later as levels, are replicas of CTMC S t in Fig.1 (a). (7) Figure 2. Proactive state estimation of the S t CTMC. C. Decision Making In the decision-making phase CR uses some policy Π for both transmission-sampling tradeoff management and for channels allocation. Let μ [bit/sec] be the transmission rate of CR over a single channel. Denote by parameter θ (0 θ 1) the proportion of the channel assigned for the transmission and the remaining part (1 θ) for the sampling. Therefore, the effective transmission rate over a single channel is θμ [bit/sec] and the rate of the sample-based estimations is (1 θ)μb [1/sec]. The constant 1/B [bit] is the number of bits required for updating the estimation Ŝ t and is technology driven. Additionally, policy Π allocates the number of channels, denoted as C t, where t stands for the time at which CR tries to access them. Figure 3. CTMC of the ultimate CR model.

5 We order the states lexicographically, i.e. (0,0),(0,1),,(0,M),(1,0),(1,1), and construct the generator matrix Q of this CTMC which is given by: Q B00 B B01 B11 A A A A = 0 0 A2 A1 A A 2 1 A channels S t are α=1 and β=2. The service rate of the packets is μ=10. The arrival rate λ takes values in the set {1, 2,, 10} which allows to examine CR s performance under different loads. Both the analytical and simulated results are presented in Fig. 4. In Fig. 4, it can be seen that both the analytical and the simulated average waiting times W of the reactive CR coincide with a high accuracy for all the arrival rates, which validates the correctness of the simulation. The proactive CR simulation runs were performed on the same simulation platform as for reactive CR, with the required changes implied by (5). where B 00 ={B 00 (i,j)}, B 01 ={B 01 (i,j)}, B 10 ={B 10 (i,j)}, B 11 ={B 11 (i,j)}, A 0 ={A 0 (i,j)}, A 1 ={A 1 (i,j)} and A 2 ={A 2 (i,j)} are (M +1) (M+1) matrices. Any element which is denoted as 0 in Q (and in other matrices) is a matrix of all zeros of the appropriate dimension. It can be seen that in our model B 01 =A 0 =diag{λ,λ,,λ} and B 10 =A 2 =diag{0,μ,2μ,,mμ}, while the matrices B 00 and B 11 =A 1 are more complicated: and ( λ+ ( M i) α+ iβ) j= i ( M i) α j=+ B00(, i j) = iβ j= 0 else ( λ+ iμ+ ( M i) α+ iβ) j= i ( M i) α j=+ A1 (, i j) = iβ j= 0 else The rate matrices presented above completely define the model and can be solved by the standard Matrix-Geometric procedure [22]. Calculating the stationary probabilities allows evaluating the performance measures of interest, mainly the average waiting time of CR s packets. The performance evaluation results are presented in the next section. III. PERFORMANCE EVALUATION In this section we evaluate the performance of the three models presented in the previous sections. Namely, we compare the performance of reactive CR, proactive (prediction-based) CR, and ultimate CR. The last model is fully analyzed in [16]. Reactive CR, is also analytically tractable by same means. Unlike the previous models, it is difficult to analyze the proactive CR system. This difficulty comes from the fact that the Markov property no longer holds for this system. When (5) is applied, between successive sample-based updates, the prediction based updates occur at deterministic intervals which are not memoryless. Therefore, in the case of proactive CR, the performance evaluation is done through simulation. For the performance comparison we consider a scenario in which there are M=3 channels, and the additional parameters in (1) that determine the dynamics of the Figure 4. Average waiting time W vs. arrival rate λ. From the demonstrated results, it can be seen that the proactive CR s waiting time is bounded from below by ultimate CR s waiting time and from above by the reactive CR s waiting time. Additionally, as expected, proactive CR demonstrates better performance as compared to reactive CR. For lower arrival rates, proactive CR s waiting time is close to the lower bound. When equal waiting times are considered, proactive system achieves higher throughput (λ) compared to reactive CR. In Fig. 5, the ratio of the reactive and the proactive waiting times is shown. It is noteworthy that for both low and high arrival rates, the proactive waiting time is more than twice lower comparatively to the reactive one. For the moderate arrival rates the average waiting times are almost equal with a relatively small advantage to the proactive CR. This result can be explained by the queueing behavior of CR s packets. For the low arrival rates, there is a high probability for the newly arriving packet to enter to an empty buffer. This implies that the significant part of the waiting time comes from the transmission (service) time. It is likely that prediction based estimation will benefit from a better spectrum utilization which actually turns into shorter service times. On the contrary, for high arrival rates, the newly

6 arriving packets queue. When relatively long queues are formed, every packet, while being transmitted, contributes to the waiting times of all the other packets waiting in the queue. Therefore, even small decrease in the average transmission time cumulatively decreases the average waiting time. For the moderate arrival rates the queues are not long enough to exhibit this effect and the performance is insignificant. Figure 5. Ratio of the reactive and proactive waiting times vs. λ. IV. SUMMMARY AND FUTURE WORK In this work we proposed a multi-step prediction method which is beneficial for CR in its attempt to maintain stable communication session in the face of the dynamically changing environment. Our study shows that the proactively operating CR achieves better performance, compared to the reactive operation mode. This is especially significant when the system is highly loaded and the prediction based decision-making significantly decreases the waiting time and stabilizes the system. As a future work we suggest to further develop the prediction method presented in this paper. As it can be seen from the results, there is still a significant gap between the proactive CR s waiting and the lower bound which remains a challenge to be committed. It is important to model the mode of operation when sensing is fully controlled by the prediction process so that the sensing is performed in the vicinity of the predicted state transitions. Finally, the proposed prediction method might be useful for the task of data fusion in collaborative sensing schemes. REFERENCES [1] Federal Communications Commission, ET Docket No Notice of proposed rule making and order, December [2] M. McHenry, "Spectrum white space measurements", New America Foundation Broadband Forum, June [3] Y. Zhao, S. Mao, J. O. Neel, and J. H. Reed, Performance Evaluation of Cognitive Radios: Metrics, Utility Functions, and Methodology, Proceedings of the IEEE, vol. 97, no. 4, pp , [4] Q. Zhao, L. Tong, A. Swami, and Y. Chen, Decentralized Cognitive MAC for Opportunistic Spectrum Access in Ad Hoc Networks: A POMDP Framework, IEEE Journal on Selected Areas in Communications, vol. 25, no. 3, pp , April [5] D.Willkomm, J. Gross, and A.Wolisz, Reliable link maintenance in cognitive radio systems, in Proc. IEEE DySPAN, pp , November [6] M. Di Felice, K. R. Chowdhury, A. Kassler, L. Bononi, ``Adaptive Sensing Scheduling and Spectrum Selection in Cognitive Wireless Mesh Networks," in Proc. of the IEEE ICCCN, Maui, Hawaii, August 1-4, 2011, pp [7] Y. Zhang, Spectrum handoff in cognitive radio networks: Opportunistic and negotiated situations, in Proc. IEEE ICC, pp. 1 6, June [8] C.-W. Wang and L.-C. Wang, Modeling and analysis for reactivedecision spectrum handoff in cognitive radio networks, in Proc. IEEE GlobeCom, [9] L. Yang, L. Cao, and H. Zheng, Proactive channel access in dynamic spectrum networks, Physical Communication (Elsevier), vol. 1, pp , June [10] T. Clancy and B. Walker, Predictive dynamic spectrum access, in Proc. SDR Forum Technical Conference, Orlando, FL, November [11] S. Yarkan and H. Arslan, Binary time series approach to spectrum prediction for cognitive radio, in Proc. IEEE Vehicular Technology Conference (VTC), pp , October [12] S.-U. Yoon and E. Ekici, Voluntary spectrum handoff: A novel approach to spectrum management in CRNs, in Proc. IEEE International Conference on Communications (ICC), [13] C. Song and Q. Zhang, Intelligent dynamic spectrum access assisted by channel usage prediction, in IEEE INFOCOM Conference on Computer Communications Workshops, 2010, pp [14] S. Geirhofer, J. Z. Sun, L. Tong, and B. M. Sadler, Cognitive frequency hopping based on interference prediction: Theory and experimental results, ACM SIGMOBILE Mobile Computing and Communications Review, vol. 13, no. 2, pp , [15] Y.-C. Liang, Y. Zeng, E. Peh, and A. T. Hoang, Sensing-throughput tradeoff for cognitive radio networks, in Proc. IEEE Int. Conf. Commun.(ICC), June 2006, pp [16] B. Oklander and M. Sidi, Modeling and Analysis of System Dynamics and State Estimation in Cognitive Radio Networks, PIMRC 10 (CogCloud Workshop), pp , [17] B. Oklander and M. Sidi, Cross-Entropy Optimized Cognitive Radio Policies, in NETWORKING 2011 Workshops, vol. 6827, V. Casares- Giner, P. Manzoni, and A. Pont, Eds. Springer Berlin / Heidelberg, 2011, pp [18] S. Chen and L. Tong, Maximum Throughput Region of Multiuser Cognitive Access of Continuous Time Markovian Channels, Work, vol. 29, no. 10, pp , [19] V.G. Kulkarni, Modeling, analysis, design, and control of stochastic systems, Springer, New York, [20] S. Geirhofer, L. Tong, and B. M. Sadler, Cognitive medium access: constraining interference based on experimental models, IEEE J. Sel. Areas Commun., vol. 36, pp , Feb [21] P. Tehrani and Q. Zhao, Separation principle for opportunistic spectrum access in unslotted primary systems, rd Annual Conference on Information Sciences and Systems, pp , [22] M.F. Neuts, "Matrix Geometric Solutions in Stochastic Models", John Hopkins University Press, 1981.