Abstract
This paper analyzes multistepahead spectrum prediction for Cognitive Radio (CR) systems using several future states. A slotbased scenario is used, and prediction is based on the Support Vector Machine (SVM) algorithm. The aim is to determine whether multistepahead spectrum prediction has gains in terms of reduced channelswitching and increased network throughput compared with shortterm prediction. The system model is simulated in software using an exponential onoff distribution for primaryuser traffic. A classical energy detector is used to perform sensing. With the help of simplifications, we present new closedform expressions for the detection probability under AWGN and Rayleigh fading channels which allows the appropriate number of samples for these scenarios to be found. The performance of the proposed predictor is thoroughly assessed in these scenarios. The SVM algorithm had low prediction error rates, and multistepahead idlechannel scheduling resulted in a reduction in channel switching by the SU of up to 51%. An increase in throughput of approximately 4% was observed for multistepahead prediction with three future states. The results also show channelswitching savings can be achieved in a CR network with the proposed approach.
Index Terms
Spectral vacancies; spectrum sharing; cognitive radio
I. INTRODUCTION
Since the publication of the seminal work by Mitola [^{1}[1] J. Mitola and G. Q. Maguire, “Cognitive radio: making software radios more personal,” IEEE Pers. Comm., vol. 6, no. 4, pp. 13–18, Aug., 1999, DOI. 10.1109.98.788210.], Cognitive Radio (CR) has become an effective technology for solving the challenges generated by the growing demand for wireless communications. The concept of CR has already been implemented in the IEEE 802.22 [^{2}[2] IEEE Draft Standard for Information Technology ”Telecommunications and information exchange between systems  Wireless Regional Area Networks (WRAN)  Specific requirements  Part 22: Cognitive Wireless RAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: Policies and procedures for operation in the TV Bands,” in IEEE P802.22/D1.0, December 2010, vol., no., pp.1598, 20 Dec. 2010] standard but can be further refined to improve the spectrum and energy efficiency of wireless devices. A device with cognitive capacity is called a secondary user (SU) and can coexist with primary users (PUs), which are native devices on a certain frequency band. An SU is able to check opportunistically if a channel is idle and, if so, occupy it [^{3}[3] Z. Wei and B. Hu, “A Fair MultiChannel Assignment Algorithm With Practical Implementation in Distributed Cognitive Radio Networks,” IEEE Access, vol. 6, pp. 1425514267, Mar., 2018, DOI. 10.1109.ACCESS.2018.2808479.].
Cognitive devices can perform spectrum sharing with a PU in three ways: underlay, overlay and interweave [^{4}[4] A. Goldsmith, S. A. Jafar, I. Maric and S. Srinivasa, “Breaking Spectrum Gridlock With Cognitive Radios: An Information Theoretic Perspective,” Proceedings of the IEEE, vol. 97, no. 5, pp. 894–914, May, 2009, DOI. 10.1109.JPROC.2009.2015717.]. In the first approach, underlay, the SU can transmit simultaneously with the PU; however, the cognitive device must use mechanisms to prevent it interfering with the PU’s communication so that it is effectively transparent to the PU. In the overlay method the PU implements a mechanism involving specific keywords and techniques that report the current channel state to the SU, which is provided with data to enable it to perform interferencefree transmission. In the interweave approach the SU has no prior knowledge of the PU signal or channel state and implements a mechanism for listening to the current channel state called spectrum sensing. This enables it to transmit if the PU status is idle.
Spectrum sensing can be performed in different ways, including matched filter detection, cyclostationary feature detection and energy detection [^{5}[5] M. A. Abdulsattar and Z. A. Hussein, “Energy detection technique for spectrum sensing in cognitive radio: a survey,” International Journal of Computer Networks and Communications, vol. 4, no. 5, pp. 223242, Sep., 2012, DOI. 10.5121.ijcnc.2012.4514.]. The last of these is the most widely used technique because it does not require knowledge of the transmitted signal’s properties, the channel state or even the modulation scheme used. The technique was first described in [^{6}[6] H. Urkowitz, “Energy detection of unknown deterministic signals,” Proceedings of the IEEE, vol. 55, no. 4, pp. 523531, Sep., 1967, DOI.10.1109.PROC.1967.5573.], in which a simple mechanism for detecting radiosignal energy is discussed. Two important metrics used in energydetector design for spectrum sensing are detection probability and falsealarm probability [^{7}[7] S. Atapattu, C. Tellambura and H. Jiang, “Conventional Energy Detector,” in Energy detection for spectrum sensing in cognitive radio, 1st ed. New York, NY, US: Springer, 2014, ch. 2, sec. 3, pp. 11–24.], [^{8}[8] Y. Liang, Y. Zeng, E. C. Y. Peh and A. T. Hoang, “SensingThroughput Tradeoff for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp. 13261337, Apr., 2008, DOI. 10.1109.TWC.2008.060869.]. Closed expressions for these two metrics in fading channels and lowSNR scenarios can be found in the literature [^{9}[9] S. Atapattu, C. Tellambura and H. Jiang, “Spectrum Sensing via Energy Detector in Low SNR,” 2011 IEEE International Conference on Communications (ICC), Kyoto, pp. 1–5,, DOI. 10.1109.icc.2011.5963316.].
Using an energydetection scheme, Liang et al [^{8}[8] Y. Liang, Y. Zeng, E. C. Y. Peh and A. T. Hoang, “SensingThroughput Tradeoff for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp. 13261337, Apr., 2008, DOI. 10.1109.TWC.2008.060869.] developed models with optimal sensing duration to increase data throughput for the SU network and with a high detection probability and low falsealarm probability. The higher the detection probability, the more protected the primary users will be. However, from the perspective of the SUs, the lower the probability of false alarm, the more likely the channel is to be reused when it is available. In [^{8}[8] Y. Liang, Y. Zeng, E. C. Y. Peh and A. T. Hoang, “SensingThroughput Tradeoff for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp. 13261337, Apr., 2008, DOI. 10.1109.TWC.2008.060869.], the authors describe the operation of an SU with only two stages: sensing an effective transmission of information. The SU randomly chooses one of the available channels for sensing.
Although it is possible for an SU to search randomly for idle channels, this is costly in terms of energy and search time. To ensure more successful sensing results, PU occupancy patterns can be analyzed and the future states of a channel predicted. The SU listens to the states of the channels and, after processing historical data, predicts future channel occupancy [^{10}[10] S. Nandakumar et al., “Efficient Spectrum Management Techniques for Cognitive Radio Networks for Proximity Service,” IEEE Access, vol. 7, pp. 4379543805, Apr., 2019, DOI. 10.1109.ACCESS.2019.2906469.]. This procedure is called spectrum prediction. As the SU now knows which channels are most likely to be busy, it can selectively perform spectrum sensing. This is done first on channels that are most likely to be idle. Then, using a mechanism that allows coordination between SUs [^{11}[11] A. M. Masri, C. Chiasserini, C. Casetti and A. Perotti, “Common control channel allocation in cognitive radio networks through UWB communication,” Journal of Communications and Networks, vol. 14, no. 6, pp. 710 718, Dec., 2012, DOI. 10.1109.JCN.2012.00037.], the appropriate channel is chosen. Spectrum prediction yields savings in sensing energy for SUs [^{12}[12] A. Shahid et al., “CSIT: channel state and idle time predictor using a neural network for cognitive LTEAdvanced network,” Eurasip Journal on Wireless Communications and Networking, vol. 2013, no. 1, pp. 203–219, Dec., 2013, DOI. 10.1186.168714992013203.] and a significant increase in the throughput of the CR network [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.].
In [^{14}[14] G. Ding et al., “On the limits of predictability in realworld radio spectrum state dynamics: from entropy theory to 5G spectrum sharing,” IEEE Communications Magazine, vol. 53, no. 7, pp. 178–183, Jul., 2015, DOI. 10.1109.MCOM.2015.7158283] Ding et al study the fundamental limits of prediction of real scenarios, showing that it is valid to use pattern analysis schemes to predict the use of spectrum. Different prediction algorithms have been extensively used in the context of cognitive radio as it can be synthesized in surveys [^{15}[15] X. Xing, T. Jing, W. Cheng, Y. Huo and X. Cheng, “Spectrum prediction in cognitive radio networks,” IEEE Wireless Communications, vol. 20, no. 2, pp. 90–96, Apr., 2013, DOI. 10.1109.MWC.2013.6507399] and [^{16}[16] G. Ding et al., “Spectrum Inference in Cognitive Radio Networks: Algorithms and Applications,” IEEE Communications Surveys and Tutorials, vol. 20, no. 1, pp. 150–182, Firstquarter, 2018, DOI.10.1109.COMST.2017.2751058]. For instance, the work of Chen and Yang [^{17}[17] X. Chen and J. Yang, “A spectrum predictionbased frequency band preselection over deteriorating HF electromagnetic environment,” China Communications, vol. 15, no. 9, pp. 10–24, Sep., 2018, DOI. 10.1109.CC.2018.8456448] analyzes correlations in HF electromagnetic environment in both time and frequency and developed an algorithm to predict spectrum usage in CR scenarios.
Supervised Machine Learning (ML) algorithms are of interest for spectrum prediction in CR as they can perform occupancy inference from the collected traffic data in real time. SUs can use this type of algorithm to predict spectrum occupancy in a slotbased wireless communication system. The sequence of past slots is a data set called the observed window, and the sequence of data predicted for the future is called prediction window.
Studies on spectrum prediction using ML algorithms include the work developed by Tumuluru et al [^{18}[18] V. K. Tumuluru, P. Wang and D. Niyato, “A Neural Network Based Spectrum Prediction Scheme for Cognitive Radio,” 2010 IEEE International Conference on Communications, pp. 1–5, Cape Town, May, 2010, DOI. 10.1109.ICC.2015.5502348.], in which the use of neural networks for spectrum prediction in CR networks is reported for the first time. Using a model known as the Multilayer Perceptron (MLP) with specific layers and shortterm prediction, the authors achieved better spectrum usage and savings in sensing energy. The use of neural networks in CR is also addressed in other works, such as [^{12}[12] A. Shahid et al., “CSIT: channel state and idle time predictor using a neural network for cognitive LTEAdvanced network,” Eurasip Journal on Wireless Communications and Networking, vol. 2013, no. 1, pp. 203–219, Dec., 2013, DOI. 10.1186.168714992013203.], [^{19}[19] Z. Tang and S. Li, “Deep Recurrent Neural Network for Multiple Time slot Frequency Spectrum Predictions of Cognitive Radio,” KSII Transactions on Internet and Information Systems (TIIS), vol. 11, no. 6, pp. 30293045, Oct., 2017, DOI. 10.3837.tiis.2017.06.013.], [^{20}[20] N. Shamsi, A. Mousavinia and H. Amirpour, “A channel state prediction for multisecondary users in a cognitive radio based on neural network,” 2013 International Conference on Electronics, Computer and Computation (ICECCO), pp. 200–203, Ankara, Nov., 2013, DOI. 10.1109.ICECCO.2013.6718263.] and [^{21}[21] A. Agarwal, S. Dubey, M. A. Khan, R. Gangopadhyay and S. Debnath, “Learning based primary user activity prediction in cognitive radio networks for efficient dynamic spectrum access,” 2016 International Confer ence on Signal Processing and Communications (SPCOM), pp. 200–203,Bangalore, Jun., 2016, DOI. 10.1109.SPCOM.2016.7746632.]. In [^{12}[12] A. Shahid et al., “CSIT: channel state and idle time predictor using a neural network for cognitive LTEAdvanced network,” Eurasip Journal on Wireless Communications and Networking, vol. 2013, no. 1, pp. 203–219, Dec., 2013, DOI. 10.1186.168714992013203.], Shahid et al adopted an MLP neural network, while in [^{19}[19] Z. Tang and S. Li, “Deep Recurrent Neural Network for Multiple Time slot Frequency Spectrum Predictions of Cognitive Radio,” KSII Transactions on Internet and Information Systems (TIIS), vol. 11, no. 6, pp. 30293045, Oct., 2017, DOI. 10.3837.tiis.2017.06.013.], Tang and Li used a hidden multiple layer neural network.
Other types of ML algorithms described in the literature that can be used for spectrum prediction include the Hidden Markov Model (HMM) [^{22}[22] Z. Chen, N. Guo, Z. Hu and R. C. Qiu, “Channel state prediction in cognitive radio, Part II: Singleuser prediction,” 2011 Proceedings of IEEE Southeastcon, pp. 50–54, Nashville, TN, Mar. 2011, DOI. 10.1109.SECON.2011.5752904.], nearest neighbor [^{22}[22] Z. Chen, N. Guo, Z. Hu and R. C. Qiu, “Channel state prediction in cognitive radio, Part II: Singleuser prediction,” 2011 Proceedings of IEEE Southeastcon, pp. 50–54, Nashville, TN, Mar. 2011, DOI. 10.1109.SECON.2011.5752904.], classification trees [^{23}[23] Soltani, S., and Mutka, M. W., “A decision tree cognitive routing scheme for cognitive radio mesh networks,” Wireless Communications and Mobile Computing, vol. 15, no. 10, pp. 14051417. 2015, DOI. 10.1002/wcm.2418], maximum likelihood [^{24}[24] Canavitsas, A., Silva Mello, and M. Grivet, “Spectral Vacancies Prediction Method for Cognitive Radio Applications,” Journal of Microwaves, Optoelectronics and Electromagnetic Applications, vol. 15, no. 1, pp. 18–29, Mar., 2016, DOI. 10.1590.2179.10742016v15i1581] and Bayesian estimators. In [^{25}[25] X. Chen, J. Yang and G. Ding, “Minimum Bayesian Risk Based Robust Spectrum Prediction in the Presence of Sensing Errors,” IEEE Access, vol. 6, pp. 29611–29625, May, 2018, DOI. 10.1109/ACCESS.2018.2836940], Chen et al developed the Minimum Bayesian Risk based Robust Spectrum Prediction algorithm which outperforms NeuralNetworks prediction. Finally, in [^{21}[21] A. Agarwal, S. Dubey, M. A. Khan, R. Gangopadhyay and S. Debnath, “Learning based primary user activity prediction in cognitive radio networks for efficient dynamic spectrum access,” 2016 International Confer ence on Signal Processing and Communications (SPCOM), pp. 200–203,Bangalore, Jun., 2016, DOI. 10.1109.SPCOM.2016.7746632.], Agarwal et al study two variations of an ML algorithm known as Support Vector Machines (SVM)  SVM with a linear kernel and SVM with a Gaussian kernel – and found that the former yielded the better predictions. The SVM algorithm was also explored in [^{40}[40] Mushtaq, M. T., Khan, I., Khan, M. S., and Koudelka, O. “Signal detection for QPSK based cognitive radio systems using support vector machines,”. Radioengineering, vol. 24, no. 1, pp 192198. Apr. 2015. DOI: DOI. 10.13164/re.2015.0192
https://doi.org/DOI. 10.13164/re.2015.01...
] where this ML classifier technique is used successfully for the detection of the QPSK signals in CR systems.
According to the amount of estimated future slots, two classes are defined, named shortterm or longterm prediction. While it may seem nontrivial to define the correct amount of future slots that is encompassed by the expressions shortterm prediction and longterm prediction. Sapankevych and Sankar [^{26}[26] N. Sapankevych and R. Sankar, “Time Series Prediction Using Support Vector Machines: A Survey,” IEEE Computational Intelligence Magazine, vol. 4, no. 2, pp. 24–38, May, 2009, DOI. 10.1109/MCI.2009.932254] define shortterm prediction as onestep ahead prediction while longterm prediction refers to the case where the prediction window consists of multiple slots [^{15}[15] X. Xing, T. Jing, W. Cheng, Y. Huo and X. Cheng, “Spectrum prediction in cognitive radio networks,” IEEE Wireless Communications, vol. 20, no. 2, pp. 90–96, Apr., 2013, DOI. 10.1109.MWC.2013.6507399]. In our work the term shortterm prediction is associated to a singleslot prediction window. For several slots ahead, we prefer to use the expression “multistepahead” since “longterm” would be better applied to cases with much larger slot amounts than those studied in this paper. Multistepahead slot prediction is in the early stages of development with enormous challenges ahead [^{15}[15] X. Xing, T. Jing, W. Cheng, Y. Huo and X. Cheng, “Spectrum prediction in cognitive radio networks,” IEEE Wireless Communications, vol. 20, no. 2, pp. 90–96, Apr., 2013, DOI. 10.1109.MWC.2013.6507399] due the error accumulation problem. Multistepahead prediction is reported in [^{27}[27] R. Min et al. “Interference avoidance based on multistepahead pre diction for cognitive radio,” 2008 11th IEEE Singapore International Conference on Communication Systems, Guangzhou, Nov., 2008, DOI. 10.1109.ICCS.2008.4737177.], where Min et al describe an algorithm based on multiple slots prediction is proposed to forecast the interference time ratio culminating to avoid interference in the opportunistic spectrum access (OSA). In [^{12}[12] A. Shahid et al., “CSIT: channel state and idle time predictor using a neural network for cognitive LTEAdvanced network,” Eurasip Journal on Wireless Communications and Networking, vol. 2013, no. 1, pp. 203–219, Dec., 2013, DOI. 10.1186.168714992013203.] only multiple idle slots are accounted for prediction using a Neural Network.
Approaches using Neural Network for multiple slots analysis were also found in references [^{19}[19] Z. Tang and S. Li, “Deep Recurrent Neural Network for Multiple Time slot Frequency Spectrum Predictions of Cognitive Radio,” KSII Transactions on Internet and Information Systems (TIIS), vol. 11, no. 6, pp. 30293045, Oct., 2017, DOI. 10.3837.tiis.2017.06.013.] and [^{28}[28] B. Shawel et al. “Convolutional LSTMbased LongTerm Spectrum Prediction for Dynamic Spectrum Access,” 2019 27th European Signal Processing Conference (EUSIPCO), A Coruna, Sep., 2019, DOI. 10.23919.EUSIPCO.2019.8902956.]. In [^{19}[19] Z. Tang and S. Li, “Deep Recurrent Neural Network for Multiple Time slot Frequency Spectrum Predictions of Cognitive Radio,” KSII Transactions on Internet and Information Systems (TIIS), vol. 11, no. 6, pp. 30293045, Oct., 2017, DOI. 10.3837.tiis.2017.06.013.] Tang and Li analyses Deep Recurrent Neural Network with several hidden layers is used to learn spectrum occupancy for WiFi channels. In [^{28}[28] B. Shawel et al. “Convolutional LSTMbased LongTerm Spectrum Prediction for Dynamic Spectrum Access,” 2019 27th European Signal Processing Conference (EUSIPCO), A Coruna, Sep., 2019, DOI. 10.23919.EUSIPCO.2019.8902956.] Shawel et al employ Convolutional Long ShortTerm Memory (ConvLSTM) Deep Learning Neural Network is employed for longterm prediction to learn joint spatialspectraltemporal dependencies in spectrum utilization. Multistepahead prediction efforts are also presented by Sun et al [^{29}[29] J. Sun et al. “LongTerm Spectrum State Prediction: An Image Inference Perspective,” IEEE Access, vol. 6, pp. 4348943498, Jul., 2018, DOI. 10.1109/ACCESS.2018.2861798] and by Ge et al [^{30}[30] C. Ge, Z. Wang and X. Zhang, “Robust LongTerm Spectrum Prediction With Missing Values and Sparse Anomalies,” IEEE Access, vol. 7, pp.16655–16664, Jan., 2019, DOI. 10.1109/ACCESS.2018.2889161], where both works employ time frequencyday spectrum tensor model used for longterm prediction. The proposal in [^{30}[30] C. Ge, Z. Wang and X. Zhang, “Robust LongTerm Spectrum Prediction With Missing Values and Sparse Anomalies,” IEEE Access, vol. 7, pp.16655–16664, Jan., 2019, DOI. 10.1109/ACCESS.2018.2889161] outperforms mechanisms presented in [^{29}[29] J. Sun et al. “LongTerm Spectrum State Prediction: An Image Inference Perspective,” IEEE Access, vol. 6, pp. 4348943498, Jul., 2018, DOI. 10.1109/ACCESS.2018.2861798], fixing the problem of missing data and sparse anomalies.
Bayhan and Alagoz [^{31}[31] S. Bayhan and F. Alagoz, “Scheduling in Centralized Cognitive Radio Networks for Energy Efficiency,” IEEE Transactions on Vehicular Technology, vol. 62, no. 2, pp. 582–595, Feb., 2013, DOI. 10.1109.TVT.2012.2225650] and Chang et al [^{32}[32] P. Chang et al., “Performance analysis of channel switching with various bandwidths in cognitive radio,” 2013 The twelfth International Conference on Networks (ICN), pp. 29–33, Seville, Jan., 2013, DOI. 10.1109.ICECCO.2013.6718263.], discuss the channelswitching cost associated with CR, as a consequence of the need for radiocircuit reconfiguration when switching channels.
Shortterm prediction in conjunction with channelsensing is described in [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.], which reported gains in terms of throughput using MLP prediction. In [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.], the prediction stage in the framework proposed by [^{8}[8] Y. Liang, Y. Zeng, E. C. Y. Peh and A. T. Hoang, “SensingThroughput Tradeoff for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp. 13261337, Apr., 2008, DOI. 10.1109.TWC.2008.060869.] was added prior to the sensing stage to allow the SU to perform sensing only on channels predicted as idle. Both studies [^{8}[8] Y. Liang, Y. Zeng, E. C. Y. Peh and A. T. Hoang, “SensingThroughput Tradeoff for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp. 13261337, Apr., 2008, DOI. 10.1109.TWC.2008.060869.] and [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.], considered only an additive Gaussian white noise (AWGN) channel and did not analyze a fading channel.
To the best of the authors’ knowledge, joint analysis of multistepahead prediction and sensing in fading environments was not reported in literature. In addition, multistepahead prediction study with SMV was still not validated. The main contributions of this work are:

The multistepahead joint prediction sensing analysis for the purpose of resourceful channel usage in CR network. This scheme allows channelscheduling to be implemented as the SU can choose the channel with the largest number of consecutive time slots predicted as idle allowing for a lower number of channels switching. The prediction is realized with SVM ML, attaining a low probability of prediction error. Expressions for the probability of a cognitive radio network with multiple channels and multistepahead prediction are theoretically derived.

A new SU frame with multistepahead prediction and sensing is defined and it is determined whether there is a resulting increase in throughput in the CR network. For this research and future studies, the handoff (channelswitching) is very important and must be analyzed for a more realistic pointofview of SU frame. The handoff affects the entire framework of the SU, as the time spent by the SU in this process decreases the transmission and the production of results consistent with the real scenarios. For this reason, this work introduces an algorithm that tries to prevent as much as possible the handoff of channels.

A simplified expression for determining the detection probability of the energy detector for Rayleigh fading channels is proposed which allows the number of required samples for reliable detection in fading scenarios to be accurately determined. This is motivated because Rayleigh fading channel severely attenuates the signal and impacts primarily energy detection other than spectrum prediction. Consequently, a low probability of detection influences the data feeding the predictor algorithm, resulting in a severe reduction of predictor performance.
The results show that there was an improvement in the energydetector performance in Rayleigh fading scenarios. There was a reduction in channel switching and an increase in CR network throughput when multistepahead prediction schemes were used for both an AWGN channel and a Rayleigh fading scenario. The rest of this work is divided as follows Section II describes the system model used here. Section III shows the proposed improvements. Section IV presents the results of the simulation. Finally, in section V conclusions are drawn.
II. System Model
Figure 1 shows a CR network consisting of a SU transmitter and a SU receiver which coexist with native PU users. This Figure also shows a primary base station that establishes communication with several PU equipment, each link is established using a single channel. The PU equipment can access N_{C} licensed channels, which can also be accessed opportunistically by the SU equipment. In Fig. 1, the SU device is sensing all the N_{C} licensed channels. When a channel is available, the SU can access it to transmit to the corresponding cognitive receiver. The SU receiver is aware of the channel in use by the SU transmitter by means of a Common Control Channel (CCC) with limited bandwidth. Interference between an SU and PU can occur if spectrumdetection errors occur, in which case the SU device transmits based on the erroneous assumption that the analyzed channel is idle. The occupancy of any given channel due to PU activity is assumed to be independent of occupancy in any other channel. One PU can occupy only one channel at a time and the channels are assumed to be subject to Rayleigh fading.
When designing a wireless system, the Rayleigh fading model is one of the most appropriate to consider, as it serves the purpose of modeling a transmission without line of sight, such as dense urban areas [^{7}[7] S. Atapattu, C. Tellambura and H. Jiang, “Conventional Energy Detector,” in Energy detection for spectrum sensing in cognitive radio, 1st ed. New York, NY, US: Springer, 2014, ch. 2, sec. 3, pp. 11–24.].
A stochastic process with two states models PU traffic occupancy: busy or idle. Simulations were performed with an exponential onoff traffic distribution model, in which the interval when the channel is busy follows an exponential distribution with mean μ_{1} and the interval when it is idle has mean μ_{0}. The system model is composed of multiple channels, each one occupied by one PU.
The history of PU occupancy is modeled by binary states denoted s_{i} ∈ {0, 1}, where s_{i} is the state of the slot being analyzed. A busy slot is represented by 1, and an idle slot by 0.
III. Proposed Improvements
In the works referred to in the previous sections the slot or frame is divided into stages. In [^{8}[8] Y. Liang, Y. Zeng, E. C. Y. Peh and A. T. Hoang, “SensingThroughput Tradeoff for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp. 13261337, Apr., 2008, DOI. 10.1109.TWC.2008.060869.] only two stages are presented: sensing and transmission; in [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.], in contrast, the frame is divided into three stages: prediction, sensing and transmission. In order to deal with multistepahead prediction we made two modifications to the SU frame structure, these can be seen in Fig. 2, which shows a series of larger frames, made up of an initial frame and F – 1 subsequent frames, where F is the number of predicted future states. The first frame has a duration T and is divided into four stages: prediction, with a duration τ_{P}; sensing, with a duration τ_{S}; channelswitching latency or delay, with a duration τ_{SC}; and the effective transmission of information, lasting T – τ_{P} – τ_{S} – τ_{SC}. The next F – 1 frames are segmented into up to three stages in a similar manner: sensing, channelswitching latency and transmission. In these frames the actual transmission has a duration T – τ_{S} – τ_{SC}. After the F – 1 threestage frames, the SU begins the prediction cycle again with the initial frame divided into four stages.
SU slot or operating frame with multistepahead prediction, sensing and channel switching. The effective transmission time is denoted either as T – τ_{P} – τ_{S} – τ_{SC} or T – τ_{S} – τ_{SC}.
The prediction stage, which occurs only in the initial frame, is performed with an ML algorithm. In this stage, the SU estimates the state of N_{C} channels based on historical data and selects only those that are considered idle to perform sensing. In the second stage (sensing), a channel that has been predicted to be idle is chosen at random and the energydetection technique is used to evaluate the actual state of the channel. Data transmission takes place if the channel is in fact idle. Channel switching occurs if the SU determines that the current channel will be busy [^{31}[31] S. Bayhan and F. Alagoz, “Scheduling in Centralized Cognitive Radio Networks for Energy Efficiency,” IEEE Transactions on Vehicular Technology, vol. 62, no. 2, pp. 582–595, Feb., 2013, DOI. 10.1109.TVT.2012.2225650], [^{32}[32] P. Chang et al., “Performance analysis of channel switching with various bandwidths in cognitive radio,” 2013 The twelfth International Conference on Networks (ICN), pp. 29–33, Seville, Jan., 2013, DOI. 10.1109.ICECCO.2013.6718263.]. Channel switching results in latency because RF (radio frequency) circuitry must be reconfigured. If the predicted channel is the same as that already occupied by the SU, this stage is not counted, increasing the effective information transmission time. This model is more realistic than previous schemes because it considers the channelswitching latency and does not repeat the prediction stages.
The channelswitching latency (handoff) affects the entire SU frame, the time spent with handoff impacts the effective transmission decreasing the throughput and it is relevant for the analysis. Its consideration is very important as this work presents an algorithm that tries to avoid channel switching as much as possible.
A. SVM and Prediction Stage
Prediction in the context of CR can be performed through different techniques described in the literature including Machine Learning (ML) algorithms. ML algorithms can be divided into two categories, classifiers and regressors. Classifiers perform the classification by estimating discrete values. One example is the Support Vector Machine (SVM) algorithm, this was developed in [^{33}[33] V. N. Vapnik, “Methods of Pattern Recognition,” in The Nature of Statistical Learning Theory, 1th ed. New York, NY, US: SpringerVerlag, 1995, ch. 5, sec. 1, pp. 123–167.] and it is used in many areas of science such as market prediction, energy load estimation, among others.
Like other ML techniques, standard SVM performs data classification, it is considered a nonprobabilistic binary linear classifier. It takes a training stage with a set of samples taken from the total space problem data. The algorithm performs a process of categorizing the input data into just one of two classes. One way of viewing the operation of the algorithm is to treat each input data as a point in a hyperplane. The algorithm then finds a line with the maximum distance between two types of data categories. After executing the algorithm, the output is associated with only one of these categories. The purpose of the algorithm is to maximize the differences between the two categories to achieve correct classification.
The main reasons for choosing the SVM technique instead of the MLP neural network as a prediction tool are the small number of free parameters and the guarantee of converging to the optimal solution [^{26}[26] N. Sapankevych and R. Sankar, “Time Series Prediction Using Support Vector Machines: A Survey,” IEEE Computational Intelligence Magazine, vol. 4, no. 2, pp. 24–38, May, 2009, DOI. 10.1109/MCI.2009.932254]. Although the training phase of the two tools is computationally expensive, at the time of execution with the real data set, both have the advantage of being very efficient.
Given a data set x(t), where t is a series of discrete samples t = {0,1,2,3,4,5, N – 1}, an estimated value in the future is defined as y(t + δ). The classification aims at defining the following equation:
where w is the weight of the prediction function and ε is called limit value. The function ϕ(x) is the kernel function which is used when the input data space is not linear. The kernel function is a procedure to map the x(t) data to a higher dimension and then to perform linear regression. Several kernel functions meet the necessary conditions for mapping, such as hyperbolic, Gaussian and polynomial tangents [^{26}[26] N. Sapankevych and R. Sankar, “Time Series Prediction Using Support Vector Machines: A Survey,” IEEE Computational Intelligence Magazine, vol. 4, no. 2, pp. 24–38, May, 2009, DOI. 10.1109/MCI.2009.932254]. In the training phase, the objective is to find the optimal weights and limit values. One of the criteria is to find values for w with similar levels between them, this is verified by the Euclidean norm. Another criterion performed in the training phase is to reduce the error generated in the value estimation process; the residual error is given by:
where L(·) is a cost function which depends on the input x(t), prediction y(t) and regression function (1). Lagrange multipliers are used to solve this kind of convex optimization problem, which can be executed in linear arrangement in consequence of the kernel mapping process.
In this work, we used the linear kernel instead of the Gaussian kernel. Empirical tests showed a higher performance for the linear kernel which is aligned with the work of [^{21}[21] A. Agarwal, S. Dubey, M. A. Khan, R. Gangopadhyay and S. Debnath, “Learning based primary user activity prediction in cognitive radio networks for efficient dynamic spectrum access,” 2016 International Confer ence on Signal Processing and Communications (SPCOM), pp. 200–203,Bangalore, Jun., 2016, DOI. 10.1109.SPCOM.2016.7746632.] that presented superior performance of the linear kernel.
For a given channel η ∈ N_{C}, the observed window (pastdata window) has length L and is defined as
The training phase consists of providing the algorithm with a large amount of data, previously known and in this case, separated in several observed windows and its associated futuredata windows. The algorithm in its training phase acts to minimize the error between the values of the predicted future window and the already known futuredata window.
The MATLAB 2018 software was used to generate the simulation environment. This work utilizes the multiclass model for Support Vector Machine [^{35}[35] Allwein, E., Schapire, R. and Singer Y. “Reducing multiclass to binary: A unifying approach for margin classifiers.”ÂăJournal of Machine Learning Research, vol. 1, pp. 113âĂŞ141, Dec., 2000.] presented in MATLAB native Statistics and Machine Learning Toolbox. As mentioned before, we adopted the linear kernel parameter and the SVM algorithm performs the classification for multiple classes. Although we use binary data to define spectrum occupation or idle states, in our implementation we chose to leave the observed window in binary state and we chose to perform a simple operation in the futuredata window by aggregating the binary values within a future window with decimal value by performing a simple binarydecimal conversion. This simple conversion takes place before entering the data in the predictor algorithm, and this scheme is first used in the training phase. For example, considering F = 3, the algorithm defines 2^{F} = 8 possible different classes, a direct result of the binary combination of the three predicted slots. In its training phase, therefore, the algorithm makes the association between an observed window (in binary format) with a decimal number. In the validation phase when the predictor algorithm receives an observed window, it returns a decimal value (multiclass). After performing the prediction by the SVM algorithm in the validation phase of the real data in a multiclass format, we perform the inverse decimalbinary conversion. As stated, the input data (observed window) are not aggregated into multiple classes but are fed into the predictor as binary data.
The predicted vector
In this work, imperfect prediction was considered because the SVM technique can make erroneous predictions, causing the predicted value for slot
B. Sensing Stage
Channels that are predicted to be idle are selected for the second stage of the SU frame, the sensing stage. Energy detection [^{6}[6] H. Urkowitz, “Energy detection of unknown deterministic signals,” Proceedings of the IEEE, vol. 55, no. 4, pp. 523531, Sep., 1967, DOI.10.1109.PROC.1967.5573.] is a wellknown sensing technique in which the output is proportional to the energy of the received signal. The amount of energy detected is compared with a threshold, and a state corresponding to either the presence or absence of a signal at the receiver is returned. The result can be presented as a binary hypothesis on occupancy:
Noise is represented by n(t), h is the channel gain, x(t) is the PU signal, and y(t) is the signal received at the SU. Under hypothesis H_{0} only noise is present at SU receiver, while under hypothesis H_{1} the PU signal is also present at the SU receiver side. The channeloccupancy probabilities, which are shown in Section II for both hypotheses, are functions of traffic density. We also assume slow or quasistatic fading such that the channel gain h remains constant over several timeslots.
Noise samples n(t) are assumed to be AWGN with zero mean and variance
where λ is the detection threshold.
Closedform equations for P_{d} and P_{f} in AWGN channels have already been derived in [^{8}[8] Y. Liang, Y. Zeng, E. C. Y. Peh and A. T. Hoang, “SensingThroughput Tradeoff for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp. 13261337, Apr., 2008, DOI. 10.1109.TWC.2008.060869.], [^{34}[34] S. Atapattu, C. Tellambura and H. Jiang, “Performance Measurements,” in Energy detection for spectrum sensing in cognitive radio, 1st ed. New York, NY, US: Springer, 2014, ch. 4, sec. 1, pp. 41–59.], as well as the approximations
Where N represents the number of samples and
In scenarios with low SNR, i.e., low values of γ, it is more difficult to detect a signal effectively and the energy detector therefore needs more samples.
According to [^{8}[8] Y. Liang, Y. Zeng, E. C. Y. Peh and A. T. Hoang, “SensingThroughput Tradeoff for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp. 13261337, Apr., 2008, DOI. 10.1109.TWC.2008.060869.], the minimum number of samples, N, required for effective detection in an AWGN channel is:
Equation (8) shows that for the AWGN channel model the number of samples depends only on the design values of
Knowing that
Combining (5) and (10) gives the unprecedented closedform expression for P_{d} at lowSNR regime:
This equation is an excellent approximation for (9), as can be seen in section IVB, and greatly simplifies the algebraic manipulation required, as can be seen below.
C. Rayleigh Channel Energy Detector
The instantaneous detection probability P_{d} depends on the SNR and the number of samples as can be seen in (5), and may also be affected by the state of the wireless channel. Shadowing and fading effects on the channel, for example, make it necessary to evaluate the average detection probability
In a Rayleigh fading scenario, the distribution of the SNR is
In the above expression, _{2}F_{1} is a Gauss hypergeometric function of the form _{2}F_{1}(a, b, c, z) [^{37}[37] I. S. Gradshteyn and I. M. Ryzhik, “Hypergeometric Functions,” in Tables of Integrals, Series, and Products, 7th ed. San Diego, CA, US: Elsevier Academic Press, 2007, ch. 9, sec. 1, pp. 1005–1048.]. This equation is a compact form for
D. Transmission Stage
The last stage of the SU frame is the effective transmission of information based on the prediction and sensing stages. We will present the same calculations developed in [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.] for F = 1, next we will extend the calculations for F > 1.
When prediction is made for only one future state, i.e., F = 1, and considering only one channel, let
According to [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.], considering the N_{C} channels, the prediction probability indicating idle channel availability is
and the probability of all the channels being predicted to be busy is
When this last event happens, the SU selects a random channel to sense. At no time do the prediction results affect the sensing result.
The joint probability distribution of events prediction, sensing and the true state for only one channel
Extending the analysis to multiple future states (F > 1), for the sake of simplicity we first consider F = 2, i.e., the SU algorithm analyzes only two future states, and then generalize the results to any F. For only one channel, the probability of predicting both states as idle is P_{0(l)} = (P_{0(s)})^{2}. The probability of predicting the first state to be idle and the next to be busy is P_{1(l)} = (P_{0(s)})(P_{1(s)}). Similarly, the probability of predicting the first state to be busy and the next to be idle is P_{2(l)} = (P_{1(s)})(P_{0(s)}). Finally, the probability of predicting both states to be busy is P_{3(l)} = (P_{1(s)})^{2}.
Note that there are B = 2^{F} different combinations of idlebusy prediction results when considering F future slots. Let b ∈ {0,1,…, (B – 1)} denotes the decimal representation of a combination of idlebusy prediction results. For instance, considering three future slots, b = 5 means that the prediction result is (busy, idle, busy), which is represented by the binary sequence {101}. Then, for any F the probability of a combination of idlebusy prediction result can be computed as
where ξ is the number of idle predicted states and κ = F – ξ is the number of busy predicted states.
Now, considering the N_{C} channels and multiple slots, the prediction probability indicating idle channel availability can be considered as a multinomial experiment. This kind of experiment consists of a number N_{C} of trials, since each channel can be viewed as independent of each other. Each attempt can result in any one of B possible outcomes: O_{0}, O_{1},…, O_{B}_{–1}. In the previous example considering F = 2, the four possible outcomes (or events) are: O_{0} = {00}, O_{1} = {01}, O_{2} = {10}, O_{3} = {11}. The probabilities P_{0(l)}, P_{1(l)},… P_{B}_{–1(l)}, are associated to each possible outcome. Let define the weight vector (k_{0}, k_{1},…, k_{B}_{–1}) which specify the number of times each outcome O_{b} occurs, such that k_{0} + k_{1} + L+ k_{B}_{–1} = N_{C}. The probability associated with this vector is given by:
where,
is the multinomial coefficient. Note that this is the probability that O_{0} occurs k_{0} times, O_{1} occurs k_{1} times, …, and O_{B}_{–1} occurs k_{B}_{–1} times. Still using F = 2 we set another example, in order to facilitate understanding of the prediction technique with multiple slots. Under the perspective of multiple channels, considering N_{C} = 3, the weight vector has four elements (k_{0}, k_{1}, k_{2}, k_{3}) and a possible value for the vector could be (2,1,0,0) as 2 + 1 + 0 + 0 = 3.
This means that O_{0} occurs two times, O_{1} occurs one time and there are no occurrences for both O_{2} and O_{3}. The probability of this event is given by:
The prediction probability indicating idle channel availability across the N_{C}channel network is a union of probabilities like the one shown above.
Therefore, among all possible state combinations of vectors, we are only interested in those that involve idlestate sequences starting at
The other two combinations (that happen with probabilities P_{2(l)} and P_{3(l)}) start their sequences with busy state and are not evaluated by the scheduling algorithm. Another example can be visualized if we consider F = 3, which leads to B = 2^{3} = 8 possible different prediction probabilities denoted as P_{0(l)}, P_{1(l)},…, P_{7(l)}. In this last case the scheduling scheme will analyze only four predicted sequences:
The elements of the vectors elected to compose the aforementioned union should satisfy
By performing the analysis for the entire CR network made up of N_{C} channels, we get an extension of the result presented in [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.]. The generalized equation for the probability of the entire network with multiple channels being idle in multiple future states is therefore
Equation (22) is original, and takes into account all cases where there is a sequence of idle channels starting with
Which accounts for the events: all channels busy in all future states or only some channels busy in future states.
In the case of two future states, three more columns are added to Table III of [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.]. As the number of future states increases, the number of rows in the table increases exponentially. Assuming the case where F = 2 and considering the analysis of only one channel, if the prediction is idle, the sensing is idle and the true state is also idle for all F = 2 future states analyzed we will have the extension of the result of [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.] and the result in this particular case is the square of the first row, third column of Table III of [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.]. The total quantity of possible combination for F = 2 and just one channel is 2^{(2×3)} = 64 rows, generalizing we have ψ = 2^{(F×3)} different probability of true channel state, prediction and sensing with F = 2 and just one channel.
The theoretical probability distribution of true channel state, prediction and sensing for F > 1 and the entire network (multiple channels), can be found by multiplying the probabilities of the first term of equations from third column of Table III of [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.] and the probability equations for the whole network, (22)[22] Z. Chen, N. Guo, Z. Hu and R. C. Qiu, “Channel state prediction in cognitive radio, Part II: Singleuser prediction,” 2011 Proceedings of IEEE Southeastcon, pp. 50–54, Nashville, TN, Mar. 2011, DOI. 10.1109.SECON.2011.5752904. and (23)[23] Soltani, S., and Mutka, M. W., “A decision tree cognitive routing scheme for cognitive radio mesh networks,” Wireless Communications and Mobile Computing, vol. 15, no. 10, pp. 14051417. 2015, DOI. 10.1002/wcm.2418:
where g ∈ 0,1, which selects equations (22) or (23). The index ψ is described above and ψ ∈ 1,…,2^{(F×3)}. The product inside the brackets in (24)[24] Canavitsas, A., Silva Mello, and M. Grivet, “Spectral Vacancies Prediction Method for Cognitive Radio Applications,” Journal of Microwaves, Optoelectronics and Electromagnetic Applications, vol. 15, no. 1, pp. 18–29, Mar., 2016, DOI. 10.1590.2179.10742016v15i1581 is associated to the quantity of future states analyzed, thus we have a sequence of multiplications of the eight rows in Table III of [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.] and as a result w ∈ 1,…,8.
The throughput of a CR network is defined as the total amount of data transmitted divided by the total transmission time. If a channel is sensed busy, the SU will not transmit data and the throughput will be zero, i.e., C_{0} = 0, where index 0 indicates the nontransmission state. If a channel is sensed idle and is indeed idle, and if the gain of the channel, h, which is subject to Rayleigh fading, is assumed to be an ergodic process [^{38}[38] K. D. Rao, “Introduction,” in Channel coding techniques for wireless communications, 1st ed. New Delhi, India, Springer, 2015, ch. 1, sec. 4, pp. 1–20.], [^{39}[39] V. Kuhn, Wireless communications over MIMO channels: applications to CDMA and multiple antenna systems, 1st ed. Chichester, UK, John Wiley et Sons, 2006, ch. 2, sec. 2,pp. 51–90.], the throughput of the channel will be
This is the throughput in the best case because there is no interference from the PU in the chosen channel.; γ_{S} is the SNR between the transmitting and receiving SU,
As multistepahead prediction estimates F states into the future, the prediction stage does not need to be run more than once, so there is a slight increase in network throughput. When the channel is sensed idle but is actually occupied by the PU, the throughput will be reduced as there will be interference from the PU in the channel. Therefore
corresponds to the transmission capacity in the least favorable circumstances. The network throughput, R, is given by
Both summations refer to cases where sensing was performed but the actual channel state changes the associated throughput. Equation (28) is normalized to generate dimensionless values by dividing it by the upper limit R_{S} = P(H_{0})C_{1} + P(H_{1})C_{2}:
E. Channel Scheduling
Channel scheduling increases the efficiency of a CR network by reducing the amount of channel switching, reducing transmission pauses and making communication more stable. Channel switching is investigated in [^{12}[12] A. Shahid et al., “CSIT: channel state and idle time predictor using a neural network for cognitive LTEAdvanced network,” Eurasip Journal on Wireless Communications and Networking, vol. 2013, no. 1, pp. 203–219, Dec., 2013, DOI. 10.1186.168714992013203.] in the context of increased transmission quality in LTE networks. In multichannel communication using timeslots, the user should remain on the same channel for as long as possible as channel switching involves handoff mechanisms that can result in computational costs and delays for the end user.
In this context, a change in the chosen channels for sensing compared with other studies found in the literature was developed. Because the multistepahead predictor can estimate multiple slots ahead, it determines which channels will be idle longer and which will have the greatest number of sequential idle slots.
The proposed algorithm implemented in the SU looks for the channel with the greatest possible number
(a) Channel selection with the most sequential future idle slots; (b) The pseudo code for the algorithm.
The proposed algorithm also yields an improved result for F = 1 and gives preference to the channel that had already been chosen in the previous state, avoiding a potentially unnecessary channel change. The pseudo code for the algorithm can be verified in Algorithm 1 (depicted in Fig. 3b).
IV. Results
In this work we used a training set with T_{r} = 1000 sample slots, and the total number of validation slots per simulation round was set to S = 30000, the same value as that used in [^{12}[12] A. Shahid et al., “CSIT: channel state and idle time predictor using a neural network for cognitive LTEAdvanced network,” Eurasip Journal on Wireless Communications and Networking, vol. 2013, no. 1, pp. 203–219, Dec., 2013, DOI. 10.1186.168714992013203.]. Simulations were performed for training and performance evaluation. As described in Section IIIA, each SU was trained with different slots to avoid biased results. For the remainder of the simulation, the same design values as those in [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.] were used according to Table I.
Where the SNR of the PU sensed by the SU complies with the design described in Section IIIC. The procedures, steps, equations and algorithms^{1} presented in Sections II and III were implemented through the MATLAB® 2018 Software from Mathworks® in a personal computer (PC), where the “Statistics and Machine Learning Toolbox“ and “Neural Network Toolbox” are required. The hardware of the PC is a Core i57300HQ CPU @2.5 GHz, 8GB DDR4@ 2400MHz. The algorithms were tested using the following MATLAB functions: “fitcknn”, “fitctree”, “fitcsvm”, “fitecoc”, “predict”, “network” and “train”. It was possible to perform several computer simulations that validate the main contributions of this work and present a comparison with what was provided in the literature.
A. Imperfect Prediction
The SVM technique was chosen after a thorough comparison between several ML techniques. Four machine learning algorithms were compared, namely: kNearest Neighbor [^{22}[22] Z. Chen, N. Guo, Z. Hu and R. C. Qiu, “Channel state prediction in cognitive radio, Part II: Singleuser prediction,” 2011 Proceedings of IEEE Southeastcon, pp. 50–54, Nashville, TN, Mar. 2011, DOI. 10.1109.SECON.2011.5752904.], Classification Tree[^{23}[23] Soltani, S., and Mutka, M. W., “A decision tree cognitive routing scheme for cognitive radio mesh networks,” Wireless Communications and Mobile Computing, vol. 15, no. 10, pp. 14051417. 2015, DOI. 10.1002/wcm.2418], Neural Network [^{18}[18] V. K. Tumuluru, P. Wang and D. Niyato, “A Neural Network Based Spectrum Prediction Scheme for Cognitive Radio,” 2010 IEEE International Conference on Communications, pp. 1–5, Cape Town, May, 2010, DOI. 10.1109.ICC.2015.5502348.] and SVM. Each algorithm was tested with a set of data used in this work, that is, a set of spectrum occupation slots with the possible states 1 or 0, with their traffic following the Poissonbinomial distribution.
Figure 4 shows the probability of prediction error,
The performance of predictors measured in terms of the probability of prediction error as a function of the number of predicted future slots. The traffic density for all simulations was set to ρ=0.65.
A point that weighed heavily in favor of choosing the SVM tool is that it always converges to the optimal result [^{26}[26] N. Sapankevych and R. Sankar, “Time Series Prediction Using Support Vector Machines: A Survey,” IEEE Computational Intelligence Magazine, vol. 4, no. 2, pp. 24–38, May, 2009, DOI. 10.1109/MCI.2009.932254]. This is not guaranteed by the Neural Network, the second best ML algorithm in terms of probability of wrong detection. Another point that was taken into consideration in our analysis was the computational cost. In our study, both the neural network algorithm and the SVM algorithm spent a very similar amount of time for its execution in the training phase, with a discrete difference in favor of the SVM ML algorithm. In the data validation phase (execution of the real data) the SVM technique operated about 17% faster than the neural network algorithm. Finally, to the best of our knowledge the authors are unaware of any multistepahead prediction application with SVM.
Predictor performance is measured in terms of the probability of prediction error
Figure 5 shows the probability of prediction error (which is the performance benchmark of the predictor) as a function of traffic density. For the cases where the traffic density is very high or very low, the predictor has an excellent performance obtaining results very similar, although different, for the two curves. In both cases, the traffic density is extremely high or extremely low and the uncertainty of future states is low. The predictor tends to be more accurate in these cases because these scenarios are more static. The fact that the probability of error of the SVM predictor is approximately 10% in both cases is associated with the residual error equation (2) being defined as R_{emp}(f) = 0.1. The predictor achieves this same level of performance, although the Rayleigh channel causes more dynamics in the traffic pattern, showing excellent performance of the predictor. In cases where the traffic density is close to ρ = 0.5, the uncertainty of the predictor assumes the highest level since there the scenarios are more dynamical.
B. The appropriate number of samples for the Rayleigh fading channel
Figure 6 shows the very high degree of similarity between the curves of P_{d} as a function of N generated by the equations in [^{34}[34] S. Atapattu, C. Tellambura and H. Jiang, “Performance Measurements,” in Energy detection for spectrum sensing in cognitive radio, 1st ed. New York, NY, US: Springer, 2014, ch. 4, sec. 1, pp. 41–59.] and equations (9) and (13) in the present paper. There is a minimal difference between the calculated number of samples for both cases. In computational terms it was observed that computing N using (13) is less complex and 4.54 times faster than using equation (4.2) of [^{34}[34] S. Atapattu, C. Tellambura and H. Jiang, “Performance Measurements,” in Energy detection for spectrum sensing in cognitive radio, 1st ed. New York, NY, US: Springer, 2014, ch. 4, sec. 1, pp. 41–59.].
Theoretical detection probability as a function of number of samples for an AWGN channel and a Rayleigh fading channel for the proposed approach and the literature.
Performance gains can be achieved during the sensing stage when the correct number of samples is used in the system design. In the case of the Rayleigh channel, there was an increase in energydetector performance when we used the specific design for this channel type.
Figure 7 shows two simulations for detection probability values as a function of SNR. In the first simulation we used the design for an AWGN channel in a Rayleigh fading channel, while in the second simulation the design specifically intended for a Rayleigh fading scenario was used.
For design values of P_{f} = 0.1, P_{d} = 0.9, and γ = –20dB in an AWGN channel, N = 66,351 samples were used. When this number of samples was used in a fading scenario, the performance of the energy detector was adversely affected. In this unfavorable case, the detection probability was approximately P_{d} = 0.8, corresponding to a performance loss of approximately 12%. This result shows the importance of analyzing fading scenarios. If only the project for the AWGN was considered but the channel is Rayleigh, the results would show a degradation in the performance of the energy detector. The simulated detection probability P_{d} = 0.9 when the correct design for a Rayleigh channel was used can also be seen in Figure 7. The correct number of samples N_{Ray} = 66,718 for a Rayleigh channel was determined from (13).
C. Channel Scheduling
In this simulation we used the specific design for a Rayleigh channel with a past observation window of L = 10, future observation window of F = 5 and traffic density values ranging from ρ = 0.1 to ρ = 0.9. Figure 8 shows a comparison of the amount of channel handoff with and without multistepahead scheduling, which was described in Section IIIE. In the scheduling scheme, the predictor uses the multistepahead algorithm to choose the channel with the largest number of future idle slots. For low values of ρ most channels are idle, and when no decision criterion is used by the SU there is a large amount of channel handoff. When the multistepahead prediction scheme is used, channel handoff is limited for low values of ρ and increases as ρ increases, but decreases when ρ = 0.9. For ease of interpretation, the amount of channel handoff was normalized by dividing the number of channel hops by the number of slots analyzed. For ρ = 0.6 there was a saving of up to 42% in the number of channel hops when multistepahead scheduling was used, and for ρ = 0.5 the result of Figure 8 was 51%. When the traffic density is close to ρ = 0.9, it is possible to observe that the number of handoff is very low and the two curves are very close. In this case, most channels are occupied during several time intervals. The SU does not perform the transmission because it is most often in the stop state. The two algorithms perform similarly in this extreme case and the network throughput is severely affected by the high traffic density
D. Throughput of the Cognitive Radio Network
Figure 9 shows the normalized throughput R_{Norm} as a function of traffic density for an AWGN scenario. Two simulations were performed for F = 1: one without channel scheduling and one with scheduling, as proposed in Section IIIE. Two simulations were also performed for F = 3. In all four simulations the same number of past points (L = 15) was used. Curves of the theoretical normalized capacity for an AWGN channel with
A gain in terms of throughput is observed when multistepahead prediction is used. Figure 9 shows that the curve for F = 3 with scheduling was extremely close to the curve for F = 1 without scheduling. The curve for F = 1 is also generated in [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.] which analyses the case for single step prediction. For ρ = 0.5 the increase in throughput was about 4%. This increase is a result of multistepahead prediction based on the structure proposed in Section III, which ensures an increase in the effective transmission time. Figure 9 also compare the cases with scheduling and without scheduling. In the case of multistep prediction without scheduling the average probability of prediction error is slightly greater than the case with single step prediction due the error accumulation problem. The scheduling algorithm implemented in the SU improves the cognitive network throughput performance; the factor that contributes to this increase is that the channelscheduling algorithm always chooses the channel with the greatest number of predicted idle slots. Thus, the transmission has the least amount of hops possible.
In the case of multistepahead prediction, accumulation of error causes the SU predictor to perform slightly less than the singlestepahead predictor for ρ < 0.3. For multistep, the algorithm tries unsuccessfully to generate scheduling, ultimately generating unnecessary channel hopping. These changes cause loss of performance in the network throughput. The onestep forward algorithm has a more robust prediction and less channel change for these cases. For the other cases from ρ ≥ 0.3 there is a performance gain by the multistepahead prediction. As much as there is a problem of error accumulation, the algorithm can choose more coherently channels with the largest number of free channels, through scheduling.
Figure 10 shows normalized throughput as a function of traffic density in a Rayleigh fading scenario. Two simulations were performed for F = 1 (with and without scheduling) and two for F = 3 (with and without scheduling).
Normalized throughput R_{Norm} of the CR network for Rayleigh fading scenarios with F = 1 and F = 3.
The theoretical curves for the Rayleigh channel based on these properties are also shown. As in the previous simulations, a value of
The results presented in this Section showed significant improvements when compared to some results presented in the literature. First, an improvement of up to 4% in the normalized transfer rate of the cognitive radio network (secondary user network) was found when using the prediction with multistep ahead compared to the work [^{13}[13] J. Yang and H. Zhao, “Enhanced Throughput of Cognitive Radio Networks by Imperfect Spectrum Prediction,” IEEE Communications Letters, vol. 19, no. 10, pp. 1738–1741, Oct., 2015, DOI. 10.1109.LCOMM.2015.2442571.]. This result was possible because the enhanced structure of the SU framework is different from what had already been published in the literature. Our work also presented a channel scheduling scheme for multiple steps that had not been explored in the literature, this approach allowed the SU to choose the channel that has the best availability for the longest time. We also used the Support Vector Machine (SVM) machine learning technique, which had a lower probability of prediction error compared to other techniques found in the literature [^{18}[18] V. K. Tumuluru, P. Wang and D. Niyato, “A Neural Network Based Spectrum Prediction Scheme for Cognitive Radio,” 2010 IEEE International Conference on Communications, pp. 1–5, Cape Town, May, 2010, DOI. 10.1109.ICC.2015.5502348.], [^{22}[22] Z. Chen, N. Guo, Z. Hu and R. C. Qiu, “Channel state prediction in cognitive radio, Part II: Singleuser prediction,” 2011 Proceedings of IEEE Southeastcon, pp. 50–54, Nashville, TN, Mar. 2011, DOI. 10.1109.SECON.2011.5752904.] and [^{23}[23] Soltani, S., and Mutka, M. W., “A decision tree cognitive routing scheme for cognitive radio mesh networks,” Wireless Communications and Mobile Computing, vol. 15, no. 10, pp. 14051417. 2015, DOI. 10.1002/wcm.2418]. This ML algorithm achieved the best results not only for one point in the future but for multiple points in the future. Finally, we present a new way of finding the probability of detection of the energy detector for the channel with Rayleigh fading that is simpler and faster to perform than the equation found in [^{34}[34] S. Atapattu, C. Tellambura and H. Jiang, “Performance Measurements,” in Energy detection for spectrum sensing in cognitive radio, 1st ed. New York, NY, US: Springer, 2014, ch. 4, sec. 1, pp. 41–59.].
V. Conclusions
This work focused on the formulation of multistepahead spectrumprediction schemes for fading channels. Innovative analytical expressions for the probability of a cognitive radio network with multiple channels and multistepahead prediction are theoretically derived. The energydetector sensing technique was analyzed for the Rayleigh fading scenario, and a new detectionprobability equation for lowSNR scenarios was derived. Using this equation, the exact number of samples required to meet the system design requirements was calculated. This approach also resulted in improvements in the throughput of the CR network. Using multistepahead an algorithm was explored which permit SU prioritize channels that are most likely to be idle longer so there is a saving in terms of handoff periods for users. The proposed approach also reduces the number of repetitions of time spent on predictions in SU frame, generating throughput gains for the entire network. Excellent levels of prediction error were achieved using the SVM technique. Prediction error was found to depend on PU traffic, which was included as a variable parameter to improve the simulation. The main suggestions for future research include realize an energyefficient multistep prediction algorithm for different fading scenarios and propose a system model were SUs employing multistep prediction can cooperate with each other providing enhanced network throughput. The continuous study of efficient techniques for the use of the spectrum opens space for new practical models of cognitive radio to be implemented in new generations of wireless communication systems.
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Publication Dates

Publication in this collection
11 Nov 2020 
Date of issue
Dec 2020
History

Received
18 Apr 2020 
Reviewed
04 May 2020 
Accepted
01 Oct 2020