Multi-Attributes, Utility-Based, Channel Quality Ranking Mechanism for Cognitive Radio Networks

: Cognitive radio is an intelligent wireless solution that aims to enhance the access to the radio spectrum. In this technology, secondary users sense the radio spectrum, select the best channel among a pool of free channels, and determine the optimal transmission parameters to meet their quality-of-service requirements while maximizing the spectral efﬁciency. Over the past decade, several channel-ranking mechanisms have been proposed. However, these mechanisms consider only the remaining idle time of the channel and exclude some crucial parameters. This convincingly demonstrates a strong need for a new channel quality-ranking model that jointly considers several parameters to select the best communication channel for transmission. This paper proposes a utility model that integrates several important parameters for ranking channels. First, we underline the importance of the process of the channel quality ranking. Then, we describe a multi-attributes, utility-based, channel quality-ranking model. Finally, we describe a series of experiments and their results, which show that our model effectively ranks the best communication channels ﬁrst.


Introduction
Wireless devices and traffic have been exponentially growing, causing a huge demand for radio frequency channels [1][2][3]. Current fixed frequency allocation has resulted in an inefficient utilization of radio spectrum resources due to two main reasons: the licensed frequency channels are not or are scarcely used while unlicensed bands, such as Wi-Fi bands, are heavily used. Cognitive radio (CR) technology has been proposed to enhance the access to the radio spectrum and overcome its scarcity by enabling dynamic access. Secondary users (SUs) can perform spectrum sensing and access the free channels while the primary user (PU) is idle.
Energy detection [4][5][6][7][8][9] computes the energy of the received sample as the squared magnitude of the Fast Fourier Transform (FFT) averaged over the number of samples. Then, this energy is compared to a threshold to decide on the presence or the absence of the primary user. Specifically, if this energy is higher than the threshold, the primary user is declared to be present; otherwise, the primary user is absent. Energy detection is a simple and fast technique that does not require any prior knowledge about the primary user signal, and it is very sensitive to noise, which makes the detection performance of this technique at low signal-to-noise ratio (SNR) values unreliable.

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Development of a utility ranking-based model for channel quality ranking, • Use of a nonlinear regression algorithm to determine the weights corresponding to each parameter, • Validation the proposed model, • Highlight the challenges and future directions related to channel quality ranking.
The rest of this paper is organized as follows: the second section describes the proposed model, the third section describes the experiments and the results, the fourth section further discusses the proposed model and how it can be extended, and in the last section, conclusions and perspectives are drawn.

Methodology
The proposed model involves three main processes: spectrum sensing, channel quality estimation, and channel ranking. As shown in Figure 1, the first step of this model consists of performing spectrum sensing using either energy detection [4][5][6][7][8][9], cyclostationary features detection [10][11][12][13][14][15], or matched filter detection [16,17]. This spectrum-sensing process determines the list of free frequency channels. The second process involves the estimation of the parameters related to the quality of each free frequency channel, such as the occupancy of the channel, SNR, information capacity of the channel, bit error rate, etc. The channel ranking calculates the global utility of each frequency channel and then ranks all the free channels. The frequency channel with the highest utility value is chosen as the best channel for transmission. In the "ACTION" function, the selected frequency channel is used for communication.
The proposed utility function is described as follows. Let us consider that the radio spectrum is divided into M frequency channels, of which N frequency channels are free. F = { f 1 , f 2 , . . . , f N } denotes the list of these N free channels for which the quality of the channel is increasing as the subscript of the frequency is increasing.  Figure 2 shows the expected utility function of the frequency channels. The x-axis represents the list of frequencies from f 1 to f 100 , and the y-axis represents the expected utility ranging from 0 to 1.
The frequency channel f 1 has the lowest quality, and as we increase the subscript of the frequency, the quality of the channel increases until reaching the frequency with the highest frequency that correspond to the channel with the best quality.
The utility function of these parameters can be approximated by a sigmoid function, which is expressed as: where w i denotes the weight associated with the parameter x i , and N is the number of features used to estimate the quality of the channel. Equation (1) can be rewritten as: where x is the N-dimensional vector made of the parameters x i , w is the N-dimensional vector made of the weights w i , and T is the transpose operator. To find the weight w i corresponding to each utility parameter x i , we define the cost function as: where y is the expected global utility and m is the number of training data. Then, the problem of finding the weights can be solved by minimizing the following cost function: To minimize the cost function, we use the Gradient Descent algorithm. This algorithm updates all the weights simultaneously until the convergence to a global minimum. These weights are updated using the following formula: where α is the learning rate and ∂ ∂w j J(w) is the partial derivative regarding the weights w j .
Consider n parameters that are encompassed in the global utility function. All of these parameters are updated simultaneously, and Equation (5) can be rewritten as: . . .
The partial derivative ∂ ∂w j J(w) becomes the following: where m is the number of element in the training set. Thus, Equation (5) above can be rewritten as: The performance of the gradient descent is related to two main parameters: the learning rate and the number of iterations. When the learning rate is smaller, the chance that the gradient descent converges to a global minimum of the cost function is higher. As we increase the value of the learning rate, the gradient descent can miss the global minimum and can diverge. With a small learning rate value, the gradient descent runs for a large number of iterations to find the global minimum. As we increase the number of iterations, the convergence time increases as well. Finding the optimal values of the learning rate and the number of iterations is necessary for the convergence of this algorithm in an acceptable time.

Results
To validate the proposed model, we consider a scenario in which the quality of frequency channels is determined using two parameters: the information capacity and the availability of the channel. However, more parameters can be easily included to evaluate the quality of the channel without any change in the proposed model. These two parameters are important in channel ranking. To illustrate the importance of the first parameter in channel ranking, we consider a scenario in which a secondary user has to choose between two channels: channel one, with a capacity C 1 , and channel two, with a capacity C 2 . If C 1 is more significant than C 2 , the secondary user will choose the first channel since it allows him to transmit at a higher data rate. To illustrate the importance of the second parameter, let us take, for instance, two channels with occupancies of 10% and 90%. A secondary user, who has to choose between these channels, will select the first one as it is less occupied.
The information capacity, C, refers to the maximum rate at which data can be transmitted across the channel without errors. This parameter can be determined based on the bandwidth of the channel and the received signal-to-noise ratio, as given by: where C is measured in bits per second or bits per transmission, B is the bandwidth, and SNR is the signal-to-noise ratio.
The Shannon information capacity theorem states that for a prescribed channel bandwidth B and a received SNR, a signal can be transmitted without error even when the channel is noisy, provided that the actual signaling rate R in bits per second, at which data is transmitted through the channel, is less than the information capacity C.
The availability of the channel refers to the holding time or the time that a secondary user can benefit from using a channel until the arrival of the primary user signal. The availability of a specific channel can be derived from its occupancy. The frequentist method [32], for instance, gives a simple statistical computation of the channel occupancy as: where N 0 denotes the number of observations in which the frequency channel is occupied, and N denotes the total number of observations. The first step of this experiment was the determination of the weights w 1 and w 2 corresponding to each parameter of the utility. For this reason, a dataset has to be generated to train our model and determine the optimal value of these weights. To generate this dataset, we considered a list of 100 frequency channels with different values of capacity and occupancy. For each frequency channel, we computed its corresponding utility; we then calculated the capacity of each frequency channel considering the SNR value and the bandwidth B using the Shannon formula given in Equation (9). Different values of bandwidth are considered in this experimental setup depending on the bands. For instance, for Wi-Fi 2.4 GHz, a bandwidth of 20 MHz is considered. Then, according to the standard IEEE 802. 11ac, we selected a combination of a modulation and a coding rate that allow secondary users to achieve a maximum data rate less or equal to the capacity of this channel, i.e., R ≤ C. To illustrate this process, we consider an example of a channel that has a capacity of 80 Mbps, and then, according to Table 1, we can achieve a data rate of 78 Mbps, if we select QPSK modulation with a coding rate of 3/4. Once we determined the data rate that can be achieved by each frequency channel with the modulation technique and coding rate, we used the maximum data rate in addition to the holding time to rank these 100 frequency channels. For instance, the frequency channel that has a high data rate and a higher holding time is ranked first, and the frequency channel that has a low data rate and short holding time is ranked last. Finally, we attributed a utility value to each frequency channel that reflects its ranking. Channels ranked on the top of the list have high values of the utility, while the channels ranked last have small values of the utility.
The generated dataset was divided into two parts: training and testing data. The training dataset represented 75% of the overall data, and the testing data represented 25%. The Gradient Descent algorithm determines the optimal values of weights corresponding to each parameter by solving the optimization problem, given by Equation (7). To find the appropriate learning rate and the number of iterations to use with the Gradient Descent algorithm, we varied the learning rates and compared the outputs of the Gradient Descent in terms of error function and convergence time. The learning rate and the number of iterations that have a low error function and a short convergence time are chosen for the Gradient Descent setting.
Once the weight corresponding to each parameter is determined, the model can predict the utility function of each channel frequency, and this predicted utility is used to rank the list of frequency channels, which are given in Table 2. This list considers four bands from Global System for Mobile (GSM) and Wi-Fi: GSM 850 MHz, GSM 1900 MHz, Wi-Fi 2.4 GHz, and Wi-Fi 5.8 GHz. This table also gives the list of frequency ranges, the channel spacing, and the number of channels for each band. These frequency channels are considered because they are the most used ones in wireless communication. It is worth mentioning that the experiments have been carried out on Matlab (R2016a, MathWorks corporate, Natick, MA, USA) running on a machine with a processor intel(R) Core (TM) i7-6700 CPU 3.40 GHz. Examples of results are given in Figures 3-6. Figure 3 shows the error function, or the cost function, of the Gradient Descent algorithm versus different values of the learning rate α . As it can be observed, the error function is minimal (0.04) for a value of learning rate of 0.01. As we increase the learning rate, the error function increases to reach a value of 0.07 when the learning rate is 0.028. Figure 4 shows the convergence time of the gradient descent as a function of the number of iterations for a learning rate equal to 0.01. As observed, the convergence time increases as the number of iterations increases. The convergence time for 20,000 iterations is equal to 0.26 s. Figure 5 shows the error function as a function of the number of iterations for a learning rate equal to 0.01. As one can see, the cost function or the error function decreases as the number of iterations increases. For a number of iterations greater than 20,000, the error function remains constant.
Based on the results of Figures 3-5, we have chosen a learning rate of 0.01 and a number of iterations equal to 20,000 to determine the weights of our model. Figure 6 shows both the experimental and the calculated global utility using the testing dataset. The x-axis represents the list of frequencies from f 1 to f 100 . The y-axis represents the utility function. From this figure, one can see that the calculated utility with the estimated weights using the proposed model fits the experimental utility.     Table 3 shows the obtained values of the global utility for several values of the capacity and the occupancy. As one can see, the utility function tends toward zero with increasing values of the occupancy and decreasing values of the capacity. Thus, based on the obtained ranking, the best channels are the desirable ones. For instance, the 1850 MHz frequency with a capacity of 0.14 and an occupancy of 34% is better than 1856.4 MHz with a capacity of 0.14 and an occupancy of 37%. In addition, the first ranked channel 5725 MHz has the highest capacity and the lowest occupancy. In contrast, the last channel in the ranking is 5815 MHz, which has the lowest capacity and the highest occupancy. According to the results obtained in Table 3, a secondary user can use the channel frequency of 5725 MHz to achieve a higher data rate and a high holding time for the frequency channel, which minimizes the number of switching from a channel to another, therefore reducing the power consumption from the process of sensing and ranking. The channel 5725 MHz has a capacity of 266.32 Mbps, and according to the standard IEEE 802.11ac, if we use a modulation 64-QAM with a coding rate of 3/4, the secondary user can achieve a data rate of up to 243 Mbps. In contrast, the algorithms that rank the channels using only the remaining idle time, i.e., the channel with the lowest occupancy, which gives the secondary user a high holding time of the channel, are selected. However, selecting the channel with the lowest occupancy does not mean necessarily that this channel has the highest capacity, which makes the secondary users unable to transmit with a high data rate to meet their requirements in terms of quality of service.

Discussion
The proposed model was evaluated experimentally using two parameters: the information capacity and the occupancy of the free channel, which was determined by using spectrum sensing. These two parameters involve several other parameters. For instance, the capacity in its calculation involves two main parameters, which are the bandwidth of the channel and the level of noise represented by the signal-to-noise ratio. The data rate is also considered, which involves a modulation and coding techniques. One of the advantages of the proposed model is its modularity as one can easily include as many parameters as needed to evaluate the quality of the channel. For instance, one crucial parameter that can be included in the channel quality ranking is the bit error rate. In the case of the communication systems, the reliability is commonly expressed using the bit error rate (BER). The BER can be defined as the ratio between the number of corrupted bits and the total number of transmitted bits during a period of time. The knowledge of the BER associated with each channel at any time can help to evaluate the quality of the channel, and thus, can improve the quality of service by enabling the selection of a channel with a minimum BER for transmission. Clearly, the smaller the BER, the more reliable the communication system is. To measure the BER, several techniques have been proposed [33]. For instance, the authors of [34] have proposed a technique that measures the BER in the Additive White Gaussian Noise (AWGN) channel using as few as 32 pilot samples to estimate the BER with an error of 0.00066.
The signal-to-interference-plus-noise-ratio (SINR) is another crucial parameter in channel quality ranking, especially in cognitive radio networks [35], since interference is one of the critical factors that affects the performance of communication in these networks. The SINR is the relative ratio between the power of the transmitted signal and the interference power added to the noise power. This parameter is affected by several parameters such as shadowing and path loss.
Another aspect that has to be considered in channel quality ranking is the security risk associated with each specific channel. The cognitive radio network is subject to several attacks that can create a denial of service [36][37][38]. For instance, if a channel is jammed, the communication is interrupted. To avoid jamming attacks, it is possible to calculate, for instance, the probability that a channel will be jammed. A secondary user can choose the channel with a lower attack probability.
Another advantage of the proposed model is that it involves several parameters in the process of the selection of the best communication channel, which contrasts to other models that consider only one parameter, such as the occupancy of the channel. The selection of the best channel based on the occupancy can lead to the selection of a channel with a high remaining idle time, but this channel can have a low bandwidth or can experience a high level of noise, which does not allow secondary users to achieve a high data rate. This clearly show the outperformance of the proposed model compared with other techniques.
Once the selection of the best channel is done, secondary users can choose the optimal parameters of transmission such as the modulation technique, the coding rate, and the power of transmission that allow them to achieve the maximum data rate. Several algorithms can be applied in this stage, such as genetic algorithms discussed in the introduction section. Table 4 gives a comparison between ranking mechanisms. This table shows that our algorithm ranks the channels based on the capacity that involves in its calculation the bandwidth, level of noise within a channel, and the occupancy. A machine-learning model is used to predict the utility value of each frequency channel. The model involves several parameters jointly in the process of the channel ranking. The selection of the channel with the lowest occupancy and the highest capacity enables secondary users to transmit with a high data rate during a long period. However, most of the existing algorithms rank channels based only on the availability, which can lead to the selection of a channel with low occupancy, but it can be of low quality. Some other algorithms such as the one given in [27][28][29][30][31] consider the quality of the channel, but this occurs only after the selection of the channel to adapt the parameters of transmission according to the condition of the selected channel.

Conclusions
In cognitive radio, secondary users have to sense and select the best frequency channel that meets their requirements regarding the quality of service and security before transmitting data. Several channel quality ranking mechanisms have been proposed for helping secondary users in their choice. Nevertheless, most of these ranking mechanisms include the occupancy as a parameter and exclude other key parameters such as channel capacity. In addition, most of these existing ranking techniques consider parameters separately in ranking. In this paper, we have proposed an aggregate utility function of several parameters. The weight associated with each parameter is determined using the nonlinear regression. Our findings demonstrate that the proposed model produces good results and can help secondary users in selecting the best channel for communication. To further improve our research, we plan to investigate the validity of our model with other important parameters, especially those related to security.