A Quantization-Based Multibit Data Fusion Scheme for Cooperative Spectrum Sensing in Cognitive Radio Networks

Spectrum sensing remains a challenge in the context of cognitive radio networks (CRNs). Compared with traditional single-user sensing, cooperative spectrum sensing (CSS) exploits multiuser diversity to overcome channel fading, shadowing, and hidden terminal problems, which can effectively enhance the sensing performance and protect licensed users from harmful interference. However, for a large number of sensing nodes that need high bandwidth of the control channel for data transmitting, CSS increases cooperative overhead. To address this problem, we investigated the soft decision fusion strategy under a limited bandwidth of the control channel and proposed a simple quantization-based multibit data soft fusion rule for CSS for its simple structure and easily implementation. Under the quantization-based sensing strategy, each cooperative secondary user (SU) adopts an energy detector for local spectrum sensing. Each SU transmits quantized multibit data that sends local sensing information, instead of forwarding local one-bit hard decision results or original observation statistics, to the fusion center (FC). Furthermore, the closed-form expressions of the quantization levels and the quantization thresholds are analytically derived. Simulation results indicate that the detection performance of the proposed method approaches that of the conventional soft fusion rule with less cooperative overhead and outperforms the hard decision rules. Extensive simulations also show that multibit quantization fusion achieves a desirable tradeoff between the sensing performance and the control channel overhead for CSS.


Introduction
Cognitive radio is a promising technology to solve the problem of spectrum resource scarcity and improves the efficiency of spectrum utilization. In cognitive radio networks (CRNs), secondary users (SUs) can opportunistically access the specific spectrum channel that is assigned to primary users (PUs) for data transmission [1]. This process requires accurate and reliable spectrum sensing at SUs before the SUs start to communicate. More precisely, spectrum sensing technology plays a key role in identifying which portion of the licensed channels is available for SUs. Therefore, spectrum sensing has been attracting significant interest in the context of CRNs in recent years.
In the spectrum sensing process, various transmission impairments of the sensing channels (i.e., the wireless channels between the PUs and the SUs), such as severe fading, shadowing, and hidden terminal problems, have a crucial impact on the system's detection performance [2]. Thus, the detection performance of local single-user sensing is limited and may not be reliable. In order to enhance the above investigate quantized soft data combing, they are still not tractable enough to be used as a cost function for parameter optimization. The computational complexity of such a scheme is high. The closed-form expressions of the quantization thresholds are not given. Therefore, an efficient and simple quantization-based multibit data fusion scheme is indispensable for CSS in CRNs.
In this paper, a simple quantization-based multibit data soft fusion rule for CSS is presented to achieve a desirable tradeoff between sensing performance and control channel overhead. Under this scheme, each local SU adopts an energy detector to estimate the energy of received signal during a sensing interval. This energy value is compared with a pair of quantization thresholds and then produces multibit data. The FC collects quantized multibit data from all SUs and performs inverse quantization based on the received data of each SU. A global test statistic, namely, the sum of the inverse quantization values, is constructed at the FC to decide whether a PU signal is present or absent. The main contributions of this paper are concluded as follows.
(1) We propose a simple quantizer design scheme. From the global false alarm probability at the FC perspective, we first determine the center quantization thresholds at each secondary user according to Neyman-Pearson criteria. This scheme is different from the scheme proposed in [17]. Meantime, we establish the "3σ" rule to design the quantization interval, and closed-form expressions of the quantization levels and thresholds are derived. Compared to the suboptimal linear-quantization multibit combining (SLMC) scheme in [24], which employs a numerical search algorithm to find the optimal quantization interval, we provide a computationally affordable method to determine quantization parameters.
(2) We also analyze the detection performance of CSS based on the soft fusion rule (equal gain combining) and the hard decision rule, and investigate the tradeoff between control channel overhead and sensing performance under the proposed scheme. Furthermore, the effects of the number of cooperative SUs, the number of quantization bits, and the number of samples for local sensing on detection performance are examined. Simulation results may be useful to determine parameters to meet the required performance in a practical CSS system. (3) Lastly, extensive numerical simulation experiments are performed to demonstrate the proposed quantization fusion rule and compare it with soft fusion, hard decision, the SLMC [24] scheme, and semi-soft [12] fusion rules. Overall, the proposed quantization scheme achieves a desirable tradeoff between the sensing performance and the control channel overhead, with low computational complexity.
The rest of the paper is organized as follows. The system model and detection problem is formulated in Section 2. The proposed simple quantization-based multibit data fusion scheme as the associated procedure of the algorithm is given in Section 3. Numerical simulation results under different scenarios are presented in Section 4. Finally, the main conclusions are summarized in Section 5.

The System Model and Problem Formulation
We consider a CSS system in CRNs, including a PU, M spatially distributed SUs, and an FC. Specifically, each SU performs local spectrum sensing. Due to the control channel bandwidth and energy supply limitations, the local sensing results from SUs have to be quantized before transmitting them to the FC. Assume that the control channel is error-free, this is reasonable by using an efficient channel coding mechanism to mitigate the noise and interference in the reporting phase. Let the null hypothesis (H 0 ) and the alternative hypothesis (H 1 ) denote that a PU signal is absent and present, respectively. Figure 1 shows the basic structure of a quantization-based CSS system.  Figure 1. The structure of quantization-based cooperative spectrum sensing (CSS) system with M secondary users (SUs) and a fusion center (FC).
According to the structure model given in Figure 1, the detection problem can be described as follows. Whether a PU signal is present or not is decided by combining M independent, individual local sensing nodes quantized data at the FC, and a global test statistic is constructed for making a final decision on the presence/absence of the PU signal by a certain fusion rule under a global false alarm probability constraint.

Local Spectrum Sensing
Spectrum sensing can be formulated as the following binary hypothesis testing problem [25]: where xi(n) denotes the i-th SU received signal sample at time instant n, s(n) is the primary signal with a received power of  2 s (the effect of fading can be absorbed in  2 s ), wi(n) represents the i-th SU additive white Gaussian noise (AWGN) at time instant n with zero mean and known variance  2 i . Furthermore, assume that the noise wi(n) and primary transmitted signal s(n) are independent of each other.
The energy detector is used for the local sensing due to its low complexity and needing no a priori knowledge about the PU signal. The i-th SU received energy Ti over the N samples is given as when N is large enough, using the central limit theorem (CLT), the test statistics Ti follows an asymptotically Gaussian distribution with mean and variance as [26]  where  ( , ) N is a normal distribution with mean u and variance  ,  i is the SNR, and is the variance of the PU signal.

Local Hard Decision Fusion
In the hard decision fusion, each SU after a specific sensing interval then makes a binary decision independently about the presence or absence of a PU signal. Each i-th SU sends its one-bit decision di to the FC via a common control channel, where The FC combines local decision results from all cooperative SUs by a certain fusion rule for making a final decision. The general form of the hard fusion rule can be expressed as According to the structure model given in Figure 1, the detection problem can be described as follows. Whether a PU signal is present or not is decided by combining M independent, individual local sensing nodes quantized data at the FC, and a global test statistic is constructed for making a final decision on the presence/absence of the PU signal by a certain fusion rule under a global false alarm probability constraint.

Local Spectrum Sensing
Spectrum sensing can be formulated as the following binary hypothesis testing problem [25]: where x i (n) denotes the i-th SU received signal sample at time instant n, s(n) is the primary signal with a received power of σ 2 s (the effect of fading can be absorbed in σ 2 s ), w i (n) represents the i-th SU additive white Gaussian noise (AWGN) at time instant n with zero mean and known variance σ 2 i . Furthermore, assume that the noise w i (n) and primary transmitted signal s(n) are independent of each other.
The energy detector is used for the local sensing due to its low complexity and needing no a priori knowledge about the PU signal. The i-th SU received energy T i over the N samples is given as when N is large enough, using the central limit theorem (CLT), the test statistics T i follows an asymptotically Gaussian distribution with mean and variance as [26] where N(µ, σ) is a normal distribution with mean u and variance σ, γ i is the SNR, and γ i = σ 2 s /σ 2 i , σ 2 s is the variance of the PU signal.

Local Hard Decision Fusion
In the hard decision fusion, each SU after a specific sensing interval then makes a binary decision independently about the presence or absence of a PU signal. Each i-th SU sends its one-bit decision d i to the FC via a common control channel, where The FC combines local decision results from all cooperative SUs by a certain fusion rule for making a final decision. The general form of the hard fusion rule can be expressed as In Equation (5), the fusion rule is OR-logic when K = 1, AND-logic when K = M, and MAJORITY-logic when K > M/2 . The global probability of detection Q d and global probability of false alarm Q f for AND, OR, and K-out-of-M (KM) rules are given as follows:

Soft Decision Fusion
In soft decision fusion, every cooperative sensing node sends its complete test statistics to the FC. The statistics from all cooperative nodes are then constructed via a global test statistic by the soft fusion rule. The soft fusion rule can be adopted as equal gain combining (EGC), maximal ratio combining (MRC), and the optimal likelihood ratio test (LRT) [27]. In this paper, FC compares the sum of all cooperative nodes test statistics with a predefined decision threshold. The global probability of detection Q d and the probability of false alarm Q f using the EGC fusion rule at the FC is given as where M is the number of cooperative nodes, λ c is the predefined decision threshold in FC, Q(x) is the Q-function, and Q(x) is given as Figure 2 shows the global probability of detection versus the global probability of false alarm of the hard OR and AND fusion rules and the soft (EGC) fusion rule. The detection performances of these rules were evaluated. Ten thousand independent Monte Carlo simulation trials verified the theoretical results. Assume that all nodes have an SNR of −12 dB, the number of cooperative SUs M is 6, and the samples N is 400. We observed that the soft fusion rule achieved a higher detection probability than either of the hard fusion rules, and that the detection probability of the hard OR rule outperformed AND rule. Meanwhile, the theoretical results are well matched with the simulation results.

q-Bit Quantizer
In this work, the computed local test statistics Ti has to be quantized before it is sent to the FC. The FC combines these quantized versions of Ti using the EGC fusion rule to make the final decision. Generally, each SU adopts a q-bit quantizer, the test statistics Ti is compared with a set of and  i denote the quantization levels and quantization interval at each SU. The quantization rule is given as In Equation (15) and  , ik denote the (k − 1)-th and k-th quantization boundaries at SU i, respectively. Figure 3 shows the proposed q-bit quantizer. Figure 3. Proposed q-bit quantizer.

Multibit Combining and Decision Making
Under the multibit cooperative detection scheme, the quantization interval and thresholds should be determined firstly. Since the probability density function (PDF) of the energy test statistics Ti is available for each sensing node, we designed a "  3 " rule to determine the quantization interval  i , which can be calculated as

q-Bit Quantizer
In this work, the computed local test statistics T i has to be quantized before it is sent to the FC. The FC combines these quantized versions of T i using the EGC fusion rule to make the final decision. Generally, each SU adopts a q-bit quantizer, the test statistics T i is compared with a set of quantization and ∆ i denote the quantization levels and quantization interval at each SU. The quantization rule is given as In Equation (15), ψ i (•) represents the quantization process at SU i, and d i ∈ {0, 1} q denotes a binary codeword. λ i,k−1 and λ i,k denote the (k − 1)-th and k-th quantization boundaries at SU i, respectively. Figure 3 shows the proposed q-bit quantizer.

q-Bit Quantizer
In this work, the computed local test statistics Ti has to be quantized before it is sent to the FC. The FC combines these quantized versions of Ti using the EGC fusion rule to make the final decision. Generally, each SU adopts a q-bit quantizer, the test statistics Ti is compared with a set of and  i denote the quantization levels and quantization interval at each SU. The quantization rule is given as In Equation (15) and  , ik denote the (k − 1)-th and k-th quantization boundaries at SU i, respectively. Figure 3 shows the proposed q-bit quantizer. Figure 3. Proposed q-bit quantizer.

Multibit Combining and Decision Making
Under the multibit cooperative detection scheme, the quantization interval and thresholds should be determined firstly. Since the probability density function (PDF) of the energy test statistics Ti is available for each sensing node, we designed a "  3 " rule to determine the quantization interval  i , which can be calculated as

Multibit Combining and Decision Making
Under the multibit cooperative detection scheme, the quantization interval and thresholds should be determined firstly. Since the probability density function (PDF) of the energy test statistics T i is available for each sensing node, we designed a "3σ" rule to determine the quantization interval ∆ i , which can be calculated as where After ∆ i is determined, the quantization energy levels E i,k 2 q k=1 and thresholds λ i,k 2 q k=0 can be given by In Equations (22) and (23), λ i,2 q /2 is the center threshold of quantization as λ i,2 q /2 = λ c /M, the calculation of λ c is based on Equation (13) according to Neyman-Pearson criterion for a given Q f = α.
The FC collects all cooperative SUs quantized data, and the global test statistic T c is constructed as the sum of the received quantized data. That is, where ψ −1 i (•) represents the inverse of the quantization process at SU i, ψ −1 i (q i ) represents the quantization levels E i,k 2 q k=1 at SU i, which is determined by Equation (22), and T c is compared with a predefined global decision threshold, λ c , which is determined according to Equation (13) to decide whether a PU is present or absent, i.e., The detection performance of the CSS with multibit quantized data is measured by the global detection probability Q d = Pr( T c ≥ λ c |H 1 ) and the global false alarm probability The procedure of the proposed quantization-based multibit data soft fusion scheme consists of three main steps: a sensing request, energy detection, and decision making. When FC broadcasts a spectrum sensing request, the FC obtains the estimation of noise power σ 2 i of each SU, then computes the center quantization threshold and reports it to each SU. After all SUs receive the threshold, each SU performs energy detection and produces multibit data that is transmitted to the FC through the control channel. The FC computes the sum of the inverse quantization vale for final decision making. The procedure of the proposed scheme is summarized in Algorithm 1.

Algorithm 1. Proposed Quantization-Based Multibit Data Fusion Scheme
Sensing request: 1: The FC broadcasts a spectrum sensing request, and each SU reports its noise power σ 2 i to the FC for computing the center threshold of quantization λ i,2 q /2 = λ c /M according to (13). Energy detection: 2: The i-th SU computes its energy T i and quantizes data q i according to Equations (2) and (15) The computational complexity of our proposed algorithm is low. Since the quantization parameters are obtained based on closed-form analytical expressions, it is tractable enough to be used. For identically distributed SU observation statistics, the computational complexity increases linearly in 2 q − 1. For non-identically distributed observation statistics, the complexity increases linearly in M × (2 q − 1).

Simulation Results and Valuations
In this section, simulation results are presented to evaluate the performance of a quantization-based multibit data fusion CSS scheme. Without loss of generality, we assume that the PU signal s(n) is also a Gaussian random process with mean zero and variance σ 2 s as the SNR, and noise variance σ 2 i = σ 2 = 1 for all cooperative SUs. We also consider, as references, the SLMC [24] scheme and the semi-soft fusion rule [12] for ideal control channel environment. The decision statistics of SLMC are given as In the SLMC fusion rule, u i ∈ {0, 1, . . . , 2 q − 1}, the decision threshold λ u at FC is selected in {0, 1, . . . , M(2 q − 1)}, which is a positive integer.

Detection Performance
Firstly, we evaluate the detection performance of the proposed quantization-based soft fusion rule. We set parameters such that M = 6 total cooperative SUs, each SU received samples is N = 400 at a certain sensing interval, and the SNR is −12 dB for all SUs. Figure 4 presents the ROC curves of the proposed multibit quantization detector with the hard OR and AND fusion rules, the soft fusion (EGC) rule, the SLMC fusion scheme, and the semi-soft fusion scheme. The detection probability of the 3-bit quantization-based soft fusion rule outperforms the SLMC fusion rule, the semi-soft fusion rule, and the hard fusion rules. Meanwhile, compared to the soft (EGC) fusion rule, the performance loss of the proposed scheme is negligible. To further evaluate the effect number of quantization bits on detection performance, the results in terms of the probability of detection for different quantization bits are given in Figure 5. We also found that the performance gain saturates when quantization bits are greater than 4. In particular, the detection performance of 4-, 5-or 6-bit quantization-based soft fusion rules is comparable to the soft fusion (EGC) rule without quantization. However, in practice, the number of quantization bits selected depends on the tradeoff between the available resource and the system's required performance. For instance, the 2-bit and 3-bit quantization detector achieves a probability of detection of about 0.7 and 0.8 with less cooperative overhead, respectively, when the probability of false alarm is fixed at 0.1.   We also verify the performance of the proposed quantization-based multibit soft fusion scheme with different values of quantization bits q and different values for global probability of false alarm  , where we opt q = 2, 4, 6, and  = 0.1, 0.01, 0.001. From Figure 6, it can be observed that 4-bit and 6-bit quantization-based soft fusion rules achieve comparable detection performance for each value of  , but outperform those achieved by 2-bit quantization-based soft fusion. Furthermore, for a given SNR that is less than −8 dB, the probability of detection is improved by increasing the probability of false alarm and the number of quantization bits.   We also verify the performance of the proposed quantization-based multibit soft fusion scheme with different values of quantization bits q and different values for global probability of false alarm  , where we opt q = 2, 4, 6, and  = 0.1, 0.01, 0.001. From Figure 6, it can be observed that 4-bit and 6-bit quantization-based soft fusion rules achieve comparable detection performance for each value of  , but outperform those achieved by 2-bit quantization-based soft fusion. Furthermore, for a given SNR that is less than −8 dB, the probability of detection is improved by increasing the probability of false alarm and the number of quantization bits. We also verify the performance of the proposed quantization-based multibit soft fusion scheme with different values of quantization bits q and different values for global probability of false alarm α, where we opt q = 2, 4, 6, and α = 0.1, 0.01, 0.001. From Figure 6, it can be observed that 4-bit and 6-bit quantization-based soft fusion rules achieve comparable detection performance for each value of α, but outperform those achieved by 2-bit quantization-based soft fusion. Furthermore, for a given SNR that is less than −8 dB, the probability of detection is improved by increasing the probability of false alarm and the number of quantization bits.

Detection Probability versus the Number of Samples
In general, increasing the samples of the received signal improves the spectrum sensing detector's performance. Unfortunately, increasing the sensing interval will increase delay in spectrum sensing and lead to a loss in opportunities for spectrum access. Figure 7 shows the detection probability versus the SNR under various numbers of samples for the proposed 2-bit quantization fusion rule. Figure 7 shows that the detection probability is improved when the number of samples increases from 40 to 80 and from 80 to 120. It is also clear that this is true for the soft (EGC) fusion rule. For instance, given SNR = −6 dB, M = 4, and Qf = 0.05, if the required detection probability is 0.8, we can select an N of at least 80.  Figure 8 shows that the 5-bit quantization-based soft fusion rule achieves a performance comparable to the soft (EGC) fusion rule with various numbers of samples. For a fixed N, increasing quantization bits q of each cooperative SU can enhance the probability of detection. We also found that the performance gain of the proposed fusion rule is relatively higher between quantization bits q = 2 and 3 than the quantization bits q = 3 and 5, respectively. For example, if the required detection probability is more than 0.9, based on Figure 8, we can determine the required number of samples to meet the desired detection probability under SNR = −8 and −16 dB, respectively. In order to meet the detection probability Qd = 0.9, for −8 dB, the proposed quantization fusion rule requires the number of samples to be approximately 230, 200, and 150 with quantization bits q = 2, 3, and 5, respectively. Similarly, for −16 dB, quantization bits q = 2, 3, and 5 require the number of samples to be about 7600, 6000, and 5200, respectively. Therefore, at low SNR conditions, more bits and a large number of samples are required to further improve detection performance.

Detection Probability versus the Number of Samples
In general, increasing the samples of the received signal improves the spectrum sensing detector's performance. Unfortunately, increasing the sensing interval will increase delay in spectrum sensing and lead to a loss in opportunities for spectrum access. Figure 7 shows the detection probability versus the SNR under various numbers of samples for the proposed 2-bit quantization fusion rule. Figure 7 shows that the detection probability is improved when the number of samples increases from 40 to 80 and from 80 to 120. It is also clear that this is true for the soft (EGC) fusion rule. For instance, given SNR = −6 dB, M = 4, and Q f = 0.05, if the required detection probability is 0.8, we can select an N of at least 80.

Detection Probability versus the Number of Samples
In general, increasing the samples of the received signal improves the spectrum sensing detector's performance. Unfortunately, increasing the sensing interval will increase delay in spectrum sensing and lead to a loss in opportunities for spectrum access. Figure 7 shows the detection probability versus the SNR under various numbers of samples for the proposed 2-bit quantization fusion rule. Figure 7 shows that the detection probability is improved when the number of samples increases from 40 to 80 and from 80 to 120. It is also clear that this is true for the soft (EGC) fusion rule. For instance, given SNR = −6 dB, M = 4, and Qf = 0.05, if the required detection probability is 0.8, we can select an N of at least 80.  Figure 8 shows that the 5-bit quantization-based soft fusion rule achieves a performance comparable to the soft (EGC) fusion rule with various numbers of samples. For a fixed N, increasing quantization bits q of each cooperative SU can enhance the probability of detection. We also found that the performance gain of the proposed fusion rule is relatively higher between quantization bits q = 2 and 3 than the quantization bits q = 3 and 5, respectively. For example, if the required detection probability is more than 0.9, based on Figure 8, we can determine the required number of samples to meet the desired detection probability under SNR = −8 and −16 dB, respectively. In order to meet the detection probability Qd = 0.9, for −8 dB, the proposed quantization fusion rule requires the number of samples to be approximately 230, 200, and 150 with quantization bits q = 2, 3, and 5, respectively. Similarly, for −16 dB, quantization bits q = 2, 3, and 5 require the number of samples to be about 7600, 6000, and 5200, respectively. Therefore, at low SNR conditions, more bits and a large number of samples are required to further improve detection performance.   Figure 8 shows that the 5-bit quantization-based soft fusion rule achieves a performance comparable to the soft (EGC) fusion rule with various numbers of samples. For a fixed N, increasing quantization bits q of each cooperative SU can enhance the probability of detection. We also found that the performance gain of the proposed fusion rule is relatively higher between quantization bits q = 2 and 3 than the quantization bits q = 3 and 5, respectively. For example, if the required detection probability is more than 0.9, based on Figure 8, we can determine the required number of samples to meet the desired detection probability under SNR = −8 and −16 dB, respectively. In order to meet the detection probability Q d = 0.9, for −8 dB, the proposed quantization fusion rule requires the number of samples to be approximately 230, 200, and 150 with quantization bits q = 2, 3, and 5, respectively. Similarly, for −16 dB, quantization bits q = 2, 3, and 5 require the number of samples to be about 7600, 6000, and 5200, respectively. Therefore, at low SNR conditions, more bits and a large number of samples are required to further improve detection performance.

Detection Probability versus the Number of Cooperative SUs
To further evaluate the detection performance of the proposed fusion rule, Figure 9 shows the probability of detection versus the SNR for various M with 3-bit quantization. It is shown that the detection probability increases by increasing the number of cooperative SUs. It is also clear that, when SNR is greater than −10 dB, the probability of the detection gain is high between M = 2, M = 4, and M = 6 cases of the proposed fusion rule. However, the detection probability gain is relatively low between the M = 8 and M = 10 cases of the proposed fusion rule. For instance, if we require a detection probability Qd of 0.8 at an SNR of −6 dB, the required number of cooperative SUs is no less than 8 for 3-bit quantization.  Figure 10 shows the detection probability in terms of the number of cooperative SUs varying from 2 to 10, where q = 2, 3, and 5, and SNR = −12 dB. It is shown that the detection performance is improved by increasing the number of quantization bits and cooperative SUs. Under certain q and SNR values, we can use the obtained curve to determine the number of cooperative SUs for a required sensing performance. For instance, to meet the required detection probability Qd = 0.9 at SNR = −12 dB, the required cooperative SUs M is 14, 13, and 12 in cases of the proposed quantization fusion rule where quantization bits q = 2, 3, and 5, respectively. The results presented in Figure 10 also show that the performance gain between 2-bit, 3-bit, and 5-bit cases of the proposed quantization-based multibit data soft fusion rule can be negligible when the number of cooperative SUs is more than 14. It is also clear that we can increase the number of cooperative SUs M or quantization bits q to meet the required detection probability.

Detection Probability versus the Number of Cooperative SUs
To further evaluate the detection performance of the proposed fusion rule, Figure 9 shows the probability of detection versus the SNR for various M with 3-bit quantization. It is shown that the detection probability increases by increasing the number of cooperative SUs. It is also clear that, when SNR is greater than −10 dB, the probability of the detection gain is high between M = 2, M = 4, and M = 6 cases of the proposed fusion rule. However, the detection probability gain is relatively low between the M = 8 and M = 10 cases of the proposed fusion rule. For instance, if we require a detection probability Q d of 0.8 at an SNR of −6 dB, the required number of cooperative SUs is no less than 8 for 3-bit quantization.

Detection Probability versus the Number of Cooperative SUs
To further evaluate the detection performance of the proposed fusion rule, Figure 9 shows the probability of detection versus the SNR for various M with 3-bit quantization. It is shown that the detection probability increases by increasing the number of cooperative SUs. It is also clear that, when SNR is greater than −10 dB, the probability of the detection gain is high between M = 2, M = 4, and M = 6 cases of the proposed fusion rule. However, the detection probability gain is relatively low between the M = 8 and M = 10 cases of the proposed fusion rule. For instance, if we require a detection probability Qd of 0.8 at an SNR of −6 dB, the required number of cooperative SUs is no less than 8 for 3-bit quantization.  Figure 10 shows the detection probability in terms of the number of cooperative SUs varying from 2 to 10, where q = 2, 3, and 5, and SNR = −12 dB. It is shown that the detection performance is improved by increasing the number of quantization bits and cooperative SUs. Under certain q and SNR values, we can use the obtained curve to determine the number of cooperative SUs for a required sensing performance. For instance, to meet the required detection probability Qd = 0.9 at SNR = −12 dB, the required cooperative SUs M is 14, 13, and 12 in cases of the proposed quantization fusion rule where quantization bits q = 2, 3, and 5, respectively. The results presented in Figure 10 also show that the performance gain between 2-bit, 3-bit, and 5-bit cases of the proposed quantization-based multibit data soft fusion rule can be negligible when the number of cooperative SUs is more than 14. It is also clear that we can increase the number of cooperative SUs M or quantization bits q to meet the required detection probability.  Figure 10 shows the detection probability in terms of the number of cooperative SUs varying from 2 to 10, where q = 2, 3, and 5, and SNR = −12 dB. It is shown that the detection performance is improved by increasing the number of quantization bits and cooperative SUs. Under certain q and SNR values, we can use the obtained curve to determine the number of cooperative SUs for a required sensing performance. For instance, to meet the required detection probability Q d = 0.9 at SNR = −12 dB, the required cooperative SUs M is 14, 13, and 12 in cases of the proposed quantization fusion rule where quantization bits q = 2, 3, and 5, respectively. The results presented in Figure 10 also show that the performance gain between 2-bit, 3-bit, and 5-bit cases of the proposed quantization-based multibit data soft fusion rule can be negligible when the number of cooperative SUs is more than 14. It is also clear that we can increase the number of cooperative SUs M or quantization bits q to meet the required detection probability.  The sensing performance with a different number of cooperative SUs, M, is shown in Figure 11 for quantization bits q = 2, 4, and 6. When the number of cooperative SUs is relatively high, the performance gain improves slightly by increasing the quantization bits q. Hence, diversity information among different cooperative SUs further improves detection performance.

Conclusions
In this paper, we propose a simple quantization-based multibit data fusion scheme for CSS in CRNs. Compared with the hard decision rule (which reports one-bit data to the FC) and the soft fusion rule (which reports observed original statistics to the FC), under our scheme, each SU only reports q-bits quantized data to the FC. From the perspective of global false alarm probability at the FC, we determined the center quantization threshold according to the Neyman-Pearson criterion. Meantime, we establish the "  3 " rule to design the quantization interval. The closed-form expressions of quantization levels and quantization thresholds were derived. We also investigated the impact of the number of quantization bits, the SNR, the number of samples, and the number of cooperative SUs on the sensing performance. Extensive numerical simulation results were used to evaluate the proposed quantization fusion rule in comparison with hard decision, soft fusion, SLMC fusion, and semi-soft fusion rules. Simulation results demonstrated that the proposed fusion rule achieved better performance with low computational complexity, and a desirable tradeoff between the detection performance and the control channel's communication overhead. In our future work, spectrum sensing data falsification, also known as byzantine attack [28], will be involved in the proposed quantization-based multibit data fusion scheme. The sensing performance with a different number of cooperative SUs, M, is shown in Figure 11 for quantization bits q = 2, 4, and 6. When the number of cooperative SUs is relatively high, the performance gain improves slightly by increasing the quantization bits q. Hence, diversity information among different cooperative SUs further improves detection performance.  The sensing performance with a different number of cooperative SUs, M, is shown in Figure 11 for quantization bits q = 2, 4, and 6. When the number of cooperative SUs is relatively high, the performance gain improves slightly by increasing the quantization bits q. Hence, diversity information among different cooperative SUs further improves detection performance.

Conclusions
In this paper, we propose a simple quantization-based multibit data fusion scheme for CSS in CRNs. Compared with the hard decision rule (which reports one-bit data to the FC) and the soft fusion rule (which reports observed original statistics to the FC), under our scheme, each SU only reports q-bits quantized data to the FC. From the perspective of global false alarm probability at the FC, we determined the center quantization threshold according to the Neyman-Pearson criterion. Meantime, we establish the "  3 " rule to design the quantization interval. The closed-form expressions of quantization levels and quantization thresholds were derived. We also investigated the impact of the number of quantization bits, the SNR, the number of samples, and the number of cooperative SUs on the sensing performance. Extensive numerical simulation results were used to evaluate the proposed quantization fusion rule in comparison with hard decision, soft fusion, SLMC fusion, and semi-soft fusion rules. Simulation results demonstrated that the proposed fusion rule achieved better performance with low computational complexity, and a desirable tradeoff between the detection performance and the control channel's communication overhead. In our future work, spectrum sensing data falsification, also known as byzantine attack [28], will be involved in the proposed quantization-based multibit data fusion scheme.

Conclusions
In this paper, we propose a simple quantization-based multibit data fusion scheme for CSS in CRNs. Compared with the hard decision rule (which reports one-bit data to the FC) and the soft fusion rule (which reports observed original statistics to the FC), under our scheme, each SU only reports q-bits quantized data to the FC. From the perspective of global false alarm probability at the FC, we determined the center quantization threshold according to the Neyman-Pearson criterion. Meantime, we establish the "3σ" rule to design the quantization interval. The closed-form expressions of quantization levels and quantization thresholds were derived. We also investigated the impact of the number of quantization bits, the SNR, the number of samples, and the number of cooperative SUs on the sensing performance. Extensive numerical simulation results were used to evaluate the proposed quantization fusion rule in comparison with hard decision, soft fusion, SLMC fusion, and semi-soft fusion rules. Simulation results demonstrated that the proposed fusion rule achieved better performance with low computational complexity, and a desirable tradeoff between the detection performance and the control channel's communication overhead. In our future work, spectrum sensing data falsification, also known as byzantine attack [28], will be involved in the proposed quantization-based multibit data fusion scheme.