Various linear and nonlinear classification algorithms are explored to choose an ML technique that works best in the given problem and, FKNN is found superior. The FKNN in Fig. 3 operates to find the shortest distance between data and evaluate the closest neighbors to the training data pattern. FKNN is more leisurely to implement in finding a solution to the problem. This technique classifies a new test data (feature vector) based on the distance of the new test data from multiple nearby neighbors. The FKNN generalizes the data referring to attributes of training samples, where the given query point finds several training instances closest to the query point. This classification is based on the majority voting to classify the objects. The FKNN is a simple algorithm that operates on the shortest distance of a query instance to the training sample.

For x1 as the sample data and x2 as the data test/testing data. The distance formed (d) using the k-nearest neighbor (KNN) is as

where i is the data variable and P as the dimension of the data.

Proper selection of the KNN parameters depends on the data requirements. A high value k reduces the noise effect but drawing the line between classes becomes blurred. Therefore, the k value is selected after fine-tuning through cross-validation. The KNN classifier that effectively solves the given problem is the FKNN algorithm. The tuning parameters for the FKNN have a total neighbor of two. The distance metric in the FKNN is Euclidean distance. Similarly, the distance weights are equal, and the data standardization option is turned on.

This section shows the design procedure to construct the data set for the ML classifier. The soft energy statistics in Eq. (3) attain suitable sensing samples for a given detection, false alarm, and SNRs as

(5)Pf=Q((β−μ0)(σ02))=Q((β−K)(2K)),

Here Pf is the probability of false alarm, β is the threshold value. μ0 and σ02 are the mean and variance when H0 is true. Similarly, the result of detection probability Pd when the H1 is true is

(6)Pd=Q((β−μ1)(σ12))=Q((β−K(ηj+1))(2K(ηj+1))),

In Eq. (6), μ1 and σ12 are mean and variance for the jth when H1 is true with ηj as the SNRs. The FKNN finds the optimal number of sensing samples in this work using the probability of detection function. Therefore, expressing the detection probability in Eq. (6) in terms of the false alarm probability in the AWGN channel conditions leads to the following [7]

(7)Pd=Q((2Q−1(Pf)−Kηj)(2(ηj+1))).

The Q(.) and Q−1(.) are the complementary and inverse complementary distribution functions of the standard Gaussian. In Eq. (7), to find optimal sensing samples K for a given detection and false alarm probabilities needs the solution of a non-convex function, which is hard to get in real-time. Therefore, the result in Eq. (7) is employed to generate a data set and train the FKNN scheme compared with traditional methods. The trained model is finally used to estimate the value of optimal sensing samples that are employed in the throughput, sensing cost, and soft fusion combination schemes. The feature vector or example of a data point in the dataset is represented with a vector as

(8)x=(ηj,Pf,K,Pd)

This feature vector consists of SNRs ηj, false alarm probability Pf, detection probability Pd, and samples K. The detection probabilities are obtained for the different combinations of the SNRs, false alarms, and several samples to get the dataset. The FKNN model is trained using the (ηj,Pf,Pd) as input and Kj as the output feature. The FKKN estimates the reconfigurable sensing samples for the jth SU as

(9)Kj=FKNN([PfPdηj])

The trained model is used to estimate the optimum sensing sample Kj based on the new values of SNRs, detection and false alarm requirements. A reconfiguration of the sensing parameters such as Kj results in increased throughput and reduce in sensing cost. The channel capacity formula is employed to measure the SUs throughput as

(10)C=∑j=1M(Cj)=∑j=1M(B×log2⁡(1+ηj)).

Here Cj is the channel capacity with channel bandwidth B. The throughput for an SU using Eq. (10) in a time slot T is given by:

(11)H=∑j=1MHj=∑j=1M(Cj×(T−τj)).

In Eq. (11), Hj is the jth user throughput with τj sensing time and (T−τj) as the data transmission duration. The result in Eq. (11) shows the throughput is linear dependent on the data transmission duration with fixed T. Therefore, for a fix T reduction in the sensing duration τj leads to a higher throughput. As τj=Kjfs has the sampling frequency fs as a fixed parameter. Therefore, higher sensing throughput is obtained by lowing the τj through reduced sensing samples Kj. In the non-configurable CRN, the parameter K is fixed, while the suggested re-configurable network estimates the optimum results Kj using the FKNN algorithm and varies based on the sensing environment. The energy spent in sensing is directly proportional to the sensing duration and is represented as

(12)S(i)=∑j=1M(Ej(i)×τj),where, S(i) is the sensing energy consumed by the cooperative users in the ith sensing interval and Ej is the sensing energy spent by the jth user based on the reconfigured sensing samples Kj. The increase in Kj=τj×fs is expected to increase the sensing cost of the system in Eq. (12).

The FC combines soft energy reports of all SUs in the final decision. The famously soft and hard combination schemes used at the FC are the EGC, MGC, and majority voting schemes. The EGC method combines the soft information and assigns equal weight to each SU decision. This result is compared with the numerical set threshold to decide the spectrum as

(13)GEGC(i)={H1:1M∑j=1M(Ej(i)×τj)≥(β)H0:otherwise.

The cooperative detection and false alarm probabilities of the EGC scheme based on its global decision are

(14)Pd_EGC=Pr{1M∑j=1M(Ej(i)×τj)≥(β)|H1},

(15)Pf_EGC=Pr{1M∑j=1M(Ej(i)×τj)≥(β)|H0}.

In the MGC, each received signal branch is multiplied by a weight proportional to the branch gain. The branches with strong signals get amplification while the weak signals are attenuated with these weights. The FC with MGC scheme assigns higher weights to the decision of the SUs with higher SNR and low weights to the SUs with low SNR

(16)GMGC(i)={H1:∑j=1M(wj×(Ej(i)×τj))≥(β)H0:otherwise,where wj=η(j)∑j=1Mη(j). The cooperative detection and false alarm probabilities of the MGC are measured based on the individual sensing reports as

(17)Pd_MGC={∑j=1M(wj×(Ej(i)×τj))≥(β)|H1},

(18)Pf_MGC={∑j=1,M(wj×(Ej(i)×τj))≥(β)|H0}.

A precise flow diagram in Fig. 4 shows the training and testing strategy of the FKNN-based hybrid scheme at the FC.

Case 1 addresses the throughput, energy cost, and error probabilities at different levels of the SNRs and detection probabilities for the SFS and compared with the reconfigured sample estimation of the SFKNN, SDT, and SLR in Figs. 5–10. Fig. 5 exhibits the throughput performance achieved with the SFKNN, SFS, SDT, and SLR schemes. These results confirm that the SFS achieves low channel throughput confronted with the SFKNN, SLR, and SDT at different levels of the SNRs. Also, the results reveal that an increase in the SU SNRs leads to an increase in throughput performance. Likewise, the throughput performance of the SFKNN, SLR, SDT, and SFS in the case of a single user is shown in Fig. 6 at different levels of the detection probabilities. The result in Fig. 6 shows a dominant performance of the SFKNN scheme compared with SFS, SDT, and SLR. The proposed SFKNN results in Figs. 5 and 6 are next followed by the SDT scheme, while the SFS gets the minimum throughput results.

The energy cost relation for the SFKNN, SDT, SLR, and SFS schemes at different levels of the SNRs and detection probability are shown in Figs. 7 and 8. Fig. 7 shows that SFS consumes more sensing energy with a high sensing cost for the SFS as compared with the SFKNN, SDT, and SLR. Similarly, the energy cost function of the SFS, SFKNN, SLR, and SDT in Fig. 8 against the increasing requirement of target detection probabilities proves high energy cost for the SFS compared with the SFKNN, SDT, and SLR.

The energy cost relation in Figs. 7 and 8 show the SNR and detection probability demands to measure the system energy cost. In Fig. 7 energy cost of the system decreases with increasing SNRs demand of the SUs, while in case of the high demand of the PU detection probability the system energy cost increases. To achieve high detection probability, more time is consumed by the SUs in sensing resulting in the high energy cost of the system.

Finally, the error probability results in sensing the PU channel while employing SFS, SFKNN, SDT, and SLR schemes are shown in Figs. 9 and 10. The error probability results in Fig. 9 infer the dominant performance of the SFKNN as compared with SDT, SLR, and SFS-based individual user sensing. An increase in the value of the SNRs and fixed detection probability in Fig. 9 lowers the SFKNN error probability related to the SLR, SFS, and SDT based schemes. Fig. 10 depicts the error probability results for the SFKNN, SLR, SDT, and SFS under fixed SNRs and changing detection probability. Fig. 10 shows that SFKNN has minimum sensing error followed by the SDT and SLR schemes, while the SFS performance is poor due to high sensing error. It is observable that increasing demand for high detection probability and SNRs at the SU leads to reduce error probability of the system.

It is concluded from the results in case 1 that SFKNN has the best sensing performance when individual SU sense the PU activity. The SFKNN effectively finds the optimum number of sensing samples to achieve high throughput, minimum energy cost, and low sensing error. An increase in the sensing time for the FS produces better sensing accuracy with the cost of more sensing energy and reduces the channel throughput.

Case 2 illustrates the error probabilities in the FC decision while employing EGC, MGC, and count combination schemes for global decisions. Here ML techniques such as FKNN and FS-based DT are used to find the optimal sensing samples that further lead to minimum sensing error with lower energy cost and high average throughput. It can be seen from the result in case 2 that the proposed FKNN based combination has improved average throughput with low energy cost and minimum error in sensing the PU channel.

Fig. 11 shows the average throughput of the cooperative SUs against raising SNRs with target detection probability for the FKNN, DT, and FS schemes. This shows a high average throughput accomplishment of the FKNN compared with the DT and FS when target SNRs for the cooperative SUs increases. The proposed scheme is followed by the DT algorithm, while the FS has a low average throughput. Fig. 12 shows the average throughput performance for the proposed FKNN, DT, and FS-based schemes at different levels of the target detection probabilities under fixed SNRs. The results in the figure show that for the demand of improved detection probability of the SUs severe decrease in the average throughput of the DT and FS-based combination schemes is observed. The simple FS scheme has the least average throughput performance at all values of the target detection probabilities.

Figs. 13 and 14 show the comparison of the energy cost of the CSS for the proposed FKNN algorithm, DT, and FS against varying SNRs and target detection probabilities. It is visible from the results in Fig. 13 that the FKNN estimated sensing samples have low energy costs in CSS as compared with the DT and FS for increasing demand of SNRs and fixed detection probabilities. The FKNN results are followed by the DT, while the FS shows a higher energy cost. Fig. 13 shows the high energy cost in CSS by the DT scheme compared with the FS scheme when the SNRs are below −13 dB. The DT scheme in these results dominates the FS scheme as the SNR is allowed to pass −13 dB.

Fig. 14 address the energy cost in CSS against the increasing demand of detection probabilities and fixed SNRs. The result shows that the proposed FKNN algorithm has the minimum energy cost at various detection probabilities. The DT scheme in Fig. 14 shows that to meet the demands of high detection probability for the DT-based CSS, the energy cost increase more compared with the FKNN.

The FKNN is less affected in energy cost for the increasing demands of detection probabilities and SNRs compared with the DT and FS technique.

It can be seen from the results given in Figs. 11–14 that the FKNN based CSS attains high average throughput with minimum energy cost as compared with the DT and FS schemes. To exhibit the cost paid by the proposed scheme in terms of error probabilities, simulation results are illustrated in Figs. 15 and 16. These results are achieved for the MGC, EGC, and count decision schemes, while employing FKNN estimated samples, DT estimated samples and FS techniques. Fig. 15 shows that FKNN based MGC, EGC, and count decisions have the minimum sensing error at all values of the SNRs when the target detection probability is fixed. The MGC with FKNN (MGC-FKNN), EGC with FKNN(EGC-FKNN), and Count with FKNN (Count-FKNN) results are followed by the DT algorithm based on MGC with DT (MGC-DT), EGC with DT (EGC-DT), and Count with DT (Count-DT). The MGC with FS (MGC-FS), EGC with FS (EGC-FS), and Count with FS (Count-FS) are shown to have high sensing errors in detecting PU channels. Similarly, Fig. 16 shows the error probability results against the varying target detection probabilities and fixed SNRs. The EGC-FKNN produces improved detection with minimum sensing error at different levels of the target detection probabilities. The Count-FS, EGC-FS, and MGC-FS schemes have their worst sensing performance with high sensing error in the global decisions. It can be concluded from the results in case 2 that the employment of FKNN for sensing PU channel achieves higher average throughput, low energy cost, and minimum sensing error for the EGC, MGC, and Count decision schemes.