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In order to avoid the undesired interference with the activities of the primary users in cognitive radio networks, the secondary users are required to be able to predict the behavior of the primary users so as to leave the channel before the arrival of such licensed owner of the spectrum. While a number of existing literatures on cognitive radio spectrum prediction employ the use of propagation curves for predicting the spectrum holes otherwise known as TV white space, these models are built based on measurements conducted in regions that are different from Nigeria, suitability in terms of usage may therefore vary due to environmental factors and terrain profile. This work evaluates the efficacy of the developed model in predicting the cognitive spectrum availability in Nigeria. Models capable of predicting spectrum occupancy in the time domain using discrete-time two-state Markov chain with an appropriate Duty Cycle (DC) model and also a modified m-bell shaped exponential equation were formulated. The result obtained in all cases considered shows that the formulated models are appropriate to be used in any environment if the parameters were carefully extracted from the data. This work has also demonstrated that the accuracy of Markov chain models depends on the level of usage of a spectrum under consideration and may therefore not give desirable results when employed in some other spectrum.

The continuous demand for wireless communication technologies and systems has reached a peak where existing capacity cannot meet increasing demand without means of improving the efficiency of spectrum utilization. The Owned spectrum allocation policy also known as the fixed spectrum allocation policy has led to Spectrum Scarcity [

Pursuant to this, a lot of researches have been carried out in the area of Cognitive Radio Network for Opportunistic Access. This has facilitated digital switchover which has completely taken place in most developed countries while a similar switchover process is still underway or being planned in many other countries around the world. A treaty agreement which mandated the digitization of broadcasting in Europe, Africa, Middle East and the Islamic Republic of Iran by a target date of June 17, 2015 was signed on June 16, 2006 during the Regional Radio Communication Conference (RRC-06) of the International Telecommunication Union (ITU) in Geneva. Nigeria was however among other 52 countries in the continent of Africa that was unable to make the transition from analogue to digital terrestrial broadcasting [

Efforts are now being made to have a digital switchover in other countries such as Nigeria that were unable to meet the previous deadline. When this is eventually done, the quantity of the spectrum available will be needed in order to make effective and efficient use of it. However, models are needed in order to carry out spectrum availability measurements since the behavior and performance of a secondary network depend on the spectrum occupancy patterns of the primary system. A realistic and accurate modeling of such patterns becomes essential and extremely useful in the domain of cognitive radio research [

This work evaluates the efficacy of the developed models in predicting the cognitive spectrum availability in Nigeria. Our contributions are in formulating a model capable of predicting spectrum occupancy in the time domain using an adopted discrete-time two-state Markov chain with an appropriate Duty Cycle (DC) model and also in formulating a deterministic based model using a modified m-bell shaped exponential equation. The performance of the proposed models was evaluated using throughput as metric and by performing Kolmogorov Smirnov test. The details of the proposed models evaluation are also presented in this paper.

The rest of this paper is arranged as follows; In Section 2, we present reviews of related works. We describe the methodology that was employed in formulating our proposed model, in Section 3, we also give the details of the performance metric used in the same section. In Section 4, we present the results obtained using the models formulated and also present our evaluation results while Section 5 offers conclusions and discusses areas for future work.

Cognitive radio spectrum management is very important as a key technology for future wireless communications and mobile computing, it is not surprising that a lot of literatures exists on Cognitive Radio Network (CRN). In this section, we review some of the literatures relevant to this work.

Predictive models can be classified into either deterministic or stochastic models. Both of which are used in predicting the cognitive radio spectrum availability depending on the traffic pattern. A deterministic model defines an exact relationship between variables, and the output is fully determined by the parameter values and the initial conditions. The system properties and the input are perfectly known [

Spectrum occupancy modeling is widely known to be the process of extracting information about the state of a spectrum (busy or idle) at a particular time. Once the busy/idle information has been extracted from the captured measurement data, it can be used for the development of spectrum occupancy models. Spectrum occupancy models are models that aids predicting the future state of a spectrum, such state can either be busy or idle. Determining the spectrum usage of the PUs however is by no means straightforward [

According to the work in [

The authors in [

The work in [

In [

In another relevant work, modeling and characterization of unused part of the spectrum known as white spaces for underlay cognitive radio networks was considered [

This work assumed the spectrum usage ON/OFF (busy and idle) periods to be independently distributed from each other and the sampling interval to be greater than the Primary User’s (PU) ON/OFF times represented with “1” and “0” respectively which were formulated from the estimated duty cycle of each spectrum considered. Traffic patterns were obtained from the spectrum usage features exhibit by the PU of the spectrums considered. The traffic patterns obtained were simply represented as case 1, case 2, case 3 and case 4 in this paper.

Case 1 shown in

The experimental design approach adopted in this work involves using the present behavior of the primary users to predict their future behavior. This adopted approach has been used in several existing works as found in [

Secondary Users (unlicensed users) are not allowed to make use of a channel unless such a channel is idle. Our proposed model is a modification of the approach in [

Looking at the pattern, a model developed for such a pattern will be used for

the idle time prediction. The idle time prediction subsystem predicts the next idle period of the channel. Given the present state of the channel as idle with some set of constraints, the system is capable of predicting how long the channel will remain in an idle state. The time comparator flag compares the PU’s predicted state holding time, say t_{p} (which is the total time the PU is expected to be absent) with the total time needed by the SU to transmit, say t_{c}. If t_{c} < t_{p}, the SU is expected to complete its transmission before the arrival of the PU and data transmission follows, else the SU is expected to switch channel and return to find another free channel.

This work focuses on the transition processes from channel history to idle time prediction. Channel sensing and channel switching were therefore not considered. As discussed previously, the traffic patterns were derived from the channel history as a function of the duty cycle. The considered deterministic patterns were then used to predict the future states of the spectrum. The details of the discrete-time two-state Markov chain with appropriate Duty Cycle (DC) models adopted in this work has been presented in our previous work [

Some traffic patterns possess bell curve shapes leading to formulation of a bell shaped exponential equation [

The bell shaped exponential equation is represented as [

Ψ ( t ) ≈ Ψ min + ∑ m = 0 M − 1 A m e − ( ( t − T m ) 2 ) σ m 2 (3.1)

where;

Ψ ( t ) is the duty cycle at time t, Ψ min is the minimum duty cycle that can be found on the traffic pattern, M is the total number of bells found on the traffic pattern, m is the bell index, A_{m}_{ }is Amplitude at bell m, T_{m} is the period at bell m and σ m is the standard deviation at bell m.

From

Ψ ( t ) ≈ Ψ min + [ A 0 e − ( t − T 0 ) 2 σ 0 2 + A 1 e − ( t − T 1 ) 2 σ 1 2 + A 2 e − ( t − T 2 ) 2 σ 2 2 ] (3.2)

The performances of the models were evaluated using throughput as a metric. Generated distributions were also evaluated by observing the disparities between each empirical distribution and the corresponding hypothesized distribution using Kolmogorov-Smirnov test.

Throughput is a good performance metric for the cognitive radio system and it is defined as the percentage of time during which a cognitive radio can successfully transmit without colliding with the PU [

by comparing the predicted duty cycle with the empirical duty cycle. The evaluation was done by classifying the differences into three; False Positive, False Negative and Accurate Prediction. An outcome is classified as false positive if the model predicted duty cycle (which is referred to as the probability that a channel is busy) is greater than the actual one, and false negative if otherwise. A prediction is said to be accurate if the predicted duty cycle is the same as the actual one. A prediction that is either false positive or accurate is classified as successful transmission since a collision with the PU in this case will be avoided. A false negative prediction is regarded as unsuccessful transmission since a collision is unavoidable in such cases. The throughput is thus calculated as:

Throughput = No of successful transmission Total No of transmission ∗ 100 (3.3)

Since the prediction accuracy is being tested and not how effective the channel was utilized, a modified Equation (3.3) can be written as;

Throughput = No of Accurate prediction + No of False Positive Total no of Prediction ∗ 100 (3.4)

Kolmogorov Smirnov test can be performed on any given two samples say A and A_{0} with size s_{1} and s_{2} respectively if it is required to test whether such samples come from the same distribution. If the Observed Cumulative Distribution Function (OCDF) of the sample A is A(x) and the OCDF of the sample A_{0} is A_{0}(x), then Kolmogorov-Smirnov test may be an appropriate test to determine whether these two samples come from the same distribution. To, test the hypothesis that A is equal to a particular distribution A_{0}, it is required to decide between these two hypotheses say H_{0} and H_{1} [

H 0 : A = A 0 ; H 1 : A ≠ A 0 (3.5)

Kolmogorov-Smirnov test statistics is given as

D s 1 , s 2 = max x [ | A ( x ) − A 0 ( x ) | ] (3.6)

This according to the author in [_{0}(x). Where D s 1 , s 2 is the least upper bound of all point-wise differences [ | A ( x ) − A 0 ( x ) | ] .

Function KSDIST can be used to determine the p-value of the two-sample Kolmogorov-Smirnov test at x for samples of size say s_{1} and s_{2} and function KSINV can also be used to determine the critical value for significance level p of the two-sample Kolmogorov-Smirnov test for samples of size s_{1} and s_{2} [_{s} can be used to test the hypothesis that a random sample came from a population with a specific distribution function A(x). If

max x | A ( x ) − A 0 ( x ) | ≤ D s , ∝ (3.7)

Then, the sample data is a good fit with A(x). Hypothesis test result on MATLAB simulation tool returns a logical value of either “0” or “1”. Value h = 1 indicates the rejection of the null hypothesis at the alpha significance level while value h = 0 indicates a failure to reject the null hypothesis at the alpha significance level. Asymptotic p-value of the test is returned as a scalar value in the range (0, 1) which is interpreted as the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis.

As an update on our previous work presented in [

The prediction output from the modified m-bell shaped exponential equation and Markov chain model were presented using duty cycle concept. The proposed modified m-bell shaped exponential equation used for case 2 showed a better agreement with the empirical duty cycle.

Most of the channels found in case 1, case 3 and case 4 are channels that are consistently and constantly being used, channels that are always busy or always idle and channels in which primary user resides in one state for a long period of time before switching to another state, making them suitable to be modeled using discrete time two state Markov chain model. Results show that discrete time Markov chain model is appropriate to predict these types of patterns. This may be due to the fact that, prediction using discrete-time Markov chain model depends on the transition probabilities which do not change with sweep time (the duration of time in which the channel is being sampled in order to determine the state of such channel) but with period (the time it requires to make a complete process).

The transition probabilities were computed from the behavior of the primary users in one period thus the transition probability remained constant for every period. For channels that are under consistent and constant usages, channels that are always busy or always idle and channels with primary users of such channels residing in one state for a long period of time before switching to another state, the changes in transition probabilities will be very negligible leading to an accurate prediction from the model. Case 2 however shows few disparities because some of the channels in it are not being consistently used. In such a case, the changes in transition probabilities per sweep time will be slightly different from the transition probabilities per period leading to a less accurate prediction from the model. The results obtained in all cases shows a reasonable agreement with the observation in [

Case 3 and case 4 are special cases of spectrum usage in which the spectrum usage during the weekdays differ from the spectrum usage at weekends. This is inevitable because spectrum usage depends on the habits found in such an environment. For example, in Nigeria, TV and radio transmitter’s broadcasting period on weekdays differ from weekends. These differences can be observed on the traffic patterns of case 3 and case 4. Markov chain model was used to model the usage of the spectrum on weekdays and weekends.

Stochastic distribution models may be used to model spectrums with non-deterministic patterns. Modeling of these cases using stochastic distribution models were not considered in this work. This work however modified the existing bell shaped exponential equation to model the spectrum usage presented in case 2. It was observed that, the bell shaped exponential equation model is accurate and appropriate if carefully modified for modeling any spectrum usage with bell curves characteristics regardless of the environment. In order to adopt such a model in any environment, the input parameters however must also be carefully estimated.

The results obtained were evaluated using throughput and Kolmogorov Smirnov test.

Case | Method | False + (%) | False − (%) | Accurate (%) | Throughput (%) |
---|---|---|---|---|---|

1 | Markov | 41.67 | 16.67 | 41.67 | 83.33 |

2 | Markov | 41.67 | 33.33 | 25.00 | 66.67 |

2 | MBSEM | 0.00 | 4.17 | 95.83 | 95.83 |

3 (Weekdays) | Markov | 4.16667 | 20.8333 | 75 | 79.17 |

3 (Weekends) | Markov | 25 | 8.33333 | 66.6667 | 91.67 |

4 (Weekdays) | Markov | 4.16667 | 4.16667 | 91.6667 | 95.83 |

4 (Weekends) | Markov | 16.6667 | 8.33333 | 75 | 91.67 |

Kolmogorov Smirnov test was also performed so as to determine whether there is significant difference between the empirical distributions and the predicted distributions. The approach discussed in [

For case 1, the D-stat obtained was 0.167, while the D-crit was 0.376. Since 0.167 < 0.376, the result is accepted at significance level of 0.05. This test was also used to evaluate the distributions obtained for case 2, case 3 and case 4. The test returned values for D-stat lesser than D-crit in all cases at significant level of 0.05 signifying a higher level of acceptability of this research outcome. These are depicted in Tables 2-4. Other results obtained using this test can be made available on request.

DC | Case 1 | Markov | F(x) | G(x) | |F(x) − G(x)| |
---|---|---|---|---|---|

0.48 | 2 | 0 | 0.08333 | 0 | 0.083333 |

0.5 | 3 | 1 | 0.20833 | 0.04167 | 0.166667 |

0.52 | 4 | 4 | 0.375 | 0.20833 | 0.166667 |

0.54 | 7 | 8 | 0.66667 | 0.54167 | 0.125 |

0.56 | 3 | 9 | 0.79167 | 0.91667 | 0.125 |

0.58 | 3 | 2 | 0.91667 | 1 | 0.083333 |

0.6 | 2 | 0 | 1 | 1 | 0 |

24 | 24 | D-stat | 0.166667 | ||

D-crit | 0.375595 | ||||

Significant different? | No | ||||

P-value | 0.860764 |

DC | Case 2 | Markov | F(x) | G(x) | F(x) − G(x) |
---|---|---|---|---|---|

0.35 | 3 | 0 | 0.125 | 0 | 0.125 |

0.4 | 6 | 7 | 0.375 | 0.29167 | 0.083333 |

0.45 | 6 | 7 | 0.625 | 0.58333 | 0.041667 |

0.5 | 5 | 9 | 0.83333 | 0.95833 | 0.125 |

0.55 | 4 | 0 | 1 | 0.95833 | 0.041667 |

0.6 | 0 | 1 | 1 | 1 | 0 |

24 | 24 | D-stat | 0.125 | ||

D-crit | 0.375595 | ||||

Significant different? | No | ||||

P-value | 0.986779 |

DC | Case 2 | MBSEM | F(x) | G(x) | F(x) − G(x) |
---|---|---|---|---|---|

0.35 | 3 | 0 | 0.125 | 0 | 0.125 |

0.36 | 0 | 2 | 0.125 | 0.08333 | 0.041667 |

0.37 | 0 | 1 | 0.125 | 0.125 | 0 |

0.38 | 0 | 1 | 0.125 | 0.16667 | 0.041667 |

0.39 | 0 | 4 | 0.125 | 0.33333 | 0.208333 |

0.4 | 6 | 2 | 0.375 | 0.41667 | 0.041667 |

0.42 | 0 | 0 | 0.375 | 0.41667 | 0.041667 |

0.44 | 0 | 2 | 0.375 | 0.5 | 0.125 |

0.45 | 6 | 2 | 0.625 | 0.58333 | 0.041667 |

0.46 | 0 | 2 | 0.625 | 0.66667 | 0.041667 |

0.49 | 0 | 2 | 0.625 | 0.75 | 0.125 |

0.5 | 5 | 2 | 0.83333 | 0.83333 | 0 |

0.52 | 0 | 0 | 0.83333 | 0.83333 | 0 |

0.54 | 0 | 4 | 0.83333 | 1 | 0.166667 |

0.55 | 4 | 0 | 1 | 1 | 0 |

24 | 24 | D-stat | 0.208333 | ||

D-crit | 0.375595 | ||||

Significant different? | No | ||||

P-value | 0.621609 |

Note: DC means Duty Cycle. F(x) is the cumulative percentage of the empirical distribution; G(x) is the cumulative percentage of the distribution obtained using Markov chain model; D-stat is the maximum absolute difference between the two distributions; D-crit is the critical value.

It is hoped that, the results presented in this paper will provide useful information for Nigerian Communications Commission and any other bodies that may be interested in spectrum management in Nigeria and any other country. Furthermore, the models presented in this paper will facilitate spectrum usage with limited interference to the activities of the licensed users of the spectrum. We hope this paper will provide relevant information for future work towards enhancing spectrum usage.

The evaluation was repeated at the significance level of 0.01 with the results showing an agreement between the empirical distributions and the predicted distributions in all cases.

The higher values obtained for p-value signify the degree of validity of the results. As the statistical difference between the empirical distributions and the predicted distributions increases, the p-value reduces.

The p-value of 0.86 was obtained in case1, 0.98 and 0.62 for both instances considered in case 2, 0.99 and 0.86 for case 3 (weekdays and weekends respectively) and 1 and 0.99 for case 4 (weekdays and weekends respectively). This further confirms the reliability of research outcomes documented in this paper.

This paper establishes a predictive model for cognitive radio spectrum availability. This research has produced a discrete time based model that is suitable for predicting the cognitive radio spectrum available in Southwest, Nigeria. The work demonstrated that, though traffic models are not appropriate to be used in the environment other than the ones, they were initially built for Markov chain based models as well as bell shaped exponential equation based models are appropriate to be used in any environment if the parameters were carefully extracted from the data. This work has also demonstrated that, the accuracy of Markov chain models depends on the level of usage of a spectrum under consideration and may therefore not give desirable results when employed in some other spectrum. Bell shaped exponential equation model was also proposed as a more suitable model that will be useful in modeling spectrum that exhibits a bell shaped characteristic.

Future Research AreasNigeria is yet to fully make the digital switchover and it is expected that when the switchover is eventually complete, there will be a large number of spectrums that will be available for use by the unlicensed devices. Since this work expects the Nigerian Communications Commission (NCC) to adopt FCC regulations of avoiding interference with the activities of the licensed devices, it is important for the unlicensed devices to be able to accurately predict the arrival time of the licensed devices so as to leave the band before the arrival of the licensed devices. While this research has adopted the method of formulating the behavior of the licensed devices of the spectrum, this approach is not completely suitable as no system can be implemented in real life with a model that is built based on assumptions. Future research may therefore consider empirical data using a spectrum analyzer to obtain more training data on the behavior of the licensed devices for more accuracy. In which case, the obtained threshold frequency can then be used to determine the presence of the licensed devices.

It is also important to consider patterns other than the deterministic ones considered in this work, while to avoid interference on any channel, an unlicensed device must be able to perform proactive channel switching. Channel switching was also not considered in this work and future research in this area may be a necessity.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Okegbile, S., Oluwaranti, A. and Aina, S. (2018) On Evaluating the Efficacy of Predictive Models for Cognitive Radio Spectrum Availability in Nigeria. Wireless Engineering and Technology, 9, 49-65. https://doi.org/10.4236/wet.2018.93005