Sage Journals: Discover world-class research

Abstract

Spectrum sensing has gained new aspects with the advent of cognitive radio and opportunistic spectrum access techniques. Spectrum sensing plays a vital role in cognitive radio networks, and its reliability determines the success of transmission. It also enables the spectrum access for unlicensed users, enhancing the spectral utilization. The successful integration of primary users and secondary users requires the secondary users to be capable of efficient sensing and keeping precise track of the primary transmissions. There exists an inherent sensing-throughput trade-off in the time-division multiple access–based hierarchical cognitive radio networks. The sum rates of the cognitive radio networks depend on the sensing performance and can be maximized by reducing the sensing errors. In this work, we investigate the optimal sensing parameters of imperfect sensing for opportunistic spectrum access–based cognitive radio networks. The optimal sensing operating points are analyzed for different sensing durations and known primary user activities. First, the sum rate gain and sum rate loss are presented for the non-cooperative network, in terms of perfect channel sensing, and imperfect channel sensing, with and without optimal sensing pairs. Next, the trade-off between cooperative gain and cooperation overhead is examined for the multiuser cognitive radio networks. The sum rate is derived, using the optimal operating point, to investigate the cooperative sensing trade-off for different number of cooperative users in the multiuser cognitive radio network.

Keywords

Cognitive radio opportunistic spectrum access spectrum sensing sensing-throughput trade-off

Introduction

Cognitive radio (CR) networks have emerged as effective techniques for mitigating the spectrum scarcity and spectrum under-utilization issues in wireless systems.^1,2 The users are divided into a multitiered hierarchy in CR systems, and primary users (PUs) have the priority of spectrum access over the unlicensed, that is, secondary users (SUs).^2,3 The CR technologies allow the SUs to exploit the spectrum holes opportunistically for the transmission of their packets. The coexistence of PUs with SUs is subject to the condition that a certain level of quality-of-service (QoS) is guaranteed to the PUs. Therefore, reliable spectrum sensing is a crucial part of CR networks, as SUs are allowed to access the licensed band only under the constraint that the PU is protected.⁴ The SUs detect the primary transmissions in opportunistic spectrum access (OSA)-based networks through the spectrum sensing performed by one or more nodes.^2,3 If an SU detects a PU activity, then it vacates the channel and switches to another idle channel, or waits if no idle channel is available.^3,4

The techniques used for spectrum sensing include energy detection (ED), cyclo-stationary detection, and matched-filter detection. However, the energy-based ED technique is considered to be the most practical method, as it does not require prior knowledge of the PU signal parameters. A PU signal is detected simply, based on the comparison of the sensed energy with a predefined threshold. The major limitation of the ED scheme is that such a method performs well only in moderate and high signal-to-noise ratio (SNR) scenarios.² Different energy-based approaches such as cooperative sensing, beam forming, and multiple antennas can be used to enhance the sensing performance.^5,6

The sensing parameters (e.g. detection thresholds and sensing durations) and physical layer transmission parameters (e.g. transmission rates and powers) have direct impacts on the performance of CR systems. The opportunistic access for the SUs is determined by the results of spectrum sensing.⁷ The longer time devoted to sensing increases the detection probability, enhancing the overall sensing performance. However, it provides less time for transmission, for the SUs.¹ Hence, there exists an inherent trade-off between the durations of sensing and transmission in the CR networks. The total achievable sum rate of the CR network depends on the sensing performance and can be enhanced by reducing the sensing errors. Moreover, the sum rate degradation due to the imperfect sensing can be reduced significantly using optimal sensing parameters.

The sensing performance of the energy-based approaches can be enhanced significantly by cooperative spectrum sensing (CSS). The cooperation between the multiple SUs mitigates the fading and shadowing effects by exploiting the spatial diversity. The CSS approach not only enhances the detection performance in the fading environments but also alleviates the hidden terminal problem.⁵ In CSS-based schemes, SUs collectively sense the channel, share the sensing results, and detect the PU activity. Common CSS approaches include centralized, decentralized, and relay-assisted schemes. In the centralized cooperative sensing approach, a central identity called the fusion center (FC) collects local sensing results from all the considered SUs and makes a final decision about the availability of the spectrum.⁵ The FC also manages the access policies for the SUs.³ Cooperation between the SUs results in cooperative gain, that is, performance improvement. However, it also incurs cooperation overheads, that is, the extra time needed for the cooperation. Hence, a cooperative sensing trade-off also exists in the multiuser CR networks.

The cognitive radio wireless sensor network (CR-WSN) is a specialized ad hoc network of distributed wireless sensors where CR techniques can be used with the OSA approach. The CR-WSNs consist of spatially distributed energy-constrained, self-configuring wireless sensor nodes with CR capabilities.⁸ However, the resource- and power-constraint problems of the sensor nodes need to be addressed for the implementation of complex detection algorithms in the CR-WSN.⁹ The overlay-based approaches for CR-WSN allow the SUs to transmit through standard orthogonal methods. Hence, such approaches have implementation complexities, due to the energy- and hardware-constraint nodes, for obtaining accurate and timely knowledge about the spectrum holes.⁹ The overlap of SU transmissions with the PU signals in the time, frequency, and space domains in the underlay-based approaches relieves the burden of spectrum sensing.¹⁰ However, such strategies work under the constraint that the interfering effect of the SU transmitters on the PU receivers must be known. The underlay CR approaches can be further distinguished according to the degree of cooperation required between two systems, that is, the PUs and SUs.¹⁰ Importantly, most application areas of the CR-WSN are very critical in terms of the delay and correctness of data. However, sensing errors due to the imperfect sensing cause a long waiting delay, frequent channel switching, and significant performance degradation in the CR-WSNs.⁸ The efficient analyses of optimal sensing operating points, aimed at minimizing the sensing errors, can be useful for such problem areas of CR-WSNs.

Non-orthogonal multiple access (NOMA) has recently emerged as a spectral-efficient multiple access (MA) technique for wireless networks. In NOMA, multiple users are served at the same time and frequency, but are multiplexed based on the power or code domains.¹¹ In the conventional MA if a PU occupies the channel frequently, the orthogonal spectrum allocated to the PU cannot be accessed by the SUs. However, the NOMA technique ensures that both PUs and SUs are served simultaneously without degrading the performance significantly, and it effectively improves the spectral efficiency.¹² In downlink NOMA, for example, when one base station serves two users, the key idea is to allocate higher power to the user with poorer channel conditions and lower power to the user with better channel conditions. Hence, for the user with a better channel condition, that is, with lower power, the other users signal with higher power can be decoded and canceled, and its own desired signal can be decoded without any interference, with an assumption of perfect successive interference cancelation (SIC). For the user with the worse channel, however, the desired signal power is higher than the other users interference, and the desired message can be decoded by considering the interference as noise.¹³ The use of NOMA protocols in CR systems (termed CR-NOMA) improves the spectral efficiency significantly. The cooperative schemes (i.e. with multiple SUs) can be used to exploit the spatial diversity offered by the CR-NOMA system and hence achieve more performance gain.¹²

The previous studies have demonstrated the performance gap between NOMA and conventional MA in CR networks. The integration of cooperative CR networks with NOMA brings out the capability of enhancing the spectral utilization and network reliability. However, the performance analysis of a cooperative CR-NOMA scheme requires high computational complexity. Moreover, many technological problems are associated with the NOMA techniques, in practice. Because the CR-NOMA approach does not require channel sensing, but requires channel quality estimation and power allocation, it is beyond the scope of this article. Instead, we focus on the optimization of channel sensing in cooperative CR networks employing an orthogonal approach. The performance of the orthogonal CR networks with channel sensing can be improved significantly by reducing the sensing errors. The sensing errors can be reduced by incorporating optimal sensing parameters adaptive to the different activities of PU, sensing results, sensing durations, sensing SNRs, and cooperative users.

In the first section of the article, we focus on optimizing the sensing parameters adaptively for different sensing times and known PU activities for the non-cooperative CR network, that is, a single primary link and a single secondary link. We discuss the inherent trade-off between the durations of channel sensing and data transmission for the SUs. The characteristic sensing operation in terms of optimal channel sensing parameters is investigated for different sensing times and PU activities. Moreover, the sum rates for the considered CR network are compared for the three possible cases, that is, perfect channel sensing, imperfect channel sensing with optimal sensing pairs (a pair of false alarm and detection probabilities), and imperfect channel sensing without optimal sensing pairs (the worst case of sensing operation).

In the next section, a multiuser CR network with a cooperative centralized architecture is considered. We investigate the trade-off between the cooperative gain and the incurred cooperation overhead for different number of cooperative SUs. For simplicity, we assume that the cooperative gain is limited to the improved detection performance. Moreover, only the reporting delay (i.e. sharing time) is considered for the cooperation overhead.⁵ The sharing time refers to the extra time needed for sending the local sensing results to the FC and getting the final decision about the availability of the considered channel.⁵ Using the same approach, sensing parameters are optimized in order to maximize the sum rates of both primary and secondary links. The optimal cooperative sensing trade-off for different number of SUs, with a given PU activity, is investigated with the numerical results. Simulation results show that optimal sensing operating points achieve better spectrum sensing performances and hence result in higher sum rates.

The rest of the article is organized as follows. Section “Related work” summarizes the related work. In section “System and signal model,” the system and signal models are described in detail. In section “Sum rate analysis under imperfect sensing,” we formulate the sum rates of the considered networks with the sensing errors due to imperfect sensing. Section “Simulation results and discussion” presents the simulations and discussion. Finally, section “Conclusion and future work” draws the conclusions of this article and presents the future work.

Related work

The emerging CR technology is an intelligent radio technology that enables the efficient utilization of spectrum by allowing the SUs to use the best available channel in their vicinity. There has been an explosion of research related to the CR networks in the recent years. The efficient spectrum access protocols for the OSA-based CR networks have been investigated actively.⁷ However, most of the related literature is based on the performance under the assumption of perfect spectrum sensing, which might be misleading in realistic scenarios. The sensing errors due to imperfect sensing need to be formulated precisely. In addition, most existing CSS strategies focus only on detection improvement, that is, improving the cooperative gain in sensing performance.⁵ The drawback of the CSS approach is that the reporting time increases linearly with the number of cooperative SUs. Only a few proposed CSS schemes have incorporated the cooperation overhead. Darsena et al.¹⁴ proposed an interesting spectrum sharing scheme, referred to as convolutive superposition. The proposed model allowed the SU to transmit multiple symbols in parallel over the orthogonal frequency-division multiplexing (OFDM) subcarriers of the primary system, to improve the data rate. A key feature of the proposed scheme was the improvement in the performance of the PU system with the SU transmission, without any cooperation between the two systems. Lee et al.¹⁵ proposed a dynamic spectrum aggregation approach to maximize the sum rate of the aggregate channel under collision constraints. The proposed model was analyzed in terms of the asynchronous transmission and imperfect spectrum sensing. Yin et al.¹⁶ investigated the joint optimization problem of energy harvesting, spectrum sensing, and data transmission, to maximize the achievable throughput of a single secondary device in an energy harvesting CR network. Althunibat and Granelli¹⁷ proposed an objection-based CSS scheme for CR networks using lesser number of reporting SUs, to maximize the energy efficiency. The proposed models in the above-mentioned research did not consider the performance gain achieved by reducing the sensing errors using optimal sensing operating points for the imperfect sensing scenarios. Unlike these studies, this work focuses on investigating the optimal sensing operating points adaptive to different sensing parameters.

System and signal model

One of the most challenging tasks of CR networks is to perform the channel sensing effectively and efficiently.^1,2 In this work, we consider the ED scheme for the local sensing of SUs in the proposed CR networks. We consider an OSA-based CR network with two types of users operating in the same channel.² The periodic sensing is essential in OSA-based CR networks, as SUs always need to be aware of the primary transmissions. This is achieved using the frame structure shown in Figures 1 and 2. The SU cannot perform sensing and transmissions simultaneously, because of the single radio frequency (RF) transceiver.⁷ Hence, the frame structure for the SU in the non-cooperative scenario consists of a sensing duration, $τ$ , and a transmission duration, T − τ, as shown in Figure 1. For a given detection threshold, a longer sensing duration will increase the detection probability, thereby reducing the interferences to the PUs. However, such an approach will decrease the time left for data transmission, reducing the sum rate of the secondary network. This phenomenon is called the inherent sensing-throughput trade-off in the CR network.⁵ At the end of each sensing slot, the SU transmits if the channel is sensed to be idle. If the channel is sensed to be occupied, the SU waits for the next frame. We assume that the SU in the considered network is equipped with a single narrowband antenna as only a single channel is considered for the sensing. It is assumed that all transmissions are slotted with a given slot time, T. It is also assumed that the packet transmission of an SU is synchronized with that of the PU at each slot.¹

Figure 1.

Frame structure of SU in conventional OSA-based CR network.

Figure 2.

Frame structure of SUs in conventional OSA-based cooperative CR network.

Next, a multiuser CR network with a cooperative centralized architecture is considered. In order to vacate a channel in a timely manner on the appearance of a PU, each frame of the SU consists of a sensing duration, $τ$ , sharing time, $T_{sh}$ , and the remaining duration for the transmission of the packets, as shown in Figure 2. The sharing time, $T_{sh}$ , refers to the total extra time required for the cooperation operations.⁵ In our work, we assume that the cooperation gain depends only on the sensing duration, $τ$ , whereas the sharing time, $T_{sh}$ , is required for the entire cooperative overhead. We, also, assume that the sharing time increases linearly with the number of cooperating users. A better sensing performance can be achieved in lesser time using cooperative sensing. However, cooperative sensing also incurs cooperation overhead.⁵ The optimal sensing operating points need to be investigated to achieve an optimal cooperative sensing trade-off between cooperative gain and cooperation overhead. It is assumed that cooperating SUs use a common control channel (CCC)² and that they are perfectly synchronized by the FC, with sensing results available instantly and concurrently at the FC.⁵ We assume that all SUs are selected for the cooperation in cooperative sensing.

Sum rate analysis under imperfect sensing

The channel sensing performance for the ED scheme can be analyzed in a closed form and is evaluated mainly by two probabilities, that is, detection probability $(P_{D})$ and false alarm probability $(P_{FA})$ .^18,19 $P_{D}$ denotes the probability that an SU declares the channel busy when it is being occupied by the PU, and $P_{FA}$ denotes the probability that the SU declares the channel busy if the channel is idle. Hence, $P_{D}$ indicates the protection level for the PU, and $P_{FA}$ determines the channel access chances for the SU.²⁰ The optimal sensing can be achieved by the selection of optimal sensing operating points depending on the parameters of the considered networks. The receiver operating characteristic (ROC), which is described by $P_{D}$ as a function of $P_{FA}$ , provides the metric for the performance evaluation of the considered ED scheme.^6,20 We assume that the PU signal is a complex-valued phase-shift keying (PSK) signal. For such an assumption, the ROC is expressed by⁷

$P_{D} = Q (\frac{1}{\sqrt{1 + 2 γ}} (Q^{- 1} (P_{FA}) - γ \sqrt{N_{s}}))$ (1)

where $Q (x) = 1 / \sqrt{2 π} \int_{x}^{\infty} e^{- u^{2} / 2} du$ is the Gaussian Q-function;⁷ $γ$ is the sensing SNR of the PU, received at SU; and $N_{s}$ is the number of sensing samples. Hence, the probabilities of the sensing errors depend on the sensing SNR at the SU and the required number of sensing samples.

We next consider the total achievable sum rate of the CR network under imperfect spectrum sensing with sensing errors due to channel fading and noise. Under imperfect spectrum sensing, the false alarm event is the case when the channel is falsely detected to be busy and channel is not used by the PU or SU. On the contrary, the case when the SU incorrectly detects the channel to be idle for transmission is considered to be miss-detection. Under this case, the PU and SU packets interfere with each other with a miss-detection probability $(1 - P_{D})$ . We consider a collision model for miss-detection in which the PU and SU packets collide with each other and no data are transmitted.¹ Hence, we assume that it does not contribute to the overall sum rate of the network. In each time slot, the channel is occupied by a PU with a certain probability which is called a primary activity probability factor (PAPF).¹ In our work, we assume that PAPF is known to SU. The total achievable sum rate of the proposed CR system, under the collision model, is given by

$C_{sum} = ζ P_{D} C_{1} + \frac{T - τ}{T} (1 - ζ) (1 - P_{FA}) C_{2}$ (2)

where $ζ$ denotes PAPF, that is, the probability for PU to send the packet at a given time slot. $C_{1}$ and $C_{2}$ denote the channel capacities of the primary link (unaffected by any SU transmission) and the secondary link (unaffected by any PU transmission), respectively, and are given by

$C_{1} = \log_{2} (1 + γ_{p})$ (3)

$C_{2} = \log_{2} (1 + γ_{s})$ (4)

where $γ_{p}$ and $γ_{s}$ are the SNRs of the primary and secondary transmissions, respectively.

In a multiuser CR network, we assume that the distances between the cooperating SUs are negligible when compared to the distance to the primary transmitter. Therefore, each channel gain is assumed to have the same variance, and the received sensing SNRs of the PU at all cooperative SUs will be the same, given by $γ_{c}$ .^3,5 Hence, the ROC for all the cooperative CR users can be expressed as

$P_{D, k} = Q (\frac{1}{\sqrt{1 + 2 γ_{c}}} (Q^{- 1} (P_{FA, k}) - γ_{c} \sqrt{N_{s}}))$ (5)

where $P_{D, k}$ and $P_{FA, k}$ are the detection and false alarm probabilities, respectively, of the kth SU.

We consider a logical or (OR) combining rule as the data fusion technique at the FC. As per the OR rule, the FC declares the presence of a PU if at least one SU detects the PU. Otherwise, the FC determines the absence of a PU. Hence, the OR rule decreases the interference level for the PU, but it may result in lower spectrum utilization. The probability of detection and the probability of false alarm, of the final decision at the FC, are given by

$P_{D, C} = 1 - Π_{k = 1}^{N_{CR}} (1 - P_{D, k})$ (6)

$P_{FA, C} = 1 - Π_{k = 1}^{N_{CR}} (1 - P_{FA, k})$ (7)

For the multiuser CR network, we consider a realistic scenario of imperfect spectrum sensing, with a collision model for the miss-detection. The average channel capacity is considered for all the SUs, when the PU is not present and the SU needs to transmit its packet. Hence, the total achievable sum rate of the proposed CR system, under the collision model, is given by

$\begin{matrix} C_{sum, c} = ζ P_{D, C} C_{1} \\ + \frac{T - (τ + T_{sh})}{T} (1 - ζ) (1 - P_{FA, C}) C_{2, C} \end{matrix}$ (8)

where $P_{D, C}$ , and $P_{FA, C}$ are the probability statistics of the final decisions at the FC. $C_{1}$ and $C_{2, C}$ denote the channel capacities of the primary link (unaffected by any SU transmission) and the secondary link (unaffected by any PU transmission), respectively, and are given by

$C_{1} = \log_{2} (1 + γ_{p})$ (9)

$C_{2, C} = \frac{1}{N_{CR}} \sum_{i}^{N_{CR}} \log_{2} (1 + γ_{i, s})$ (10)

Here, $N_{CR}$ represents the number of cooperating SUs, $γ_{p}$ represents the SNR of the primary link, and $γ_{i, s}$ is the SNR for ith SU.

Simulation results and discussion

In this section, the simulation results are presented. For the results, the total frame duration and sensing duration for the SUs are assumed to consist of 1000 and 100 samples, respectively. The received SNR of the PU’s signal at each SU is set to be −10 dB. The SNRs for the primary and secondary links are assumed to be 10 dB. First, we investigate the inherent trade-off between the durations of spectrum sensing and data transmission for the CR network with a single secondary link. The trade-off between the sum rates of the primary and secondary links can be adjusted using the channel sensing parameters, that is, a pair of false alarm and detection probabilities. The ROC for the considered ED scheme given by equation (1) is concave, that is, $P_{D}$ is a concave function of $P_{FA}$ . As expressed by the ROC, the more miss-detection events occur at lower false alarm probabilities, and the CR users have less chance to access the channel at high false alarm probabilities. Figure 3 shows the sensing performance improvement as the sensing time increases. This is because of the fact that the probability of sensing errors, including miss-detections and false alarm events, for the considered ED scheme, depends on the number of sensing samples, that is, sensing interval, as given by equation (1)

Figure 3.

ROC curves depending on the number of sensing samples.

A longer sensing time means shorter transmission time for the SU. Hence, the channel sensing parameters need to be optimized for a given sensing time, to maximize the overall sum rate of the considered CR network. Figure 4 shows the sum rates for the perfect and imperfect channel sensing cases, for a given PU activity. The perfect sensing case without sensing error achieves the maximum sum rate, which corresponds to perfect time sharing between the PU and SU, with a parameter of PAPF. However, the imperfect sensing cases show the sum rate degradation. However, the degradation of sum rate depends on the operating point on the ROC curve, that is, $P_{FA}$ and the associated $P_{D}$ . The maximum achievable sum rate for the imperfect sensing can be obtained by choosing the optimal $P_{FA}$ , $P_{D}$ on the ROC at each PAPF. At $PAPF = 0$ , the sum rate is entirely contributed by the SU. At $PAPF = 1$ , the sum rate is entirely contributed by the PU. As PAPF increases, a higher $P_{FA}$ is the optimal approach because it increases the $P_{D}$ and the sum rate of the overall network.

Figure 4.

Sum spectral efficiency as a function of primary activity probability factor (PAPF), with perfect and imperfect sensing for each false alarm probability.

Figure 5 shows the sum rates under perfect and imperfect channel sensing with the upper bounds (optimized sensing pair) and lower bounds (worst sensing pair) for different PU activities. It is shown that a higher sum rate gain can be achieved with the optimal sensing pair at each PAPF. We define the sum rate gain as the improved sum rate because of using the optimal operating points. Figure 5 also shows that the sum rate gain is the lowest at $PAPF = 0.5$ . This sum rate degradation is due to a larger number of miss-detections and false alarm events when the PU and SU get the channel with equal access probability. Moreover, the sum rate for $PAPF = 1$ is higher than that for $PAPF = 0$ . This is because the PU contributes more to the overall sum rate of the network, as the PU can use its entire frame duration to transmit data.

Figure 5.

Sum spectral efficiency comparison under perfect and imperfect channel sensing with upper and lower bounds for different PAPFs.

Figure 6 shows the optimal operating point of sensing, in terms of false alarms, for each PU channel access probability, that is, PAPF. It is shown that the higher values of optimal false alarms are needed with the increase in the PAPF. This is because the achievable sum rate of the proposed network is majorly contributed by the primary link as the PAPF increases. Therefore, the operating point is selected for increasing the detection probability instead of reducing the false alarms.

Figure 6.

Optimal false alarm probability (PFA) as a function of PAPF.

Figure 7 shows the sum rates under perfect and imperfect channel sensing with upper bound (optimized sensing pair) and lower bound (worst sensing pair) for different sensing samples. A unique optimized sensing pair exists for each number of sensing samples to get the maximum sum rate with imperfect sensing. It is also shown that the sum rate under imperfect channel sensing with the optimized sensing pairs increases for lesser sensing samples. This is due to the dominance of the detection improvement of $P_{D}$ for PU as compared to the reduction in the factor $(T - τ / T) (1 - P_{FA})$ for the SU. Moreover, the sum rate decreases for higher number of sensing samples. This is because the reduction in the factor of $(T - τ / T) (1 - P_{FA})$ for the SU dominates the detection improvement for PU.

Figure 7.

Sum spectral efficiency comparison under perfect and imperfect channel sensing with upper and lower bounds for different number of sensing samples.

Figure 8 shows the false alarm probability associated with the upper and lower bounds, for different number of sensing samples. As shown, when both the PU and SU contribute to the overall sum rate of the network, increasing the sensing samples ensures lesser false alarm events; hence, the optimal value of false alarm probability decreases. However, as the number of sensing samples approaches the maximum possible number of samples, the sum rate is majorly contributed by the PU. Hence, to maximize the sum rate of the primary link, $P_{D}$ must be higher. Therefore, from the ROC, a higher $P_{D}$ gives higher optimized $P_{FA}$ . It is shown in Figure 8 that the $P_{FA}$ approaches 1 as the sensing samples approach to the maximum possible samples for a given frame.

Figure 8.

False alarm probability associated with upper and lower bounds for different number of sensing samples.

Now, we investigate the cooperative sensing trade-off between the cooperative gain and the cooperative overhead for different number of cooperative SUs. We consider the improved detection performance and hence the improved sum rate, for the cooperative gain. Moreover, only the reporting delay, that is, sharing time, is considered for the cooperative overhead. Figure 9 shows the sensing performance improvement with multiple cooperative SUs.

Figure 9.

ROC curves for different number of cooperative users.

Figure 10 shows the improved sum rate performance of the multiuser CR network. The result shows that the sum rate improvement is significant only at lower $P_{FA}$ values. This is because, at lower $P_{FA}$ values, the SUs tend to utilize the channel more frequently with their enhanced sensing performance, which, in turn, enhances the total sum rate of the network. At higher $P_{FA}$ values, the SUs get less chance to utilize the channel, and the enhanced detection performance mostly contributed by the primary link is in a trade-off with the sharing time needed for cooperation. Hence, the total sum rate of the network remains the same.

Figure 10.

Sum spectral efficiencies for different number of cooperative users.

Figure 11 shows the maximum achievable sum rates of a multiuser CR network using the optimal operating point for the cooperating SUs at a given PAPF. The result validates the inherent cooperative sensing trade-off between improved detection performance and sharing time needed for the cooperation. With fewer users, the improved detection performance dominates, when compared to the sharing time, and it increases the overall sum rate of the network. However, with a higher number of cooperative users, the sharing time increases and is dominated, which decreases the overall sum rate of the network. Hence, if the number of SUs is more than the optimal number, for the given sensing parameters, the sum rate decreases because of the cooperation overhead.

Figure 11.

Sum spectral efficiency with optimized sensing pair for different number of cooperative users.

Conclusion and future work

The sum rate degradation due to the imperfect sensing can be reduced significantly by minimizing the sensing errors in the conventional orthogonal CR networks. In this article, we investigate the optimal sensing operating points, adaptive to different sensing parameters for time-division multiple access (TDMA)-based hierarchical CR networks, to maximize the achievable sum rates of the considered networks. First, the sensing efficiency was analyzed in terms of the optimal channel sensing parameters, for different sensing durations and PU activities in the non-cooperative scenario. The comparison of sum rates, in terms of the sum rate gains and sum rate losses under perfect and imperfect sensing with upper and lower bounds of sensing pairs, was proposed. The trade-off between cooperative gain and cooperation overhead, using the optimal operating point, was examined for different number of cooperative SUs in the multiuser CR network. Our results validated that it was necessary to consider the cooperative sensing trade-off for selecting the number of cooperative users, to utilize the benefits of the cooperative sensing. The extensions to the more advanced scenarios with the cooperative CR-NOMA scheme can be considered in future works.

Footnotes

Handling Editor: Donatella Darsena

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This research was supported by the MSIT (Ministry of Science and ICT),Korea,under the ITRC (Information Technology Research Center) support program (IITP-2017-2016-0-00313) supervised by the IITP (Institute for Information & Communications Technology Promotion) and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03030757).

References

Optimal primary pilot power allocation and secondary channel sensing in cognitive radios. IET Commun 2016; 10(5): 487–494.

Zhang

et al . Energy-efficient design of channel sensing in cognitive radio networks. Comput Electr Eng 2015; 42: 207–220.

Rajasekharan

Eriksson

Koivunen

Cooperative game-theoretic approach to spectrum sharing in cognitive radios. Signal Process 2015; 106: 15–29.

Elmahdy

El-Keyi

ElBatt

et al . Optimizing cooperative cognitive radio networks performance with primary QoS provisioning. IEEE T Commun 2017; 65(4): 1451–1463.

Akyildiz

Balakrishnan

Cooperative spectrum sensing in cognitive radio networks: a survey. Phys Commun 2011; 4(1): 40–62.

Suliman

Lehtomaki

Umebayashi

On the effect of false alarm rate on the performance of cognitive radio networks. EURASIP J Wirel Comm 2015; 2015(1): 1–15.

Stotas

Nallanathan

On the throughput and spectrum sensing enhancement of opportunistic spectrum access cognitive radio networks. IEEE T Wirel Commun 2012; 11(1): 97–107.

Joshi

Nam

Kim

SW.

Cognitive radio wireless sensor networks: applications, challenges and research trends. Sensors 2013; 13(9): 11196–11228.

Darsena

Gelli

Verde

An opportunistic spectrum access scheme for multicarrier cognitive sensor networks. IEEE Sens J 2017; 17(8): 2596–2606.

10.

Darsena

Gelli

Verde

. Non-cooperative superposition relaying for multicarrier cognitive networks. In: Proceedings of the IEEE 27th annual international symposium on personal, indoor, and mobile radio communications (PIMRC), Valencia, 4–8 September 2016, pp.1–6. New York: IEEE.

11.

Ding

Peng

Poor

HV.

Cooperative non-orthogonal multiple access in 5G systems. IEEE Commun Lett 2015; 19(8): 1462–1465.

12.

Chen

Cooperative non-orthogonal multiple access in cognitive radio. IEEE Commun Lett 2016; 20(10): 2059–2062.

13.

Zabetian

Baghani

Mohammadi

. Rate optimization in NOMA cognitive radio networks. In: Proceedings of the 8th international symposium on telecommunications (IST), Tehran, Iran, 27–28 September, pp.62–65. New York: IEEE.

14.

Darsena

Gelli

Verde

Convolutive superposition for multicarrier cognitive radio systems. IEEE J Sel Area Comm 2016; 34(11): 2951–2967.

15.

Lee

Vahid

et al . Practical spectrum aggregation for secondary networks with imperfect sensing. IEEE T Veh Technol 2016; 65(7): 5474–5484.

16.

Yin

Achievable throughput optimization in energy harvesting cognitive radio systems. IEEE J Sel Area Comm 2015; 33(3): 407–422.

17.

Althunibat

Granelli

An objection-based collaborative spectrum sensing for cognitive radio networks. IEEE Commun Lett 2014; 18(8): 1291–1294.

18.

Atapattu

Tellambura

Jiang

Spectrum sensing via energy detector in low SNR. In: Proceedings of the 2011 IEEE international conference on communications (ICC), Kyoto, Japan, 5–9 June 2011, pp.1–5. New York: IEEE.

19.

Atapattu

Tellambura

Jiang

Conventional energy detector. In: Atapattu

Tellambura

Jiang

(eds) Energy detection for spectrum sensing in cognitive radios. New York: Springer-Verlag, 2014, pp.11–26.

20.

Peh

Liang

. Optimization for cooperative sensing in cognitive radio networks. In: Proceedings of the 2007 IEEE wireless communications and networking conference (WCNC), Kawloon, China, 11–15 March 2007, pp.27–32. New York: IEEE.