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May 28, 2018 - data rates, area traffic capacity, energy efficiency, spectrum efficiency, and spectrum utilization are the key performance indicators that can be ...
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Sum Utilization of Spectrum with Spectrum Handoff and Imperfect Sensing in Interweave Multi-Channel Cognitive Radio Networks Waqas Khalid

ID

and Heejung Yu *

ID

Department of Information and Communication Engineering, Yeungnam University, Gyeongsan 38541, Korea; [email protected] * Correspondence: [email protected] Received: 1 May 2018; Accepted: 21 May 2018; Published: 28 May 2018

 

Abstract: Fifth-generation (5G) heterogeneous network deployment poses new challenges for 5G-based cognitive radio networks (5G-CRNs) as the primary user (PU) is required to be more active because of the small cells, random user arrival, and spectrum handoff. Interweave CRNs (I-CRNs) improve spectrum utilization by allowing opportunistic spectrum access (OSA) for secondary users (SUs). The sum utilization of spectrum, i.e., joint utilization of spectrum by the SU and PU, depends on the spatial and temporal variations of PU activities, sensing outcomes, transmitting conditions, and spectrum handoff. In this study, we formulate and analyze the sum utilization of spectrum with different sets of channels under different PU and SU co-existing network topologies. We consider realistic multi-channel scenarios for the SU, with each channel licensed to a PU. The SU, aided by spectrum handoff, is authorized to utilize the channels on the basis of sensing outcomes and PU interruptions. The numerical evaluation of the proposed work is presented under different network and sensing parameters. Moreover, the sum utilization gain is investigated to analyze the sensitivities of different sensing parameters. It is demonstrated that different sets of channels, PU activities, and sensing outcomes have a significant impact on the sum utilization of spectrum associated with a specific network topology. Keywords: 5G networks; cognitive radio; interweave; sum utilization of spectrum; spectrum handoff; spatial and temporal variations

1. Introduction The forthcoming fifth-generation (5G) wireless networks are expected to provide high-speed seamless multimedia services with low latency and excellent reliability [1]. The scope of 5G services is not limited to personal wireless communications but extends to the services associated with mobile gadgets, wearable devices, sensors, actuators, machines, robots, vehicles, and other applications [2]. 5G technology is expected to be a combination of cooperative heterogeneous networks of multi-tier communication systems and different radio access technologies [3,4]. The heterogeneous feature in 5G technology will provide orders-of-magnitude improvement, including 1000 times higher data volume per area, 10–100 times more connected devices, 10–100 times higher user data rates, one-tenth the energy consumption, and sub-millisecond end-to-end latency. However, the challenges faced by 5G systems are manifold because of the heterogeneity in terms of services, classification of devices, deployment scenarios, environments, and mobility [4,5]. In addition to its heterogeneous nature, another major challenge surrounding 5G is the random and diverse high-volume user data [5,6]. A large number of users, i.e., active connections, having different quality of service (QoS) requirements,

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is also a challenging task for 5G networks [6]. Hence, to provide the services promised by 5G, is also a challenging 5G networks [6]. and Hence, provideare therequired services[2,6]. promised by 5G, innovative changes in task both for wireless technologies core to networks innovative changes in both wireless technologies and core networks are required [2,6]. Aspects such as mobility, latency, widespread coverage, Internet of Things (IoT) services [7], such as mobility, latency,energy widespread coverage, Internet of Things (IoT) services [7], peak peak Aspects data rates, area traffic capacity, efficiency, spectrum efficiency, and spectrum utilization data rates, area traffic capacity, energy efficiency, spectrum efficiency, and spectrum utilization are the are the key performance indicators that can be regarded as technical requirements for 5G networks key performance indicators that can be regarded as technical requirements for 5G networks [2,8]. Hence, [2,8]. Hence, 5G technology requires new radio frequencies with wider spectrum bands to deliver the 5G technology requires new radio frequencies with wider spectrum deliver the promised promised performance improvements. The ITU-R IMT-2020 (5G) bands visiontoincludes three usage performance improvements. The ITU-R IMT-2020 (5G) vision includes usage scenarios; enhanced scenarios; enhanced mobile broadband (eMBB), massive machine typethree communication (mMTC), and mobile broadband (eMBB), massive machine type(URLLC) communication (mMTC), and ultra-reliablespectrum and low ultra-reliable and low latency communications [8]. In this regard, a multi-layer latency communications (URLLC) [8]. In thisfor regard, a multi-layer spectrum approach, shown in approach, as shown in Figure 1, is proposed a wide range of proposed scenarios, useascases, and Figure 1, is proposed for a wide range of proposed scenarios, use cases, and requirements associated requirements associated with 5G. The spectrum distribution includes the 2–6 GHz range (C-band), withabove-6-GHz 5G. The spectrum includes the 2–6 Each GHz band-range range (C-band), the above-6-GHz range, the range, distribution and the below-2-GHz range. has specific characteristics to and the below-2-GHz range. Each band-range has specific characteristics to make it suitable for make it suitable for certain deployment scenarios. The low range has good propagation aspects to certainit deployment scenarios. The low range has good propagation to make for make suitable for the coverage, though it is limited in capacity. The aspects mid-range offersitasuitable reasonable the coverage, thoughand it is capacity limited infor capacity. The mid-range a reasonable coverage mixture of coverage 5G services, because itoffers is suitable for the mixture coverageoffor urban and capacity for 5G services, because it is suitable for the coverage for urban deployment, along deployment, along with the increased capacity. The high range is needed for 5G services such as with the increased capacity. The high is needed for 5G servicesthe such as ultra-high-speed ultra-high-speed mobile broadband, but range has limited coverage. Recently, highly uncongested 60mobile broadband, hasmillimeter limited coverage. Recently, the highly 60-GHz band, known GHz band, known but as the radio (mmWave) band, has uncongested become the next major frequency as the millimeter radio (mmWave) band, has become the next major frequency band for wireless band for wireless communication services, because of its short-range and wider-area applications. communication because of its mmWave short-range and wider-area Researchers have Researchers haveservices, started investigating communication in applications. various scenarios. The band is started investigating mmWave communication in various scenarios. The band is capable of delivering capable of delivering high-speed services, though with less range, and can be ideal for small-cell high-speed services, though with less range, and can be ideal for small-cell networks [9]. networks [9]. Below 2GHz (Low Frequencies) Coverage Layer

2-6 GHz (Mid-range Frequencies)

eMBB, URLLC, mMTC (wide-range and deep coverage)

eMBB, URLLC, mMTC (no deep coverage)

Coverage & Capacity Layer

Above 6 GHz (High Frequencies) Data Layer

eMBB (extremely high data rates)

Figure 1. Proposed multi-layer bands and usage scenarios for 5G. Figure 1. Proposed multi-layer bands and usage scenarios for 5G.

1.1. Background and Motivation 1.1. Background and Motivation The key requirements for 5G technology include near-zero delay, high reliability, device support The key requirements for 5G technology include near-zero delay, high reliability, device support for heterogeneous networks, spectrum flexibility, and energy efficiency. Spectrum allocation is for heterogeneous networks, spectrum flexibility, and energy efficiency. Spectrum allocation is considered one of the major problems among the mentioned requirements [1,9]. The static spectrum considered one of the major problems among the mentioned requirements [1,9]. The static spectrum allocation policies are inefficient for meeting the ever-growing demand of spectrum resources, which allocation policies are inefficient for meeting the ever-growing demand of spectrum resources, which are needed for high-speed wireless access in 5G cellular networks [10]. Radio resources have become are needed for high-speed wireless access in 5G cellular networks [10]. Radio resources have become increasingly scarce because of the static spectrum allocation approaches. The unlicensed users cannot increasingly scarce because of the static spectrum allocation approaches. The unlicensed users cannot access the licensed bands, making the bands under-utilized [6,10]. Spectrum allocation flexibility and access the licensed bands, making the bands under-utilized [6,10]. Spectrum allocation flexibility spectrum utilization efficiency can be achieved with different proposed technologies, such as LTEand spectrum utilization efficiency can be achieved with different proposed technologies, such as WiFi aggregation (LWA) [11], operations in millimeter-wave band [12], LTE over the unlicensed band LTE-WiFi aggregation (LWA) [11], operations in millimeter-wave band [12], LTE over the unlicensed (LTE-U) [13], multicasting [14,15], layer-division multiplexing [14,16], ultra-dense small cells in 5G band (LTE-U) [13], multicasting [14,15], layer-division multiplexing [14,16], ultra-dense small cells in architecture [17], non-orthogonal multiple access (NOMA) [18–20], and software-defined cognitive radio network (SD-CRN) [21–25].

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5G architecture [17], non-orthogonal multiple access (NOMA) [18–20], and software-defined cognitive radio network (SD-CRN) [21–25]. LTE-U has emerged as an effective way to improve the spectral efficiency and capacity of wireless networks. Using LTE-U along with superior techniques such as carrier aggregation (CA), the performance of wireless networks can be improved significantly. However, an effective coexistence mechanism between LTE-U and Wi-Fi systems is necessary. Millimeter wave communications leverage the large-bandwidth potentially available at mmWave frequency band to provide the high data rates, and is considered to be a promising technology for the next-generation cellular networks. However, the performance evaluation of mmWave mobile communication systems, such as quantitative analysis of system-level propagation performance, and architecture evaluation need to be explored. Multicasting is a popular technique to simultaneously convey data to a group of terminals through point-to-multipoint communications, with positive impact on capacity and spectrum efficiency of the cellular systems. However, multicast traffic over 5G networks does not involve the end-user devices only, but also machine-type communications for IoT. In future broadcasting systems, layer-division multiplexing has been proposed to enable mobile TV on top of conventional terrestrial digital TV services, increasing the efficiency of the spectrum. In 5G systems, vehicular-to-everything (V2X) communications will also gain higher interest considering the ultra-dense and high-load scenarios. NOMA is one of the promising radio access techniques for performance enhancement and greater spectrum efficiency in 5G systems. In NOMA, multiple users are served at the same time and frequency, but are multiplexed based on the power or code domains. The integration of NOMA protocols with CR systems improves the spectral efficiency significantly. However, the performance analysis of a cooperative CR-NOMA schemes requires high computational complexity. Furthermore, in a possible radio-band assignment for 5G networks, different frequency bands will be used for macro cells and ultra-dense small cells. Such a 5G architecture will require intelligent spectrum sensing using CR technology to aggregate the spectrum bandwidths for small and large cells. The software-defined cognitive radio network (SD-CRN) is a promising technology to mitigate the spectrum scarcity and spectrum under-utilization issues in wireless systems. Enabling CR features in dense 5G networks can maximize the spectrum utilization. The users are generally categorized into a multi-tiered hierarchy in CR systems; primary users (PUs) have priority of spectrum access over the secondary users (SUs) [24]. Dynamic spectrum access techniques enable time-division multiple access (TDMA)-based spectrum sharing between the PUs and SUs, without requiring any major modifications in the primary systems [22–24]. The three possible paradigms of spectrum access in CRNs include overlay, underlay, and interweave [25,26]. In underlay schemes, SU and PU may transmit simultaneously under the constraint of SUs’ interference to the PU. On the contrary, in overlay schemes, SU not only transmits its own signal, but also assists the primary transmissions through some relaying techniques. In interweave-based schemes, SU is capable of exploiting the spectrum opportunities via spectrum sensing, hence enhancing the utilization efficiency of spectrum. In interweave CR (I-CR) systems, SUs are allowed to opportunistically exploit the primary network, without interrupting the primary transmissions significantly. The successful integration of the PU with SUs is subject to the condition that a certain QoS level for a PU must be guaranteed, and can be accomplished through spectrum sensing. Hence, reliable spectrum sensing, using software-defined radio technology and an advanced cognition engine, is the most crucial part of CRNs [25–28]. Spectrum sensing is performed either independently or in a cooperative manner. If a SU detects PU transmission, it needs to release the channel and switch to another idle channel if one is available, or wait if no vacant channel is available. Energy detection (ED), spectral detection, and waveform detection are the common spectrum sensing techniques in I-CRN [27]. The ED scheme is one of the conventional channel sensing approaches. It provides relatively low computational complexity because it relies on PU signal power detection. In addition, a priori knowledge of the PU signal is not required. However, a major drawback for the ED scheme is that it has poor sensing performance in low-SNR conditions. Cooperative spectrum sensing (CSS) is one of the efficient approaches used to combat the hidden terminal problems, deep

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fading, and shadowing effects. CSS approaches exploit the spatial diversity by deploying multiple distributed SUs [28]. In such a case, a central node, i.e., a fusion center (FC), makes a final decision on the availability of considered channel by combining the local sensing information of multiple SUs. The FC applies data fusion techniques, such as equal gain combining, maximal ratio combination, and Bayesian fusion, or decision fusion techniques such as the AND, OR, and K-OUT-N rules [27,28]. When multiple SUs exist, better sensing performance can be achieved while allocating less time to the sensing operations [19,29]. 1.2. Related Work The performance of the opportunistic spectrum access (OSA)-based I-CRNs has been lavishly published. A substantial amount of research has been dedicated to the CR architecture, to its operating principle, mobility, and spectrum sensing performance both in perfect and realistic imperfect sensing scenarios [28–37]. Nevertheless, analytical modelling of the spectrum utilization due to dynamic nature of the PU is a challenging task [30–37]. In our own prior contribution [19], we studied the improvement of the sum rate by optimizing the sensing operating point, e.g., the sensing threshold, in conventional orthogonal CR networks, because sensing errors, i.e., missed-detection events and false alarms, cannot be avoided in real-time spectrum sensing. We also investigated the optimal sensing operating points, adaptive to different sensing parameters, to maximize the achievable sum rates of the considered networks. Bradonjic et al. [30] discussed the operation of the CR networks over a dynamic bandwidth in both time and space. The integration of users in CRN requires SUs to be capable of efficient sensing and keeping precise track of the primary transmissions. The unique characteristic of SUs co-existing with PUs is the dynamic nature of the spectrum availability. The CRN operates over a dynamic bandwidth (i.e., both in time and space) that inherently forms clusters. Hence, it is important to consider both the spatial and temporal dimensions of spectrum opportunities on the basis of PU activities. The network topologies, based on the interaction between the integrated users, depend on the physical proximity and availability of the spectrum holes. Specifically, Ozger et al. [34], and Sun et al. [37] discussed the utilization of spectrum for different network topologies. For the communicating SU nodes, the packet must be transmitted to the corresponding receiver without any significant error, along with the correct detection of spatial-temporal spectral opportunity. However, the transmitted packet may be severely damaged by the poor channel conditions, thus degrading the transmission reliability. Moreover, Mehrnoush et al. [31] analyzed the impact of spectrum handoff on the performance of considered CRN. Spectrum handoff occurs when a channel is being utilized by a SU and a PU appears. Thus, the SU needs to vacate the channel and migrate to another channel in order to transmit a packet successfully. In a nutshell, spectrum-aware communication in CRNs requires timely and accurate detection of the spatial-temporal spectrum access opportunities, efficient spectrum mobility (spectrum handoff) when required, and successful transmission of the SU and PU packets. 1.3. Contribution of the Paper This paper further develops our research on the utilization of spectrum [32,33]. In Ref. [32,33], we formulated and analyzed the utilization of spectrum for the SUs and PU, i.e., sum utilization of spectrum. In Ref. [33], we considered different SU and PU co-existing scenarios, and investigated the sum utilization of spectrum, with retransmission capability for the SU, to ensure the reliable packet delivery. We characterized the gain in the sum utilization of spectrum with the SU retransmission capability, as SU was allowed to retransmit its packet during the PU mean inactive duration, and SU packet length, in order to improve the link reliability. In our previous studies, sum utilization of spectrum was characterized while considering the single channel. By contrast, in this study, we formulate and analyze the utilization of spectrum policy for multi-channel scenarios, with the aid of sensing and handoff capabilities. We investigate the utilization of spectrum for PU and SU, with SU opportunistically operating on various PU channels. We derive closed-form expressions for sum

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utilization of spectrum, evaluating the impact of spectrum handoff under different network topologies. Our performance results show that the spectrum handoff approach, based on sensing outcomes and PU interruptions, enhances the sum utilization of spectrum. 2. System Model In this section, we present the system model, assumptions, and spectrum sensing design. We assume a decentralized interweave TDMA hierarchical CR network, with nodes self-organizing into a network [19,29,33]. In the study, we consider a CRN with N narrowband channels, with each narrowband channel licensed to a PU. It is assumed that a SU employs an ED scheme. The performance metric in term of detection probability and false-alarm probability measures the performance of the ED scheme. On the basis of the probability density function (PDF) of the test statistic, complex-valued phase-shift keying signaling, and circularly symmetric complex Gaussian noise [32–34], the closed-form expressions of sensing probabilities are considered. The SU is assumed to be equipped with a single narrowband antenna to sense the considered channel. This assumption would be applied to real-world hardware-constrained CRNs. A SU performs sensing procedure in a sequential order, with a fixed sampling frequency and constant transmit power, to locate the spectrum holes. The considered channels are assumed to be idle or busy depending on the sensing outcomes. We assume that the SU transmitter is always ready to transmit the packet, provided that considered channel is available [36]. The secondary network cannot guarantee on-time services, i.e., QoS is not guaranteed. The suitable traffic pattern for the secondary network can be best-effort data. Therefore, we assume that the secondary traffic is back-logged, i.e., the secondary queue always has a data to be transmitted. It is also assumed that the SU has the switching capability to drive multiple spectrum handoffs. We assume that the spectrum sensing procedure is executed until handoff operation is initiated. In this study, spectrum handoff delay is not considered, and is assumed that the handoff is executed immediately when necessary. In addition, the sensing duration is assumed to be identical at each channel. We consider a single set of communicating SU nodes for the system, and that the sensing procedure is performed at each channel. For ease of reference, we summarize our commonly used notations in Table 1. Table 1. Summary of Notations. Notation

Description

PFA PD PMD Td.1 ts PON POFF R S A B PS Rp γ Ω Ns

Probability of false alarm Probability of detection Probability of miss-detection Transmission duration over first channel Sensing duration PU active state probability PU inactive state probability PU mean inactive duration PU mean active duration RV to define OFF duration RV to define ON duration Packet size Data rate SNR of PU signal at SU PU deployment density Number of sensing samples

The time slots in OSA-based frame structure of SU over different channels is shown in Figure 2. The frame structure consists of sensing time and transmission time over the given set of channels. After the sensing procedure is complete, the SU transmits in the unoccupied channel for the transmission time. The available transmission time in the jth channel, i.e., after the ( j − 1)th handoff,

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is Td.1 − ( j − 1) ts . It is assumed that if the jth channel is found free, the SU will be able to transmit the corresponding packet in the available transmission duration, and will not sense the next channel, Sustainability 10, x FOR REVIEWwe assume the upper limit for the allowable number of handoffs, 6 of 18 i.e., (j + 1)th2018, channel. InPEER this study, i.e., N, and also, that the transmission duration over the considered channel is enough to transmit the transmit the corresponding If the Nth channel is found for the next timecorresponding packet. If thepacket. Nth channel is found busy, the SUbusy, waitsthe forSU thewaits next time-slot to sense slot to sense the first channel again. For a given detection threshold, an inherent tradeoff [19] exists the first channel again. For a given detection threshold, an inherent tradeoff [19] exists in the frame in the frame structure betweentime the and sensing time and time transmission over the considered channel. structure between the sensing transmission over the time considered channel. It is assumed It is assumed the packet transmissions and PU are synchronized that the packetthat transmissions of SU and PU of areSU synchronized at each slot. at each slot.

Handoff Execution Channel 1 ts

Td.1

Channel 2 ts

Td.1- ts

N-1

1 Channel N

ts

Td.1- (N-1)ts

Sensing procedure duration Transmission procedure duration Figure 2. Pattern of N-channel usage by SU. Figure 2. Pattern of N-channel usage by SU.

We assume that the PU is authorized to use a fixed spectrum, which is divided into a set of We assume that the∈PU to that use aPU fixed spectrum, which dividedchannels into a set narrowband channels [1, is] .authorized We assume traffic across all the isprimary is of narrowband channels j ∈ 1, N . We assume that PU traffic across all the primary channels is [ ] independent and identically distributed. Therefore, the utility performance in a case that the handoff independent and identically utility performance a case that the handoff channel is randomly selecteddistributed. is the sameTherefore, as that inthe a case that the handoffinchannel is sequentially channel is randomly selected is the same as that in a case that the handoff channel is sequentially selected. Hence, activity of a PU over the channels is sensed in a sequential order, starting from the selected. Hence, activity of achannel PU over in a sequential order, starting from the first channel. If the current is the idle,channels a packetisissensed transmitted to the corresponding receiver. If first channel. If the current channel is idle, a packet is transmitted to the corresponding receiver. If the the channel is busy, the SU switches to the next channel with the aid of spectrum handoff, and senses channel is busy,inthe switches theactivity next channel with the aid is ofmodeled spectrumbyhandoff, and senses the PU activity theSU next channel.toThe of PU on a channel discrete-time semithe PU activity in the next channel. activity of PU3.on a channel is modeled by discrete-time Markov (two-state) process [36–40], asThe shown in Figure The states alternate between the OFF and semi-Markov process [36–40], as shown in Figure 3. The alternate between the ON states. The(two-state) ON state represents that channel is occupied by the PU, states and the OFF state represents OFF and ON is states. The ON by state thatthe channel occupied by PU, and state that channel not occupied therepresents PU. Without loss ofisgenerality, wethe assume thatthe theOFF length of represents that channel is not occupied by the PU. Without the loss of generality, we assume that the OFF and ON durations is represented by the random variables A and B, respectively, and follows length of OFF and ON durations is represented by the random variables A probabilities and B, respectively, exponential distribution with means R and S, respectively. At any time, the that theand PU follows exponential distribution with means R and S, respectively. At any time, the probabilities that is in ON, and OFF states are given by PON = S/(S + R), and POFF = R/(S + R), respectively. Furthermore, the is in ON, OFF states given bychannel PON = are S/(Sindependent + R), and Pof = R/(S + R), respectively. OFFthose it is PU assumed that and the states of the are considered of the other channels. Furthermore, it is assumed that the states of the considered channel are independent of those of the other channels.

B

ON

A

OFF

Figure 3. Activity model for the PU.

ON states. The ON state represents that channel is occupied by the PU, and the OFF state represents that channel is not occupied by the PU. Without the loss of generality, we assume that the length of OFF and ON durations is represented by the random variables A and B, respectively, and follows exponential distribution with means R and S, respectively. At any time, the probabilities that the PU is in ON, and states are given by PON = S/(S + R), and POFF = R/(S + R), respectively. Furthermore, Sustainability 2018,OFF 10, 1764 7 of 18 it is assumed that the states of the considered channel are independent of those of the other channels.

B

A

ON

OFF

Figure 3. 3. Activity for the the PU. PU. Figure Activity model model for

To model the imperfections of the channel sensing by incorporating sensing errors [33–36], the states of the considered channel are represented by missed-detections and false-alarm probabilities, and are calculated by the activity of PU and estimated sensing outcomes. A detection event occurs when a SU successfully senses an occupied channel, and a false alarm indicates a busy status for an idle channel (i.e., the transmission opportunity is wasted). As shown in our previous work [19], a higher detection probability results in better protection for the PU, and a higher false alarm probability means less chance for the SU to utilize the channel. The utilization of the spectrum can be improved with the selection of the optimal sensing operating point depending on the sensing parameters (e.g., SNR) and sensing duration [33]. In the considered ED scheme, the detected signal is squared and integrated over the observation interval, and then the output is compared to a fixed threshold to make a local decision. In this study, the sum utilization of spectrum, i.e., joint utilization of spectrum by the SU and PU, is considered. Thus, the sensing performance under the QoS constraints for PU or SU can be formulated [37]. We consider the sensing performance subject to a QoS constraint for the PU, i.e., the probability of detection is set at a desired value (to give a desired level of protection to the PU), and the probability of false alarm is obtained at a given SNR or sensing duration. The receiver operating characteristic with given assumptions is expressed as j

PFA = Q

q

j

2γ j

+ 1Q

−1

j ( PD ) + γ j

q

j Ns

 (1) j

where j ∈ [1, N ] is the channel index, PD (detection probability) and PFA (false alarm probability) are the sensing pair on the jth channel, γ j is the SNR of the PU signal at the SU on the jth channel, j Ns is the number of sensing samples of the SU on the jth channel, and Q(·) and Q−1 (·) denote the complementary distribution function of the standard Gaussian and its inverse, respectively. The four possible cases of sensing outcomes and PU activities, i.e., PON PD , PON PMD , POFF PFA , and POFF (1 − PFA ), are considered for the proposed analysis, and are assumed to be identical for all channels. In detail, PON PD refers to a scenario where the activity of a PU on a channel is represented by the ON state, and the state is correctly detected by a SU. PON PMD refers to the case where the PU is in the ON state, but the state is incorrectly detected by the SU, and a missed detection occurs. POFF PFA refers to the case where the PU is in the OFF state, but the state is incorrectly detected by the SU, and a false alarm occurs. Similarly, POFF (1 − PFA ) refers to the scenario where the PU is in the OFF state, and the state is correctly detected by the SU. A CR transmitter, i.e., SU, switches to the next channel for the two cases, i.e., PON PMD and POFF PFA . In our work, we assume that the sum utilization of spectrum is contributed only when a SU detects the state of the considered channel correctly, i.e., POFF (1 − PFA ) and PON PD . The access contention for the SUs is not considered. 3. Sum Utilization of Spectrum In this section, we consider different PU and SU co-existing network topologies and describe the formulation and analysis of sum utilization of spectrum for different sets of channels. We consider two topological models, i.e., topology-1, and topology-2, as shown in Figure 4, to investigate both the spatial and temporal variation conditions on the set of idle channels between the communicating SUs [30]. The sum utilization of spectrum is evaluated for both topological models separately. Topology-1

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considers the identical sets of idle channels for the communicating SUs, because both SUs are within the coverage range of the same PU. As shown in Figure 4, the communicating SUs, i.e., SU-ATx and SU-ARx , or the SU-BTx and SU-BRx , lie within the communication range of the same primary network (PRN). Hence, the variation conditions on the set of idle channels is temporal only. For topology-2, communicating SUs are subjected to activity from a possibly different set of PUs. The PU coverage range is comparable to that of the SUs. As shown in Figure 4, the communicating SUs, i.e., SU-ATx and SU-ARx , are within the communication range of different PRNs, i.e., PRN-3 and PRN-2, respectively. Hence, the 2018, variations ofPEER the idle channels are both spatial and temporal. Sustainability 10, x FOR REVIEW 8 of 18

SU-BTx SU-ATx

SU-BRx SU-ARx

PRN

(a)

PRN-3

SU-ATx

SU-BRx

PRN-2 PRN-1

SU-CRx

SU-CTx SU-ARx SU-BTx

(b) Figure 4. PU model. Figure 4. PU and and SU SU co-existing co-existing network network topologies: topologies: (a) (a) topology-1 topology-1 model; model; (b) (b) topology-2 topology-2 model.

The considered channel j can be found busy under two scenarios: the PU state is ON and the The considered channel j can be found busy under two scenarios: the PU state is ON and the state state is correctly detected, and the PU state is OFF and a false alarm occurs. The probability that the is correctly detected, and the PU state is OFF and a false alarm occurs. The probability that the channel channel j is found busy is expressed as j is found busy is expressed as j j j (2) j PB = PON PDj + POFF PFA j (2) P = P P + P P B ON D OFF FA Furthermore, the channel j can be found idle under two scenarios: the PU state is OFF and the state Furthermore, is correctly detected, and the PUbe state is ON is not detected. Thethe probability channel j is the channel j can found idleand under two scenarios: PU statethat is OFF and the found is expressed as and the PU state is ON and is not detected. The probability that channel j state isidle correctly detected, j j j is found idle is expressed as PF = POFF (1 − PFA ) + PON PMD (3) j j Under the two-state model, denotej the events to consider the OFF and ON states, (3) PF H =0 and PO F H F 1 ( 1 - P F A ) + PO N P M D respectively, of the PU in the current channel. Given Equation (3), channel j in a given time-slot can and H1detection. denote the events consider OFF and ON states, Under the two-state model,ofHa0missed also be regarded as idle because The actualtofree channelthe j, without a false alarm, respectively, of the PU in the current channel. Given Equation (3), channel j in a given time-slot canj, is estimated. Thus, the probability of detecting the spectrum opportunity, for the current channel also be regarded is expressed as as idle because of a missed detection. The actual free channel j, without a false alarm, j j is estimated. Thus, the probability of detecting spectrum for the current channel j,(4) is PD.SO = the POFF (1 − PFAopportunity, ) expressed as j j PD .S O = PO F F ( 1 - PF A )

(4)

After detecting the spectral opportunity correctly, the communicating SUs require a successful transmission condition. The successful transmission of a packet depends on the activity of PU, i.e., the PU must not access the licensed spectrum band during the transmission of SU packet. Hence, the

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After detecting the spectral opportunity correctly, the communicating SUs require a successful transmission condition. The successful transmission of a packet depends on the activity of PU, i.e., the PU must not access the licensed spectrum band during the transmission of SU packet. Hence, the probability of no activity during the sensing and transmission periods for a single-channel scenario is defined as   PT1 = Pr A ≥ ts + ( Ps1 /R p ) (5) PT1 =

Z∞

1

ts + Ps1 /R p

P 1 −t/R [(− 1 )(ts + Rsp )] e dt = e R R

(6)

Similarly, the probability of no activity during the sensing and transmission periods, for the jth channel among a set of N channels, is defined as j PT

=

Z∞

j

j ts + Ps /R p

P 1 −t/R [(− 1 )(ts + Rsp )] e dt = e R R

(7)

j

where Ps1 , and Ps , denote the packet size (in bits) in the first, and the jth channels, respectively. In this study, we assume that the number of bits Ps1 are transmitted in the available transmission −ts time Td.1 of the first channel. After the first handover, Ps2 (i.e., Ps1 Td.1 ) bits are transmitted in T d.1

j

T

−( j−1)t

s the available transmission time Td.1 − ts of the second channel. Moreover, Ps (i.e., Ps1 d.1 T ) d.1 bits are transmitted on the jth channel, after the j − 1 handover, in the available transmission time Td.1 − ( j − 1)ts . If the transmission duration is reduced after handoff, the number of transmitted bits is also reduced with the ratio of transmission duration. A channel error [40] occurs when the SNR of a received packet is low because of path loss or a deep fading. The probability of obtaining an error-free packet over the jth channel, because of channel errors only for the cognitive transmission, can be expressed as j

j

Pe− f ree = (1 − BER(γs )) Ps

(8)

where γs is the SNR of the secondary transmission (i.e., transmitted power), and BER is the bit error rate for BPSK in the Rayleigh fading channel and can be expressed as [40] BER(γs ) =

1 4γs

(9)

We assume that the probability of an error-free transmission of packets that are transmitted in the case of a missed detection is one because the primary and secondary packets collide. In this study, we use the probability PUT.PU = PON PD for the PU utilization over the given channel set. The probability of sum utilization of spectrum for topology-1 depends on the probability of detecting the spectrum opportunity at the transmitting and receiving SU nodes, probability of no activity during transmission, probability of error-free transmission, and the PU’s own utilization probability. From Equations (4), (6), and (8), and PU utilization probability, the probability of sum utilization of spectrum for a single-channel scenario under topology-1 can be expressed as 2 1 1 1 PU.T p−1 = ( PD.SO ) PT Pe− f ree + PUT.PU

(10)

For the multi-channel scenario, the number of bits in a packet is reduced in each try after handoff; hence, the weighting factor is introduced to consider the utilization as per the transmitted number −ts of bits in each channel. The weighting factor W 1 = Td.1 is considered for the second channel T d.1

−ts because Ps1 Td.1 bits are transmitted in the available transmission time. Moreover, the weighting T d.1

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−( j−1)t

T

−( j−1)t

s s factor W j = d.1 T is considered for the jth channel, after the j − 1 handoff, because Ps1 d.1 T d.1 d.1 bits are transmitted in the available transmission time. Hence, the probability of sum utilization of spectrum, with the set of N channels under topology-1, can be expressed as

PU.T p−1 = PUT.PU + ∑ j

j −1 N j=1 ( PSW )



2 j j j PD.SO PT Pe− f ree W j−1

 (11)

Next, we investigate the sum utilization of spectrum under topology-2. Let T be the union region of all those PRNs having coverage areas of the communicating SUs. In such a case, the probability of sum utilization of spectrum for topology-2 must be characterized for the two scenarios S1 and S2. S1 refers to a scenario in which no PU is present within region T. S2 refers to a scenario in which there are k PUs present within region T. We assume that PUs are deployed with a uniform distribution with density Ω. Thus, the probability that no PU is present within region T can be expressed as [34] PnoPU = e(−ΩT )

(12)

For the S1 case, the probability of detecting the spectrum opportunity at both SU communicating nodes, and the probability that no PU is present within region T, are considered for the sum utilization of spectrum for the SU. From Equations (4), (8) and (12), the probability of sum utilization of spectrum for the SU, for a single-channel scenario under S1 of topology-2, is expressed by PU.T p−2.S1 = PnoPU ( PD.SO )2 Pe1− f ree

(13)

For the S2 scenario, assume that k.PUs, and PUs.OFF, are the required events that represent the k PUs present within region T, and those PUs have an OFF state during SU transmission. The probability that there are k PUs in the region T is expressed in [34] as P[k.PUs] = e(−ΩT )

(ΩT )k k!

(14)

Hence, the probability that k PUs are present within region T, and are in the idle state during SU transmission over the first channel, can be expressed as [34] Pk1.IPUs = Pr [k.PUs ∩ PUs.OFF ]

(15)

Pk1.IPUs = P[k.PUs] P[ PUs.OFF k.PUs]

(16)



(ΩT )k  1 k PT k!

(17)

Pk1.IPUs = e{(−ΩT )(1− PT )} − e(−ΩT )

(18)

Pk1.IPUs =

∑ e(−ΩT)

k =1

which can be simplified as 1

For the S2 case, the probability of detecting the spectrum opportunity at both SU communicating nodes, and the probability that k PUs present within region T have an idle state, are considered for the sum utilization of spectrum for the SU. From Equations (4), (8) and (18), the probability of sum utilization of spectrum for the SU, for a single-channel scenario under S2 of topology-2 is expressed by PU.T p−2.S2 = Pk1.IPUs ( PD.SO )2 Pe1− f ree

(19)

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Thus, from Equations (13) and (19), and PU utilization probability, the probability of sum utilization of spectrum for a single-channel scenario under topology-2 can be expressed as h  i PU.T p−2 = PUT.PU + ( PD.SO )2 Pe1− f ree Pk1.IPUs + PnoPU

(20)

The probability of sum utilization of spectrum for the SU with the set of N channels under S1 of topology-2 is expressed by j PU.T = p−2.S1



j −1 N j=1 ( PSW )



j

PD.SO

2

j

PnoPU Pe− f ree W j−1

 (21)

Similarly, the probability of sum utilization of spectrum for the SU with the set of N channels under S2 of topology-2 is expressed by j PU.T = p−2.S2



j −1 N j=1 ( PSW )



j

PD.SO

2

j

Pkj.IPUs Pe− f ree W j−1

 (22)

From Equations (21) and (22) and PU utilization probability, the probability of sum utilization of spectrum with the set of N channels under topology-2 can be expressed as    2  j j j −1 j N j −1 j PU.Topl. = P + P P P W P + P ( ) UT.PU noPU ∑ j=1 SW D.SO e− f ree −2 k .IPUs

(23)

4. Numerical Results and Discussion In this section, numerical results are provided to evaluate the performance of sum utilization of spectrum under different network topologies, PU activities, sensing parameters, and sets of channels. In our simulation setup, we consider a CRN co-existing with a PRN that is licensed to use a set of N = 5 frequency bands. The communication range of PU and SU is varied to allow different values of probabilities and sensing parameters. The licensed bands are occupied by a PU according to the PU model as shown in Figure 3. To obtain the numerical results examined in this section, the key parameters are chosen as follows: Ps1 = 1000 bits, R p = 100 kbps, R = 20 ms to 100 ms, ts = 1 ms to 10 ms, and Ω = 0.0001 m−2 . The sensing SNR at the SU is considered to be −15 dB. The SNR for the secondary transmissions over each channel is set to 30 dB, and hence, the BER value is set to 0.00025. Unless otherwise stated, we consider the fair model of the PU for the channel status, i.e., PON = POFF = 0.5. The targeted detection probability PD is set to 90%, to restrict the interference probability to the PU to 10% or less. The values of these parameters are considered accordingly to validate the characteristics of the considered set of channels and network behavior. In the simulation runs, the maximum of five channels, each occupied by a single PU, are considered. The observation period commences from the first narrowband accessible channel to the last one. Figures 5 and 6 illustrate the probability of sum utilization of spectrum with different sensing durations and sets of channels, under the topology-1 model and topology-2 model, respectively. “Multi-channel” refers to a scenario in which different numbers of narrowband channels are considered, and the sum utilization probability over different numbers of narrowband channels is summed. The number of transmitted bits in a packet in the multi-channel scenario is adjusted as per the available transmission duration over that channel, and the weighting factor is added to consider the utilization as per the transmitted number of bits. Figures 5 and 6 validate the inherent tradeoff in the utilization of spectrum of the SU for single-channel scenario over different sensing durations. With the targeted detection probability, the spectrum utilization performance for the PU is considered to be the same. The tradeoff exists for any value of PU states mean durations considering the fair model of the PU for its channel status, i.e., the same PU states probabilities. The tradeoff exists between the two probabilities, i.e., the probability of “no activity during transmission” and the probability of “detecting the spectrum opportunity”. In detail, the increase in probability of “detecting the

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spectrum opportunity” over the shorter sensing durations is dominant over the decrease in probability of “no activity during transmission.” Similarly, the decrease in probability of “no activity during transmission” over the longer sensing durations is dominant over the increase in probability of “detecting the spectrum opportunity”. Hence, our results validate that an optimal sensing duration exists for single-channel scenario. However, the optimal sensing duration depends on the handoff probability and considered sensing parameters. It can be seen that the performance of the sum utilization of spectrum improves with the number of channels. The reason is that the multiple-channel scenario considers the transmission of a packet in the next channel for each PU interruption, and hence, enhances the 10, reliability the transmitted packet. However, the performance improvement Sustainability xx FOR REVIEW 12 Sustainability 2018, 2018, 10, FOR PEER PEERof REVIEW 12 of of 18 18 is not significant when a large number of channels is considered. The reason is that in such a case, improvement is not significant when a large number of channels is considered. The reason is that in the handoff probability is not significant. Importantly, the result validates that it is necessary to such a case, the handoff probability is not significant. Importantly, the result validates that it is considernecessary the optimal number channels subject to thesubject considered network and sensing parameters in to consider the of optimal number of channels to the considered network and sensing order toparameters achieve the optimal sum utilization performance. in order to achieve the optimal sum utilization performance. 0.66 0.66

Single-Channel Single-Channel Scenario Scenario Multi-Channel Multi-Channel Scenario Scenario with with 2 2 Channels Channels Multi-Channel Multi-Channel Scenario Scenario with with 3 3 Channels Channels Multi-Channel Scenario with 4 Channels Multi-Channel Scenario with 4 Channels Multi-Channel Multi-Channel Scenario Scenario with with 5 5 Channels Channels

Probability of of Sum Sum Utilization Utilization of of Spectrum Spectrum Probability

0.65 0.65 0.64 0.64 0.63 0.63

Sensing Sensing SNR=-15 SNR=-15 dB dB & & PU PU States States Mean Mean Duration=70ms Duration=70ms

0.62 0.62 0.61 0.61 0.6 0.6 0.59 0.59 0.58 0.58 0.57 0.57 1 1

2 2

3 3

Topology-1 Topology-1 4 5 6 7 4 5 6 7 Sensing Sensing Durations Durations (s) (s)

8 8

9 9

10 10 -3 -3 xx 10 10

Figure Figure 5. 5. Sum Sum utilization utilization of of spectrum spectrum for for singlesingle- and and multiple-channel multiple-channel scenarios scenarios under under the the topologytopology1 model.

Figure 5. Sum utilization of spectrum for single- and multiple-channel scenarios under the topology-1 model. 1 model. Single-Channel Single-Channel Scenario Scenario Multi-Channel Multi-Channel Scenario Scenario with with 2 2 Channels Channels Multi-Channel Scenario Multi-Channel Scenario with with 3 3 Channels Channels Multi-Channel Multi-Channel Scenario Scenario with with 4 4 Channels Channels Multi-Channel Multi-Channel Scenario Scenario with with 5 5 Channels Channels

Probability of of Sum Sum Utilization Utilization of of Spectrum Spectrum Probability

0.66 0.66 0.65 0.65 0.64 0.64

Sensing Sensing SNR=-15 SNR=-15 dB dB & & PU States Mean PU States Mean Duration=70ms Duration=70ms

0.63 0.63 0.62 0.62 0.61 0.61 0.6 0.6 0.59 0.59 0.58 0.58 1 1

2 2

3 3

Topology-2 Topology-2 4 5 6 7 4 5 6 7 Sensing Sensing Durations Durations (s) (s)

8 8

9 9

10 10 -3 -3 xx 10 10

Figure Figure 6. 6. Sum Sum utilization utilization of of spectrum spectrum for for singlesingle- and and multiple-channel multiple-channel scenarios scenarios under under the the topologyFigure 6. Sum utilization of spectrum for singleand multiple-channel scenarios under thetopologytopology-2 model. 22 model. model.

Figures 7 and 8 show the probability of sum utilization of spectrum with different PU states mean durations, for single- and multi-channel scenarios, under the topology-1 and topology-2 models, respectively. In the legend, “multi-channel” refers to a scenario in which five narrowband channels are considered, and the sum utilization for all the possible cases over five channels is

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Figures 7 and 8 show the probability of sum utilization of spectrum with different PU states mean durations, for single- and multi-channel scenarios, under the topology-1 and topology-2 models, respectively. In the legend, “multi-channel” refers to a scenario in which five narrowband channels are considered, and the sum utilization for all the possible cases over five channels is considered. Sustainability 2018, 10, x FOR PEER REVIEW 13 of 18 As previously explained, the fair model of the PU for channel status, i.e., same PU states probabilities, is considered. The of explained, transmitted is adjusted as per the available transmission duration considered. Asnumber previously the bits fair model of the PU for channel status, i.e., same PU states in each channel, and the weighting factor is added accordingly. Again, the result shows that the probabilities, is considered. The number of transmitted bits is adjusted as per the available performance of the sum utilization of spectrum improvesfactor with isthe number of channels. transmission duration in each channel, and the weighting added accordingly. Again, The the sum resultgain shows that the for performance of the models. sum utilization spectrum with thegain number of to the utilization is shown both topology In thisofstudy, the improves sum utilization refers channels. The sum utilization gain is shown scenario, for both topology models. In this study, the sum performance improvement of the multi-channel as compared to the single-channel scenario. utilization gain refers performance improvement of the multi-channel compared the The sum utilization gain to is the achieved because of the handoff capability ofscenario, SU, andasconsidering to the single-channel scenario. The sum utilization gain is achieved because of the handoff capability transmission of a packet in the next channel for each PU interruption. It can also be seen that the sum of SU, and considering the transmission of a packet in the next channel for each PU interruption. It utilization of spectrum increases with the increase in the PU states mean durations. The PU states can also be seen that the sum utilization of spectrum increases with the increase in the PU states mean mean durations. durations The includes bothmean the PU mean active and mean considering PU states durations includes both the inactive PU meandurations. active and By mean inactive the same PU states probabilities and targeted detection probability, the spectrum utilization performance durations. By considering the same PU states probabilities and targeted detection probability, the utilizationto performance forHowever, the PU is considered to states be the mean same. duration However, indicates a longer PU for thespectrum PU is considered be the same. a longer PU a longer states mean duration indicates a longer mean inactive duration, and hence for more PU mean inactive duration, and hence morePU spectrum utilization opportunities thespectrum SU. In detail, utilizationof opportunities the SU. In detail, the probability of “nothe activity during transmission” the probability “no activityfor during transmission” increases with increase in the PU states mean increases with the increase in the PU states mean duration, thereby increasing the probability of sum duration, thereby increasing the probability of sum utilization of spectrum. This result illustrates utilization of spectrum. This result illustrates the need to identify the optimal range of PU states mean the need to identify the optimal range of PU states mean durations subject to the considered sensing durations subject to the considered sensing parameters to obtain the maximum sum utilization gain parameters to multi-channel obtain the maximum with the scenario. sum utilization gain with the multi-channel scenario. Single-Channel Scenario Multi-Channel Scenario with 5 Channels

Probability of Sum Utilization of Spectrum

0.66 0.64 0.62 0.6

Sum Utilization Gain

0.58 Sensing SNR=-15 dB & Sensing Duration=2.5ms

0.56 0.54 0.52 0.5 0.48

Topology-1

0.46 0.01

0.02 0.03 0.04 0.05 PU States Mean durations (s)

0.06

0.07

Figure 7. Probability of sum utilization of spectrum with different PU states mean durations for

Figure 7. Probability of sum utilization of spectrum with different PU states mean durations for singlesingle- and multi-channel scenarios under topology-1. and multi-channel scenarios under topology-1. Figures 9 and 10 show the probability of sum utilization of spectrum with different PU active state probabilities and PUthe mean inactive durations the single-channel scenario under topology-1 Figures 9 and 10 show probability of sum for utilization of spectrum with different PU active and topology-2, respectively. At the PU active state probability P ON = 0.1, the utilization of spectrum state probabilities and PU mean inactive durations for the single-channel scenario under topology-1 is dominantly contributedAt by the the PU SU. active At the PU active state probability PON the = 0.9, the utilization of and topology-2, respectively. state probability PON = 0.1, utilization of spectrum spectrum is dominantly contributed by the PU. The sum utilization of spectrum increases when the is dominantly contributed by the SU. At the PU active state probability PON = 0.9, the utilization of PU uses the channel more actively. In addition, the overall utilization of spectrum when dominantly spectrum is dominantly contributed by when the PU. The sumcontributed utilizationbyofthe spectrum increases contributed by the PU is higher than dominantly SU, because the PU when the PU uses the channel more actively. In addition, the overall utilization of spectrum contributes more to the overall sum utilization of spectrum when the targeted detection probability when dominantly by the PU is be higher than when dominantly byof the SU, because is set tocontributed be 0.9. Furthermore, it can seen in Figures 9 and 10 that thecontributed sum utilization spectrum with the increase in PU meansum inactive durations. explainedwhen previously, the spectrum the PUincreases contributes more to the overall utilization ofAs spectrum the targeted detection utilization performance the PU is considered to be the same because9 of the10 fixed targeted detection probability is set to be 0.9. for Furthermore, it can be seen in Figures and that the sum utilization probability. However, PU mean inactive cause more As spectrum utilization of spectrum increases with longer the increase in PU meandurations inactive durations. explained previously, opportunities for the SU, and hence the probability of sum utilization of spectrum increases. It can

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the spectrum utilization performance for the PU is considered to be the same because of the fixed targeted detection probability. However, longer PU mean inactive durations cause more14spectrum Sustainability 2018, 10, x FOR PEER REVIEW of 18 utilization opportunities for the SU, and hence the probability of sum utilization of spectrum increases. 2018, 10, xthat FOR PEER REVIEW 14 of 18 also increase in in thethe sum utilization of spectrum withwith the PU inactive It canSustainability alsobebeobserved observed thatthe the increase sum utilization of spectrum the mean PU mean inactive durations is dominant when usesthe thechannel channel more thethe performance of theof the durations is dominant when thethe SUSUuses moreactively. actively.However, However, performance also be observedofthat the increase in the sumthe utilization of spectrum with actively. the PU mean inactive sum utilization spectrum converges when PU uses the channel more The reason sum utilization of spectrum converges when the PU uses the channel more actively. The reason is is that durations is dominant when the SU uses channel more actively. However, the performance ofand the that the SU’s utilization of spectrum is atthe a minimum when PU uses the channel more actively, the SU’s utilization of spectrum is at a minimum when PU uses the channel more actively, and the sum utilization of spectrum converges uses the performance channel moreof actively. reason is PU the PU mean inactive durations only when affect the thePU utilization the SU.The The results meanthat inactive durations only affect theisutilization performance thethe SU. The results validated the SU’s of spectrum at the a minimum PU of uses channel more andthat it validated thatutilization it is important to identify range of when PU states probabilities subject toactively, the targeted is important to identify the range of PU states probabilities subject to the targeted detection probability the PU mean inactive durations only affect the utilization performance of the SU. The results detection probability and PU states mean durations to achieve the required sum utilization validated that it durations is importanttotoachieve identifythe therequired range of PU probabilities subject to the targeted and PU states mean sumstates utilization performance. performance. detection probability and PU states mean durations to achieve the required sum utilization performance. Single-Channel Scenario Probability of SumofUtilization of Spectrum Probability Sum Utilization of Spectrum

0.66

Multi-Channel Scenario with 5 Channels Single-Channel Scenario Multi-Channel Scenario with 5 Channels

0.66 0.64 0.64 0.62 0.62 0.6

Sum Utilization Gain

Sensing SNR=-15 dB & Sensing Duration=2.5ms

Sum Utilization Gain

0.6 0.58

Sensing SNR=-15 dB & Sensing Duration=2.5ms

0.58 0.56 0.56 0.54 0.54 0.52 0.52

Topology-2 0.01

0.02 0.03 0.04 0.05 PU States Mean durations (s) Topology-2

0.06

0.07

0.01

0.02

0.06

0.07

0.03

0.04

0.05

Figure 8. Probability of sum utilization of spectrum with different states mean durations States Mean durations (s)PUPU Figure 8. Probability of sum utilization ofPUspectrum with different states mean durations forfor singlesingle- and multi-channel scenarios under topology-2. and multi-channel scenarios under topology-2. Figure 8. Probability of sum utilization of spectrum with different PU states mean durations for Single-Channel Scenario Under Topology-1 single- and multi-channel scenarios under topology-2.

Probability of SumofUtilization of Spectrum Probability Sum Utilization of Spectrum

0.9

PU Mean Inactive Duration (R) =30ms

Single-Channel ScenarioPU Under Topology-1 Mean Inactive Duration (R) =70ms

0.85 0.9

PU Mean Inactive Duration (R) =100ms PU Mean Inactive Duration (R) =30ms PU Mean Inactive Duration (R) =70ms

0.8 0.85

PU Mean Inactive Duration (R) =100ms

0.75 0.8

Region with Utilization Majorly Contributed by SU

0.7 0.75

Region with Utilization Majorly ContributedDetection Probability=.9 by SU & Sensing Duration=2.5ms

0.65 0.7

Detection Probability=.9 & Sensing Duration=2.5ms

0.6 0.65 0.55 0.6

Region with Utilization Majorly Contributed by PU

0.5 0.55 0.45 0.5 0.1

Region with Utilization Majorly Contributed by PU

0.2

0.3

0.4 0.5 0.6 0.7 PU Active State Probability

0.45

0.8

0.9

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure 9. Probability of0.1sum utilization of with different PU active state probabilities for PUspectrum Active State Probability single-channel scenarios under topology-1. Figure 9. Probability of sum utilization of spectrum with different PU active state probabilities for Figure 9. Probability of sum utilization of spectrum with different PU active state probabilities for single-channel scenarios under topology-1.

single-channel scenarios under topology-1.

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of Sum of Utilization of Spectrum Probability Probability of Sum Utilization Spectrum

Single-Channel Scenario Under Topology-2 0.9 PU Mean Inactive Duration (R) =30ms Sustainability 2018, 10, x FOR PEER REVIEW

PU Mean Inactive Duration (R) =70ms PU Mean Inactive Duration (R) =100ms

0.85 0.9 0.8 0.85 0.75 0.8 0.7

Single-Channel Scenario Under Topology-2

PU Mean Inactive Duration (R) =30ms PU Mean Inactive Duration (R) =70ms PU Mean Inactive Duration (R) =100ms

Region with Utilization Majorly Contributed by SU

Region with Utilization Majorly Contributed by SU

Detection Probability=.9 & Sensing Duration=2.5ms

0.75 0.65 0.7 0.6

Detection Probability=.9 & Sensing Duration=2.5ms

0.65 0.55 0.6 0.5 0.1 0.55

15 of 18

Region with Utilization Majorly Contributed by PU

Region with Utilization Majorly Contributed by PU

0.2

0.3

0.4 0.5 0.6 0.7 PU Active State Probability

0.8

0.9

Figure 10. Probability of sum utilization of spectrum with different PU active state probabilities for

Figure 10. Probability of 0.5 sum utilization different 0.3of spectrum 0.4 0.5with0.6 0.7 PU 0.8active 0.9state probabilities for single-channel scenarios0.1 under0.2 topology-2. single-channel scenarios under topology-2.PU Active State Probability Figure 10. of sum of spectrum with different PU active with state probabilities Figures 11Probability and 12 show theutilization probability of sum utilization of spectrum different PUfor active under topology-2. state single-channel probabilities for singleand multiple-channel scenarios under topology-1 and topology-2, Figures 11 and 12 scenarios show the probability of sum utilization of spectrum with different PU active state respectively. In the multi-channel scenario, two narrowband channels are considered, the probabilities for single- and multiple-channel scenarios under topology-1 and topology-2,and respectively. Figures 11 and 12 over showthe thetwo probability ofissum utilization of spectrum with different PU active utilization probability channels summed. As explained previously, the number of In the multi-channel scenario, two narrowband channels are considered, and the utilization probability state probabilities for singleand multiple-channel scenarios under topology-1 bits andintopology-2, transmitted bits are fixed for the first channel. Moreover, the number of transmitted the second over the two channels summed. As scenario, explainedtwo previously, the channels number of bits fixed respectively. In theis narrowband aretransmitted considered, andare the channel is adjusted asmulti-channel per the available transmission duration, and the weighting factor is added to for the first channel. Moreover, the number of transmitted bits in the second channel is adjusted utilization the channels number is summed. AsItexplained previously, number of as consider theprobability utilizationover as per thetwo transmitted of bits. can be seen in Figuresthe 11 and 12 that per the available transmission duration, and the weighting factor is added to consider the utilization transmitted bitsmean are fixed for the first channel. offor transmitted bits in thescenario second for a given PU inactive duration, the sumMoreover, utilizationthe of number spectrum the multi-channel channel is adjusted as per the available transmission duration, and the weighting factor is added tomean as peralso theincreases transmitted number of bits. It can be seen in Figures 11 and 12 that for a given when the PU uses the channel more actively. The reason is the same, as thePU PU consider the utilization as per the transmitted number of bits. It can be seen in Figures 11 and 12 that inactive duration, the sum utilization of spectrum for the multi-channel scenario also increases contributes more to the overall sum utilization of spectrum because of the targeted detectionwhen foruses a given mean inactive the sum utilization spectrum for the multi-channel scenario the PU thePU channel more duration, actively. The reason is theofsame, as the PU contributes more probability. The performance improvement for the multi-channel scenario is achieved for any modelto the also increases when the PU uses the channel more actively. The reason is the same, as the PU of channel status, i.e.,ofdifferent PUbecause states probabilities. The reason is thatprobability. the handoff The probability is overall sum utilization spectrum of the targeted detection performance contributes more to the overall sum utilization of spectrum because of the targeted detection considered tothe be the same for anyscenario PU channel status. Hence, the model transmission of a packet in i.e., the next improvement for multi-channel is achieved for any of channel status, different probability. The performance improvement for the scenario is is achieved for any model channel for each PU The interruption is that considered, andmulti-channel the sum utilization gain achieved. PU states probabilities. reason is the handoff probability is considered to be the same for any of channel status, i.e., different PU states probabilities. The reason is that the handoff probability is PU channel status. thefor transmission of astatus. packetHence, in thethe next channel for PU in interruption is 0.95 considered to beHence, the same any PU channel transmission ofeach a packet the next Single Channel Scenario Multi Channel Scenario with 2 Channels considered, and the sum utilization gain is achieved. channel for each PU interruption is considered, and the sum utilization gain is achieved. of Sum Utilization of Spectrum ProbabilityProbability of Sum Utilization of Spectrum

0.9

0.95 0.85

Sum Utilization Single Channel Scenario Multi Channel ScenarioGain with 2 Channels

0.9 0.8 0.85 0.75

Sum Utilization Gain

0.8 0.7 0.75 0.65 0.7 0.6 0.65 0.55 0.6 0.5 0.55 0.45 0.1 0.5

Sensing Duration=2.5ms & PU Mean Inactive Duration=30ms

Sensing Duration=2.5ms & PU Mean Inactive Duration=30ms

Topology-1 0.2

0.3

0.4 0.5 0.6 0.7 PU Active State Probability

0.8

0.9

Topology-1 Figure 11. Probability0.45 of sum utilization of spectrum with different PU active state probabilities for 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 single- and multiple-channel scenarios under topology-1. PU Active State Probability

Figure 11. Probability of sum utilization of spectrum with different PU active state probabilities for

Figure 11. Probability of sum utilization of spectrum with different PU active state probabilities for single- and multiple-channel scenarios under topology-1. single- and multiple-channel scenarios under topology-1.

Sustainability 2018, 10, 1764 Sustainability 2018, 10, x FOR PEER REVIEW

16 of 18 16 of 18

0.95

Single Channel Scenario Multi Channel Scenario with 2 Channels

Probability of Sum Utilization of Spectrum

0.9 0.85

Sum Utilization Gain

0.8 0.75 0.7 0.65

Sensing Duration=2.5ms & PU Mean Inactive Duration=30ms

0.6 0.55 0.5 0.1

Topology-2 0.2

0.3

0.4 0.5 0.6 0.7 PU Active State Probability

0.8

0.9

Figure 12. 12. Probability Probability of of sum sum utilization utilization of of spectrum spectrum with with different different PU PU active active state state probabilities probabilities for for Figure singleand multiple-channel scenarios under topology-2. single- and multiple-channel scenarios under topology-2.

5. Conclusions 5. Conclusions To deliver the full range of potential capabilities promised by 5G networks, efficient dynamic To deliver the full range of potential capabilities promised by 5G networks, efficient dynamic spectrum allocation schemes are required. Furthermore, heterogeneous deployment, i.e., small cells, spectrum allocation schemes are required. Furthermore, heterogeneous deployment, i.e., small cells, is is considered a major network topology in 5G networks. Such multi-tier network layouts will enhance considered a major network topology in 5G networks. Such multi-tier network layouts will enhance the coverage and capacity of the network 1000-fold. However, such architecture introduces severe the coverage and capacity of the network 1000-fold. However, such architecture introduces severe challenges for the 5G-based CRNs. The reason is that the PU will be required to be more active challenges for the 5G-based CRNs. The reason is that the PU will be required to be more active because of the small coverage area, with more active users per unit area, more base stations, random because of the small coverage area, with more active users per unit area, more base stations, random user arrivals, and spectrum movement. Besides, handover operations must be executed in multi-tier user arrivals, and spectrum movement. Besides, handover operations must be executed in multi-tier networks. Therefore, efficient handover management is needed for such networks. CRNs have great networks. Therefore, efficient handover management is needed for such networks. CRNs have great potential to enhance the spectrum utilization. In this regard, we propose the analytical formulation potential to enhance the spectrum utilization. In this regard, we propose the analytical formulation and and evaluation of spectrum utilization for the PU and SU, considering different sets of accessible evaluation of spectrum utilization for the PU and SU, considering different sets of accessible channels. channels. We consider an interweave-based CRN under different physical topologies based on the We consider an interweave-based CRN under different physical topologies based on the spatial and spatial and temporal variations of the PU activities. We present a realistic scenario of multiple temporal variations of the PU activities. We present a realistic scenario of multiple narrowband narrowband channels for the SU to utilize the licensed band more efficiently. The SU can switch to channels for the SU to utilize the licensed band more efficiently. The SU can switch to the next the next channel in the case of PU interruptions and ensures the reliability of the transmitted packet, channel in the case of PU interruptions and ensures the reliability of the transmitted packet, hence hence increasing spectrum utilization. The sum utilization of spectrum is analyzed through closedincreasing spectrum utilization. The sum utilization of spectrum is analyzed through closed-form form expressions. In addition, we evaluate the impact of different network and sensing parameters expressions. In addition, we evaluate the impact of different network and sensing parameters over over the sum utilization gain, achieved with the multi-channel scenario. Specifically, numerical the sum utilization gain, achieved with the multi-channel scenario. Specifically, numerical results results indicate that a different number of channels, PU activities, sensing outcomes, and network indicate that a different number of channels, PU activities, sensing outcomes, and network topologies topologies have significant impact on the sum utilization of spectrum. In the future, we would like have significant impact on the sum utilization of spectrum. In the future, we would like to extend to extend our approach of investigating the utilization of spectrum for more complicated scenarios our approach of investigating the utilization of spectrum for more complicated scenarios such as such as cooperative, unlicensed (femtocells), and HARQ-enabled SUs in dense CRNs. cooperative, unlicensed (femtocells), and HARQ-enabled SUs in dense CRNs. Author Contributions: Contributions: Waqas Khalid Heejung designedthe andproposed developed the and proposed idea, and also Author W.K. and H.Y. and designed andYu developed idea, also formulated the formulated themodel. mathematical model. WaqasH.Y. Khalid wrote the paper. Heejung Yu supervised and finalized the mathematical W.K. wrote the paper. supervised and finalized the manuscript for submission. manuscript for submission. Acknowledgments: This research was supported by a 2018 Yeungnam University Research Grant. Acknowledgments: was supported by of a 2018 Yeungnam University Research Grant. Conflicts of Interest:This The research authors declare no conflict interest. Conflicts of Interest: The authors declare no conflict of interest.

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