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Hybrid spectrum sharing with cooperative secondary user selection in cognitive radio networks.

1. Introduction

As a solution for the spectrum inefficiency problem, cognitive radio (CR) is an exciting and emerging technology that has attracted a great deal of attention in recent years for enhancing the utilization of limited resources [1]. In cognitive radio networks (CRNs), primary (licensed) users (PUs) coexist with secondary (unlicensed) users (SUs) in the same frequency band to achieve better spectrum utilization.

1.1 Related Work

Generally, in CRNs, three models have been considered in the literature for spectrum sharing: the interweave, underlay and overlay. In the opportunistic spectrum access (OSA) or interweave model [2-3], CRs (SUs) opportunistically access the unused licensed band, commonly referred to as "spectrum hole" only when it is detected idle. However, the main problems of the interweave models are: high sensitivity to the detection error and PU traffic pattern [3-4]. In underlay model [5-6], SUs are allowed to transmit simultaneously with the PUs as long as the interference generated by SUs to PUs below some accepted threshold. Because of the strict power constraints imposed on SUs and the interference from PUs [7], the SUs may have a bad transmission performance which is a major problem in underlay approaches. In the overlay model, the SUs simultaneously transmit with the PUs over the same spectrum provided that the SUs may help the PUs such that PUs can transmit by cooperative communication techniques, such as advanced coding or cooperating relaying techniques [8]. However, due to the mutual interference between PUs and SUs, the overlay approach may still experience a secondary transmission performance degradation.

A spectrum sharing protocol by jointly considering interweave and overlay models was proposed in [9]. To facilitate the spectrum sharing protocols, dirty paper coding and perfect spectrum sensing are used in [9]. Hybrid spectrum sharing protocols by jointly considering overlay and underlay models have been proposed in [10-12]. In [13], under hybrid spectrum sharing protocol, an optimal transmission allocation scheme to achieve maximum energy-efficiency is investigated. In this work, the authors considered one PU pair and one SU pair, in which they interfere with each other. Moreover, a proper spectrum sharing model is selected by SUs based on the state of the PUs.

Because of the adversity of the common channel between PTx and PRx pair, it is impossible to establish a direct link (DL) between them. In order to solve this problem, cooperative relay has been introduced into CRNs as in [14] and various relay selection strategies have been proposed such as [15-16]. The relay nodes assist the primary system so that the PTx-PRx pair can transmit more data via this relay link while transmitting to the DL. In addition, using a relay node between source and destination gives an extra benefit of reducing the overall path loss [17]. By this way, it is possible to increase system throughput and spectrum efficiency.

Spectrum sharing protocols considering amplify-and-forward (AF) relaying have been proposed in [18-19] and decode-and-forward (DF) relaying were investigated in [20-21]. In [18], a cooperative relaying spectrum sharing CR system considering constraints on the average received-interference at the PRx is investigated where AF relays are employed to help in the SUs communication process. There is no DL between source and associated destination nodes and the communication is established in a dual hop fashion with the help of a relay. In [20], a single STx partially acts as a DF relay for the primary system consisted of a simple transmitter-receiver pair. The DF based spectrum sharing protocol was generalized to a multi-user scenario where multiple secondary transmitters compete for opportunistic access of the primary user's spectrum by assisting them [21]. In [22], the authors extended the work in [21] by considering a more general scenario where the primary system is a dual hop selective relaying network and secondary nodes may act either as relays for the primary system or serve as secondary access transmitters. But in their work, they did not consider any DL between PTx and PRx as well as extra relays are used to assist the primary.

1.2 Our Main Contributions

In this paper, our main contributions can be summarized as follows:

1) A novel cooperative hybrid spectrum sharing model by jointly considering interweave and underlay schemes so that the SUs can access the licensed spectrum along with the PU.

2) We investigate the ergodic capacity and outage probability of the primary system with cooperative relaying.

3) We evaluate the outage probability of the SUs by considering the following three cases based on PU activity.

* If the data rate of PTx to PRx achieves [R.sub.PT].

* If the data rate of PTx to PRx falls below [R.sub.PT] over the DL but achieves [R.sub.PT] on the relaying link.

* If the PTx-PRx pair is idle or primary system is in outage.

The above three cases are mutually exclusive. So, the outage probability of the each case is calculated separately. Then, the total outage probability is calculated to establish the relationship among the above cases.

4) It is shown that, both the PU and SUs are able to achieve performance improvement in terms of outage probability when the active secondary transmitter is located farther away from the PRx. It is also shown that the ergodic capacity of the PU with cooperative relaying degrades when the active secondary transmitter becomes closer to the PRx.

5) Closed-form expressions of the outage probabilities are derived and validated by the simulation results. Moreover, interference limited environment is considered.

The main advantage of our proposed spectrum sharing model is that our scheme provides better spectrum utilization compared to the individual consideration of either interweave or underlay scheme.

The cooperative relaying scheme proposed in [23] has been incorporated in this research paper for the clarity of the presentation of our current work. But the notable differences between this work and [23] are as follows. In [23], we only proposed a cooperative SU selection scheme for an underlay CRN. But in this work, we have proposed a hybrid spectrum sharing model with joint consideration of underlay and interweave schemes. The main contributions of the current work have been summarized above.

1.3 Organization of the Paper

The rest of this paper is organized as follows. In section 2, we introduce the system model. In section 3, SU selection schemes are illustrated. Section 4 describes the outage probability analysis. Analytical results validated by simulation results are given in section 5. Finally, we conclude this paper in section 6.

2. System Model

2.1 System Description

We consider a hybrid spectrum sharing model by jointly considering interweave and underlay schemes for CRNs consisting of a primary transmitter (PTx) and a primary receiver (PRx) as well as a group ofM STx-SRx pairs. The proposed system model is shown in Fig. 1.

Secondary transmitters are divided into two groups. In the first group, K (K [member of] M) active secondary transmitters [ST.sub.i], i [member of] (1, 2, ..., K} which may opportunistically use the PU spectrum or may transmit data with the coexistence of PTx below a certain interference threshold to the PRx. In the second group, N=M-Kinactive secondary transmitters [ST.sub.j], j [member of] (1, 2, ... , N)} which are in idle state, act as relays to assist the primary system. In [22], a group of secondary transmitters as well as relays participate in the cooperation procedure to assist the primary system and one of the nodes is selected as a best relay node to forward the primary information. During the best relay selection procedure, no secondary spectrum access is allowed. The secondary transmitters may compete for the secondary spectrum access in the second transmission phase after the successful selection of the best relay for the primary system when the primary system is not in outage. But in our proposed method, only the inactive secondary transmitters will participate in the relay selection procedure to cooperate the PU. At the same time, an active secondary transmitter may transmit its data to the corresponding receiver causing interference below the certain threshold to the PRx. The active secondary transmitter causes interference to the PRx when the DL between PTx and PRx exists or to the [ST.sub.j] as well as the PRx during cooperation. Similarly, the PTx causes interference to the SRx when an active secondary transmitter transmits data to its corresponding receiver. Moreover, SUs or CRs interfere with each other when more than one SUs transmit simultaneously. When the data rate between the PTx and PRx over the DL falls below [R.sub.PT] then the primary transmission from PTx to PRx is performed over two transmission phases via the help of the best inactive secondary transmitter which acts as a DF relay to the primary system. Moreover, we consider signal to noise plus interference ratio (SNIR) over links PTx-PRx, PTx-[ST.sub.j] (Rej), [ST.sub.j]-PRx and [ST.sub.i]-SRi.

2.2 Channel Model

Assume that the channels over all links are subject to Rayleigh flat fading plus additive white Gaussian noise (AWGN) because large-scale fading is almost constant and can be mitigated by the power control over a long period of time whereas small-scale fading can not. Each node is a single antenna system and a half duplex radio. Also assume that the channel coefficients remain static during the both transmission phases. Let, link gain [[alpha].sub.i.j] between nodes i and j is an exponentially distributed random variable with a mean value [[lambda].sub.i,j] [24]. To get the desired effect of the position of the active secondary transmitter with respect to the PRx, we consider [[lambda].sub.i,j] = [(1/[d.sub.i,j]).sup.n] where [d.sub.i,j] denotes the distance between node i and j and n is the path loss exponent. The transmit power at PTx, [ST.sub.i] and [ST.sub.j] is denoted as [P.sub.PT], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] respectively.

We assume that PTx and each STx adopt adaptive power allocation scheme as follows:

* The PTx may increase its transmit power to the peak.

* When a STx acts as a relay to forward the primary information, it uses the same transmit power as the PTx.

* If the PU is in idle state or primary system is in outage, a STx can increase its transmit power to reach the maximum.

* In addition, if the PU is present, only a STx limits its transmit power to satisfy a predefined interference threshold to the PRx.

2.3. Secondary Transmission Scheme with State Transition

The state transition scenario of the secondary transmitters is shown in Fig. 2. Assume that at most one STx-SRx pair may change its state from inactive to active at any time instant. The state [S.sub.STi] = 1 denotes active while [S.sub.STi] = 0 denotes inactive where [S.sub.STi] represents the state of the ith STx among Msecondary transmitters. From Fig. 2, it is clear that the STx may be in any of the following state scenarios:

1) The first level of the state diagram in Fig. 2 shows that if none of the secondary transmitters is able to achieve the secondary target date rate [R.sub.ST] then all the secondary transmitters are in inactive states. In such scenario, no secondary transmission is allowed. So, all the secondary transmitters participate in the relay selection procedure to forward the primary information if the data rate of the DL between PTx and PRx falls below [R.sub.PT].

2) The second level in Fig. 2 shows that only one STx may be active at a time. This happens when the PU is present. So, all the remaining secondary transmitters are inactive. In this scenario, an active secondary transmitter may transmit in parallel with the PTx satisfying a predefined interference threshold to the PRx. If the active secondary transmitter fails to achieve [R.sub.ST] then it goes to the initial state i.e., first level in the state diagram.

3) When the PU is absent or the PU fails to achieve [R.sub.PT] over the DL as well as relaying link then there is no primary transmission in the channel. In such scenario, at most two among M secondary transmitters may be active at a time which is shown in the third level of the state diagram in Fig. 2. One of the active secondary transmitters may become opportunistic secondary i.e., it transmits as like as the PU and another active secondary transmitter may transmit satisfying certain interference threshold to the opportunistic SRx. If only one STx achieves [R.sub.ST] then the state goes to the second level in Fig. 2. If no secondary transmitter achieves [R.sub.ST] then all the secondary transmitters go to the initial state i.e., first or fourth level of the state diagram. Although the first and fourth levels of the state diagram are same but we have drawn them as separate level for the simplicity of our drawing.

Moreover, the secondary spectrum access policy is described in details in section 3.2. It is also assumed that primary and secondary systems use the link layer control signals like RTS and CTS to access the channel as in [15].

3. Secondary User Selection Scheme: Description and Implementation

3.1 Cooperative Secondary User Selection

When the data rate of the PU over the DL falls below [R.sub.PT] then one of the inactive secondary transmitters acts as a cooperative relay to forward the primary information. The detailed explanation of our cooperative secondary selection as a relay for the primary system is given in [23]. In this section, we will summarize the scheme for the sake of clarity of our spectrum sharing model. The achievable rate of the links PTx-PRx, PTx-to-[Re.sub.j] and [Re.sub.j]-to-PRx are given by

[R.sub.PTx-PRx] = [log.sub.2] (1 + [SNIR.sub.PTx-PRx]) (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where the scaling factor 1/2 in (2) and (3) is due to the fact that the overall transmission is divided into two phases. The SNIR of the corresponding links can be represented as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where [[eta].sub.1] ~CN(0,[[sigma].sup.2.sub.1]), [[eta].sub.2] ~CN(0, [[sigma].sup.2.sub.2]), [[eta].sub.3] ~CN(0, [[sigma].sup.2.sub.3] denote AWGN. We assume that only one active secondary transmitter (i.e., K = 1) may transmit data with the coexistence of PTx-PRx pair below a certain interference threshold to the PRx at a time when PTx-PRx pair is active. Moreover, noise powers are negligible in the interference limited environment [25]. Therefore, (4), (5) and (6) are respectively approximated as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

The equivalent end-to-end data rate of the two hop cooperative link is the minimum one of the two hops [26]. We denote S, the set of relays that can be considered for relay selection as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

We consider a similar relay selection procedure as in [23]. So, our proposed protocol selects the best relay [Re.sub.best] if it satisfies the following condition

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

After the selection of the best inactive secondary (best relay), the PTx transmits the message to the best relay in the first time slot. If the best relay is able to decode the message successfully then it will forward this message to the PRx in the second time slot. Otherwise, the best relay remains silent and the system declares an outage. Therefore, the ergodic capacity which is defined as the maximum achievable long term rate without considering any delay constraint, of the primary system with the considered relay selection of (11) can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

In our relay selection procedure, we have considered all N links. Hence, from (10), (11) and (12), it is clear that the ergodic capacity of the PU through the relaying link is the long term best relay rate among N relays without any delay constraint consideration.

3.2 Active Secondary User Selection for Secondary Spectrum Access

In this paper, we show that if all the active secondary nodes have an equal power scheme then the position of the active secondary transmitter with respect to the PRx affects the outage performance and ergodic capacity. Selection of active SU for spectrum access is described in three different possible scenarios. The proposed scenarios are:

* Scenario I (SI): A secondary node selection when the data rate of the PTx to PRx over the DL achieves [R.sub.PT].

* Scenario II (SII): A secondary node selection when the data rate of the PTx to PRx falls below [R.sub.PT] over the DL but achieves [R.sub.PT] on the relaying link PTx-[Re.sub.m]-PRx.

* Scenario III (SIII): Two secondary nodes selection for spectrum access when PTx-PRx pair is idle or primary system is in outage.

3.2.1 Secondary Node Selection in SI

Only one secondary node can access the channel in this scenario. All secondary nodes compete for spectrum access considering CSMA/CA like random access protocol [27]. Let, a secondary node [ST.sub.p] gets opportunity to access the channel causing interference to the PRx below a certain interference threshold. Then, [ST.sub.p] becomes a member of active secondary nodes i.e., p [member of] K. Now, the data rate over the links [ST.sub.p] to [SR.sub.p] is given by

[R.sub.sTp-SRp] = [log.sub.2] (1 + [SNIR.sub.STp-SRp]) (13)

According to (7), (8) and (9), the received SNIR at the SRp can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

Assume, [[sigma].sup.2.sub.PInt] = [P.sub.PInt] + [[eta].sub.SR] [approximately equal to] where [P.sub.Pint] and [[eta].sub.SR] denote interference caused by PTx at [SR.sub.p] and AWGN respectively. In CR spectrum sharing system, it is allowed to share the PU's spectrum by SU as long as the amount of interference caused by STx at the PRx is below a predefined threshold [I.sub.th], which is the maximum tolerable interference level at the PRx [5]. So, the transmission power of the SU is constrained to allow this spectrum sharing and is given as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

By putting (15) into (14), we get

[SNIR.sub.STp-SRp] = [[alpha].sub.STp-SRp][I.sub.th]/[[alpha].sub.STp-PRx][[sigma].sup.2.sub.PInt] (16)

3.2.2 Secondary Node Selection in SII

To select the secondary node for spectrum access, the following situations are considered:

* Suppose SI is happening. Afterwards, if the primary rate falls below [R.sub.PT] then the secondary transmitter [ST.sub.p] which is using the channel satisfying [I.sub.th] will use the channel as usual as in SI. All other inactive secondary transmitters will participate in the relay selection procedure according to section 3.1. Assume that the active secondary node will ignore the primary cooperation control messages i.e., it will not respond to the PU request message for cooperation.

* Among the inactive secondary transmitters, only the nodes which satisfy (10), start their countdown timers to cooperate the primary system. So, other inactive secondary transmitters are free to compete for secondary spectrum access.

* If PTx[right arrow][Re.sub.best][right arrow]PRx link is established, then all other inactive secondary transmitters except Rebest will compete for secondary spectrum access as in [27].

The data rate of the active secondary is calculated as in SI.

3.2.3 Secondary Node Selection in SIII

We assume that if the PTx-PRx pair is idle then they will be considered as in outage. Hence, when the primary system is in outage, two secondary nodes get the opportunity to access the primary spectrum. One of the secondary transmitters will opportunistically use the PU's spectrum i.e., it acts as like as the PU and at the same time another STx coexist satisfying [I.sub.th] to the opportunistic SRx at the same spectrum band. It is assumed that all the secondary nodes keep information about the [Re.sub.best] of the immediate previous cooperating transmission phase. So, the [Re.sub.best] ([ST.sub.oppr]) will be the opportunistic secondary during the outage of the primary system. Remaining secondary transmitters will compete for spectrum access as in [27] satisfying [I.sub.th] to the opportunistic SRx and let [ST.sub.q], q [member of] M \ {[ST.sub.oppr]} succeeds to access the spectrum. Then, [ST.sub.oppr] and [ST.sub.q] become members of active secondary groups Ki.e., K = 2. Now, the data rate over the links [ST.sub.q] to [SR.sub.q] and [ST.sub.oppr] to [SR.sub.oppr] are given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

[R.sub.SToppr-SRoppr] = [log.sub.2] (1 + [SNIR.sub.SToppr-SRoppr]) (18)

The opportunistic STx acts like a PU when the primary system is in outage. So, the transmission power [P.sub.SToppr] of the [ST.sub.oppr] does not need to consider interference constraint. But [ST.sub.q] must satisfy [I.sub.th] to the [SR.sub.oppr]. So, the transmission power of the [ST.sub.q] needs to constrain i.e., [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Therefore, according to (7), (8) and (9), the received SNIR at the [SR.sub.oppr] and [SR.sub.q] can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

Assume [[sigma].sup.2.sub.q] = [P.sub.Intoppr] + [[eta].sub.q] [approximately equal to] [P.sub.Intoppr] where [P.sub.Intoppr] and [[eta].sub.q] denote interference caused by [ST.sub.oppr] at the [SR.sub.q] and AWGN respectively.

4. Outage Analysis

4.1 Outage Probability of the Primary System

The primary system is in outage if the following two conditions occur: (i) The data rate of the DL between PTx and PRx falls below [R.sub.PT] and (ii) None of the inactive secondary nodes achieves [R.sub.PT] i.e., [absolute value of S] = 0. So, the outage probability of the primary system is expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

In (21), the outage probability for the links PTx-PRx, PTx-to-[R.sub.em] and [R.sub.em]-to-PRx are given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Let, [g.sub.o] and [g.sub.1] are exponential random variables with means [[lambda].sub.0] and [[lambda].sub.1] respectively. Then, the probability density function (PDF) of X = [g.sub.0]/[g.sub.1] is expressed as [28].

[f.sub.x] (x) = [[lambda].sub.0] [[lambda].sub.1]/[([[lambda].sub.0] + [[lambda].sub.1]x).sup.2]

Similarly, all the link gains assumed in this paper are exponentially distributed random variables with their corresponding mean values which are defined in section 2. Thus, the outage probability for the links PTx-PRx can be derived as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

Similarly, the outage probability for the links PTx-to-[R.sub.em] and [R.sub.em]-to-PRx can be derived as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

By substituting (25), (26) and (27) in (21), we get the total outage probability of the primary system.

4.2 Outage Probability of the Secondary System

In this section, we will derive the outage probability of the secondary system with request target rate [R.sub.ST] by considering three scenarios of the secondary spectrum access.

4.2.1 Outage Probability of SI

The secondary system is in outage if the data rate of the DL between PTx and PRx achieves [R.sub.PT] but secondary data rate falls below [R.sub.ST]. The outage probability is therefore given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)

In (28), the outage probability for the link [ST.sub.p] to [SR.sub.p] can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Now, substituting (25) and (29) in (28), we can get the outage probability of the secondary system of SI.

4.2.2 Outage Probability of SII

The secondary system is in outage if the following situations occur simultaneously:

i) The data rate of the DL between PTx and PRx falls below [R.sub.PT].

ii) The data rate of the link PTx-[R.sub.em]-PRx achieves [R.sub.PT], and

iii) The secondary data rate falls below [R.sub.ST].

In the case of simplicity of our derivation, we assume that same STx i.e., STp transmits in SI and SII. So, the outage probability can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)

Substituting (25), (26), (27) and (29) in (30), we get the outage probability of the secondary system of SII.

4.2.3 Outage Probability of SIII

The outage of the SUs occur when the following three conditions occur simultaneously:

i) The PTx and PRx pair is idle or primary system is in outage.

ii) The data rate of the opportunistic secondary node falls below [R.sub.ST].

iii) The data rate of the secondary node satisfying [I.sub.th] falls below [R.sub.ST].

The outage probability of the secondary system is therefore expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (31)

In (31), the outage probability for the link [ST.sub.q]-[SR.sub.q] and [SR.sub.oppr]-[SR.sub.oppr] are written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (32)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (33)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Now, substituting (21), (32) and (33) in (31), we get the outage probability of the secondary system of SIII.

The three scenarios described in section 3.2 in the selection of active secondary transmitter for spectrum access are mutually exclusive. So, the outage probability of the each scenario is calculated separately. However, by summing (28), (30) and (31), we can get the total outage probability of the secondary system as follows:

[P.sup.S.sub.OUT] = [P.sup.S,(SI).sub.OUT] + [P.sup.S,(SII).sub.OUT] + [P.sup.S,(SIII).sub.OUT] (34)

5. Simulation Results and Discussions

In this section, we present the simulation and theoretical results to study the performance of our proposed spectrum sharing model. PTx and PRx are located at (0, 40) and (100, 40) respectively. To reduce the number of model parameters, we assume that all the inactive secondary transmitters which act as relays are located at approximately the same distance between PTx and PRx as in [29-30] and variable location of active secondary transmitter is considered to show that the ergodic capacity and outage probability are affected by the position of the active secondary transmitter with respect to the PRx. Moreover, slow fading is considered in this paper. So, to get the effect of all relays, fading co-efficient of each relay is independent to each other. Assume, path loss exponent n=2 and meter is the unit of distance here.

In Fig. 3 and Fig. 4, we show the simulation result of the ergodic capacity of the primary system with a cooperative SU selection as a function of SNIR. Here, we assume [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and SNIR varies from 0 dB to 18 dB. It can be observed from Fig. 3 that the ergodic capacity of the primary system monotonically increases with SNIR for both direct transmission (DT) and with the considered relay selection of (11) as expected. In addition, it is clear from Fig. 3 that the better ergodic capacity can be achieved with increasing N. Fig. 4 shows the impact of the position of the active secondary transmitter with respect to the PRx. Ergodic capacity decreases as the active secondary transmitter becomes closer to the PRx. If two active secondary transmitters have same transmit power then closer one to the PRx causes more interference to the PRx because of shorter distance.

In Fig. 5 and Fig. 6, we show the outage probability of the primary system as a function of SNIR in dB. Simulation results are verified by theoretical results developed in section 4 and they match with each other in all cases. Fig. 5 shows the outage probability decreases with increasing SNIR as well as N. It can be observed that the proposed spectrum sharing model with cooperative relays shows better outage performance than non-cooperative network. In Fig. 6, we show the outage probability of the primary network with the varying position of the active secondary transmitter. It can be observed that primary outage increases as the active secondary transmitter becomes closer to the PRx. If two active secondary transmitters have the same transmit power, the closer one with respect to PRx causes more interference to the PRx which is clear from Fig 6. On the contrary, we can say that if each active secondary transmitter satisfy a fixed interference threshold i.e., [I.sub.th] then their position with respect to the PRx as well as relay nodes do not impact on the performance of the primary outage probability which is clear from (7), (8) and (9).

In Fig. 7 and Fig. 8, we show the outage probability of the secondary system in SI and SII respectively. We assume [I.sub.th]/[[sigma].sup.2.sub.Pint] varies from 0 dB to 18 dB and inactive secondary transmitters (relay sets) are located at (60, 40). To clarify the comparison, we assume the distance between STx and SRx is 100 meters in all cases. We also verified the theoretical results with simulation results and they are well matched with each other. It can be observed from Fig. 7 and Fig. 8 that the outage probability of the secondary network decreases with increasing [I.sub.th]. In addition, the outage performance improves when the active secondary transmitter is located farther away from the PRx. It is also obvious that secondary outage increases with an increasing [R.sub.ST].

In Fig. 9, we show the outage probability of secondary network in SIII with different values of [R.sub.ST] and [I.sub.th]. We consider two cases of [R.sub.ST] where [R.sub.ST] = 0.5 bits/sec/Hz and [R.sub.ST] = 1 bits/sec/Hz respectively. Two cases of [I.sub.th] where [I.sub.th] = 5 dB and [I.sub.th] = 10 dB are considered. Inactive secondary transmitters (relay sets) are located at (60, 40) and the distance between STx and SRx is 100 meters in all cases as in SI and SII. Theoretical results are also verified by simulation results. Here, we assume [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and SNIR varies from 0 dB to 18 dB. During computation of the secondary outage probability, we assume same primary outage probability [P.sup.P.sub.OUT] i.e., fixed [P.sup.P.sub.OUT] for all four cases described above. We can observe from Fig. 9 that secondary outage increases with a decreasing [I.sub.th]. It is also observed that secondary outage increases with an increasing Rst. Distance between two active secondary transmitters (i.e., opportunistic STx and STx satisfying [I.sub.th] with respect to SRoppr) is same for all four cases.

If we compare Fig. 7, Fig. 8 and Fig. 9 then it is obvious that better secondary outage performance is found for SIII because of the increasing number of secondary transmission as well as primary system is in outage. It is also noted that in SI and SII the primary system is not in outage.

In Fig. 10, we show the total outage probability of the SU with different values of Rst. Here, we assume [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] varies from 0 dB to 18 dB. Three cases of [R.sub.ST] where [R.sub.ST] = 0.5 bits/sec/Hz, [R.sub.ST] = 0.75 bits/sec/Hz and [R.sub.ST] = 1 bits/sec/Hz are considered. Inactive secondary transmitters (relay sets) are located at (60, 40) and the distance between STx and SRx is 100 meters in all cases as in SI, SII and SIII. For above three cases of [R.sub.ST], we considered same [P.sup.P.sub.OUT] as well as same distance between two active secondary transmitters (i.e., opportunistic STx and STx satisfying [I.sub.th] with respect to SRoppr). Theoretical results are validated by the simulation results. It can be observed from Fig. 10 that [P.sup.S.sub.OUT] increases with increasing [R.sub.ST]. It is also observed that [P.sup.S.sub.OUT] decreases with increasing values of [I.sub.th].

However, in this paper, we have proposed a hybrid spectrum sharing model with joint consideration of the interweave and underlay schemes. We have considered interference limited environments in our proposed model. In addition, our proposed system model differs than others. In our model, inactive secondary transmitters act as cooperative nodes for the PU and active secondary transmitter coexist with the PU satisfying [I.sub.th]. It is also shown that ergodic capacity and outage probably improve when the active secondary transmitter is located farther away from the PRx. Therefore, it is too difficult to compare our model with other spectrum sharing models (e.g., [22]). Furthermore, it will be considered as a future work.

Most of the modern communication systems are coded system. In this paper, we have considered DF relaying because it shows the following advantages over AF relaying: (i) DF relaying is better for coded systems as well as (ii) in [31], it is shown that single antenna multi-hop Rayleigh-fading relay channels under the DF protocol achieve higher ergodic capacity than under the AF one.

6. Conclusion

In this paper, we have proposed a hybrid spectrum sharing protocol with cooperative SU selection. Best cooperative secondary node is selected based on SNIR between the links PTx-to-[ST.sub.j] and [ST.sub.j]-to-PRx i.e., the [ST.sub.j] which achieves best primary request target rate on the relaying link. We have investigated the ergodic capacity, outage probability of the primary network with cooperative relaying as well as the outage probability of the secondary network and these are affected by the position of the active secondary transmitter with respect to PRx. The ergodic capacity and outage probability of the primary system improve when more number of inactive secondary transmitters i.e., relays participate in the cooperation procedure. Moreover, the outage probability of the secondary network improves as the number of active secondary transmitter increases as well as the primary system is in outage. We also derived closed-form expressions for the outage probability of both the primary and secondary systems. In addition, analyzing the impact of the access delay on the capacity in the two cooperative relay phases will be considered in future work.

http://dx.doi.org/10.3837/tiis.2013.09.001

Received July 4, 2013; revised August 26, 2013; accepted September 21, 2013; published September 30, 2013

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[31] G. Farhadi and N. Beaulieu, "On the ergodic capacity of multi-hop wireless relaying Systems," IEEE Trans. Wireless Comm., vol. 8, no. 5, pp. 2286-2291, May, 2009. Article (CrossRef Link). Md Fazlul Kader received the B. Sc. Engineering degree in computer Science and engineering (CSE) from Chittagong University of Engineering and Technology (CUET), Bangladesh in 2005. From 2007 onwards he is a faculty member of the Dept. of Applied Physics, Electronics and Communication Engineering, University of Chittagong, Bangladesh. He is currently working toward the M. Sc. Engineering degree in the Department of CSE, CUET, Bangladesh. His major research interests include cognitive radio networks, cooperative communications, computer network, pattern recognition etc.

Md Fazlul Kader (1), Asaduzzaman (2) and Md. Moshiul Hoque (2)

(1) Department of Applied Physics, Electronics and Communication Engineering, University of Chittagong Chittagong, Bangladesh [e-mail: f.kader@cu.ac.bd]

(2) Department of Computer Science & Engineering, Chittagong University of Engineering & Technology Chittagong, Bangladesh [e-mail: asad@cuet.ac. bd,mo shiulh@yahoo .com]

* Corresponding author: Md Fazlul Kader

Asaduzzaman received the B. Sc. Engineering degree in electrical and electronics engineering from Chittagong University of Engineering and Technology, Bangladesh, in 2001. From 2001 onwards he has been serving as a faculty member in the Department of Computer Science and Engg., Chittagong University of Engineering and Technology (CUET), Chittagong, Bangladesh. He received his Ph.D. from the Department of Electrical Engineering, University of Ulsan, Korea in 2010. His major research interests include wireless communication systems with emphasis on cooperative communications and MIMO systems, wireless sensor networks, modulation and coding techniques, cognitive radio, etc.

Md. Moshiul Hoque received his B. Sc. in electrical and electronics engineering from Chittagong University of Engineering and Technology (CUET), Bangladesh and MSc in Computer Science and Engineering from Bangladesh University of Engg. & Tech. (BUET), in 2001 and 2005 respectively. Hoque received his Ph.D in science & engg. in 2012 from Saitama University, Japan. In 2001, he joined as a lecturer in CUET and became an associate professor in 2012. His major research interests include sensor network, wireless network security, human robot interaction and computer vision. He is a student member of IEEE, Robotics Society of Japan.
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Author:Kader, Fazlul; Asaduzzaman; Hoque, Moshiul
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