The 2013 International Conference on Advanced Technologies for Communications (ATC'13)

Multi-hop Transmission with Diversity Combining Techniques Under Interference Constraint Tran Trung Duy, Vo Nguyen Quoc Bao Telecommunications Department Posts and Telecommunications Institute of Technology, Vietnam Email: [email protected], [email protected].

Abstract—In this paper, we study performance of multi-hop cooperative transmission protocols in underlay cognitive radio networks. In the considered protocols, secondary relays and secondary destination employ combining techniques such as selection combining (SC) and maximal ratio combining (MRC) to combine the packets received from the secondary source and previous secondary relays. We derive asymptotic closed-form expressions of outage probability over Rayleigh fading channel. Monte Carlo simulations are presented to verify the derivations. Index Terms—Underlay cognitive radio, cooperative diversity, multi-hop transmission, combining techniques, outage probability.

Cooperative diversity protocols [1] can be used efficiently to enhance the performance of secondary networks in interference constraint environments [2]–[4]. In such schemes, secondary users (SUs) can currently use the frequency band with primary users, provided that the interference created by secondary operations is lower than a given threshold. In [4], the secondary destination uses selection combining technique (SC) to combine the signals received from the secondary source and relay. In [5], the performance of an incremental underlay protocol with maximal ratio combining technique (MRC) employed at the destination was investigated. So far, almost published works related to diversity relaying in underlay network have mainly focused on dual-hop schemes. However, the multi-hop relaying protocol in which a secondary source communicates with a secondary destination via a number of secondary relays has become a promising technique. In [6] and [7], the authors considered the multi-hop underlay transmission scheme over Rayleigh fading channel and Nakagami-m fading channel, respectively. In these schemes, the direct transmission is used at each hop to forward the secondary signal. In [8], a multi-hop cooperative transmission protocol in underlay cognitive network was proposed and analyzed. In this scheme, the combining techniques were not employed at the relays and the destination. In addition, because only the active relay, which is nearest to the destination, is allowed to retransmit the source data to the destination, the obtained diversity order of this protocol is equal to two . To further enhance the diversity gain, in this paper, we propose the multi-hop cooperative transmission protocols in underlay cognitive radio networks. In the proposed protocols, the packet which is transmitted by a secondary source or a secondary

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I. I NTRODUCTION

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Multi-hop diversity transmission in underlay cognitive networks.

relay, can be received by a secondary destination and other relays. Different from the protocol proposed in [8], the relays in our schemes sequentially decode the packet and then forward it to the destination if they can decode it successfully. Moreover, the secondary destination and secondary relays are equipped with the combiners such as selection combining (SC), and maximal ratio combining (MRC) to combine the received packets. For the performance evaluation and comparison, we derive the asymptotic closed-form expressions of the outage probability over Rayleigh fading channel. Then, we perform Monte Carlo simulations to verify the derivations. The results show that the proposed schemes obtain full diversity order which equals to the number of hops. In addition, the outage performance is significantly effected by the number of hops and the position of the primary user. The rest of the paper is organized as follows. The system model of the proposed schemes is described in Section II. In Section III, the performance evaluation is analyzed. The simulation results are presented in Section IV. Finally, the paper is concluded in Section V. II. S YSTEM M ODEL Let us consider an M -hop secondary network in which the secondary source N1 communicates with the secondary destination node NM +1 via M -1 secondary relay nodes Nk , k ∈ {2, 3, ..., M }. The relay nodes are numbered with respect to their distance to the destination; i.e., the relay NM is nearest and the relay N2 is the furthest. In Fig. 1, we present the 3-hop transmission scheme under the interference constraint given by the primary user (PU). Assume that each node

The 2013 International Conference on Advanced Technologies for Communications (ATC'13)

has a single half-duplex radio and a single antenna. Due to half-duplex constraint, a time-division channel allocation is occupied in order to realize orthogonal channels. The operation of the proposed protocols is performed, similarly to the scheme proposed in [9] as follows: At the first time slot, the source N1 broadcasts its packet, which can be received by the destination and all of the relays. If the relay N2 can decode the packet successfully, it generates an ACK message to inform. Then, this node forwards the packet in the next time slot. Otherwise, the relay N2 sends a NACK message to inform the decoding status. Next, let us consider the operation at the relay N3 . If it can receive packets transmitted by the source N1 and relay N2 , it combines them by using SC (or MRC) technique and do decoding. Similar to the operation of the relay N2 , if this node can decode the packet successfully, it sends the ACK message to inform and forward the packet at the next time slot. Otherwise, it generates the NACK message. Sequentially, the relays N4 , N5 , ..., NM decode the source packet and broadcast the control messages to inform their decoding status. Finally, the destination NM +1 combines the received packets and does decoding. If it cannot decode the packet successfully, the packet is dropped. III. P ERFORMANCE A NALYSIS We assume that the channels between any two terminals are subjected to block and flat Rayleigh fading. Let hX,Y denote the channel coefficient between a transmitter X and a receiver Y , where X ∈ {N1 , N2 , ..., NM } and Y ∈ {N2 , N3 , ..., NM +1 , PU}. For ease of presentation, we denote the channel gains as follows: γi,j = |hNi ,Nj |2 and ψk = |hNk , PU |2 . To take path loss into account, these parameters can be modeled as a function of distance between two nodes [10] as λi,j = dβNi ,Nj and Ωk = dβNk ,PU , where β is path loss exponent, dNi ,Nj and dNk , PU are the distances between Ni and Nj , and between Nk and PU, respectively. In underlay cognitive network, the transmit power of a secondary transmitter Ni is given as [10]: PNi = Qth /ψk

(1)

where Qth is interference constraint required by the primary user PU. From (1), the instantaneous Signal-to-Noise Ratio (SNR) received at the node Nj due to the transmission of the node Ni is given as γi,j (2) ΨNi ,Nj = PNi |hNi ,Nj |2 = Q ψi where N0 is variance of the additive noise at the node Nj , and Q = Qth /N0 . Now, we consider the case that the destination cannot decode the source packet successfully. Let us denote W as set of relays, i.e., W = {N2 , N3 , ..., NM }. We denote VS as the set of relays which decoded the packet successfully and forwarded the packet to the destination. We can assume that VS = {Ni1 , Ni2 , ..., NiT } where VS ⊂ W, and T is the cardinality of VS with 0 ≤ T ≤ M − 1. Next, the destination

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and the remaining relays which cannot decode the packet successfully are assumed to belong the set VF , i.e., VF =  NiT +1 , NiT +2 , ..., NiM −1 , NM +1 where VS ∪ VF = W and iT +1 < iT +2 < ... < iM −1 . For example, if T = 0, then VS = {∅} and VF = {N2 , N3 , ..., NM , NM +1 }, which means that all of the relays and the destination cannot decode the packet received from the source. For another example, if T = M − 1, then VS = {N2 , N3 , ..., NM } and VF = {NM +1 }. In this case, all of the relays can successfully decode the packet and forward it to the destination, but the destination cannot receive the packet correctly. Hence, the total end-to-end outage probability of the proposed protocols can be formulated as follows: X PCout = PC (V S ) (3) VS

where PC (VS ) is the probability for each case of the decoding sets VS , C ∈ {SC, MRC} denotes the combining technique employed at the relays and destination. In this paper, we assume that a receiver cannot decode the packet successfully if the received SNR at that node is lower than a pre-determined threshold γth . • Case 1: Selection Combining (SC) Let us consider the relay Nij (1 ≤ j ≤ T ) belonging to the set VS . The received SNR at the output combiner of this node is given as   max ΦSC ΨN1 ,Nij , ΨNit ,Nij (4) ij = t=1,2,...,j−1

For the relay Nij (T + 1 ≤ j ≤ M − 1) belonging to the set VF , the received SNR at this node can be expressed as   max ΦSC ΨN1 ,Nij , ΨNiv ,Nij (5) ij = Niv ∈VS , iv
Also, the SNR received at the destination can be given as !
max ΨN1 ,NM +1 , ΨNit ,NM +1 (6) ΦSC M +1 = t=1,2,...,T

From (4), (5) and (6), we can formulate the probability PSC (VS ) as  SC  Φi1 ≥ γth , ..., ΦSC iT ≥ γth ,  SC  SC PSC (VS ) = Pr  ΦiT +1 < γth , ..., ΦiM −1 < γth ,  (7) ΦSC M +1 < γth

and ΦSC have common RVs Since RVs ΦSC ij M +1 ψ1 , ψi1 , ...., ψiT , they are not independent. Therefore, if we set x1 = ψ1 , xi1 = ψi1 , ..., xiT = ψiT , the probability PSC (VS ) conditioned on X = {x1 , xi1 , ..., xiT } can be expressed as PSC (VS |X) =

T Y

j=1

× ×

h i Pr ΦSC ≥ γ |X th ij

M −1 Y

h i Pr ΦSC ij < γth |X

j=T +1  Pr ΦSC M +1

< γth |X



(8)

The 2013 International Conference on Advanced Technologies for Communications (ATC'13)

h i Considering Pr ΦSC ij ≥ γth |X in (8); by using (4), we can calculate it as   i h λ1,ij γth x ≥ γ |X = exp − Pr ΦSC th 1 ij Q   j−1 Y λi ,i γth exp − t j (9) × xit Q t=1

At high Q values, i.e., Q → +∞, we can approximate (9) by h i Pr ΦSC (10) ij ≥ γth |X ≈ 1 h i Next, Pr ΦSC ij < γth |X in (8) can be formulated as  i  h λ1,ij γth < γ |X = 1 − exp(− ) Pr ΦSC x th 1 ij Q  Y  λi ,i γth × xiv ) (11) 1 − exp(− v j Q Niv ∈VS iv
By using 1 − exp (−1/x) ≈ 1/x, we obtain an asymptotic x→+∞ expression of (11) at high Q region as i λ γ h Y λiv ,ij γth 1,ij th x1 xiv (12) Pr ΦSC ij < γth |X ≈ Q Q Niv ∈VS , iv
Next, it is similar to obtain

From (10), (12) and (13), PSC (VS |X) can be approximated as follows: M −1 Y λ1,ij γth λ1,M +1 γth x1 x1 Q Q

• Case 2: Maximal Ratio Combining (MRC) If the MRC technique is employed, the received SNR at the output combiner of the node Nij (1 ≤ j ≤ T ) is given as

ΦMRC = ΨN1 ,Nij + ij

×

Niv ∈VS , iv
(18)

Niv ∈VS , iv
ΦMRC M +1 =

ΨN1 ,NM +1 +

T X

ΨNit ,NM +1

(20)

Similar as Case 1, we can obtain the probability for each case of the set VS as PMRC (VS ) = # " R +∞ R +∞ PMRC (VS |X) fψ1 (x1 ) ... 0 dx1 dxi1 ...dxiT 0 fψi1 (xi1 ) ...fψiT (xiT )

(21)

where,

j Y λiv ,ij γth λit ,M +1 γth xiv xit (14) Q Q t=1

PMRC (VS |X) =

T Y

j=1

×

h i Pr ΦMRC ≥ γth |X ij

M −1 Y

j=T +1

PSC (VS ) = 0

ΨNit ,Nij

Also, the received SNR at the relays Nij (T + 1 ≤ j ≤ M − 1) and the destination can be respectively given as X ΦMRC = ΨN1 ,Nij + ΨNiv ,Nij , (19) ij

In addition, because

R +∞

j−1 X t=1

j=T +1

Y

j

j=1 Nit ∈VF ,it >ij

t=1

T  λ1,M +1 γth Y  λit ,M +1 γth x xit (13) < γ |X ≈ Pr ΦSC th 1 M +1 Q Q t=1

PSC (VS |X) ≈

where Gij is the number of the nodes Nit belonging to the set VF received the packet transmitted by the nodes Nij of the set VS . After some manipulation, we obtain an asymptotic expression for PSC (VS ). Combining this result with (3), the out total end-to-end outage probability PSC at high Q value is expressed by a closed-form expression as    M −T MQ −1 γth λ (M − T )! × 1,ij  Ω1 Q X  j=T +1  out PSC ≈ (17) Q   T !
γth Gij  Q   VS λij ,it Gij ! Ωi Q

# " R +∞ PSC (VS |X) fψ1 (x1 ) (15) ... 0 dx1 dxi1 ...dxiT , fψi1 (xi1 ) ...fψiT (xiT )

so, substituting (14) into (15) yields    M −T M −1 Y γth   PSC (VS ) ≈ λ1,ij Q j=T +1 Z +∞ M −T × Ω1 (x1 ) exp (−Ω1 x1 )dx1 0    Gij Q γth T λ Y i ,i j t Q   × N  (16) t ∈VF ,it >ij R i+∞ Gij j=1 Ω (x ) exp(−Ω x )dx i i i i i j j j j j 0

133

h i Pr ΦMRC < γ |X th ij

  (22) × Pr ΦMRC M +1 < γth |X h i At first, it is easy to obtain Pr ΦMRC ≥ γth |X ≈ 1 as Q → ij +∞. Next, by setting h Z1 = Qγ1,ij /xi1 and Zv = Qγiv ,ij /xiv , we can express Pr ΦMRC < γth |X as ij i h < γth |X = Pr ΦMRC ij " # (23) P = Pr Z1 + Zv < γth Niv ∈VS , iv
It is worth noting that the probability density function (PDF) λ1,ij x1 λ1,i x1 z of Z1 and Ziv are fZ1 (z) = exp(− Qj ) and Q λi

,i

xi

λi

,i

xi z

v j v fZiv (z) = exp(− v Qj v ), respectively. ThereQ fore, at high Q values, we obtain the corresponding asymptotic

The 2013 International Conference on Advanced Technologies for Communications (ATC'13)

PDFs as fZ1 (z) ≈ λ1,ij x1 /Q and fZiv (z) ≈ λiv ,ij xiv /Q. From that, an asymptotic expression for the moment generatP Ziv can be ing function (MGF) of RV Z = Z1 + Niv ∈VS , iv
given as

Y

MGFZ (s) = MGFZ1 (s)

MGFZiv (s)

Niv ∈VS , iv
≈

λ1,ij x1 . Q

Y

Niv ∈VS , iv
λiv ,ij xiv 1 . 1+Hi j Q s

(24)

where Hij is the number of the nodes Niv belonging to the set VS , which transmitted the packet to the node Nij . From (24), we obtain an asymptotic PDF of Z as fZ (z) ≈ λ1,ij x1

Y

Niv ∈VS , iv
z Hij λiv ,ij xiv !
1+Hi j Hij !Q

(25)

Hence, the corresponding cumulative density function (CDF) is given as FZ (z) ≈ λ1,ij x1

z 1+Hij λiv ,ij xiv ! (26)
1 + Hij !Q1+Hij

Y

Niv ∈VS , iv
Combining (26) and (23), we can obtain h i Pr ΦMRC < γ |X ≈ λ1,ij x1 th ij

Y

λiv ,ij xiv

v

Next, we evaluate the diversity order of the proposed protocols. First, the diversity gain can be defined as log (PCout ) Q→+∞ log (Q)

DC = − lim

From (17) and (30) into (31), the diversity gain DC of the proposed schemes can be given by   T X (32) Gij  DMRC = DSC = min M − T + VS

j=1

It is worth noting that in all possible cases of VS , there T P are three cases in which the value (M − T + Gij ) is j=1

minimum, i.e., VS = {∅} and VF = {N2 , N3 , ..., NM +1 }; VS = {NM } and VF = {N2 , ..., NM +1 } /NM ; and VS = {N3 , N4 , ..., NM } and VF = {N2 , NM +1 }. Because in these T P cases, (M − T + Gij ) = M , we hence conclude that the j=1

1+Hij

γth

×! (27)
1 + Hij !Q1+Hij   Similarly, an asymptotic expression of Pr ΦMRC M +1 < γth |X at high Q value can be given as T Y   Pr ΦMRC < γ |X ≈ λ x λit ,iM +1 xit th 1,M +1 1 M +1 t=1

(28)

DMRC = DSC = M

Y

λiv ,ij xiv

Niv ∈VS , iv
× λ1,M +1 x1

T Y

λit ,iM +1 xit

t=1 1+Hi

1+T γth γth j × !
(1 + T )!Q1+T 1 + Hij !Q1+Hij

(29)

Substituting (29) into (21) and after some simple manipulation, out we can obtain an asymptotic closed-form expression of PMRC

134

(33)

IV. N UMERICAL R ESULTS AND D ISCUSSION In this section, we present Monte Carlo simulation results to verify the theoretical results and to compare the performance of the protocols discussed in the previous sections with the protocol proposed in [8]. In simulation environment, we consider a two-dimensional plane in which the co-ordinates of the nodes Nj , j ∈ {1, 2, ..., M + 1}, and the primary user are ((j − 1) /M, 0), and ( xPU , yPU ), respectively. Therefore, the distances are q calculated as follows: dNi ,Nj = |i − j|/M 2

From the results obtained above, the conditioned probability PMRC (VS |X) in (22) can be expressed as follows: PMRC (VS |X) ≈ λ1,ij x1

(31)

diversity of the proposed schemes equals the number of hops:

Niv ∈VS , iv
1+T γth × (1 + T )!Q1+T

at high Q region as P out PMRC = PMRC (VS ) VS  M   M −T Q     λ1,ij (M − T )! Ωγ1thQ       j=T +1    (30)    T Gij P !
Q Q γ th ≈ × λij ,it Gij ! Ωi Q  j VS    j=1 Nit ∈VF ,it >ij     Q   1 1     × (T +1)! 1+Hij )! ( Ni ∈VS , iv
2 , where i ∈ ((j − 1) /M − xPU ) + yPU and dNj ,PU = {1, 2, ..., M + 1}. In Fig. 2, we present the end-to-end outage probability of the protocols as a function of Q in dB. In this simulation, we fix the parameters as follows: M =3, β = 3, γth = 1, and xPU = yPU = 0.5. As we can see in this figure, the outage performance is better when MRC technique is used. Moreover, the proposed schemes obtain a better performance as compared with the scheme proposed in [8]. It is because that our schemes obtain the diversity order of 3, while that of the scheme in [8] is 2. It is also seen that at high Q value, the theoretical results converge to the simulation results, which verifies the derivations.

The 2013 International Conference on Advanced Technologies for Communications (ATC'13)

in underlay cognitive radio networks. By employing different combining techniques at relays and destination, the diversity order of the proposed protocols equals to the number of hops. In addition, in the case that MRC is used, the proposed protocol provides higher performance, as compared to that of the SC case. Finally, the proposed schemes obtain the better performance as compared with the scheme proposed in [8].

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Fig. 3. Outage probability as a function of the number of hops (M ) when Q=0 (dB), γth = 1, and β = 3.

Fig. 3 shows the effect of the number of hops on the outage performance. In this figure, the results are performed by Monte Carlo simulations with Q=0 (dB), γth = 1, and β = 3. Again, we can see from Fig. 3 that the proposed schemes outperform the scheme in [8]. Moreover, the performance of all of the schemes decrease with the increasing the number of hops. Finally, it can be seen that the outage probability of the protocols significantly decreases if the primary user is far the secondary network. It is due to the fact that with same interference level Qth , the average transmit power of the secondary transmitters is higher when the distance between them and the primary user is large. V. C ONCLUSION In this paper, we proposed and analyzed the outage performance of the multi-hop cooperative transmission protocols

135

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