Proposed EERA-2P with Network Cod- Cod-ing (EERA-2PNC) Scheme

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1 + λBS, if (l = DL, r = 0, u ∈ Md) or (l = DL, r 6= 0, u = 0), w + λU E,u, if (l = UL, r = 0, u ∈ Md) or (l = UL, r = Ω(u), u ∈ Mr), 1 + λRS,r, if l = DL, r = Ω(u), u ∈ Mr,

1 + λRS,r, if l = UL, r 6= 0, u = 0,

(3.3) where λ_BS, λ_RS,r, and λ_{U E,u} are Lagrangian multipliers of (3.2c), (3.2d), and (3.2e), respectively. Compared to λ^l_r,u as obtained from (2.9) for the EERA-4P scheme, the parameter λ^l_r,u acquired in (3.3) for the EEEA-2P scheme requires additional conditions to specify the designated cases since there only exist two phases to allocate the transmission links. Similarly, the value of subchannel assignment ρ^n,l_r,uwill be relaxed from the distinct values of {0, t_τ} for τ = 1, 2 into a continuous interval of [0, t_τ] in order to convert the original formulation into a convex optimization problem. The subgradient method will be employed to provide the updating process of the Lagrangian multipliers and the phase duration t_τ. As a results, the power allocation, subchannel assignment, and phase duration can be obtained by adopting the EERA-2P scheme for the two-phase relaying networks.

3.3 Proposed EERA-2P with Network Cod-ing (EERA-2PNC) Scheme

By adopting the networking coding technique, the EERA-2PNC scheme is designed to further improve the performance of the EERA-2P algorithm for the two-phase bidirectional relaying networks. The concept of network cod-ing is utilized by the RS to combine both the DL and UL data transmissions

together into a single transmission for the corresponding receivers. For in-stance, it is considered that RS r is in charge of relaying data packets for both the BS and UE u. If u possesses a UL packet PU L for the BS and the BS has a DL packet P_DL for u, they will separately transmit the packet to the RS r on different subchannels in the first transmission phase. In the second phase, by adopting the network coding scheme, the RS r will deliver the packet P_nc = P_{U L}⊕ P_DL to both the BS and UE u on an identi-cal subchannel, where ⊕ represents the exclusive or operation. Afterwards, the BS receives the combined packet P_nc and will perform the operation of P_nc⊕ P_DL = (P_{U L}⊕ P_DL) ⊕ P_DL = P_{U L}, which can consequently obtain the packet P_{U L} initiated from UE u. Similar operation will also be executed by u, i.e., P_nc ⊕ P_{U L} = (P_{U L}⊕ P_DL) ⊕ P_{U L} = P_DL, in order to acquire P_DL transmitted from the BS.

Note that the RS r will deliver the combined packet P_nc with the lower data rate which is limited by both the RS→UE and the RS→BS communi-cation links. Consequently, the link L^DU_r,u for r = Ω(u) and u ∈ M_r is defined for transmitting the network coded packets according to the links RS r → BS and RS r →UE u. If an RS r is transmitting data packet via the L^DU_r,u link on a subchannel n, it represents that r is delivering a combined packet P_nc to both the UE u and the BS. Furthermore, it is considered that the equivalent channel gain g^n,DU_r,u of link L^DU_r,u on the subchannel n is determined as min(gⁿ_r,0, g_r,uⁿ ). The set Φ^2,nc_τ which consists of all communication links in the τ th phase for the proposed EERA-2PNC scheme can be defined as

Φ^2,nc_τ =

( {(l, r, u)| (l, r, u) ∈ Φ²₁}, if τ = 1,

{(l, r, u)| (l, r, u) ∈ Φ²₂ or (l = DU, r = Ω(u), u ∈ M_r)}, if τ = 2.

(3.4) where Φ²₁ and Φ²₂ respectively correspond to the communication links of first

and second phases as defined in (3.1) for the EERA-2P scheme. It can be observed that both the EERA-2P and EERA-2PNC schemes share the same types of communication links in the first phase; while additional network coded link is included in the second phase of EERA-2PNC method. The optimization problem of minimizing weighted energy for the EERA-2PNC scheme can be formulated as

(ρ,ε,t)min

XN n=1

Ã

C_r,0^{n,U L}+ X

u∈Mr

C_r,u^n,DU

!

≥ R^{req,U L}_r,0 , ∀r. (3.5k)

It can be seen that the power constraints for both the BS in (3.5c) and the UE in (3.5e) is the same as that for the EERA-2P scheme; while that for the RS in (3.5d) additional considers the energy consumption for the network coded link ε^n,DU_r,u in the constrained equation. The QoS constraints in (3.5h)-(3.5k) are extended from (3.2h) in order to fully consider the QoS requirement for the EERA-2PNC scheme with the network coded links, which are specifi-cally addressed in (3.5j) and (3.5k) for the RS→UE and the RS→BS links respectively. Moreover, the parameter λ^l_r,u for the EERA-2PNC scheme can be obtained as

λ^l_r,u =

( 1 + λRS,r, if l = DU, r = Ω(u), u ∈ M2,

(3.3), otherwise, (3.6)

which additional consider the case with network coded links other than the original λ^l_r,u defined in (3.3) for the EERA-2P scheme. The Lagrangian multiplier of the QoS constraint µ^l_r,ufor the EERA-2PNC scheme is redefined as

µ^l_r,u ←

( µ^{U L}_r,0 + µ^DL_r,u, if l = DU, r = Ω(u), u ∈ M₂,

µ^l_r,u, otherwise. (3.7)

Note that the resulting parameter µ^DU_r,u in (3.7) is a combination of Lagrangian multipliers, i.e., µ^DU_r,u = µ^{U L}_r,0 + µ^DL_r,u, considering the case with network coded packets. By substituting the corresponding values of λ^l_r,u and µ^l_r,u into (2.12), the EERA-2PNC scheme can determine the feasible channel n to be assigned for the link L^l_r,u. It is intuitive to observe the benefit of proposed EERA-2PNC scheme that the two data packets can be incurred at both the UL and

DL links with a single transmission of the combined packet, which can result in higher water level as ^{µU Lr,0}_λ^+µDU^DLr,u

r,u compared to the original EERA-2P scheme.

However, since the channel gain for transmitting the combined packets will be limited by min(gⁿ_r,0, g_r,uⁿ ), the packet that originally can be transmitted with link under higher channel gain will be sacrificed and only be delivered at lower data rate. Based on the formulation of proposed EERA-2PNC scheme, instead of adopting the networking coding technique, pure DL or UL packet may be transmitted if there exists large difference between the values of g_r,0ⁿ and gⁿ_r,ufor channel n. In order to clearly observe the behaviors of the various techniques, performance comparison among the proposed EERA schemes will be conducted in the next chapter.

Chapter 4