In order to achieve the requiredSIN RT h for bothIU Es and HIZU Es in the HetNet
system, we need to optimally choose D2D links, effectively allocate the RBs to the D2D links and adjust power for these links. We formulate a MILP model to address this problem. The notations used in this model are listed in Table 6.1.
Table 6.1: Glossary of D2D MILP Model
Notation Definition
K Set of all Resource Blocks (RBs)
F Set of all Free Indoor UEs (F IU Es)
L Set of all Legacy Indoor UEs (LIU Es)
O Set of all Outdoor UEs in HIZone (HIZU Es)
M Set of all MBSs
Df o A binary variable whose value is 1 iff is connected to o
for D2D else 0, where fF, oO Ck
f o A binary variable whose value is 1 iff is connected to o
for D2D using RBk else 0, where fF, oO, kK hk
f A binary variable whose value is 1 if f is using RB k for
D2D link else 0, where fF, kK
Gxy Channel gain between two nodes x and y, where nodes
can be IU Es, HIZU Es, MBSs or Femtos pk
f Normalized power emitted by f in RB k, 0 ≤ pkf ≤ 1,
where fF, kK
In order to minimize battery drain of F IU Es, one of the main objectives1 is to
minimize the overall power consumed by the D2D links as expressed in Equation (6.1):
minX
f F
X
kK
pkf (6.1)
Equation (6.2) sets an upper bound on the number of HIZU Es that can be served by each F IU E. Similarly, Equation (6.3) restricts the number of F IU Es serving each HIZU E.
1Another alternate optimization goal can be minimization of the maximum power (min(max(pk
f)) consumed by D2D links where all the constraints are identical to the proposed D2D MILP model.
X oO Df o ≤ α ∀f F (6.2) X f F Df o ≤ β ∀oO (6.3) X f F X oO Df o = ψ ∀oO (6.4)
In order to limit the total number of D2D links that would be established in a TTI, we introduce Equation (6.4). The values of α, β and ψ can be fine tuned as per the requirements of the operator. The binary variable Ck
f o is 1 when F IU E f
and HIZU E o are communicating by using RB k. Hence, Ck
f o can never be 1 when
there is no D2D link between f and o. This is ensured by Equation (6.5). Here, η represents the maximum number of RBs that can be assigned to each D2D link.
X
kK
Ck
f o ≤ η × Df o ∀f F, oO (6.5)
Equation (6.6) ensures that the maximum number of times a particular RB k can be reused by an F IU E f is 1. X oO Ck f o ≤ 1 ∀f F, kK (6.6) hk
f is set to be 1 if F IU E f is using the RB k. This is ensured by Equation (6.7).
hkf = Cf ok ∀f F, oO, kK (6.7)
The constraint in Equation (6.8) ensures that the normalized power emitted byF IU E f in a particular RB k is 0 when it is not used by f .
pkf ≤ hkf ∀f F, kK (6.8)
The Pd
max is the maximum power of a D2D link. Once the MILP model is solved,
transmission power of an F IU E f in a RB k is calculated as pk
f × Pmaxd . Gf l gives
the gain from the F IU E f to the LIU E l. Sk
l is an input parameter whose value
constraint in Equation (6.9) ensures that the maximum interference power that is received by l is less than the allowed threshold value (Il). Il is computed for a given
value ofSIN RT h of IU Es.
X
f F
(Gf l× Slk× pkf × Pmaxd ) ≤Il ∀lL, kK (6.9)
The L.H.S. of Equation (6.10) is the SINR received by HIZU E o from F IU E f . To ensure good connection, the SINR of each D2D link is maintained above a predefined threshold λo which could vary across HIZU Es.
Inf ∗ (1 − Ck f o) +Gf opkfPmaxd No+ X mM GmoPmacro+ X aBk GaoPmaxf + X f0F \f Gf0 op k f0P d max ≥ λo ∀f F, oO, kK (6.10) Here, Bk is the set of all Femtos using the RB k in a given TTI. Similarly, Gao is the
channel gain from Femto a to o, Gf o is the channel gain from f to o and Gmo is the
channel gain from MBS m to o, calculated by using PL model (shown in chapter 3). The need to use Inf ∗ (1 − Ck
f o) is that if Cf ok = 0 then Inf ∗ (1 − Cf ok ) becomes
a large value and the expression can be ignored safely. Without the virtual infinite value, Equation (6.10), ensures that all the F IU Es provide a minimum SIN RT h to
a particularHIZU E. The MILP will always be infeasible if we do not use the virtual infinite value, as not all F IU Es can maintain a SIN RT h (λo) for an HIZU E. The
Equation (6.10) can be rewritten as follows,
Inf ∗ (1 − Cf ok ) +Gf opkfPmaxd ≥ {(λoNo+λo X mM GmoPmacro+λo X aBk GaoPmaxf + λo X f0F \f Gf0 op k f0P d max)} ∀f F, oO, kK (6.11) Finally, the D2D MILP model is formulated as follows,
minX
f F
X
kK
By solving this MILP model, we achieve the following: • Get best F IU Es as relays for establishing D2D links • Assign RBs to each of the D2D links established
• Adjust the transmit power for each of the D2D links and minimize the overall power emitted by guaranteeing SIN RT h for LIU Es and HIZU Es served by
F IU Es.
As shown later in Section 6.5, the above D2D MILP model ensures fairness for both indoor and outdoor users by assuring certain minimumSIN R for all IU Es and HIZU Es. But the computation time of this D2D MILP model is high and it may not converge in real-time for any practical usage by Femtocells. For some cases, the problem can be infeasible. To overcome this shortcoming, we propose a two-step D2D heuristic algorithm in the next sub-section.