D2D Heuristic Algorithm

D2D heuristic algorithm has two steps: one step for selecting D2D pairs and allocating RBs, and other step for setting the powers of D2D pairs. Below we present these two steps.

Step 1: Heuristic D2D Pair and Resource Allocation (hDPRA)

Proposed hDPRA (refer Algorithm 3) checks whether a particular F IU E f can connect to an HIZU E o using an RB k. For this we define a parameter, Win- to-Loss (W2L) Ratio (γ) for all possible (f , o, k) combinations, as expressed in Equation (6.12). γ_{f o}k = _X Gf o o0Ok G_{f o}0 + X l0Lk G_{f l}0 + X f0Fk G_f0 o (6.12)

Here,Ok(⊂O) represents the set of HIZU Es receiving data using the RB k, Lk(⊂L)

represents the set ofLIU Es receiving data from Femto using the RB k and Fk(⊂F )

represents the set of F IU Es transmitting data to HIZU Es using the RB k. The numerator in the R.H.S. of Equation (6.12) represents the gain betweenf and o, hence it acts as an approximate measure (since the transmission power is not considered) for signal strength. The values G_{f o}0, G

f l0 and Gf0o, in the denominator represent

the channel gain between f and o0, f and l0, and f0 and o, respectively and they act as an approximate measure of the interference caused by the interfering links. The

Algorithm 3 Heuristic D2D Pair and Resource Allocation (hDPRA) Algorithm Input 1 : F , O, L

Input 2 : Optimal Femto Locations (Obtained by solving M inN F model)

Input 3 : γ, α and β values

Output : Df o, Cf ok , hkf Initialization (); 1: Df o ← 0 ∀ f F , oO 2: Ck f o ← 0 ∀ f F , oO, kK 3: Compute γk

f o ∀f F, oO, kK and store in γ matrix

4: αf ← 0 ∀ f ∈ F { Count for number of HIZU Es connected to each F IU E } 5: βo ← 0 ∀ o ∈ O { Count for number of F IU Es serving each HIZU E } 6: σ∗ _{← { }}

7: while size(γ) 6= 0 do

8: (fmax, omax, kmax) ← max(γ);

9: if Updated W2L values of entries in σ∗ _{> γ then}

10: Dfmaxomax ← 1 11: Ckmax fmaxomax ← 1 12: αfmax + + 13: βomax + + 14: if αfmax == α then 15: Remove γk fmaxo ∀ oO, kK 16: end if 17: if βomax == β then 18: Remove γk f omax ∀ f F, kK 19: end if 20: Remove γkmax fmaxomax 21: if Updatedγkmax f o < γ then 22: Removeγkmax

f o {Removes all f and o pairs using RB kmax fromγ matrix }

23: end if

24: σ∗ ← σ∗ U (fmax, omax, kmax)

25: else

26: Remove γkmax fmaxomax 27: end if

numerator and denominator are two opposing parameters to the W2L ratio. Hence, larger the value of γk

f o, higher the possibility of the particular combination (f , o) to

have a D2D link using RB k. W2L ratio will be higher in case RB k is not used by some Femtos for serving their UEs in a given TTI i.e., the value of X

l0Lk

G_{f l}0 will reduce in Equation (6.12).

σ∗ _{is the set that contains the triplet (f}∗_{, o}∗_{, k}∗_{) if f}∗ _{and o}∗ _{are having a D2D}

link using RB k∗_{. Every element in σ}∗ _{should have its W2L ratio greater than γ,}

an operator defined parameter which gives control over the number of D2D links that can be formed. Initially σ∗ _{is a null set. We start by computing the W2L}

ratio for each (f, o) pair for all possible RBs and store them in the γ matrix. From this set, the maximum W2L ratio is found and this gives the corresponding triplet (fmax, omax, kmax). On adding this particular triplet to σ∗, there will be additional

interference (Gfmaxo∗) to the existing (f

∗_{, o}∗_{) pairs who are using RB k}

max for their

data transmissions. Hence,γkmax

f∗_o∗ values have to be recalculated and checked whether they remain greater than γ. If all of these values remain greater than γ, the triplet (fmax, omax,kmax) is added to σ∗ and the recalculated γfkmax∗_o∗ values are stored in the γ matrix, otherwise triplet (fmax, omax, kmax) is not added to σ∗. In case triplet

(fmax, omax, kmax) is added toσ∗, the αfmax and βomax values are incremented, where αfmax is the count for the number of HIZU Es connected to F IU E fmax and βomax is the number of F IU Es connected to HIZU E omax. If αfmax value reaches the maximum limit α, then all the γk

f o values for F IU E fmax are removed from the γ

matrix. Similarly if βomax reaches the maximum limit ofβ, then all the γ k

f o values for

HIZU E omax are removed from theγ matrix. W2L ratio in the γ matrix is updated

∀ f , o which are using RB kmax. If any of the updatedγkf omax is lesser thanγ, then that

value is removed from the γ matrix and is not considered during the next iteration. Finally, it removes γkmax

f∗

maxo∗max from the γ matrix and continues to the next iteration until all the entries are removed from the γ matrix.

Step 2: Heuristic D2D Power Allocation (hDPA)

Using outputs of the hDPRA from the Step 1 Algorithm 3, namely Df o,Cf ok , hkf,

as the input in the Step 2 we solve an LP model which adjusts the power for each of the D2D links. The LP model is formulated similar to D2D MILP model presented earlier but with fewer constraints as given below.

minX

f F

X

kK

pk_f ≤ hk_f ∀f F, kK (6.14) X f F (Gf l× Slk× pkf × Pmaxd ) ≤ Il ∀lL, kK (6.15) Inf ∗ (1 − C_{f o}k ) +Gf opkfPmaxd ≥ {(λoNo+λo X mM GmoPmacro+λo X aBk GaoPaf em+ λo X f0F \f G_f0 op k f0P d max)} ∀f F, oO, kK (6.16) Finally, the LP model for D2D power control is formulated as follows,

minX

f F

X

kK

pk_f s.t, (6.14), (6.15), (6.16).

The proposed two-step D2D heuristic algorithm is fair to both the IU Es and HIZU Es by choosing the D2D links, allocating resources to the D2D links and adjusting their transmission power levels.