Basic notations and definitions. As also discussed in the previous subchapter, the set of BSs is denoted with B = {b1, b2, . . . , b|B|}, whereas the set of D2D links is L = {l1, l2, . . . , l|L|} (randomly distributed in a hexagonal multi-cell topology). The |·| notation declares the cardinality of a set. All BSs have the same number of resources Kb. However, the available RB pool for each b ∈ B is different and depends on the discussed FFR scheme, as shown in Table 3.1. In the context of this work, each association of a D2D link with a BS implies the occupation of a single RB. As a consequence, the total number of D2D associations with a specific BS will be equal to the number of RBs allocated by the same BS. Let us further define by clb the cost of a D2D link l connected to BS b; this can be considered as the average path-loss (distance-based) of connecting both nodes n1 and n2 of a D2D pair at the same BS and is estimated as follows: clb = PLn1,b + PLn2,b (3.3) where PLni,b = 128.1 + 37.6 log10 rni,b is the path loss (in dB) between BS b and DUE ni, for i = 1, 2. In the previous formula, rni,b is the DUE-BS distance (in kilometres). For the estimation of clb, PLni,b values are converted from dB values to ratios. For current and emerging cellular networks, where connected DUEs might have subsequent direct (D2D) and cellular UL/DL transmissions, this cost metric represents the need to stay “as close as possible” to the serving BS to support both communication types that can happen in short and sequential time Table 3.1: Resource availability per cell according to differentiated FFR Cell id (b) Inner-region D2D Outer-region D2D
