Basic notations and definitions Sample Clauses

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 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 b = 1 b = 2 · i* b = 2 · i + 1 {F3} ∪ {F4} {F2} ∪ {F4} {F2} ∪ {F3} {F1} ∪ {F3} ∪ {F4} {F1} ∪ {F2} ∪ {F4} {F1} ∪ {F2} ∪ {F3} *i = 1, 2, 3, . . . epochs (the lower the value of clb the bigger the probability to associate with the closest BS). Furthermore, because in this work the focus is turned on the UL, a user’s association with a BS should be preferably decided by its estimated path loss to it and not by the traditional downlink received signal-based criterion in cellular networks [24]. To this end, and based on the aforementioned analysis for ensuring reduced signalling overhead, the D2D links that are characterized by association ambiguity (i.e. two nodes should be normally associated with different BSs) are coupled with the BS that achieves the minimum average path loss for each pair of nodes. In order to formulate the problem of the D2D cell association and formulate it mathematically, the following binary variable needs to be defined: ylb = 1, if link l is connected to BS b 0...
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