Allocation of Slots

6.2.5.1 Maximizing the Minimum User Rate

In this section, the allocation of slots is evaluated if the distributed concept for orthogonal medium access is applied with the objective of the maximization of the minimum user rate. In order to show the impact of the adaptive algorithm for the allocation of slots, the adaptive algorithm is compared to the corresponding non-adaptive one introduced in Section 5.2. Since the non-adaptive algorithm is only defined in the distributed concept for reuse medium access, this concept is applied for the comparison although an orthogonal medium access is considered.

The comparison between the adaptive and non-adaptive algorithm is mainly affected by the number of UEs in the cell. In Fig. 6.21, the average minimum user rate

depending on the number of UEs is given. The all-adaptive and non-adaptive instances are given as references. Additionally two instances are given serving for the actual comparison between the adaptive and non-adaptive algorithm for the allocation of slots. The abbreviations used in the legend indicate the subproblems solved by the BS or RS: design of Grids of Beams (GoB), allocation of Resource Blocks (RB) and allocation of slots (slot). A line drawn over an abbreviation denotes a non-adaptive algorithm. If the adaptive algorithm is applied for the allocation of slots, the non-adaptive algorithm is applied for the allocation of power and bits. Hence, gains are only achieved by the adaptive algorithm for the allocation of slots. The comparison reveals that the adaptive allocation of slots increases the minimum user rate especially for small number of UEs. The gain decreases if more UEs are in the cell. If the number of UEs is quite low, the number of UEs served by an AP fluctuates strongly. Hence, the number of slots allocated to the APs also fluctuate strongly in order to balance the user rates within the cell. However, this effect vanishes for a very large number of UEs. The instances using the adaptive and non-adaptive algorithm for the allocation of slots outperform the non-adaptive instance clearly. Hence, it is not essential in order to outperform the non-adaptive instance if the adaptive or non-adaptive algorithm for the allocation of slots is applied.

number of UEs av er ag e m in im u m u se r ra te in b it s/ slo t all-adapt.

BS: GoB, RB, power, slot| RS: RB, power BS: GoB, RB, power, slot | RS: RB, power non-adapt. 5 10 15 20 25 30 35 40 0 50 100 150 200 250 300 350 400

Figure 6.21. Comparison of various instances to show the influence of the adaptive algorithm for the allocation of slots, Gt = 3 for all APs.

6.2 Distributed Concept for Orthogonal Medium Access 135

6.2.5.2 Maximizing the Sum Rate

In this section, the allocation of slots is evaluated if the distributed concept for orthogonal medium access is applied with the objective of the maximization of the sum rate. A comparison is made between the adaptive algorithm and the non-adaptive one. Since the non-adaptive one is only defined in the distributed concept for reuse medium access, this concept is applied for the comparison.

In Fig. 6.22, the average sum rate as a function of the number of UEs is illustrated. The abbreviations used in the legend show again which subproblems are solved non-adaptively and adaptively by the BS or RS. The all-adaptive and non-adaptive instances are given as references. Only the snapshots are considered in which the minimum user rate is achieved by all UEs, except for the non-adaptive concept. The results are only shown if the relative frequency of outages is less than 5%. The performance of the adaptive algorithm for the allocation of slots is revealed if

number of UEs av er ag e su m ra te in b it s/ slo t all-adapt.

BS: GoB, RB, power, slot| RS: RB, power BS: GoB, RB, power, slot | RS: RB, power non-adapt. 5 10 15 20 25 30 35 40 0 1000 2000 3000 4000 5000 6000

Figure 6.22. Comparison of various instances to show the influence of the adaptive algorithm for the allocation of slots, Gt = 3 for all APs, Rmin = 10 bits/slot.

the instance using the non-adaptive algorithms for the allocation of power and bits and the adaptive algorithm for the allocation of slots is compared to the instance using the non-adaptive algorithms for the allocation of power and bits and for the allocation of slots. The comparison shows that the adaptive algorithm leads to two advantages. At first, the adaptive algorithm leads to an relative frequency of outages

smaller than 5% even for 40 UEs where each one has a minimum rate of 10 bits/slot. The non-adaptive one cannot provide this. If more than 30 UEs are in the cell, the average sum rate is not depicted any longer for the corresponding instance since the relative frequency of outages exceeds 5%. At second, the average sum rate is improved. For 5 UEs until 15 UEs, the absolute gain in terms of average sum rate is nearly constant. Hence, the relative gain is large especially for small number of UEs as already shown in Section 6.2.5.1, where the objective is the maximization of the minimum user rate. For larger number of UEs, the average sum rate achieved by the instance using the non-adaptive algorithms for the allocation of power and bits and for the allocation of slots decreases. The APs must allocate more resource blocks to links in order to achieve the minimum user rate and not in order to maximize the sum rate. This is avoided if the adaptive algorithm for the allocation of slots is applied.