Greedy Algorithm

Due to high computation complexity of ILP, we further propose a heuristic algorithm to perform power allocation efficiently. This proposed algorithm is based on greedy approach.

Same as our ILP formulation, the objective of our greedy algorithm aims to maximize the total payoff of the cell. Clearly, the constraints specified in our ILP formulation such as QoS requirement, power capacity, and SINR should be also held in our greedy algorithm.

The detail of the proposed algorithm is presented in Algorithm 8.

Our algorithm operates in per RB fashion. It means that the BS allocates one RB with the required transmission power to a SS in each time. Initially, the available transmission power of the BS is equal to its power capacity. In each time that a RB is allocated to a SS, the corresponding power consumption is deduced from the available transmission power.

Algorithm 8 Greedy Algorithm

Input: 1. The location of all SSs and BS.

2. Power capacity of BS.

3. SS MCS.

Output: 1. Power allocation 2. Payoff for the cell Phase I: Investigation:

For each sⁱ_j ∈ Sⁱ do For each b∈ B do

1. For each p_l∈ P do

a. Calculate the corresponding payoff for each (sⁱ_j, b, p_l).

b. Record the smallest p_l which can sustain the required MCS.

End For

2. Record a RB bj which leads to the largest payoff P Fj.

End For End For End Phase I.

Phase II: Allocation:

For j= 1 to |Si| do

1. Check whether QoS requirement of sⁱ_j is satisfied or not.

2. If there is at least one SS with unsatisfied QoS requirement.

Dorecord one with the largest payoff among these SSs with unsatisfied QoS.

Else

Dorecord one SS with the largest and non-negative payoff

End For End Phase II.

The algorithm should terminate when the available transmission power cannot support the requirement of SS. There are two phases in our algorithm: investigation and allocation. In the investigation phase, the BS calculates the payoff among all available RBs for each SS and records one with the maximum payoff. As mentioned earlier, the SS can operate in different MCS which is an input of our problem. Therefore, in this phase, the BS focuses on not only maximizing the payoff of each SS but also make sure that it can support enough transmission power to sustain the required MCS.

With the information gathering in the investigation phase, the BS starts to make de-cisions of allocating RB to SS in the allocation phase. In order to ensure that the QoS guaranteed service can be provided, all SSs are classified into two categories: required and optional. The first category indicates the SS which QoS requirement has not been satisfied.

On the other hand, the second category stands for the SS with satisfied QoS requirement.

Due to the characteristic of delay sensitivity, the QoS requirement for real time traffic is based on the maximum delay requirement. We use the same method as ILP to calculate this requirement as shown in (5.4). The requirement for non-real time and best effort traffic is based on the minimum guaranteed bandwidth as agreed during admission control since less strict QoS requirement is needed. If there are SSs fallen into the first category, the BS must allocate RBs to these SSs in order to meet the requirement of providing QoS guaranteed service. At this time, the BS starts to select one SS with the largest payoff among the SSs in the first category and allocate the corresponding RB to this SS. After allocating the RB, the BS marks that RB as unavailable and deduce the required transmission power from available power of BS. If there are no SSs in the category of required, it means that the QoS requirement of all SSs has been reached. At this time, the BS can select one SS with the largest payoff and allocate the corresponding RB to that SS. This allocated RB is marked as unavailable and should not be allocated to any other SS in the future.

After allocating a RB to a SS, the BS repeats these two phases until all RBs are unavail-able. In addition to no available RBs, this algorithm terminates when one of the following

conditions are met: 1) the BS does not have enough available transmission power. 2) all SSs have negative payoff. The first condition ensures that the BS has enough available transmission power to sever each selected SS. This matches the power capacity constraint shown in (5.2) in our ILP formulation. As stated in (5.1), our objective is to maximize the payoff of the cell. It is necessary to ensure that all allocated RBs contribute positive payoff.

Thus, the algorithm should end when no SSs have positive payoff.

Complexity. Our greedy algorithm comprises two phases. Thus, the complexity of this al-gorithm can be calculated as the sum of complexity of individual phase. In the investigation phase, each SS takes O(|B|) time to go through all RB. Each RB takes O(|P |) time to find the optimal power level. Thus, the total complexity in this phase is O(|Sⁱ||B||P |), ∀i ∈ N.

In the allocation phase, the BS takes O(|Sⁱ|) time to go through all SS to meet the require-ments in the phrase. Thus, the total time for a BS to allocate one RB is O(|Sⁱ||B||P | + |Sⁱ|) and there are total |B| RBs. Consequently, total complexity for the greedy algorithm is O(|R| · (|Sⁱ||B||P | + |Sⁱ|)).

Correctness. The greedy algorithm leads us to a valid power allocation due to the follow-ing constraints maintained by the algorithm - 1) The BS ensures that it has enough available transmission power and is able to support the corresponding MCS before allocating a RB.

2) The SS in required category must be served before allocating RB to the SS in optional category. This ensures that the QoS requirement of each SS can be satisfied. 3) Once a RB is allocated to a SS, it is marked as unavailable. it avoids that one RB is shared by more than one SS. 4) All RBs allocated to a SS contribute positive payoff. Thus, this leads us to maximum payoff for the cell. The correctness of the proposed algorithm is verified through simulation presented in the next section.