AUTOCUIDADO NIVEL DE CALIDAD

In this section, we want to find an optimal mathematical solution for the resource allocation challenge described in the previous section. To this end, we will provide a solution for the case of one video quality level in Subsection 5.2.1 which we will extent in Subsection 5.2.2 for using multiple video quality levels and a group of priority and non-priority class users. It is important that UEs which are located farther away from the base station also get enough resources to reach a certain target rate. So there has to be a certain level of fairness in

assigning resources to the UEs. It is explicitly not the intention to maximize the overall data rate like in opportunistic scheduling. The situation that may arise in that case is that UEs that are located near the base station are allocated more resources because they will achieve high data rates with relatively few resources, unlike UEs which are further away from the base station, that will need more resources for a lower data rate [32]. With opportunistic schedulers, it may be that UEs who are located farther away will hardly be allocated any resources, which for PSS usage is unacceptable.

5.2.1. Single video quality level

For the case of one video quality level our goal is to have as many UEs as possible to achieve this quality level, while using a minimal amount of resources. This quality level corresponds to a required data rate, which is indicated by the target rate 𝑅𝑇.

We consider a network with a single cluster (as in Figure 5-1), with K users (UEs) (1 ≤ k ≤ K), a relay station r and a base station b. A user can only be connected to either the relay station or base station at one point in time, so they are divided into two groups. The first group of users, indicated with 𝐾_𝑟, send their video streams through the relay station. The second group of users, indicated with 𝐾_𝑏, send their video streams directly to the base station. The

frequency spectrum is divided into resource blocks (RBs). The total number of resource blocks available is M (1 ≤ m ≤ M).

The achievable rate 𝑅_𝑘𝑚𝑘_{in bits per second (bps) for the kth user using 𝑚}

𝑘 resource blocks per

unit of time is given by:

𝑅_𝑘𝑚𝑘 ₌ { min [(𝑚_𝑘∗ 180𝐾ℎ𝑧) ∗ 𝜎 ∗ 𝑙𝑜𝑔2(1 + 𝑆𝐼𝑁𝑅_𝑘,𝑟𝑚𝑘_), ((𝑚_𝑟∗ 180𝐾ℎ𝑧) ∗ 𝜎 ∗ 𝑙𝑜𝑔2(1 + 𝑆𝐼𝑁𝑅_𝑟,𝑏𝑚𝑟_{)) / |𝐾} 𝑟| ] , 𝑣𝑖𝑎 𝑟𝑒𝑙𝑎𝑦 𝑠𝑡𝑎𝑡𝑖𝑜𝑛 (𝑚_𝑘∗ 180𝐾ℎ𝑧) ∗ 𝜎 ∗ 𝑙𝑜𝑔2(1 + 𝑆𝐼𝑁𝑅_𝑘,𝑏𝑚𝑘_{), 𝑑𝑖𝑟𝑒𝑐𝑡 𝑡𝑜 𝑏𝑎𝑠𝑒 𝑠𝑡𝑎𝑡𝑖𝑜𝑛} (5.1)

Where |𝐾_𝑟| is the number of users in group 𝐾_𝑟 and 𝑚_𝑟 is the amount of resource blocks used by the relay station per unit of time to send |𝐾_𝑟| video streams to the base station. 𝑆𝐼𝑁𝑅_𝑘,𝑟𝑚𝑘_, 𝑆𝐼𝑁𝑅_𝑟,𝑏𝑚𝑟 _{and 𝑆𝐼𝑁𝑅}

𝑘,𝑏

𝑚𝑘 _{are calculated according to Formula (4.3), depending on the distances} k-r, r-b and k-b, respectively, and the number of resource blocks used on the particular link.

The received power must be higher than the minimum threshold so that the receiver can reconstruct the data from the received signal. On the other hand, the power of the receive signal must not be too high so that it starts to interfere with carriers of adjacent resource blocks. The minimum receive power at the relay station and the base station per resource block is described by 𝑃_𝑚𝑖𝑛𝑟𝑒𝑐. Because we are using fixed transmission power for all UEs and the relay station 𝑃_𝑚𝑖𝑛𝑟𝑒𝑐 limits the number of resource blocks that can be used for a certain link. The maximum receive power at the relay station and the base station per resource block is described by 𝑃_𝑚𝑎𝑥𝑟𝑒𝑐 which limits the fixed transmission power. This latter receive power constraint is less important given the low transmission powers used.

The total number of resources used must not exceed the total available resources. When the collection of users connected to the base station is notated as 𝐾𝑏 and the users connected to

the relay station as 𝐾_𝑟 the resources constraint can be described as:

∑ 𝑚𝑘,𝑏+ ∑ 𝑚𝑘,𝑟+ 𝑚𝑟,𝑏

𝑘∈𝐾𝑟

≤ 𝑀

𝑘∈𝐾𝑏 (5.2)

Here 𝑚_𝑘,𝑏 indicates the amount of resources used by a user connected to the base station,

𝑚𝑘,𝑟 the amount of resources used by users connected to the relay station on that link, and 𝑚_𝑟,𝑏is the amount of resources used by the relay station to support the total rate of the video streams routed via the relay station.

The optimization problem can be formulated using the objective function below. Here K is the set of subsets 𝐾𝑏 and 𝐾𝑟 {1, … , 𝑘} and I_{𝑅

𝑘𝑚𝑘 ≥ 𝑅𝑇} is the indicator function which equals 1 if 𝑅_𝑘𝑚𝑘 _{≥ 𝑅} 𝑇 and 0 otherwise. (5.3) subject to: C1: ∑_{𝑘∈𝑘𝑏}𝑚_𝑘,𝑏+ ∑_{𝑘∈𝑘𝑟}𝑚_𝑘,𝑟+ 𝑚_𝑟,𝑏 ≤ 𝑀 C2: 𝑃_𝑘𝑚 ≥ 𝑃_𝑚𝑖𝑛𝑟𝑒𝑐, ∀𝑚, 𝑘 C3: 𝑃_𝑟𝑚 ≥ 𝑃_𝑚𝑖𝑛𝑟𝑒𝑐, ∀𝑚, 𝑟 C4: 𝑃_𝑘𝑚 ≤ 𝑃_𝑚𝑎𝑥𝑟𝑒𝑐_{, ∀𝑚, 𝑘} C5: 𝑃_𝑟𝑚 _{≤ 𝑃} 𝑚𝑎𝑥𝑟𝑒𝑐, ∀𝑚, 𝑟

Constraint C1 describes the resource block allocation constraint. Constraint C2 till C5 are the minimum and maximum power constraints.

The maximization in (5.3) results in a list with possible UE distributions across the groups 𝐾𝑟

and 𝐾_𝑏 and associated resource allocations (𝑚₁, … , 𝑚_𝑘, 𝑚_𝑟). Selecting the distribution that uses the least amount of resources in total is the solution where the maximum number of UEs have a data rate that is equal to or higher than the target rate while using a minimum amount of resources.

Reference [33] also provides a solution for resource allocation in a network that consists of UEs, relay stations and a receiver. In our case, the latter is the base station. The difference is that in [33] the network contains multiple relay stations and multiple transmission paths are used at the same time. In our research only one relay station is used and a UE can only use one transmission path at the same time (i.e. via the relay or direct to the base station). In reference [33] the optimisation problem is solved with a heuristic approach where they use equal power allocation across the subcarriers of a resource block. Because of this the power constraint is ignored which simplifies the original problem. This solution is not suitable to our research. We use fixed transmission power for all UEs and the relay station so if a

transmitting entity is closer to its intended receiver it will have more power per resource block and ultimately send more data within a resource block. Also, it is indicated that when it is not possible for all UEs to meet their rate requirements that UEs are given a rate close to their requirement. In our research this would be a waste of resources because when the target rate for a certain quality video stream is not met the target rate is lowered to a lower video quality level. As a result of the approach in [33] the UE is receiving way too many resources for the new target rate. The excess of resources assigned to a particular UE can be better assigned to other UEs, which will allow as many UEs as possible to achieve the highest possible target rate.

5.2.2. Multiple video quality levels

When using one video quality level it will likely occur that some UEs will meet the target rate and are able to send their video streams, while others will not meet the target rate and have no video connection at all. For public safety applications this is totally unacceptable. Therefore several video quality levels are applied, as described in chapter 3. For using multiple video quality levels our first goal is to have as many UEs as possible to achieve the minimal video quality level. The second goal is to have as many UEs as possible to achieve a higher video quality level. So "more UEs having less increase in video quality" is preferable to "less UEs having much increase in video quality". The last goal is to achieve the prior goals while using a minimal amount of resources.

The multiple video quality levels correspond to required data rates as indicated in section 3.2, which are denoted as 𝑅_𝑇(𝑖). Here the 𝑖(1 ≤ i ≤ I) indicates which target rate it concerns. Determining the achievable rate 𝑅_𝑘𝑚𝑘 _{is harder compared to the single video quality case since} it is likely that the UEs in group 𝐾_𝑟 will have different quality video streams and so do not use an equal part of the relays station’s resources. As a consequence, the UEs connected to the relay station get a proportionate share of the throughput of the relay station which depends on the throughput of the link from the UE to the relay station, as shown in Formula (5.6). The

rate of a UE directly linked to the base station using 𝑚𝑘 resource blocks, indicated with 𝑅_{𝑘,𝑈𝐸−𝐵𝑆}𝑚𝑘 _{, is calculated according to Formula (5.4). The rate for the link from a UE to the} relay station, indicated by 𝑅_{𝑘,𝑈𝐸−𝑅𝑆}𝑚𝑘 _{, is calculated according to Formula (5.5).}

𝑅_{𝑘,𝑈𝐸−𝐵𝑆}𝑚𝑘 _{= (𝑚} 𝑘∗ 180𝐾ℎ𝑧) ∗ 𝜎 ∗ 𝑙𝑜𝑔2(1 + 𝑆𝐼𝑁𝑅𝑘,𝑏 𝑚𝑘_{) (5.4)} 𝑅_{𝑘,𝑈𝐸−𝑅𝑆}𝑚𝑘 _{= (𝑚} 𝑘∗ 180𝐾ℎ𝑧) ∗ 𝜎 ∗ 𝑙𝑜𝑔2(1 + 𝑆𝐼𝑁𝑅𝑘,𝑟 𝑚𝑘_{) (5.5)} 𝑅_{𝑘,𝑅𝑆−𝐵𝑆}𝑚𝑘 _{= ((𝑚} 𝑟∗ 180𝐾ℎ𝑧) ∗ 𝜎 ∗ 𝑙𝑜𝑔2(1 + 𝑆𝐼𝑁𝑅𝑟,𝑏 𝑚𝑟_{)) ∗} 𝑅𝑘,𝑈𝐸−𝑅𝑆𝑚𝑘 ∑_{𝑖∈𝐾𝑟}𝑅_{𝑘,𝑈𝐸−𝑅𝑆}𝑚𝑘 (5.6)

The achievable rate 𝑅_𝑘𝑚𝑘_{in bits per second (bps) for the kth user using 𝑚}

𝑘 resource blocks per

unit of time is then given by:

𝑅_𝑘𝑚𝑘 _{= {}min[𝑅𝑘,𝑈𝐸−𝑅𝑆

𝑀𝑘 _{, 𝑅}

𝑘,𝑅𝑆−𝐵𝑆

𝑀𝑘 _{] , 𝑣𝑖𝑎 𝑟𝑒𝑙𝑎𝑦 𝑠𝑡𝑎𝑡𝑖𝑜𝑛}

𝑅_{𝑘,𝑈𝐸−𝐵𝑆}𝑀𝑘 _{, 𝑑𝑖𝑟𝑒𝑐𝑡 𝑡𝑜 𝑏𝑎𝑠𝑒 𝑠𝑡𝑎𝑡𝑖𝑜𝑛} (5.7) Although all first responders contribute to the same end status, not all of them are equally interesting to be followed by the Central Command Post using a high quality video stream. By applying priority amongst the first responders, scarce spectral resources can be assigned to the most interesting cases. Therefore we define two types of users: a priority class 𝑘1 and a

priority class 𝑘2. The users of priority class 𝑘1 are assigned resources to achieve the highest

possible data rate and are thus able to send a video stream with the highest quality possible. Priority class 𝑘₂ users must be assigned enough resources to achieve the minimum target rate. If enough resources are available priority class 𝑘₂ users can even achieve a higher target rate. This optimization problem is solved in three steps. First, it must be determined which

resource allocations and route combinations result in the priority UEs achieving the maximum target rate and the non-priority UEs a throughput equal to or higher than the minimum target rate. Then it has to be determined which of these combinations give as many non-priority UEs as possible a high as possible target rate. Finally, the combination that uses the least amount of resources is chosen as the optimal resource scheduling. The constraints as described for the case with one video quality level in Subsection 5.2.1 also apply here.

The optimization problem described above is computational very hard to solve. Going through all possible resource assignments and choose the optimal one, with 7 video quality levels and 2 possible routes to the base station, gives 𝐾14 _{possible combinations. The time}

required to find the optimal resource allocation is so large that this is not a practical solution. Therefore a heuristic approach will be discussed in the next section.