Clustering Algorithms

2.2.1 Static Clustering

Static clustering is a feasible way to form the clusters in the cellular network. It can be designed offline based on geographic or averaged channel characteristics. Once the planning is

determined, it will not change over time. The advantage of this clustering type is that routing CSI and user data to a central coordinator (CC) is unnecessary. Instead, it requires a distributed coordinator (DC) per cluster which controls the BSs. The cooperation only takes place in each cluster and different clusters do not communicate with each other, which reduces the overheads.

Here we propose a static clustering algorithm as follow. In each cell, we assume there is only one scheduled user, so the index for user can be ignored and the new notation H^b_bstands for the channel from the BS b to its user.

Algorithm Static Clustering Algorithm.

1: Specify the CoMP cluster size B;

2: Each user measures channel gains and calculates his pilot SINR by

SIN R^pilot_b = H^b_b ²/



 ∑

b̸=b,b∈Ib

H^bb ²+ N₀



 , ∀b, (2.28)

whereIbis set of the six first tier interfering BSs around BS b, i.e., only the pilots from the neighboring BSs are regarded as the valid interference. If SIN R^pilot_b < γ, where γ is the threshold, the user requests CoMP service to the BS b through uplink. Then BS b sends the request to its DC;

3: DC finds the remaining B− 1 BSs which should cooperate with the BS b based on the pre-defined clustering table (see Figure 2.2 for the case of B = 3), and makes them to form a cluster;

4: Go back to step3 until all the CoMP needed users are satisfied;

The clusters are formed by neighboring BSs here. Since in average, they cause stronger in-terference compared with those farther BSs. Although static clustering reduces the inter-cluster communication overhead, it inherits the fairness problem from single cell scenario that the users located at static cluster-edge still suffer from severe inter-cluster interference.

Figure 2.2: Proposed static clustering table when cluster size B = 3.

2.2.2 Dynamic Clustering

Static clustering has very limited performance gain since the variation of the channel con-dition is not fully exploited. As mentioned in the previous section, we select the neighboring BSs to form static clusters. Since on average, they are the ones which cause strong interfer-ence. Nevertheless, due to the effect of shadowing, a user might experience a better channel to a farther BS, in other words, interference does not always come from near BSs. Therefore, it is not flexible to form fixed clusters by grouping BSs which are close to each other. Besides, users at the edge of the static cluster experience much more interference from the neighboring clusters than the ones located around the center of the cluster, which causes fairness problem. In order to overcome the aforementioned problems, the idea of dynamic clustering has been intro-duced. Geographical relation is not the main concern anymore. Instead, we try to group the BSs which cause the strictest interference before any cooperation. The proposed greedy algorithm is illustrated in the following steps. Again, only one user per BS is assumed.

Algorithm Dynamic Clustering Algorithm.

1: Specify the CoMP cluster size B;

2: Each user calculates his SIN R^pilot_b as defined in (2.28). If SIN R^pilot_b < γ, the user sends CoMP request to the serving BS b;

3: The CC collects all the requests and chooses a CoMP needed user who has not been chosen so far uniformly;

4: Find the remaining B− 1 BSs which maximize the utility function J(

C₁^CoMP, . . . , C_B^CoMP) with the user chosen in step 3, where C_b^CoMPis the capacity given by (2.27). We let only the first tier BSs around the selected user to be the candidates, i.e., b∈ Ib. If the available BSs is less than B− 1, the user cannot acquire CoMP service at this time slot, then CC drops this user and picks another one uniformly;

5: Go back to step 3 until all the CoMP needed users find their partners;

We provide three choices of the utility function in this dynamic algorithm:

• Sum-rate (SR) utility:

• Proportional fair (PF) utility:

J2 =

• Weighted sum (WS) utility:

J₃ =

∑B b=1

w_bC_b^CoMP (2.31)

The purpose of the weight is to find the users who really need CoMP, i.e., the users with low SINR. So the weight is set to the reciprocal of the SINR, which is

w_b = c/q_b, (2.32)

where

q_b = log₂ (

1 + SIN R^pilot_b )

(2.33)

is the transformed SINR which approximates capacity and

c = 1

∑B b=1

q⁻¹_b

(2.34)

is a normalization factor such that

∑B b=1

w_b = 1. Note that SIN R^pilot_b is the SINR experienced by the users before CoMP. The user with larger SIN R^pilot_b will get lower weight, since the perfor-mance gain is little when apply CoMP to the users with high SINR.

Figure 2.3 shows a snapshot of the dynamic clustering result. No matter which utility func-tion is chosen, the CoMP clusters can be formed adaptively according to the change of channel conditions. Hence there are no constant cluster edges and therefore no users will suffer from more interference. However, there must exits a CC to run the dynamic clustering algorithm.

Besides, the overhead of routing the CSI and user data is higher than the static scheme.

Since the available BSs for selection are reducing through the dynamic algorithm, it benefits the user that is chosen earlier in Step 3. To circumvent this fairness issue, we have to choose the user uniformly. Therefore, on average, everyone obtains close performance gain.

Figure 2.3: A snapshot of the dynamic clustering.