Correlation Among The Approaches

In the first of this chapter, we give a simple illustration of the relation among some related approaches. Suppose that the power levels used in 2-MTS is P1 and P2, where P1 is equal to the transmission power of reduce transmission power in RPS and P2 is less than the maximum transmission power. The maximum transmission power is added in 3-MTS. Then, zero transmission power, namely mutes subframes, is added in 4-MTS. Another arbitrary transmission power is added in 5-MTS. Therefore, Fig. 4.5is the sketch map of the performance among ABS, RPS and MTS with different levels. As shown in the figure, MTS can provide better performance than ABS in most conditions even there are only two power levels. With the number of power levels of MTS increased, the performance of MTS is better than ABS and RPS. In the following section, we give a detailed numeric example to explain this result.

Figure 4.5: The sketch map of the performance relation among ABS, RPS and MTS with different levels.

4.4.2 Example

Through a simple analysis, an intuitive explanation of the idea of MTS is pro-vided. In this example, our goal is to increase the performance of macrocells without harming that of picocells. We know that RPS and ABS involves a trade-off between the performance of macrocells and picocells. We only compare the performance of MTS and ABS, because RPSs always produce more interference to picocells than ABS does. We consider a HetNet with an MBS, a PBS and a pico UE; an illustration of the network topology is shown in Fig. 4.6. The MBS has two power levels, which are denoted by P₁^m and P₂^m (P₁^m < P₂^m), respectively.

The path loss model is according to [102]..

For the viewpoint of the MBS, more transmission power leads to better perfor-mance. Therefore, the MBS tends to use as great a proportion of P₂^m as possible in this example. Therefore, we first determine a combination of P₁^m and P₂^m that produces equal or less interference to pico UEs given a number of ABS frames, which is denoted by N^A. When subframes are not muted in ABS scenarios, the maximum transmission power is used, which is denoted by P₃^m. Gmu, Gpu and Gmp are the channel gains amongst the MBS, the PBS and the pico UE, and the transmission power of the PBS is P^p. The SINR of the pico UE is shown as follows:

SINRi = P^p× G^pu P_i^m× G^mu+ N0

, i = 0, 1, 2, 3 (4.31)

where P₀ = 0, and we have four different SINR values in this example. SINR₀ and SINR3 are used in ABS scenario, and SINR1 and SINR2 are used in MTS with two power levels. We use LTE table lookup for calculating capacities, which

4.4 Numeric Example

Figure 4.6: The topology used in the simple numeric analysis.

is the function of SINRi and denote it as U(SINRi). Denote N^D and N¹ as the ABS period and the number of subframes with power level P1, respectively. We need to find a combination of P1 and P2 to produce less or equal interference to the pico UE. So, we have the following equation:

N¹ where the left-hand-side (LHS) is the capacity of MTS and right-hand-side (RHS) is the capacity of ABS scenario. To produce less or equal interference is equal to have higher or equal capacity. So, the greater or equal operation is held in (4.32). After some derivations, we have:

N¹ ≥ N^A× [U(SINR⁰) − U(SINR³)] + N^D× [U(SINR³) − U(SINR²)]

U(SINR1) − U(SINR²)

(4.33) Besides, N¹ is the number of subframes with power level P¹, therefore, 0 ≤ N¹ ≤

N^D.

Fig. ?? shows some examples in which the distances between the MBS and the PBS are 800, 500 and 300 m. The red points in the figures are the locations of the PBS, and the MBSs are on the origin. The transmission power of the PBS is set to 30 dBm, and maximum power of the MBS is 46 dBm, namely, P₃^m = 46 dBm. We set P₁^mand P₂^mto 26 dBm and 43 dBm, respectively. The red and blue lines indicate the boundaries of the CRE bias (15 and 10 dB). The boundary of the CRE bias is an ellipse according to [?]. In eICIC, the CRE bias is usually set to around 10 dB; thus, the UEs outside the blue ellipse do not associate with the PBS in most conditions.

Each point in the figures represents the position of the pico UE. The grayscale stands for the minimum proportion of P₁^m needed to produce less or equal inter-ference to the pico UE. A darker gray means that the MBS can use a lower proportion of P₁^m, and thus a higher proportion of P₂^m, to produce equal interfer-ence to the pico UE. We provide examples with different ABS proportion α, where N^A = αN^D. In our intuition, the larger α leads to less interference experienced by the pico UE. A larger proportion of P₁^m is therefore needed. Accordingly, the figures with larger α values may seem brighter. Positions with white colour mean that we cannot use P₁^m and P₂^m to produce less or equal interference to the pico UE.

From Fig. ??, the MBS can use a larger proportion of P₂^m when the distance between the MBS and the PBS is 800 m. Even if the ABS proportion is increased to 40%, the MBS can still use P₂^m in some subframes no matter where the pico UE is located with 10-dB bias. When the distance between them is decreased to 300 m, some locations of the pico UE with 10-dB bias make it impossible for

4.4 Numeric Example

(a) 800m,10%

(b) 800m,20%

(c) 800m,30%

(d) 800m,40%

(a) 500m,10%

(b) 500m,20%

(c) 500m,30%

(d) 500m,40%

4.4 Numeric Example

(a) 300m,10%

(b) 300m,20%

(c) 300m,30%

(d) 300m,40%

the MPS to produce less or equal interference to the pico UE with P₁^m and P₂^m. However, if we decrease the value of the CRE bias, the MBS can still create less or equal interference to the pico UE regardless of whether the pico UE is located with the decreased bias. For example, in Fig. 4.9(d), if we decrease the bias value to 3 dB, we find that the locations of the pico UE can make the MBS produce less or equal interference to the pico UE. According to this finding, we have the following proposition:

From this simple analysis, MTS has better performance than ABS even though there are only two power levels.

Theorem 5. Through the proposed approach, the user further from the MBS would be assigned no less power than the users close to the MBS.

Proof. According to Theorem 1, we know that a user further from the MBS would be assigned more transmission power. In the proposed approach, the transmission power is quantified into L levels instead of continuous assignment. Therefore, users with power level Ln would be further from the MBS than those with power level Ln−1. In a similar way, users with power level Ln would be nearer the MBS than those with power level Ln+1 The group of users with power level Ln is between the group of users with power level Ln−1and those with Ln+1. Therefore, the group of users with power level Ln is an annulus. We conclude that the users would be clustered into L groups, and these groups from annuluses.

U₁(P + ∆P ) − U1(P ) < U₂(P + ∆P ) − U2(P )

⇒ U¹(P + ∆P ) + U2(P ) < U1(P ) + U2(P + ∆P )

(4.34) According to (4.34), we conclude that assigning more power to the user who is further from the MBS creates more utility in the system.

Proposition 3. The macro users scheduled by the proposed algorithm would be clustered into L groups, and these groups form annuluses.