This section presents all the needed mathematical formulas that will be simulated later in MATLAB in order to evaluate the impact of the proposed scheme on the system performance. It is important to formulate the DL SINR, throughput and capacity to have clear comparison between the UEs performance before and after implementing the proposed scheme. Needless to say that, the overall network is composed of three Macrocells with two Mobile-Femtos distributed in every 1Km2 based on the used path-loss model that has been discussed earlier. Additionally, the only considered interference scenarios in this section are the interference between Mobile-Femtos and Macrocells or interference among Mobile- Femtos themselves. The Macro UE can be interfered by the DL signal of any adjacent Mobile-Femto and the same may happen for the Mobile-Femto UE with the Macrocell or any adjacent Mobile-Femto. Thus, based on equation (4.14), the received SINR for an outdoor direct Macro UE (m) on subcarrier n can be expressed as
Where, and are the transmission power of the serving Macrocell (eNB) and the neighbouring Macrocell (eNB’) on subcarrier n respectively. is the channel gain between the Macro UE m and serving Macrocell (eNB) on subcarrier n. Channel gain from neighbouring Macrocells is denoted by . Similarly, is the transmission power of neighbouring Mobile-Femto (MFemto) on sub-carrier n. is the channel gain between the Macro UE m and neighbouring Mobile-Femto (MFemto) on sub-carrier n. Whilst, has been modelled to express the Path-Loss model and x is the distance between the Macro UE and the serving eNB. is the VPL and Pnoise is the white noise power. Hence, equation 5.7 has made it clear that outdoor Macro UEs can be interfered by two interference sources, one is the interference from neibouring Macrocells signals which has been given
by
and the second is the interference from Mobile-Femtos in the same Macrocell which has been given by . Therefore, both of the interference sources have been considered together with the noise power in this
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equation in order to evaluate the impact of them on the received SINR for an outdoor Macro UE.
In contrast, the Macrocell or any adjacent Mobile-Femto can cause interference to a Mobile- Femto’s UE based on formula (4.16), thus, the received SINR of a Mobile-Femto UE (mf)on subcarrier n can be formulated as
There is a system constant loss but no channel gain over the Mobile-Femto LOS access link between the UE and the serving Mobile-Femto. The only existing channel gain ( ) is the channel gain between the Mobile-Femto UE with other adjacent Mobile-Femtos that may cause interference to the considered UE.
Hence, the Macro-UE capacity on a specific subcarrier n can be estimated via the SINR from the following equation [Lee et al., 2010]
Where BW is the available bandwidth for subcarrier n divided by the number of UEs that share the specific subcarrier and is the coding margin and in this equation it is a constant for target Bit Error Rate (BER) thatdefined by = -1.5/ln(5BER) [Nungu et al., 2014]. Here, the BER has been set to 10-6. So the overall throughput of the serving Macrocell M can be expressed as
Where, m,n here notifies the subcarrier assignment for Macro UEs. When m(D),n = 1, the subcarrier n is assigned to Macro UE m and otherwise m(D),n = 0. From the characteristics of
(5.8)
(5.9)
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the OFDMA system, each subcarrier is allocated to only one Macro UE in a Macrocell in every time slot. This implies that = 1 for k, where Nm is the number of Macro UEs in a Macrocell and k is the available PRBs. While similar expression for Mobile-Femto UEs related to the practical capacity and the overall throughput is possible except
= 3 for k ∈ FMobile-Femto. Nmf is the number of Mobile-Femto UEs in a Macrocell and FMobile-Femto is the available sub-bands allocated to Mobile-Femtos in Macrocells. This implies that the proposed scheme reuses the full frequency band three times in the considered Macrocells.
Thus, the Mobile-Femto UE capacity on a specific subcarrier n can be estimated via the SINR as the following equation shows
Where the overall throughput of the serving Mobile-Femto (MFemto) can be expressed as
After discussing the SINR, throughput and capacity, here it is important to state that the outage probability plays an essential role in the proposed scheme as it affects the network performance by affecting the data rate and throughput of UEs. If the outage probability is small, the throughput increases, and then when the throughput increases the data rate increases, thus, the performance improves and the interference decreases. However, the outage probability affects the performance of cell-edge UEs more than the Macro UEs due to their high path-loss. To find out the outage probability it is required first to identify the SINR threshold value in the range of 0dB to 30dB. Thus, the outage probability (Pout) is determined when the SINR level of a subcarrier is below the designated threshold and it can be given by
(5.11)
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Where, indicates the failed subcarrier of UE u on subcarrier n. This can occur when the penetration loss and path-loss issues are severe especially in the vehicular environment, which may affect the received SINR at the receiver side. Thus, if =1, the SINR of that subcarrier is under the SINR threshold (SINRu,n < SINRthreshold). As a result of that, the ratio between the number of subcarriers under the SINR threshold and the number of the total subcarriers is the outage probability.
The subsequent results will show that the proposed scheme is greatly capable of preventing the interference among the Macro UEs as well as the interference among the Mobile-Femto UEs. The Mobile-Femto UEs effect on Macro UEs and vice versa is less in the proposed scheme in comparison with the previous schemes. For example, the FFR-3 (frequency factor reuse 3) and NoFFR (frequency factor reuse 1) techniques assign random subcarriers to the Femto UEs, regardless of the subcarriers that have been used by the Macro UE. Therefore, the Macro UEs and the Femto UEs may use subcarriers very nearer to one another that cause interference. Due to this fact, the interference between the Macro UEs and the Femto UEs is higher than the proposed scheme. Nevertheless, the proposed scheme avoids this interference at minimal degradation and the total amount of available subcarriers for Mobile-Femto UEs is three times of the full band in this scheme. The above comparison has been summarised in Table 5.1. Also, the table shows the fact that Macro UEs have the option to choose one frequency band at a time in each Macrocell and their choice is limited on whether those UEs are in the centre zone or edge zone. In contrast, the Mobile-Femto UEs have the choice to choose between three different frequency bands at a time and their choice is again based on UEs locations and whether they are in the centre zone or edge zone. (Refer to Figure 5.3)
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Table 5.1 Comparison between the proposed and previous interference management schemes
Schemes
Macro-user Femto-user
Frequency Amount Frequency Amount
Proposed for the Mobile-Femto/ Macrocell FFR 1 Centre zone: F0 Edge zone: F1, F2 or F3 depends on the Macro UE position in each Macrocell
Divide centre and edge zones
3
Centre zone has 2 options Edge zone has 4 potions: F0, F1, F2 or F3 depends on the Mobile-Femto UE position in each Macrocell FFR-3 (reuse 3) FFR 1 Random 1
NoFFR-3 (reuse 1) Random Random
Note: Amount column implies value of and for Macro and Mobile-Femto
UEs respectively.
Obviously, all the previous mathematical analysis has built the main base for implementing the proposed interference management scheme. Accordingly, the achieved results will be discussed in the following section as these results have created a comparison between the proposed scheme, and the FFR-3 (frequency reuse factor 3) and NoFFR-3 (frequency reuse factor 1) schemes as shown in Figure 5.5.
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However, it is important to mention here the difference between the frequency reuse factor 1 and the frequency reuse factor 3. In the frequency reuse factor 1, the same frequency band in a cell is reused in each of the adjacent cells. As a result of using the same frequency, high interference occurs in this system making it impractical. On the other hand, in the frequency reuse factor 3, the allocated frequency band is divided into 3 sub-bands (possibly with equal BW) and the three sub‐bands are reused in an alternating fashion. No neighbouring cells have the same frequency in this configuration resulting in more practical frequency reuse.Thus, reusing frequencies by dividing the allocated band by a specific integer number of cells and assigning each cell one division and then repeating the assignment repeatedly produces a trade-off between network capacity and reception quality as follows:
The higher the number of divisions of the spectrum over cells (higher cell‐reuse factor), the lower the capacity of the network but the further away cells with similar frequency allocations is located resulting in lower interference.
The lower the number of divisions of the spectrum over cells (Lower cell‐reuse factor), the higher the capacity of the network but the closer cells with similar frequency allocations is located resulting in higher interference.