In this section, simulation results are obtained for the network centric clusterisation approach using the proposed algorithm. The performance metric used are the sum-rate and bit error rate (BER). The BER performance is used to measure the number of errored received bits transmitted through a given communication medium [28]. Consider the system setup in Fig. 2.3, Fig. 2.4 (showing a cluster size of Mmax = 2) and Fig. 2.5
(showing a cluster size of Mmax = 4). The performance of the algorithm is evaluated for
KBS-UE pairs where each user k is served by Mk= Mmaxnumber of BSs in each cluster.
The value of Mmax is varied to analyse the effect of the system performance against the
number of transmit BSs allowed for CoMP transmission. In this section the non-CoMP system, which is based on a single downlink transmission between each BS-UE pair, would be compared to the proposed (small size of clusters) and existing strategies (large size of clusters). Also a random clusterisation, which randomly selects each clusters without taking any network factors into consideration is evaluated and compared with the static clusterisation method (where the clusters are fixed regardless of the changing network conditions).
For the analysis required in this section, the following parameters are defined:
• ‘bernc’ and ‘rtnc’ represents the BER and sum-rate performance respectively under non-CoMP transmission and {Mk}Kk=1 = Mmax= 1.
• ‘berrc’, and ‘rtrc’ represent the BER and sum-rate performance respectively under a random clusterisation of the BS-UE pairs and {Mk}Kk=1 = Mmax= 2.
• ‘bersc’ and ‘rtsc’ represent the BER and sum-rate performance respectively under a network preset clusterisation for the given BS-UE pairs and {Mk}Kk=1 = Mmax =
2.
• ‘berdc’ and ‘rtdc’ represent the BER and sum-rate performance respectively under the proposed dynamic clusterisation of the BS-UE pairs based using the algorithm
presented in Section 2.3.2 for K = 4 BS-UE pairs. The clusterisation is dynamic and changes with the given channel conditions and {Mk}Kk=1 = Mmax= 2.
• ‘berfc’ and ‘rtfc’ represent the BER and sum-rate performance respectively under full CoMP transmission. The users receive data from all K BSs and {Mk}Kk=1 =
Mmax= K = 4. 0 5 10 15 20 25 30 35 40 10−4 10−3 10−2 10−1 100 SNR, (dB) BER bernc, Mk = 1, ∀k berrc, Mk = 2, ∀k bersc, Mk = 2, ∀k berdc, Mk = 2, ∀k berfc, Mk = 4, ∀k
Figure 2.6: BER performance with Mt = 4, Nr = 2 and K = 4 BS-UE pairs in a network
centric CA.
Figs. 2.6 and 2.7 show the BER performance and the sum-rate performance of the given system, under the different clustering strategies. It can be observed from Fig. 2.6 that ‘bernc’ and ‘berrc’ achieve poor BER performance when compared to ‘bersc’, ‘berdc’ and ‘berfc’. It can also be observed from Fig. 2.7 that ‘rtnc’ and ‘rtrc’ achieve poor
BER performance when compared to ‘rtsc’, ‘rtdc’ and ‘rtfc’. However the sum-rate performance obtained with ‘rtnc’ exceeds that obtained with ‘rtrc’ as the SNR increases. This shows that a random clusterisation approach does not provide any gain even with CoMP transmission as compared to a non-CoMP transmission with a single BS-UE pair.
0 20 40 60 80 100 120 0 5 10 15 20 25 30 35 40 SNR(dB) Sum -r at e (k bps/Hz) rtnc rtrc rtsc rtdc rtfc
Figure 2.7: Sum-rate performance with Mt= 4, Nr= 2 and K = 4 BS-UE pairs in a network
centric CA.
The proposed ‘rtdc’ is seen to achieve a higher sum-rate than ‘rtsc’, while ‘rtfc’ is seen to have the best performance when compared to all other four strategies. The channel characteristics of the wireless channel changes with time and the dynamic clusterisation takes advantage of this unique characteristics unlike the static clustering approach. As expected, the performance obtained under the dynamic method is seen to outperform the static approach. This is because unlike static clustering, dynamic cluster takes into account the changing channel conditions of the network during clustering. Dynamic clustering approach re-clusters the users using the given strategy such that the best BSs
are clustered together at every given time. This result validates the need for a dynamic cluster selection as opposed to a static or random clusterisation of BS-UE pairs as well as non-CoMP transmission.
The best BER and sum-rate performance is achieved under ‘berfc’ and ‘rtfc’ with Mk= 4
transmit BSs for the k-th user. However when compared to ‘berdc’ and ‘rtdc’ with only Mk
= 2 transmit BSs for the k-th user, a 50% reduction is expected in the backhaul overhead using the proposed solution for only a slight decrease in the performance. For instance to obtain a BER performance of 10−2, ‘berfc’ and ‘berdc’ requires an SNR of 20 dB and 22 dB. Also when the SNR is 25 dB, ’rtfc’ and ’rtdc’ obtains a sum-rate performance of 63 kbps/Hz and 61 kbps/Hz respectively. As observed, a considerable gain is not achieved with full CoMP transmission when Mmax = 4 when compared to Mmax = 2, even though
the resulting data overhead is doubled. The backhaul link is limited and could potentially cause poor synchronisation and high latency, if congested. It is therefore important to avoid full CoMP transmission with a large number of transmit BSs per user. Hence, the cluster size needs to be reduced and the members of each cluster needs to be properly selected such that the system performance is maximised with limited backhaul overhead. Using the same number of transmit and receive antennas, for K = 6 BS-UE pairs, the simulation results show the BER and sum-rate performance in Figs. 2.8 and 2.9 respectively. The proposed dynamic clusterisation presented earlier in Section 2.3.2 is applied for K = 6 BS-UE pairs. Note that to completely cancel the interference using precoding and/or beamforming at the transmitter and/or receiver respectively, there has to be available DoF at the transmitter and/or receiver. And so for the given set-up, the constraints on the transmit and/or receive antennas respectively are Mt> (K − 1) and/or
Nr > (K−1)Mmax, which means either constraint or both constraints needs to be satisfied
for complete interference cancellation. If the number of transmit antennas do not meet the constraint required to completely null the transmitted leakage to the users, the DoF at the receive antennas can be used to also mitigate the received interference.
other four strategies when SNR ≤ 10 dB. But at higher SNR values, ‘berfc’ and ‘rtfc’ are seen to achieve the worst performance. This is because for the given system set-up with Mt = 4, Nr = 2, Mmax = 6 and K = 6 BS-UE, the condition for complete interference
zero-forcing is not met, thereby causing very poor mitigation of the received interference.
0 5 10 15 20 25 30 10−3 10−2 10−1 100 SNR, (dB) BER bernc, Mk = 1, ∀k berrc, Mk = 2, ∀k bersc, Mk = 2, ∀k berdc, Mk = 2, ∀k berfc, Mk = 6, ∀k
Figure 2.8: BER performance with Mt = 4, Nr = 2 and K = 6 BS-UE pairs in a network
centric CA.
It can be seen from Fig. 2.8, that the BER performance flattens out at higher SNR values due to unavailable DoF for complete interference cancellation. Again ‘berdc’ is seen to exceed the BER performance obtained by ‘bernc’,‘berrc’ and ‘bersc’. Also from Fig. 2.9, ‘rtdc’ is seen to achieve a better sum-rate performance over 15 dB to 20 dB and ‘rtnc’ achieves a better performance from 30 dB upwards. This happens because under the given system conditions, none of the solutions meet the transmit antenna constraints.
However, ‘rtnc’ (with Mmax = 1) would obtain a less dominant interference since the
receive antenna conditions are less stringent as opposed to ‘rtdc’ (with Mmax = 2) and
‘rtfc’ (with Mmax = 6). So at higher SNR values ‘rtnc’ would experience a better SINR
and system performance due to lower level of interference compared to ‘rtdc’ and ‘rtfc’.
0 10 20 30 40 50 60 70 80 90 100 0 5 10 15 20 25 30 SNR(dB) Sum -r at e (k bps /H z) rtnc rtrc rtsc rtdc rtfc
Figure 2.9: Sum-rate performance with Mt= 4, Nr= 2 and K = 6 BS-UE pairs in a network
centric CA.
From these observations, one can see that the number of available transmit and receive antennas can affect the performance of CoMP transmission with a large cluster size under certain condition. In addition, the data overhead experienced in this case is three times more than the data overhead required under the proposed clustering approach. Even at low SNR values, the increase in performance is very trivial compared to the required increase in the data overhead. For instance at 0 dB, ‘rtfc’ and ‘rtdc’ achieve a sum-rate performance of 22 kbps/Hz with Mmax= 6 and 19 kbps/Hz with Mmax = 2.