8.4 Complexity Analysis
8.5.2 Performance Evaluation under Different g k among Users
Now we consider different gk among users with the scenario shown in Fig. 8.5. User near to the base station requests large rate ratio due to less power decay caused by path loss. Based on Fig. 8.5, the power decay for users 1 to 8 is g1 = g2 = −107.96 dB, g3 = g4 = −112.96
required rate ratios among users 2 R 4
6 5 R
6 R R
MS 1 MS 2 MS 3
MS 4
MS 5
MS 6
MS 7
MS 8
K1:K2: K3 : K4 : K5: K6: K7 : K8 = 6:6:3:3:2:2:1:1
Figure 8.5: Diagram of considered various power decay gk (path loss) and required rate ratios among users.
dB, g5 = g6 = −116.83 dB, and g7 = g8 = −120.00 dB with corresponding rate ratios η1 : η2 : . . . : η8 = 6 : 6 : 3 : 3 : 2 : 2 : 1 : 1.
The normalized capacity among users is presented in Fig. 8.6. We find that the provided subchannel allocation algorithms combined with proposed power allocation method can also match the required rate constraints well even if there are different {gk}8k=1 between users.
Different from the discussion in previous session, the adaptable power allocation here be-comes very important as users have different large-scale channel gains. Fig. 8.7 shown the normalized capacity distribution under pure equal power allocation, i.e. ignore the second stage of Fig. 8.1. We can find that the required rate constraints are no longer satisfied. The users with less power decay gk obtain larger rate than that with serious power decay, e.g.
users 1 and 2 versus users 7 and 8. It is because the effect of different gkis not compensated.
In fact, the purpose of first stage in Fig. 8.1, subchannel allocation, is to assign most suit-able subchannels to users with good instantaneous channel qualities. Then the second stage, power allocation, can make the final assignment to be consistent with the requirements for proportional rates due to (8.22) and (8.23) have considered the parameter gk.
In addition to fit the rate constraints, Fig. 8.8 shows the link SNR improvement.
Simi-1 2 3 4 5 6 7 8 0
0.05 0.1 0.15 0.2 0.25 0.3
User Index
Normalized Capacity Ratios Among Users
Required ratios
user−oriented + max−min user−oriented + max−rate subchannel−oriented + max−min subchannel−oriented + max−rate η2 = 6
η4 = 3 η3 = 3
η5 = 2 η
6 = 2
η7 = 1 η
8 = 1 η1 = 6
Different g
k among users
Figure 8.6: Normalized capacity distribution among users with proposed power allocation method. The same parameters as Fig. 8.2. The path loss gk among users are based on the assumption of Fig. 8.5, i.e. g1 = g2 = −107.96 dB, g3 = g4 = −112.96 dB, g5 = g6 = −116.83 dB, and g7 = g8 = −120.00 dB.
larly, max-min scheduling can provide better link SNR performance than max-rate schedul-ing especially under user-oriented assignment. The enhancement is 0.35 ∼ 1.44 dB for user-oriented assignment and 0.27 ∼ 0.55 dB for subchannel-oriented assignment, respec-tively. Table 8.1 displays the system capacity over all users under proposed power allocation and pure equal power allocation. It is expected that pure equal power allocation produces higher capacity due to it does not compensate the effect of different gk. However, pure equal power allocation can not meet our predetermined requirement.
Finally, we provide an extreme example that edge users request larger rate ratios than
1 2 3 4 5 6 7 8 0
0.05 0.1 0.15 0.2 0.25 0.3
User Index
Normalized capacity ratios among users
Required ratios
user−oriented + max−min user−oriented + max−rate subchannel−oriented + max−min subchannel−oriented + max−rate
η7 = η
8 = 1 η5 = η
6 =2 η3 = η4 = 3
η1 = η2 =6
Different g
k among users
Figure 8.7: Normalized capacity distribution among users with equal power allocation. The same parameters as Fig. 8.6. The path loss gk among users are based on the assumption of Fig. 8.5.
center users. In this testing, we reset rate ratios as η1 : η2 : . . . : η8 = 1 : 1 : 2 : 2 : 3 : 3 : 6 : 6 under the same power decay assumption. Fig. 8.9 shows again the provided algorithms and power allocation can almost match the predetermined requirement. However, only equal power allocation causes unbalanced results compared to the ideal ratios as shown in Fig.
8.10. Similar to Fig. 8.7, the users with less power decay gk will get larger rate than expected values; users with heavy power decay merely get lower rate than expected values.
Note that we can find resource allocation with user-oriented assignment has better per-formance than that with subchannel-oriented assignment over all provided numerical results.
It is because there exists user requested constraints in our problem now. User-oriented
as-1 2 3 4 5 6 7 8 4.5
5 5.5 6 6.5 7 7.5 8
User Index
Average weakest link SNR (dB)
user−oriented + max−min user−oriented + max−rate subchannel−oriented + max−min subchannel−oriented + max−rate
gain: 0.35 dB
gain: 0.55 dB gain: 1.44 dB
gain: 0.27 dB
Figure 8.8: Average weakest link SNR per user (corresponding to the simulation assumptions and available capacity provided in Fig. 8.6).
signment can be more flexible than subchannel-oriented assignment to allocate resources according to instantly determined results.
Table 8.1: System capacity of multiuser MIMO-OFDM systems versus various allocation algorithms (nats/sec/Hz) under different power decay gk among users.
user-oriented subchannel-oriented
Power allocation max-min max-rate max-min max-rate Satisfy rate constraints?
Provided method 11.852 12.168 11.606 11.900 Yes (shown in Fig. 8.6)
Equal power 13.435 13.732 13.362 13.613 No (shown in Fig. 8.7)
1 2 3 4 5 6 7 8
0 0.05 0.1 0.15 0.2 0.25 0.3
User Index
Normalized capacity ratios among users
Required ratios
user−oriented + max−min user−oriented + max−rate subchannel−oriented + max−min subchannel−oriented + max−rate
η8 = 6
η5 = 3 Different g
k among users
η3 = 2 η1 = 1
η7 = 6
η2 = 1
η4 = 2
η6 = 3
Figure 8.9: Normalized capacity distribution among users with proposed power allocation method. The rate constraints among users are extremely opposite to previous assumption η1 : η2 : . . . : η8 = 1 : 1 : 2 : 2 : 3 : 3 : 6 : 6. The path loss gk among users are based on the assumption of Fig. 8.5.
1 2 3 4 5 6 7 8 0
0.05 0.1 0.15 0.2 0.25 0.3
User Index
Normalized capacity ratios among users
Required ratios
user−oriented + max−min user−oriented + max−rate subchannel−oriented + max−min subchannel−oriented + max−rate
Different g
k among users
η5 = η
6 = 3
η7 = η8 =6
η3 = η
4 =2
η1 = η2 = 1
Figure 8.10: Normalized capacity distribution among users with equal power allocation. The rate constraints among users are extremely opposite to previous assumption η1 : η2 : . . . : η8 = 6 : 6 : 3 : 3 : 2 : 2 : 1 : 1. The path loss gk among users are based on the assumption of Fig. 8.5.
Chapter 9 Conclusion
9.1 Dissertation Summary
In this dissertation, we have investigated different MIMO systems for realizing personalized parallel transmissions from two kinds of perspectives: narrowband system with personal-ized broadcast and broadband system with personalpersonal-ized scheduling. The former, the MIMO broadcast systems, utilizes spatial domain to simultaneously broadcast independently per-sonalized data for multiple users. The related research topics were presented in Chapters 3, 4, and 5. The later, the MIMO-OFDM systems, utilizes frequency domain to simultaneously communicate with multiple users through subchannel assignment and scheduling. The cor-responding research issues were listed in Chapters 7 and 8. The network MIMO systems is a special application of the MIMO broadcast systems from a single-cell scenario extended to a multi-cell environment. In Chapter 6, we combine network MIMO technique with frequency partitions to personalized transmit data among multiple cells. The details of research topics in this dissertation are listed as follows.
• Is transmit or receive beamforming more suitable for designing personalized multiuser MIMO broadcast systems?
• On the performance of transmit based MIMO broadcast systems in terms of link quality improvement and coverage extension by multiuser scheduling.
• Analysis of the effects caused by channel estimation errors in the receive ZF based MIMO broadcast systems.
• Performance enhanced 3-cell network MIMO architecture design under sectorized cells and FFR.
• Joint multiuser scheduling and subchannel assignment for multiuser MIMO-OFDM systems with coverage enhancement.
• Joint subchannel and power allocation for multiuser MIMO-OFDM systems with flex-ible proportional rates among users.
The contributions from these research works are listed as follows.
1. Provide quantitative comparison and tradeoff between the transmit and the receive ZF MIMO broadcast systems in terms of sum rate, feedback requirements, and sensitivity to feedback channel variations.
2. Present analytical expressions for the link outage probability, link diversity, and reliable coverage of the transmit ZF-DPC and ZF MIMO broadcast systems.
3. Provide analytical link performance and sum rate formulas for the receive ZF MIMO broadcast systems in the presence of channel estimation errors.
4. Design low-complexity 3-cell network MIMO architectures combined with FFR and tri-sector frequency partitions.
5. Analyze the achievable reliable coverage of the spatial multiplexing based MIMO-OFDM systems under random selection, multiuser scheduling, and jointly multiuser and frequency diversity scheduling scheme.
6. Design low-complexity subchannel assignment and power allocation method for the spatial multiplexing based MIMO-OFDM systems with proportional rate constraint among users.
The following summaries the results from the above contributions.