1. Presented By Riaz (STD ID: 82081029)
Proportional Fair Power Allocation with CDF-Based Scheduling for Fair and Efficient MU OFDM Systems
System Group’s Seminar
June, 2009
Presented before
Professor Kyung Sup Kwak
Presented By
Riaz (STD ID: )
Graduate School of Information Technology and Telecommunications
Inha University, South Korea
19 April 2019

2. Telecom Engineering Lab, INHA University
Reference
Paper Title: Proportional Fair Power Allocation with CDF-Based Scheduling for Fair and Efficient Multiuser OFDM Systems
Authors: Hanbyul Seo and Byeong Gi lee
Journal: IEEE Transaction on Wireless Communications, Vol. 5, No. 5, May 2006
19 April 2019
Telecom Engineering Lab, INHA University

3. Telecom Engineering Lab, INHA University
Contents
Introduction
System Model
Opportunistic Subcarrier Allocation
Proportional Fair Power Allocation
Performance Comparison
Conclusion
19 April 2019
Telecom Engineering Lab, INHA University

4. Telecom Engineering Lab, INHA University
Introduction
In Multiuser OFDM, it is important to allocate resources fairly among the users while maximizing the system efficiency.
Shortcomings of recent works
Improper to non-real time data services or
Fairness aspect is not considered or
Based on instant service rate
In this paper, a new adaptive resource allocation scheme is proposed that can achieve fairness in terms of time-average throughput without zero-delay constraint, while maximizing the system efficiency
For sabcarrier allocationCDF based scheduling.
Tx power allocation proportional fair power allocation (PFPA): relative throughput-increment is identical in each subcarrier.
19 April 2019
Telecom Engineering Lab, INHA University

5. Telecom Engineering Lab, INHA University
System Model (1)
Consider, downlink transmission of a MU OFDM system
BW=B, Number of orthogonal subcarrier=M
Each MS measures the channel gain of each subcarrier and feeds back the CSI to BS
Each subcarrier sees frequency flat fading and the channel gain remains constant during a slot but varies slot to slot
SNR of the m-th sabcarrier signal of the k-th user at n-th slot can be expressed by
allocated Tx power
Channel gain
PSD
19 April 2019
Telecom Engineering Lab, INHA University

6. Telecom Engineering Lab, INHA University
System Model (2)
In MU OFDM, resource allocation algorithm decides which user to serve with what power for each subcarrier.
Here we assume the total Tx power constrained to S.
Once the resources are allocated to users, the instant data rate of each user is determined and the BS serves each user at this rate. The instant service rate can be shown:
Time-average throughput of each user:
Indicator function 1 or 0
19 April 2019
Telecom Engineering Lab, INHA University

7. Telecom Engineering Lab, INHA University
System Model (3)
Throughput vector
Achievable vector
Is a throughput vector if it the algorithm can yield the throughput for user k
Achievable Region
Set of all achievable vectors
Total Number of User
19 April 2019
Telecom Engineering Lab, INHA University

8. Opportunistic Subcarrier Allocation (1)
For, MU diversity gain and increased overall system capacity
We adopt CDF-based scheduling (CS) algorithm: possible to determine the performance of each user in an analytic manner
CS selects a user as:
Weighting factor
CDF of channel gain
Asymptotic behavior of channel gain of the user selected by CS:
Sufficient to consider the case of MR algorithm with identical competing users.
In this case, the channel gain of the selected user is given by
Since gk’s are RV, selected channel gains are also random. If we assume Rayleigh fading channel, gk’s are i.i.d. exponential RV with mean g.
So we can determine the distribution of selected channel gain which is a function of the number of competing users, K/, as well
19 April 2019
Telecom Engineering Lab, INHA University

9. Opportunistic Subcarrier Allocation (2)
According to extreme value theorem, the asymptotic mean of selected channel gain:
Gumbel RV
distribution
Effective Channel Gain
Can be regarded as selected channel gain, since the normalized (by selected channel gain) error between it and the selected channel gain approaches zero
19 April 2019
Telecom Engineering Lab, INHA University

10. Opportunistic Subcarrier Allocation (3)
Assume, M increases to infinity, for a given BW B.
Selection probability, Pk=
Number of selected subcarrier, nk
The effective channel gain of kth user for the average channel gain
Then by law of large of numbers, the relative number of allocated subcarrier nk/M approaches to the selection probability as M increases to infinity
So asymptotic throughput of each user:
Ratio of allocated power of kth user to total power S.
19 April 2019
Telecom Engineering Lab, INHA University

11. Proportional Fair Power Allocation (1)
Conventional power allocation algorithms have some weakness that degrade the system performance when employed in heterogeneous user channel environment.
EQ Algorithm: does not take the CSI of each subcarrier into consideration so it can not exploit the flexibility of Tx power which is inherent in MU OFDM sys.
WF Algorithm: no fairness
One may try to allocate many subcarriers to the users with low average channel gains, but it severely degrades the throughput of users in good channel condition
In order to resolve the above problems
Define a metric on the efficiency of using Tx power and then develop a new power allocation algorithm based on it.
19 April 2019
Telecom Engineering Lab, INHA University

12. Proportional Fair Power Allocation (2)
The relative throughput increment of a subcarrier
Or, the normalized increment of service rate contributed by the increment of power
Then we consider a power allocation scheme such that the resulting is identical among all subcarriers.
As this is a monotonically decreasing function of power, this scheme always allocates additional power to the subcarrier whose relative throughput-increment subject to power increment is the largest.
Consequently this PFPA scheme maximizes the sum rate over all subcarriers and yields a proportional fair property.
19 April 2019
Telecom Engineering Lab, INHA University

13. Proportional Fair Power Allocation (3)
In OFDM systems, the number of subcarrier is very large, so it may be too complex to calculate power allocation to each individual subcarrier based on PFPA.
Two-tier approach: first allocate total power user-based (inter-user) and then distribute it subcarrier-based (intra-user).
Inter-user: PFPA with effective channel gain
Intra-user: EQ or WF
Inter-user: if nk subcarriers are selected for user k, then the inter-user PA problem reduces to the problem of determining the amount of allocated power, , satisfying the condition:
The amount of allocated power is determined by the avg channel gain and the number of assigned subcarrier, not by the instant channel gain of each subcarrier.
19 April 2019
Telecom Engineering Lab, INHA University

14. Proportional Fair Power Allocation (4)
PFPA in the asymptotic case
Asymptotic relative throughput-increment
Asymptotically optimal resource allocation that exhibits the largest achievable region when the throughput of each user is given by (9). PA becomes equivalent to the PFPA also
constant
19 April 2019
Telecom Engineering Lab, INHA University

15. Proportional Fair Power Allocation (5)
Left hand side term indicates the amount of allocated power per allocated BW, which can be interpreted as
Optimal PA is similar to the WF that regards as the channel gain.
the difference is that the water level of PFPA is inversely proportional to , the throughput per allocated BW, while the water level of WF is constant for all users
19 April 2019
Telecom Engineering Lab, INHA University

16. Comparison: Achievable Region (case-1)
Fig. 1 (a)
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Telecom Engineering Lab, INHA University

17. Comparison: Achievable Region (case-2)
Fig. 1 (b)
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Telecom Engineering Lab, INHA University

18. Comparison: Amount of Allocated Resources
Fig. 2
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Telecom Engineering Lab, INHA University

19. Comparison: Average Throughput
Fig. 3
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Telecom Engineering Lab, INHA University

20. Comparison: Average Spectral Efficiency
Fig. 4
19 April 2019
Telecom Engineering Lab, INHA University

21. Telecom Engineering Lab, INHA University
Conclusion
PFPA Algorithm is proposed.
It allocates the additional power to the subcarrier whose relative through-put increment is the largest, which results in the proportional-fair allocation
Proposed PFPA is equivalent to the asymptotically optimal PA algorithm.
Results show PFPA algorithm outperforms conventional PA algorithms in terms of time-average throughput, in heterogeneous user channel environments
Thanks for your cooperation
Questions/Comments
19 April 2019
Telecom Engineering Lab, INHA University