1. A Low Complexity Algorithm for Proportional Resource Allocation in OFDMA Systems
Ian C. Wong, Zukang Shen,
Jeffrey G. Andrews, and Brian L. Evans
The University of Texas at Austin
Wireless Networking and Communications Group
November 30, 2018

2. Orthogonal Frequency Division Multiplexing (OFDM)
Adapted by current wireless standards
IEEE a/g, Satellite radio, etc…
Broadband channel is divided into many narrowband subchannels
Multipath resistant
Equalization simpler than single-carrier systems
Uses time or frequency division multiple access
channel
magnitude
carrier
subchannel
frequency
November 30, 2018

3. Orthogonal Frequency Division Multiple Access (OFDMA)
Adapted by IEEE a/d/e BWA standards
Allows multiple users to transmit simultaneously on different subchannels
Inherits advantages of OFDM
Exploits multi-user diversity
User 1
magnitude
User 2
frequency
. . .
Base Station
- has knowledge of each user’s channel state information thru ideal feedback from the users
User K
November 30, 2018

4. Resource Allocation in OFDMA
Given:
N number of subchannels
K number of users
P base station total transmit power
Hk,n - channel gain for user k on subcarrier n
BER bit error rate (maximum)
f objective function
How do we allocate the N subchannels and P total power to the K users to optimize the objective function f while satisfying the bit error rate (BER)?
November 30, 2018

5. Proportional Resource Allocation in OFDMA Systems
Maximize the overall system throughput while maintaining proportionality among users
Useful for service level differentiation
Very difficult to solve exactly
(Nonlinear Mixed-Integer Programming Problem)
N - # subchannels
K - # users
P - BTS Power
B - Bandwidth
Hk,n - channel gain
Objective function
Exclusive subcarrier assignment
Non-zero power
No subcarrier sharing
Power constraint
Proportionality constraint
November 30, 2018

6. Solution to Proportional Resource Allocation Problem [Shen et. al
Subchannel allocation step
Greedy algorithm – allow the user with the least allocated capacity/proportionality to choose the best subcarrier O(KNlogN)
Power allocation step
General Case
Solution to a set of K non-linear equations in K unknowns – Newton-Raphson methods O(nK)
High-channel to noise ratio case
Function root-finding O(nK), n=number of iterations, typically 10 for the ZEROIN subroutine
November 30, 2018

7. Proposed Low Complexity Solution
Key Ideas
Relax strict proportionality constraint
In practical scenarios, rough proportionality is acceptable
Require a predetermined number of subchannels to be assigned to simplify power allocation
Reduced power allocation to a solution of linear equations O(K)
Achieved higher capacity with lower complexity, while maintaining acceptable proportionality
Does not need a high channel-to-noise ratio assumption
November 30, 2018

8. 4-Step Approach Determine number of subcarriers Nk for each user
Assign subcarriers to each user to give rough proportionality
Assign total power Pk for each user to maximize capacity
Assign the powers pk,n for each user’s subcarriers (waterfilling)
O(K)
O(KNlogN)
O(K)
O(N)
November 30, 2018

9. Simple Example 1 = 3/4 2 = 1/4 N = 4 K = 2 P = 10 10 8 7 4 9 6 5 3
November 30, 2018

10. Step 1: # of Subcarriers/User10 8 7 4 Nk 3 1
1 = 3/4 9
2 = 1/4
N = 4
K = 2
P = 10 6 5 3 1 2 3 4
November 30, 2018

11. Step 2: Subcarrier Assignment10 8 4 7 10 10 8 10 8 7 Rk
Rtot 8 4 7 4 7
log2(1+2.5*10)=4.70
log2(1+2.5*8)=4.39 4
log2(1+2.5*7)=4.21
13.3 3 6 5 9 9
log2(1+2.5*9)=4.55
4.55 3 6 5  Nk
3/4 3
1/4 1 1 2 3 4 1 2 3 4
November 30, 2018

12. Step 3: Power per user P1 = 7.66 P2 = 2.34 10 9 8 7 1 2 3 4
November 30, 2018

13. Step 4: Power per subcarrier
Waterfilling across subcarriers for each user
P1 = 7.66
P2 = 2.34
p1,1= 2.58
p1,2= 2.55
p1,3= 2.53
p2,1= 2.34  Nk
3/4 3
1/4 1 1 2 3 4 10 8 7 9
Data Rates:
R1 = log2( *10) + log2( *8)
+ log2( *7) =
R2 = log2( *9) =
November 30, 2018

14. Simulation Parameters
Value
Number of Subcarriers (N) 64
Channel Model
6-tap, exponentially decaying power profile with Rayleigh fading
Number of Users (K)
4-16
Max. Delay spread
5 ms
BER constraint
10-3
Doppler Frequency
30 Hz
November 30, 2018

15. Total Capacity Comparison
SNR = 38dB
SNR Gap = 3.3
Based on
10000 channel
realizations
Proportions assigned randomly from {4,2,1} with probability [0.2, 0.3, 0.5]
November 30, 2018

16. Proportionality Comparison
Based on the
16-user case,
10000 channel
realizations per
user
Normalized rate proportions for three classes of users using proportions
{4, 2, 1}
November 30, 2018

17. Computational Complexity
22% average improvement
Code developed in floating point C and run on the TI TMS320C6701 DSP EVM run at 133 Mhz
November 30, 2018

18. Memory Complexity 2024 1660 1976 2480 4000 4140 8KN+4K O(KN) 4N+12K
Memory Type
*Proposed Method
*Shen’s Method
Program
Memory
Subcarrier Allocation
2024
1660
Power Allocation
1976
2480
Total
4000
4140
Data Memory
System Variables
8KN+4K
O(KN)
4N+12K
O(N+K)
4N+8K
4N+28K
4N+24K
* All values are in bytes
November 30, 2018

19. Summary O(KNlogN) O(N+nK), n9 O(N+K) O(NK) Performance Criterion
Proposed Method
Shen’s Method
Subcarrier Allocation Computational Complexity
O(KNlogN)
Power Allocation Computational Complexity
O(N+nK), n9
O(N+K)
Memory Complexity
O(NK)
Achieved Capacity
Higher
High
Adherence to Proportionality
Loose
Tight
Assumptions on Subchannel SNR
None
November 30, 2018

20. Backup Slides
November 30, 2018

21. Step 1: Number of subcarriers per user
Determine Nk to satisfy
This is achieved by
Complexity: O(K)
November 30, 2018

22. Step 2: Subcarrier Assignment
O(1)
O(KNlogN)
November 30, 2018

23. Step 2: Subcarrier Assignment
O( (N-K-N*)K )
O(N*K)
November 30, 2018

24. Step 3: Power allocation among users
From subcarrier allocation, we have
Hence, power allocation problem is reduced into solving
November 30, 2018

25. Step 3: Power allocation among users
Whose solution is:
(K)
November 30, 2018

26. Step 4: Power allocation across subcarriers per user
Waterfilling across subcarriers for each user:
O(K)
November 30, 2018