1. Ian C. Wong and Brian L. Evans ICASSP 2007 Honolulu, Hawaii
OPTIMAL OFDMA RESOURCE ALLOCATION WITH LINEAR COMPLEXITY TO MAXIMIZE ERGODIC WEIGHTED SUM CAPACITY
Ian C. Wong and Brian L. Evans
ICASSP 2007
Honolulu, Hawaii

2. Mobile Broadband Wireless Access (IEEE 802.16e, 3GPP-LTE)
Ubiquitous and high-speed video, data, and voice
Ease of deployment, lower total cost of ownership
Scalable infrastructure
Figure from

3. Orthogonal Frequency Division Multiple Access (OFDMA)
Adopted by IEEE a/d/e and 3GPP-LTE
Allows multiple users to transmit simultaneously on different subcarriers
Inherits advantages of OFDM
Exploits diversity among users
. . .
User 1
frequency
Base Station
(Subcarrier and power allocation)
User M

4. OFDMA Resource Allocation
How do we allocate K data subcarriers and total power P to M users to optimize some performance metric?
E.g. IEEE e: K = 1536, M¼ 40 / sector
Voice applications
Minimize transmit power required to support a set of data rates
Data applications
Maximize data rates subject to power constraints
Very active research area
Difficult discrete optimization problem
Brute force optimal solution: Search through MK subcarrier allocations and determine power allocation for each

5. Summary of Contributions
Previous Research
Our Contributions
Formulation
Instantaneous rate
Unable to exploit time-varying wireless channels
Ergodic rate
Exploits time-varying nature of the wireless channel
Solution
Constraint-relaxation
One large constrained convex optimization problem
Resort to sub-optimal heuristics (O(MK2) complexity)
Dual optimization
Multiple small unconstrained problems w/closed-form solutions
% optimal with O(MK) per iteration, <10 iterations

6. Weighted-Sum Capacity Maximization
Constant
weights
Powers to determine
Channel gain to noise ratio
Average power constraint
Space of feasible power allocation vectors
Subcarrier capacity

7. Dual Optimization Method
“Dualize” the power constraint
Multiple small unconstrained problems with closed-form solutions
Find optimal geometric multiplier using line search
Derived closed-form PDF of dual
1-dimensional integral per iteration
“Multi-level waterfilling”
Geometric multiplier
“Max-dual user selection”

8. Optimal Subcarrier and Power Allocation
“Multi-level waterfilling”
“Max-dual user selection”

9. Numerical Results 5 dB 8.091 8.344 10 dB 7.727 8.333 15 dB 7.936 8.539
SNR
Erg.
Rates
Inst.
No. of
Iterations
(I)
5 dB
8.091
8.344
10 dB
7.727
8.333
15 dB
7.936
8.539
Relative
Gap
(x10-6)
.0251
5.462
.0226
5.444
.0159
Initialization Complexity
O(INM) -
Runtime Complexity
O(MK)
O(IMK)
M – No. of users; K – No. of subcarriers;
N – No. of function evaluations for integration

10. Conclusion Derived downlink OFDMA resource allocation algorithms
Requires linear complexity
Maximizes ergodic weighted-sum capacity
Achieves negligible optimality gaps ( % optimal)
Extensions to discrete rate and partial CSI cases:
[1] I. C. Wong and B. L. Evans, "Optimal Resource Allocation in OFDMA Systems with Imperfect Channel Knowledge,“ IEEE Trans. on Communications., submitted.
[2] I. C. Wong and B. L. Evans, "Optimal OFDMA Resource Allocation with Linear Complexity to Maximize Ergodic Rates," IEEE Trans. on Wireless Communications, submitted.
[3] I.C. Wong and B. L. Evans, "Optimal OFDMA Subcarrier, Rate, and Power Allocation for Ergodic Rates Maximization with Imperfect Channel Knowledge," Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Proc., April 16-20, 2007, Honolulu, HI USA, accepted.