Wireless Networking and Communications Group

OPTIMAL OFDMA RESOURCE ALLOCATION WITH LINEAR COMPLEXITY TO MAXIMIZE ERGODIC WEIGHTED SUM CAPACITY

Ian C. Wong and Brian L. Evans ICASSP 2007 Honolulu, Hawaii

Wireless Networking and Communications Group

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 http://www.wi-lan.com/library/WiMAX_Intro_CES_2005.pdf

Wireless Networking and Communications Group

Orthogonal Frequency Division Multiple Access (OFDMA)

• Adopted by IEEE 802.16a/d/e and 3GPP-LTE • Allows multiple users to transmit simultaneously on different subcarriers – Inherits advantages of OFDM – Exploits diversity among users User 1 User M frequency Base Station (Subcarrier and power allocation)

Wireless Networking and Communications Group

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 802.16e:

K = 1536, M ¼ 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

M K

subcarrier allocations and determine power allocation for each

Wireless Networking and Communications Group

Summary of Contributions

Previous Research

Instantaneous rate

•Unable to exploit time-varying wireless channels

Our Contributions

Ergodic rate

•Exploits time-varying nature of the wireless channel

Constraint-relaxation

•One large constrained convex optimization problem •Resort to sub-optimal heuristics (

O

(MK 2 ) complexity)

Dual optimization

•Multiple small unconstrained problems w/closed-form solutions •99.9999% optimal with O(MK) per iteration, <10 iterations

Wireless Networking and Communications Group

Weighted-Sum Capacity Maximization

Constant weights Powers to determine Channel gain to noise ratio Space of feasible power allocation vectors Average power constraint Subcarrier capacity

Wireless Networking and Communications Group

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”

Wireless Networking and Communications Group

Optimal Subcarrier and Power Allocation

“Multi-level waterfilling” “Max-dual user selection”

Wireless Networking and Communications Group

Numerical Results

No. of Iterations (

I

) SNR

5 dB 10 dB 15 dB

Erg. Rates

8.091

7.727

7.936

Inst. Rates

8.344

8.333

8.539

Relative Gap (x10 -6 )

5 dB 10 dB 7.936

5.462

.0251

.0226

15 dB 5.444

.0159

Initialization Complexity

O(INM)

Runtime Complexity

O(MK) O(IMK) M N

– No. of users;

K

– No. of subcarriers; – No. of function evaluations for integration -

Wireless Networking and Communications Group

Conclusion

• Derived downlink OFDMA resource allocation algorithms – Requires linear complexity – Maximizes ergodic weighted-sum capacity – Achieves negligible optimality gaps (99.9999% 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.