Transcript Document 7549145
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
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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)
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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
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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
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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”
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Optimal Subcarrier and Power Allocation
“Multi-level waterfilling” “Max-dual user selection”
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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.