1 fi′′(0)
1 (K−N +|A|)FA′′(0)
= (K − N + |A|)FA′′(0)
fi′′(0). (C.11)
The proof for (5.16) is completed.
We now turn to the power allocations for channels i, j in A. By
fi(p∗i) = fj(p∗j) = FA(qA∗) (= y) (C.12) we derive
P →0lim p∗i
p∗j = lim
y→0
fi(inv)(y)
fj(inv)(y) = lim
y→0
1/fi′fi(inv)(y)
1/fj′fj(inv)(y) = 1/fi′(0)
1/fj′(0). (C.13)
C.7 Proof of Observation 1
The result for 1) is a direct consequence of the given rates of convergence, and the result for 2) follows similarly to (C.13). Hence, we omit them.
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About the Author
Shih-Wei Wang was born in Pingtung, R.O.C., in 1981. He received the B.S. and M.S. degrees in electrical engineering from the National Central University, Chungli, Taiwan, in 2003 and 2005, respectively. He is currently working toward the Ph.D. degree in the Department of Electrical Engineering, National Chiao Tung University, Hsinchu, Taiwan. He held a visiting position with Queen’s University, Kingston, Canada, in 2010. His research interests lie in information theory and convex optimization.