Single Carrier FDMA: A New Air Interface for Long Term Evolution

Appendix B

Derivations of the Upper Bounds in Chapter 7

B.1 Derivation of Equations (7.9) and (7.10) in Chapter 7

We can expand E{Ze^νZ} as follows:

We can also expand E {e^νZ} similarly as follows:

By applying (B.1) and (B.2) to Equation (7.7) in Chapter 7 for ν = , we get the following:

By dividing each side with , we obtain

Using (B.2), Equation (7.6) in Chapter 7 becomes

B.2 Derivations of Equations (7.13) and (7.14) in Chapter 7

From Equation (7.11) in Chapter 7,

Also,

Using (B.6) and (B.7), Equation (7.8) in Chapter 7 becomes

After we determine from (B.8), the upper bound in Equation ...