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Single Carrier FDMA: A New Air Interface for Long Term Evolution by David Goodman, Hyung G. Myung

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Appendix A

Derivation of Time Domain Symbols of Localized FDMA and Distributed FDMA

In this appendix, we use the symbol notations described in Figure A.1: xm (m = 0, 1, …, M − 1) represents modulated source symbols and Xk (k = 0, 1, …, M − 1) represents M samples of the DFT of xm; Yl (l = 0, 1, …, N − 1) represents the frequency domain samples after subcarrier mapping and yn (n = 0, 1, …, N − 1) represents the transmitted time domain channel symbols that are obtained from the inverse DFT (IDFT) of Yn.

A.1 Time Domain Symbols of LFDMA

For LFDMA, the frequency samples after subcarrier mapping {Yl} can be described as follows:

image

Let n = Q · m + q, where 0 ≤ mM − 1, 0 ≤ qQ − 1, and N = Q · M. Then

image

If q = 0, then

image

Figure A.1 Symbol notations for SC-FDMA modulations

image

If q ≠ 0, since image, then Equation (A.2) can be expressed as follows:

image

Thus,

A.2 Time Domain Symbols of DFDMA

For DFDMA, the frequency ...

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