Single Carrier FDMA: A New Air Interface for Long Term Evolution
by Hyung G. Myung, David Goodman
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:
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Let n = Q · m + q, where 0 ≤ m ≤ M − 1, 0 ≤ q ≤ Q − 1, and N = Q · M. Then

If q = 0, then

Figure A.1 Symbol notations for SC-FDMA modulations

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

Thus,
A.2 Time Domain Symbols of DFDMA
For DFDMA, the frequency ...
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