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

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: x_m (m = 0, 1, …, M − 1) represents modulated source symbols and X_k (k = 0, 1, …, M − 1) represents M samples of the DFT of x_m; Y_l (l = 0, 1, …, N − 1) represents the frequency domain samples after subcarrier mapping and y_n (n = 0, 1, …, N − 1) represents the transmitted time domain channel symbols that are obtained from the inverse DFT (IDFT) of Y_n.

A.1 Time Domain Symbols of LFDMA

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

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 ...