Windowing for OFDM Signals

OFDM symbols are generated one symbol at a time. When the symbols are combined consecutively, spectral regrowth occurs because of the amplitude and phase discontinuity between the consecutive symbols. Time-domain windowing is performed on OFDM symbols to improve the spectral characteristics of the transmitted signal. Thus, spectral regrowth is reduced. Transitions between consecutive symbols are smoothed by the following methods:

  • Extending the OFDM symbols cyclically based on the Windowing Method property.
    • Starting at Symbol Boundary:
      • Appending the first window length (W) samples of the symbol at the end.
      • Overlapping the cyclic prefix (CP) with samples of the previous symbol and overlapping the cyclic suffix with the CP samples of the next symbol.
    • Centered at Symbol Boundary:
      • Appending the first W/2 samples of the symbols at the end and suffix W/2 samples before CP at the beginning.
      • Overlapping the extended CP with the samples of the previous symbol and overlapping the cyclic suffix with the samples of the CP of the next symbol
  • Applying windowing to the beginning and end of the OFDM symbol. Two windows are applied, with one window being the mathematical inverse of the other.
  • Applying the first cosine window, which rolls over from 0 to 1, over the window length of samples from the beginning of the symbol after cyclic extension.
  • Applying the second cosine window, which rolls over from 1 to 0, over the last window length of samples after cyclic extension.
  • After applying windowing to all the OFDM symbols, adding the overlapped segments of the current symbol and the previous symbol, as well as the overlapped segments of the current symbol and the next symbol to maintain the required OFDM symbol length.

The windowing algorithm is controlled by the Window Length and Windowing Method properties. The selected window shape is a raised-cosine window. The shape and length of the window relative to an OFDM symbol length, along with the shaping procedure, are shown in the following image.

Table 5.
Table 6.
1) Normal Symbol with Cyclic Prefix (CP) 5) Window-half-length
2) Symbol Cyclically Extended by Window-half-length Samples from Each Side 6) 2 * Window-half-length
3) Extended Symbol Shaped by Window 7) OFDM Symbol Length
4) Superposition by Summation of Successive Symbols
Table 7.
  1. Normal Symbol with Cyclic Prefix (CP)
  2. Symbol Cyclically Extended by Window-half-length Samples from Each Side
  3. Extended Symbol Shaped by Window
  4. Superposition by Summation of Successive Symbols
  5. Window-half-length
  6. 2 * Window-half-length
  7. OFDM Symbol Length

  Windowing for DSSS Signals

For direct sequence spread spectrum (DSSS) signals, windowing ensures power ramp up and down for the entire burst. The rising half of the cosine window is applied at the beginning of the burst and the falling half of the window is applied at the end of the burst. The length of the window is specified by the Window Length property.

The following figure represents the windowing for DSSS signals.

Figure 13.