As defined by the FCC’s First Report and Order, UWB signals must have bandwidths of greater than 500 MHz or a fractional bandwidth larger than 20 percent at all times of transmission [3]. Fractional bandwidth is a factor used to classify signals as narrowband, wideband, or ultra-wideband and is defined by the ratio of bandwidth at –10 dB points4 to center frequency. Equation 1–4 shows this relationship.

where fh and f1 are the highest and lowest cutoff frequencies (at the –10 dB point) of a UWB pulse spectrum, respectively. A UWB signal can be any one of a variety of wideband signals, such as Gaussian, chirp, wavelet, or Hermite-based short-duration pulses. Figure 1–5 represents a Gaussian monocycle as an example of a UWB pulse in the time and frequency domains. The Gaussian monocycle is the first derivative of a Gaussian pulse and is given by

where represents time and is a time decay constant that determines the temporal width of the pulse. As shown in Figure 1–5, a 500-picosecond pulse generates a large bandwidth in the frequency domain with a center frequency of 2 GHz. In Figure 1–5b, the lowest and highest cutoff frequencies at –10 dB are approximately 1.2 GHz and 2.8 GHz, respectively, which lead to a fractional bandwidth of 80 percent; this is much larger than the minimum Bf
required by the FCC:

Here is the classification of signals based on their fractional bandwidth:

For example, 802.11 and Bluetooth have fractional bandwidths of 0.8 percent and 0.04 percent, respectively.