1.3 UWB Concepts
Traditional narrowband communications systems modulate continuous-waveform (CW) RF signals with a specific carrier frequency to transmit and receive information. A continuous waveform has a well-defined signal energy in a narrow frequency band that makes it very vulnerable to detection and interception. Figure 1-2 represents a narrowband signal in the time and frequency domains.
Figure 1-2 A narrowband signal in (a) the time domain and (b) the frequency domain
As mentioned in Section 1.2, UWB systems use carrierless, short-duration (picosecond to nanosecond) pulses with a very low duty cycle (less than 0.5 percent) for transmission and reception of the information. A simple definition for duty cycle is the ratio of the time that a pulse is present to the total transmission time. Figure 1-3 and Equation 1-1 represent the definition of duty cycle.
Figure 1-3 A low-duty-cycle pulse. Ton represents the time that the pulse exists and Toff represents the time that the pulse is absent.
Low duty cycle offers a very low average transmission power in UWB communications systems. The average transmission power of a UWB system is on the order of microwatts, which is a thousand times less than the transmission power of a cell phone! However, the peak or instantaneous power of individual UWB pulses can be relatively large,  but because they are transmitted for only a very short time (Ton < 1 nanosecond), the average power becomes considerably lower. Consequently, UWB devices require low transmit power due to this control over the duty cycle, which directly translates to longer battery life for handheld equipment. Since frequency is inversely related to time, the short-duration UWB pulses spread their energy across a wide range of frequencies—from near DC to several gigahertz (GHz)—with very low power spectral density (PSD).  Figure 1-4 illustrates UWB pulses in time and frequency domains.
Figure 1-4 A UWB pulse in (a) the time domain and (b) the frequency domain. Compare the bandwidth and power spectral density with those of the narrowband signal in Figure 1-2.
The wide instantaneous bandwidth results from the time-scaling property of theoretical Fourier transforms:
The notation on the left side of Equation 1-2 shows a signal, x(t), which is scaled in the time domain by a factor a; the right side represents the same signal in the frequency domain, X(f), which is inversely scaled by the same factor a. For example, a pulse with duration T of 500 picoseconds can generate a center frequency fc of 2 GHz: