Traditional narrowband communications systems modulate continuouswaveform (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.
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.

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,2 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.The wide instantaneous bandwidth results from the time-scaling propertyof 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: