*2.2.2. Sensors of narrow instantaneous bandwidth*

Strictly spoken, such sensors do not belong to UWB systems but they are doing the same job as real UWB devices if they are applied for sensing. Hence, they are worth being considered.

**Figure 3.** Principle of sine wave measurement.

Fig. 3 depicts the very basic principle. The signal source is a sine wave generator which steps or sweeps the signal frequency over the wanted bandwidth. Depending on the requirements (signal purity, frequency stability, frequency axis linearity, settling time etc.), free-running VCO's, synthesizers or DDS-circuits are in use. The receivers are based on homodyne or heterodyne down-conversion providing the complex valued frequency response function of the DUT:

$$\underline{\mathbf{G}}(f) = \frac{\mathbf{I}\{f\} + \mathbf{j}\mathbf{Q}\{f\}}{\mathbf{R}\{f\}} \xrightarrow{\text{IFFT}} \mathbf{g}\{t\} \tag{10}$$

which can be transformed via IFFT into the impulse response function. Simple implementations (e.g. many FMCW-radars) abstain from vector receivers. They only deal with the in-phase component.

Measurement principles applying sine waves provide the best suppression of noise and harmonic distortions due to narrowband filtering before signal capture. Their receiver efficiency tends to one as long as the settlement of resolution filters and signal source are negligible against the recording time. Hence, such devices often suffer from long measurement duration which leads to a strong range-Doppler coupling. The recording time can be reduced either by simultaneous measurements at different frequencies [7] (requiring complex parallel receiver and synthesizer) or by renouncing the narrowband filters (giving up the sensitivity benefits compared to the wideband approaches).
