## 3 Experiments
### Multi-Band Beamforming and Data Fusion  
The phased array antenna patterns were measured to verify the beamforming capability for transmission and reception. We set the antenna element spacing to half the wavelength at 19.25 GHz. \(\theta=-30^{\circ}\) and \(15^{\circ}\) are selected as the beam directions. The measurement of the phased array antenna patterns at the transmitter is carried out according to the following steps: First, the four transmitting elements generate the four-band LFM signal. Next, the beam is configured to scan from \(-90^{\circ}\) to \(90^{\circ}\) in \(3^{\circ}\) steps, and the required adjustments for the VODLs and PSs are calculated based on the element spacing. The oscilloscope records the signals from four transmitting elements. Finally, the digital signals are delayed and summed digitally based on two selected directions (\(-30^{\circ}\) and \(15^{\circ}\)) to simulate the superposition of the transmitted signal in the far-field. Phased array antenna pattern measurements at the receiver follow similar steps at the transmitter. The summed signals above are replicated into four copies in the digital domain and delayed based on \(-30^{\circ}\) and \(15^{\circ}\) to simulate the echo signals reflected in these directions. The signals are then converted to analog signals by an AWG and fed into four receiving elements. Similarly, adjust VODLs and PSs to scan the beam from \(-90^{\circ}\) to \(90^{\circ}\) with a step of \(3^{\circ}\). The signals from the receiving elements are summed by two combiners and then recorded by two ADCs. Finally, the data from the two channels are interleaved in the digital domain. The peak values of the pulse compression for the obtained signals in transmitter and receiver from \(-90^{\circ}\) to \(90^{\circ}\) are calculated separately. Figure 5a,b shows the transmitter's phased array antenna patterns at \(-30^{\circ}\) and \(15^{\circ}\), while Figure 5c,d shows the receiver's measurement results at the same angles. Because the setup antenna aperture is too small relative to the S-band, the phased array antenna patterns of the S-band show insignificant directionality. It can be improved by selecting the operating frequency band of the multi-band phased array system starting with the higher frequency bands (such as 8.25 GHz, 13.75 GHz, 19.25 GHz, and 24.75 GHz) and increasing the array antenna aperture. The experimental results indicate that the method is capable of multi-band beamforming for transmission and reception. We performed data fusion of four-band LFM signals with a total bandwidth of 4 GHz for multi-band detection verification. The concatenation of four signals with identical length, \(T_{0}\), and bandwidth, \(B_{0}\), produces a chirped pulse with a length of 4 \(T_{0}\) and bandwidth of 4 \(B_{0}\), thus obtaining a quadruple range resolution. When the bandwidth of the baseband signal \(B_{0}=2\,|f_{2}-f_{1}/2\,|\), the multi-band signal after down-conversion will be connected end-to-end in the spectrum. Furthermore, due to the inherent synchronization  
Figure 5: Phased array antenna patterns measured for transmission at (**a**) \(-30^{\circ}\) and (**b**) \(15^{\circ}\), and for reception at (**c**) \(-30^{\circ}\) and (**d**) \(15^{\circ}\). Schematic diagram of four-band LFM signal in time and frequency domains (**e**) before and (**f**) after data fusion. Pulse compression on (**g**) four LFM signals separately and (**h**) fused signal. and coherence among these bands, only a simple time alignment is required for the data fusion of all four bands [2]. After applying digital filtering to each band, four LFM signals in distinct frequency bands are obtained. These signals are then connected along the time axis to produce a fused LFM signal with a total bandwidth of 4 GHz, as shown in Figure 5e,f. The results of independent pulse compression on the four LFM signals are shown in Figure 5g. The peak positions of the pulse compressions for the four signals are identical.