## 3 Experiments
### Multi-Band Signal Reception and Phase Shifting for Multi-Band Phased Array Receiver  
As shown in Figure 4a, multi-band signal reception and phase shifting are experimentally verified through two selected receiving elements. One of the receiving elements is used as the reference to verify the multi-band phase control capability. Two-channel interleaving is employed to expand the instantaneous bandwidth. For easier data analysis, outputs from four channels are individually connected to four ADCs. The AWG (KEYSIGHT, Santa Rosa, CA, USA, M8196A) generates a four-band LFM signal with the bandwidth of 500 MHz and center frequencies of 2.75 GHz, 8.25 GHz, 13.75 GHz, and 19.25 GHz to simulate transmitter signals. After being down-converted by optical pulses with the repetition frequency of 5 GHz, the four LFM signals will be converted to the frequency range of 0-2.5 GHz. The center frequencies of the four LFM signals are changed to 2.25 GHz, 1.75 GHz, 1.25 GHz, and 0.75 GHz, respectively. When the bandwidth of each LFM signal is increased from 500 MHz to 1 GHz, the total signal bandwidth goes from 2 GHz to 4 GHz, which causes spectrum aliasing. Figure 4b,c illustrates the signal reception results when channel interleaving is not applied, corresponding to the bandwidth of 500 MHz and 1 GHz, respectively. By channel interleaving, the instantaneous bandwidth of the receiver is doubled to 5 GHz and spectrum aliasing no longer occurs as shown in Figure 4d. The four-band LFM signals generated by the AWG are down-converted to 2.75 GHz, 1.75 GHz, 3.75 GHz, and 0.75 GHz. This demonstrates that channel interleaving can effectively extend the instantaneous bandwidth of the receiver to increase the total bandwidth of the multi-band signal. The entire system has low losses due to its simplified optical structure and fewer components. Since differential detection has significantly suppressed common-mode noise (such as the relative intensity noise of the optical pulses in the transmitter), the noise in the received signal mainly comes from the thermal noise and relative intensity noise of the optical pulses in the receiver. It is also possible to increase the number of bands by decreasing the difference between \(f_{s2}\) and \(f_{s1}/2\). It should be noted that the missing signals at 2-3 GHz in Figure 4b-d are caused by the bandwidth limitation of the ADCs. The effective bandwidth of the ADCs at 5 GSa/s sampling rate is only 2 GHz. Figure 4: (**a**) Experimental setup for multi-band signal reception and phase shifting with channel interleaving. (**b**) Signal bandwidth of 2 GHz without channel interleaving. (**c**) Signal bandwidth of 4 GHz without channel interleaving. (**d**) Signal bandwidth of 4 GHz with channel interleaving. (**e**) Phase difference introduced by VODL. (**f**) Phase difference introduced by VODL and PS. (**g**) Phase changes when the aperture fill time, \(t_{d2}\), exceeds \(1/f_{s2}\). We conducted verification of the phase control of the multi-band signal under channel interleaving. The verification method is the same as before. First, the optical phase shifting and electrical phase shifting are independently verified. An AWG generates multi-tone signals, which consist of frequencies at 2.5 GHz, 2.75 GHz, 3 GHz, 8 GHz, 8.25 GHz, 8.5 GHz, 13.5 GHz, 13.75 GHz, 14 GHz, 19 GHz, 19.25 GHz, and 19.5 GHz. VODL2 was kept constant and VODL1 was adjusted in 10 ps increments to increase \(\Delta t_{2}\) from 0 ps to 200 ps. The multi-band phase variation is shown in Figure 4e, which follows the pattern described by \(2\pi n_{k}f_{52}\Delta t_{2}\) (where \(n_{k}\) is 1, 2, 3, 4). The four-band RMSE is 3.02\({}^{\circ}\). Subsequently, optical phase shifting and electrical phase shifting are combined to verify multi-band phase control. Assuming that the aperture fill time, \(t_{d2}\), changes from 0 to 180 ps in steps of 10 ps, VODL1 and PS1 were adjusted according to Equation (7), keeping VODL2 and PS2 unchanged.