1. Introduction

The analog down-conversion links, which transform the radio frequency (RF) to the intermediate frequency (IF), have played important role in the receiver end of microwave/millimeter-wave radar, electronic warfare, and satellite communication [1–3]. Compared with the traditional down-conversion technology that relied on electrical devices, the microwave photonic down-conversion links based on the electro-optical modulation, optical-domain process, and photoelectric detection possess notable advantages of large-bandwidth, high isolation, multi-band reconfigurability, and anti-electromagnetic interference [4,5]. Nowadays, microwave photonic down-conversion technologies have been widely studied, which include the classical technologies which are based on the cascaded electrical-optical modulators [6,7], and the optimized schemes which are based on parallel modulators [8,9]. By comparison, the cascaded structures are easy to design and implement, but the cascaded modulators lead to a large optical loss. The parallel schemes can greatly reduce the insertion loss and improve the link gain, however, the phase mismatch of the two paths leads to the instability of the received power. Generally, the dual-parallel Mach-Zehnder modulator (DPMZM) [10–12] and the dual-polarization dual-parallel Mach Zehnder modulator (DP-DPMZM) [13] are utilized to improve the stability of the received power in the parallel schemes. However, the bias voltages and RF power of each port are difficult to control and modify manually. In addition to the above-mentioned tradeoff between stability and conversion gain, in the receiver antenna of radar, the image signals and the useful signals always exist on both sides of the local oscillation. After the down-conversion by the above microwave photonic links, the useful signals will be overlapped with the image signals, which seriously impedes the accurate recognization of information [14,15]. Therefore, image-rejection technology is also an essential part of microwave photonic down-conversion systems in practical applications.

Based on the down-conversion links, the previous research on image suppression can be mainly divided into two categories. As the approach in [16,17], the up-converted radio-frequency (RF) signal is filtered by the electrical band-pass filter and then down-converted to realize the image rejection in the cascaded structures. The advantage is that the electrical filter provides a considerable out-of-band suppression ratio, thereby the image rejection ratio is greatly enhanced. However, the frequency of local RF oscillation needs to accommodate the limited frequency range of the electrical filter, which is hard to realize the reconfiguration in multiple bands. Another technology for image rejection utilizes the theory of phase coherence and has been attracting extensive interest in parallel schemes [18–21]. In the systems, the local oscillation (LO) is divided into two channels with orthogonal phases and mixed with the received RF signals in the optical domain to construct the in-phase/quadrature (I/Q) IF signals. By combining the I/Q output signals, the image intermediate-frequency (IF) signals are eliminated while the useful IF signals are enhanced, and the nonlinear distortions near the fundamental signals that deteriorate the linearity are also increased. The problem is that the image suppression ratio greatly depends on the degree of phase matching of I/Q paths, and the spurious-free dynamic range (SFDR) of the system is limited by nonlinear distortions. Accordingly, the scheme with image suppression and nonlinear suppression has been proposed [22], in which the third-order intermodulation distortions (IMD3) are greatly suppressed to improve the SFDR by adjusting the input parameters of DP-DPMZM. However, owing to the inflexible adjustment of the multiple bias voltages, the image suppression ratio is hard to improve. Furthermore, the intermodulation distortions of the image signals (MMD) that will exist near the useful fundamental signals have not been analyzed and suppressed.

In this paper, we propose and demonstrate a coherent microwave photonic down-conversion link based on I/Q image rejection and digital nonlinear compensation. By constructing the homodyne optical phase-locked loop (OPLL) between the local laser diode (LLD) and the master laser diode (MLD) in the down-conversion link, the instability of received power is practically overcome. By designing the combination structure of single sideband filtering and 90° mixing in the optical domain, the I/Q signals with quadrature phase are obtained at the link output. During the digital processing, the I/Q signal is mathematically transformed and orthogonal synthesized, so as to realize the image rejection flexibly rather than affected by the imperfect characteristics of devices in I/Q demodulation. Besides, the MMD and IMD3 that existed near the fundamental IF signals are theoretically analyzed and digitally compensated by the post-processing algorithm. Experiments are carried out to verify the performance of the proposed link. The image-rejection ratio at 17.5 GHz is measured to be 47 dB, and the compensation ratios of MMD and IMD3 after the digital process are tested to be 18.1 dB and 10.9 dB. The gain and the SFDR of the link are measured to be –21.9 dB and 108.83 dB·Hz^2/3, respectively. Therefore, the proposed photonic down-conversion link can find applications in electronic warfare and satellite communication. By increasing the sampling speed of the analog-to-digital converter (ADC), our scheme can be adapted to more application scenarios.

2. Principle of operation

The schematic diagram of our scheme is shown in Fig. 1. The received signals are carried on the master light wave by the phase modulator (PM). The local oscillator (LO) signal is modulated onto the local light wave by another PM for the down-conversion of the received RF signals. To implement the further process of image suppression, an optical band-pass filter (OBPF) is utilized to remove the –1st-order single sideband of the modulated local optical signal. After the amplification by the EDFA, the two-path optical signals are injected into the 90° optical hybrid coupler. The output light is then transformed by the balanced photodetector (BPD) to construct the I/Q photocurrent. Among them, part of the Q-channel signal is fed back to the local laser diode (LLD) via a lowpass filter (LPF) and a proportional-integral-differential (PID) controller (PID) to achieve phase synchronization between the optical carriers. Finally, the analog photocurrent is digitalized by the dual-channel ADC for digital signal processing.

 

Fig. 1. The proposed photonic down-converted link with I/Q image rejection and digital linearization. MLD: master laser diode; LLD: local laser diode; PM: phase modulator; OBPF: optical bandpass filter; EDFA: erbium-doped optical fiber amplifier; BPD: balanced photodetector; LPF: low-pass filter; BPF: band-pass filter; PID: proportional-integral-differential controller; ADC: analog-digital converter; DSP: digital signal processor.

Download Full Size | PDF

The time-varying electric field intensity of the two-path optical signals injected into the 90° hybrid can be written as:

After the 90° optical hybrid coupler, the optical signals are respectively detected by the balance photodetectors (BPD). the photocurrent of the I-path and Q-path can be given as:

In Eq. (4), we use ω_RFn and ω_IMm as the angular frequencies of useful signals and image signals. ρ_n(t) and ρ_m(t) represent the corresponding modulation depths. In order to clearly discuss the nonlinear distortions, we first assume that x contains the three-tone signals of ${\rho _1}(t )\cos ({{\omega_1}t} )$, ${\rho _2}(t )\cos ({{\omega_2}t} )$, and ${\rho _3}(t )\cos ({{\omega_3}t} )$, then x³ can be approximately expanded as:

It can be seen from Eq. (5), the components of MMD and IMD3 are generated from x³ term when RF signals with multiple frequencies are sent into the system. In the above approximate expansion, the frequency components far from the fundamental frequencies are neglected since these harmonics can be easily filtered out and will not be detected by the ADC. In addition, the modulation depth is less than 0.5 in the proposed link. Compared with the fundamental-frequency terms generated by x, the power of the fundamental-frequency terms generated by x³/6 is small and thus can be neglected in the expressions of I_i(t) and I_q(t) to simplify the subsequent derivations. Afterward, we substitute Eq. (4) and Eq. (5) into Eq. (2) and Eq. (3), the I/Q photocurrent can be rewritten as:

In Eq. (6) and Eq. (7), y and z represent the different numbers of two useful fundamental signals in the range of 1 to n. Similarly, p and q represent the different numbers of two image fundamental signals in the range of 1 to m. Referring to Eq. (5), it can be seen that the IMD3 signals and MMD signals exist near the useful fundamental signals and the image fundamental signals in both I-path and Q-path. It can also be seen that the phase of the useful IF signal in the I-path is 90° ahead of the phase in the Q-path, while the phase of the image IF signal in the Q-path is 90° ahead of the phase in the I-path. In order to eliminate the image IF signals, the Q-signal is digitalized and Hilbert transformed in which the phase of positive frequency is delayed by π/2 and the phase of negative frequency is advanced by π/2. In this state of affairs, the useful IF signals in the I- and Q-path are in phase, and the phase of the image IF signals in the I- and Q-path is opposite. Therefore, the image IF signals are eliminated by adding up I/Q component. If the impedance is represented by R, the output voltage can be written as:

As can be seen, the output voltage is composed of low-pass and band-pass components. The low-pass component includes the direct current (DC), and the intermodulation distortions of the useful and image signals. The bandpass component is composed of useful IF signals and the surrounding nonlinear distortions. As can be seen from Eq. (8), the nonlinear distortions include the IMD3 of useful IF signals and the MMD loads near the IF signals. To eliminate the MMD, the further operation can be expressed as:

In the equations, B is exactly the DC voltage of the I-path when no RF signal is sent to the PM, and A can be obtained by calculating the modulation depth. From the derivation of Eq. (9), it can be concluded that the MMD of the received signals is eliminated by the digital process. Therefore, only the IMD3 remains in the nonlinear distortions while demodulating useful IF signals. Based on the expansion formula in Eq. (5), the IMD3 can be greatly suppressed by the operations deduced in Eq. (10). It can be seen that only the useful fundamental IF signals exist at the output in our system after the digital processing, indicating that the link performance of image rejection and linearization is effectively improved.

3. Experimental results

An experiment based on the setup shown in Fig. 1 is demonstrated and performed. In the transmitter of the proposed link, the continuous optical carrier with a wavelength of 1550.07 nm and a power of 11 dBm from the tunable MLD (OEwaves, OE4028) is amplified to 17 dBm by EDFA. The RF signals are modulated to the optical carrier by the PM (Photline, MPZ-LN-20) with an electro-optical bandwidth of 20 GHz. Besides, the local RF signal is phase modulated by PM (EOSPACE, PM-DV5-40) to the optical carrier from the LLD (OEwaves, OE4030) with a wavelength of 1550.07 nm and a power of 11 dBm. The –1st-order sideband is filtered out by the OBPF operating at 1550 nm with 0.24 nm (30-GHz) bandwidth. Afterward, the output optical signal is amplified to 17 dBm by EDFA and then injected into the 90° optical hybrid (Kylia COH24) together with the optical signals from the master laser diode. Detected by a 6-GHz BPD (Discovery DSC705), the output signals from the optical hybrid are converted to the two-path photocurrent as the I/Q signal. Since the two free-running lasers are used, the beat frequency exists in the spectrum of the I/Q signal. To eliminate the effect, the Q- signal is first divided into two parts by a power divider, one of which is fed back to the active proportional-integral filter (APIF) with a 50 kHz phased-lock bandwidth, thereby generating a control voltage to tune the output frequency of LLD so that output phase of the two lasers is synchronized. To verify the performance of the system, the useful RF signals and the image RF signals are generated by the multichannel RF source (Sinlink Technologies) and sent into the PM. The local RF signal with a frequency of 17.5 GHz is introduced to another PM to realize the RF down-conversion. At the link output, the phase difference between the useful IF signals of the I and Q paths is 90°, while the phase difference between the image IF signal of the two paths is –90°, which is the basis for the digital image rejection. During the digital process, the dual-port ADC (Gage RMX-161-G20) with a sample rate of 1-GSa/s is utilized for sampling, quantizing, and encoding the I/Q signals. 100000 time-domain points of the I and Q down-converted signals are saved for subsequent processing. Taking advantage of the inherent I/Q phase difference in our system, the image part of the digital signal can be greatly rejected after the Hilbert transform and I/Q synthesis. Then, the processed signal is divided into a low-pass part V_LPF and a band-pass part V_BPF according to the spectrum position. The MMD existing near the useful IF signals can be effectively suppressed by the operation as deduced in Eq. (9), thus only the IMD3 remains, which is further suppressed by the digital process as Eq. (10). Finally, the suppression of image interference and nonlinear distortions is realized in the proposed Ku-band photonic down-conversion link.

In order to experimentally verify the performance of image rejection and nonlinear compensation, the 17.5 GHz RF signal with a power of 20 dBm is first modulated on the LLD light wave. The modulated light is filtered by the OBPF to suppress the –1st-order sideband. To observe the situation of single single-sideband suppression, an optical fiber coupler with a splitting ratio of 95:5 was utilized. The divided light wave with a higher power is sent into the 90° optical hybrid, and another one is monitored by the spectrometer (YOKOGAWA, AQ6370D). As shown in Fig. 2, the red solid line represents the optical spectrum after single-sideband suppression, and the gray dotted line represents the frequency response curve of OBPF. As can be seen from Fig. 2, the suppression ratio of the –1st-order sideband achieves 56 dB.

 

Fig. 2. Spectrum of the modulated light after filtering by OBPF.

Download Full Size | PDF

In the structure, the beat-signal from the two lasers is fed back through the designed APIF to adjust the emit wavelength of LLD to realize the phase synchronization of the RLD and LLD. On this basis, the image-rejection capability of our link is verified. Firstly, to verify the system performance for the useful RF signals reception, the 17.52-GHz RF signal with a power of 0 dBm is sent to the PM. The received waveforms of the I/Q signal as shown in Fig. 2(a) are respectively obtained after the analog-to-digital conversation. It can be seen from the waveforms that the phase of the Q-signal is about 90° ahead of the I-signal. For comparison, the 17.48 GHz image RF signal with the same power of 0 dBm is sent to the PM. The I/Q output waveforms are shown in Fig. 3(b). The results are different from that of useful signals after down-conversion, in which the phase of the I-signal is ahead of the Q-signal by about 90°. By shifting the phase of the Q signal by 90°, the I/Q paths of the useful IF signals are in phase, and the I/Q paths of the image IF signals are in the opposite phase. Therefore, the received IF signal of the Q-path is digitally performed by the Hilbert transform and extracted imaginary part to realize the 90° phase shift of the Q-signal. By adding up I-signal and the phase-shifted Q-signal, the image-rejected output signal is obtained. The output waveform and spectrum after the above digital processing is shown in Fig. 3(c) and Fig. 3(d), in which the image signal with a frequency lower than the local oscillation frequency is greatly suppressed, and the useful signal with a frequency higher than the local oscillation frequency is enhanced in the proposed photonic down-conversion link. As can be obtained from the spectrum, the conversion gain is measured to be about –20.3 dB and the received power of the useful IF signal is 47 dB higher than the image one.

 

Fig. 3. I/Q waveforms of (a) the useful IF signal and (b) the image IF signal; (c) The output waveforms and (d) the output spectrum of the useful IF signal and the image IF signal after the I/Q digital process.

Download Full Size | PDF

Furthermore, a two-tone test is utilized to verify the compensation of nonlinear-distortions. The two-tone signals with the power of 5 dBm and the frequencies of 17.513 GHz and 17.514 GHz are chosen as the useful RF input, and the signals with the power of 5 dBm and the frequencies of 17.48 GHz and 17.4785 GHz are chosen as the image RF input. As a result, the I/Q time-domain waveforms at the link output are shown in Fig. 4(a). Since several frequency components are contained within the output signals, the waveforms are relatively confused. After the digital image rejection, the output waveforms are shown in Fig. 4(b), and the corresponding spectrums are plotted in Fig. 5. As can be seen from the spectrums, the image IF signals are greatly suppressed by the digital processing so that the power of the useful IF signals is 42 dB higher than that of the image one. It can be also seen that the MMD signals with the frequencies of 11.5 MHz, 12.5 MHz, 14.5 MHz, and 15.5 MHz, and the IMD3 signals with the frequencies of 12 MHz and 15 MHz interfere with the accurate reception of the useful IF signals. Therefore, additional digital processing is introduced to compensate for the above nonlinear distortions. Firstly, the low-frequency components of the signals with the frequencies of 1 MHz and 1.5 MHz are obtained, which respectively represent the intermodulation distortion of the useful signals and the image signals. The band-pass spectrums including the useful IF signals and the nearby distortions are shown in Fig. 6(a). After the digital process derived in Eq. (9), the MMD components near the useful signal are effectively suppressed, and the corresponding spectrum is shown in Fig. 6(b). Finally, The IMD3 components are compensated by the digital algorithm explained in Eq. (10), and the digital-processed spectrum is plotted in Fig. 6(c). The suppression ratios of IMD3 and MMD are 10.9 dB and 18.1 dB, respectively.

 

Fig. 4. Under two-tone test. The output time-varying voltages (a) in the original state; (b) after the image rejection.

Download Full Size | PDF

 

Fig. 5. The spectrum comparison between the original Q signal and the image rejected signal.

Download Full Size | PDF

 

Fig. 6. The output spectrums near the fundamentals. (a) After the image rejection; (b) After the MMD suppression; (c) After the IMD3 suppression.

Download Full Size | PDF

To observe the trend of link gain and nonlinear distortions while changing the RF input power, the output power of the fundamental IF signals and MMD is measured by adjusting the RF input power from 0 dBm to 5 dBm. The measure results are plotted in Fig. 7(a) and Fig. 7(b). As can be seen, the gain of the system increases by about 8.3 dB, which corresponds to the RF gain of the microwave photonic link reaching –21.9 dB. Note that the gain increase by the digital process of the system is slightly higher than the theoretical value of 6 dB, which is caused by the inevitable estimation deviation during the several steps of the digital process. Besides, with the increase of the input RF power, the MMD power shows an increasing trend but is effectively eliminated under the digital noise floor by the nonlinear compensation. When the input RF power is 5 dBm, the MMD suppression ratio reaches 18.1 dB.

 

Fig. 7. The power variation of (a) the output IF signal and (b) the output MMD.

Download Full Size | PDF

The SFDR of our link is characterized by testing the output fundamental frequency power, output IMD3 power, and noise power spectral density, as shown in Fig. 8. Since the balanced detection structure is utilized in the system, the dominant relative intensity noise (RIN) can be greatly suppressed [23,24], thus the output power spectral density of the shot-noise is calculated to be –152 dBm/Hz corresponds to the photocurrent of 10 mA. According to the changing trend of the fundamental frequency power and IMD3 power, the measured power is fitted by straight lines with slopes of 1 and 3, respectively. The SFDR is calculated to be 108.83 dB·Hz^2/3, which indicates the great performance on the linearity of the proposed link system.

 

Fig. 8. The output power of the fundamental IF signals and the IMD3 as a function of the input RF power.

Download Full Size | PDF

4. Conclusion

In conclusion, we have theoretically analyzed and experimentally investigated a Ku band linearized photonic link based on image rejection and nonlinear compensation. By utilizing the optical homodyne phase lock, I/Q signal construction, and the digital post-process, not only the power stability caused by the two-path mismatch is improved, but also the image interference in the down-conversion link and the distortions resulting from inherent nonlinear modulation of the electro-optic devices are effectively suppressed. In our proposed link, the image-rejection ratio in the Ku-band is measured to be 47 dB. Furthermore, the two-tone test proves that the suppression ratios of MMD and IMD3 after nonlinear compensation are 18.1 dB and 10.9 dB, respectively. The shot-noise-limited SFDR of our system is measured to be 108.83 dB·Hz^2/3. With the usage of high-speed ADC, the bandwidth of the link could be extended, which has application potential in millimeter wave radar, 5 G communication, and more high-frequency systems.