1. Introduction

Phase coded (PC) pulse compression radars have inspired extensive research interests during the past several decades, owing to their superior range resolution, great detection distance, low power consumption and immunity to radio frequency interference (RFI) from adjacent radars [1,2]. The key challenge to implementing pulse compression radar arises from the generation of the PC microwave signals with a large time-bandwidth product (TBWP) and low time-sidelobe level. The PC microwave signals play a prominent role in enhancing the performance of pulse compression radar and has enabled widespread applications ranging from multiple-input multiple-output (MIMO) radar [3], high-resolution automotive radar [4] to through-wall radar [5]. Up to now, pulse compression radar transmitters have been mostly established by electronic components, such as RF synthesizer, digital-to-analog converter (DAC) and analog mixer. Generally, these components are subject to severe speed and bandwidth bottlenecks when operating in the range of tens of gigahertz, leading to a limited TBWP. Nonetheless, as the demand for higher resolution radar transmitters continues to increase, the generation of PC microwave signals with a huge TBWP and carrier frequency is becoming increasingly significant and urgent. A fascinating solution to this dilemma is to exploit photonic technologies, which have emerged as a promising candidate to meet these stringent demands.

In recent years, the photonic generation of PC microwave signals have been extensively investigated by many researchers. Initially, great efforts are dedicated to the exploration and generation of biphase coded microwave signals. A variety of methods have been proposed, such as using a phase modulator (PM) [6–11] or a polarization modulator (PolM) [12–17], based on different integrated Mach-Zehnder modulators (MZMs) [18–23], and the use of a micro-comb source followed by a waveshaper [24], etc. Although these methods are conveniently realized and provide an experimental demonstration, there are still some intrinsic limitations that need to be tackled. It is well known that the biphase coded signals are sensitive to Doppler shift and have a relatively high sidelobe plateau in the ambiguity diagram. Consequently, the polyphase coded signal is proposed to overcome these limitations owing to its characteristics of better Doppler tolerance and lower sidelobe. Recently, an approach based on a dual-parallel MZM and a PM has been proposed to generate a quadriphase coding signal [25,26]. Based on the same principle, some similar methods for generating arbitrary phase coded signal have also been presented in [27,28]. In these schemes, however, the phase shifts hinge largely upon the modulation index, which imposes stringent requirement on the amplitude of the baseband code sequences. Consequently, the high modulation index is essential for achieving a large phase shifts, which will result in nonlinear distortion in the process of electro-optic modulation and is difficult to achieve in practice. A solution to this restriction is to use a bipolar code to control the polarity of the carrier. Motivated by this idea, several methods have been reported in [29–31]. Unfortunately, only 0 and $\pi $ phase shifts can be produced, preventing the widespread application in the area of the pulse compression radar systems. Additionally, all these aforementioned techniques contain a DC pedestal (also known as background interference) due to the presence of the baseband modulated terms. This leads to a considerable reduction of output power, which in turn exacerbates the dynamic range of overall system. For this reason, numerous approaches to mitigating the background interference have been proposed in [32–35]. Using these approaches, the phase coded microwave signals without background interference can be generated, but only with a biphase coding format.

In this paper, we report and demonstrate a scheme for generating frequency-tunable biphase and quadriphase coded pulse signals without background interference based on a lumped polarization division multiplexing dual-parallel Mach-Zehnder modulator (PDM-DPMZM). The PDM-DPMZM consists of the DPMZM1 and DPMZM2, which are located in each arm of a main modulator. The DPMZM1 serves as an optical polyphase encoder, where two baseband ternary phase code sequences are encoded into a pair of orthogonal optical carriers with the aid of photonic vector modulation technique. The DPMZM2 driven by a microwave reference signal is used to generate the first- or second-order optical sidebands by varying the bias points of the modulators. After the balanced detection, a biphase or quadriphase coded pulse signal without background interference can be generated. The major advantage of our scheme is that the four phase shifts can be obtained by simply varying the polarity of a ternary code sequence, while achieving the frequency tunability by controlling the bias voltage. It should be pointed out that our proposed scheme is similar to but distinct from the approach reported in [26], where the undesired background interference is still present and the carrier frequency and frequency tunable range are limited by an electrical 90° hybrid. However, the reflection bandwidth of the PS-FBG dictates the maximum frequency tunable range in our scheme, which is approximately the 1/4 of the reflection bandwidth when the notch is located in the middle of the reflection spectrum. Finally, a proof-of-principle experiment is conducted using the Barker code and Frank code sequences. Experimental results show that the proposed scheme has yield excellent performance, which is evaluated by virtue of several significant metrics, including the peak-to-sidelobe ratio (PSR), pulse compression ratio (PCR) and ambiguity function.

2. Principle of operation

Figure 1 illustrates the schematic diagram of the proposed phase coded pulse compression radar transmitter. A lightwave from a laser diode (LD) is firstly split into the upper and lower arms by a built-in 3dB optical coupler in the PDM-DPMZM. To perform optical polyphase coding, the lightwave in the upper arm is modulated by two trains of baseband code sequences through the DPMZM1, which serves as an optical polyphase encoder for phase modulation and transformation. The lightwave in the lower arm is modulated by a microwave reference signal through the DPMZM2, which can be used to generate the first- or second-order optical sidebands by controlling modulators biasing conditions. A phase-shifted fiber Bragg grating (PS-FBG) inserted after the PDM-DPMZM is used to filter out one sideband of the modulated optical signal from the DPMZM2. Afterwards, the optical signal from PS-FBG is sent to a polarization beam splitter (PBS) via a polarization controller (PC). A pair of complementary optical signals from the PBS are directly injected to two input ports of a balanced photodetector (BPD), which converts the modulated optical signal into a phase coded electrical signal without background interference. Finally, the phase coded signal is boosted by an electrical amplifier (EA) and radiated into free space by using a transmit antenna.

 

Fig. 1. Schematic diagram of the proposed phase coded pulse compression radar transmitter using vector modulation and balanced detection. The insets of (i) and (ii) depict the magnitude responses in the vicinity of different notches, respectively. LD: laser diode; AWG: arbitrary waveform generator; MSG: microwave signal generator; PDM-DPMZM: polarization division multiplexing dual-parallel Mach-Zehnder modulator; OC: optical coupler; PR: polarization rotator; PBC: polarization beam controller; PS-FBG: phase-shifted fiber bragg grating; PC: polarization controller; PBS: polarization beam splitter; BPD: balanced photodetector; EA: electrical amplifier.

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In the DPMZM1, the MZM1 and MZM2 are both biased at the minimum transmission point (MITP), and the phase difference between the optical carriers is adjusted to be ${\pi / 2}$ radians via the main-MZM. Mathematically, assuming ${E_c}(t )= {E_1}{e^{j{\omega _c}t}}$ denotes the electrical field of the optical carrier, where ${E_1}$ and ${\omega _c}$ represent the amplitude and angular frequency, respectively. A pair of baseband code sequences applied to the MZM1 and MZM2 are given by $I(t )\textrm{ = }{V_1}i(t )$ and $Q(t )\textrm{ = }{V_2}q(t )$, where ${V_1}$ and ${V_2}$ are the amplitudes of $i(t )$ and $q(t )$, respectively. For the small signal modulation condition, at the output of DPMZM1, an optical phase coded signal with polyphase modulation formats can be expressed as

Next, the filtered polarization multiplexed signal makes an angle of 45° with respect to one principal axis of a PBS, where the angle can be determined by tuning a PC that is placed before the PBS. Hence, the optical field at the output of the PBS can be represented by

The two polarization components in Eq. (4) are then converted to the electrical domain by interfering the optical phase coded signal and optical single sidebands on an ideal square-law BPD with a responsivity of $\Re $, and the generated photocurrent from each detector of the BPD is given by

By comparing the above two equations, we can find that the DC current terms and low-frequency baseband modulation signals (i.e., background interference) are perfectly identical in forms and signs, whereas the desired phase coded signals have opposite signs. As a result, the DC current and background interference terms are removed while the desired phase coded signals are doubled when a balanced detection scheme is performed. Hence, a phase-coded signal without background interference can be obtained by coherently subtracting Eq. (6) from Eq. (5) through the use of a BPD and is given by

Close inspection of Eq. (7) indicates that two baseband code sequences are successfully encoded into the orthogonal RF carriers centered at $n{\omega _{RF}}$ after the balanced detection. Suppose that the two code sequences are identical in amplitude, i.e., ${V_1} = {V_2}\textrm{ = }V$, leading to ${\gamma _1}\textrm{ = }{\gamma _2}\textrm{ = }{{\pi V} / {{V_\pi }}}$. Let $n = 1$ when the MZM3 is biased at the MITP, $n = 2$ when the MZM3 is biased at the MATP. Using the trigonometric identities, the photocurrent is rearranged to give

From the above equations, we can see that the amplitude and phase of the resultant phase coded signal are modulated by $i(t )$ and $q(t )$, where the amplitude modulation term $a(t )$ depends on the output voltage of the two code sequences, while the phase modulation term $\varphi (t )$ possesses amplitude-independent phase shifts, which are only dictated by the ratio of $q(t )$ to $i(t )$. In our scheme, both $i(t )$ and $q(t )$ are configured as ternary code sequences, which have values of +1, −1 and 0, representing the positive, negative and zero voltage levels, respectively. Table 1 presents the mapping rule of the combined codes to phase shifts. It can be seen that the combined codes of $\{{({ + 1,0} ),({0, + 1} ),({ - 1,0} ),({0, - 1} )} \}$ are successfully mapped to four phase shifts of $\{{{{0,\pi } / {2,\pi ,{{3\pi } / 2}}}} \}$. As a consequence, a discrete quadriphase coded pulse signal can be obtained by simply exploiting the photonic vector modulation technique. It is worth noting from Table 1 that a biphase coded pulse signal can also be implemented when either of the two bipolar code sequences is set equal to zero. In this way, a quadriphase coded pulse signal can be readily converted to a biphase coded pulse signal, and vice versa.

Table 1. The mapping rule of the combined codes to phase shifts

View Table

3. Experiment results and analysis

First of all, we demonstrate the capability of our proposed scheme to generate a fundamental or frequency-doubled biphase coded pulse signal. A proof-of-principle experimental setup is constructed based on the schematic diagram in Fig. 1. A continuous-wave (CW) pump source with 13 dBm of optical power is emitted from an LD (KG-DFB-40, $\lambda = 1550.12$ nm) and coupled into a PDM-DPMZM (FTM7977HQA). The pump source as the optical carrier is then split into two branches, which travel along the transverse electric (TE) and transverse magnetic (TM) directions, respectively. A pair of electrical code sequences with a bit rate of 4 Gbps generated from an arbitrary waveform generator (Keysight M8195A) are modulated upon the corresponding orthogonal optical carriers via the polyphase encoder. A 12 GHz microwave reference signal produced by a vector signal generator (Rohde&Schwarz, SMW200A) is applied to the RF electrode of the MZM3. The first- or second-order ODSB signal can be generated by controlling the DC bias voltage of the MZM3. To cope with the bias drift of the MZMs, a bias controller is employed in our experiments to provide a long-term operational stability and a high spectral purity. Subsequently, the modulated optical signals located at two orthogonal polarization modes are recombined by a PBC. Afterwards, the lower sideband of the ODSB signal is eliminated by a PS-FBG (TeraXion). The magnitude responses of the PS-FBG are indicated as insets in Fig. 1. It can be observed that the notches with a bandwidth of 250 MHz are located at different wavelengths in the insets (i) and (ii), which correspond to the -1st and -2nd order optical sidebands, respectively. The optical signal from the PS-FBG is then oriented at an angle of $45^\circ $ relative to one principal axis of the PBS by tuning a PC. At the output of the PBS, the two complementary optical signals are detected by a high-speed integrated BPD (Finisar, BPDV2150RM) with a 43 GHz bandwidth. Finally, the generated phase coded signal is sampled and recorded by a digital storage oscilloscope (LeCroy WaveMaster 813 Zi-B).

Figure 2(a) shows the temporal waveforms of the 12 GHz biphase coded pulse signal with a duration of 32 ns and a duty cycle of 50%, and the corresponding zoom-in view for one pulse period are depicted in Fig. 2(c). As can be clearly seen, there is no obvious DC pedestal in the generated phase coded waveforms, indicating that the background interference is totally eliminated by balanced detection. In the demonstration of the fundamental frequency biphase coded pulse signal, the in-phase code sequence is an ideal 13-bit Barker code $i(t )= \{{\textrm{ + 1, + }1,\textrm{ + }1,\textrm{ + }1,\textrm{ + }1, - 1, - 1,\textrm{ + 1},\textrm{ + }1, - 1,\textrm{ + }1, - 1,\textrm{ + }1} \}$ with a bit rate of 4 Gbps, whereas the quadrature code sequence is set to be all zeros. It is worth mentioning that the following 19 bits of $i(t )$ are padded with zeros to achieve the generation of a phase coded pulse signal. Figure 1(e) displays the retrieved phase information, which is realized by the use of a phase retrieval algorithm. This algorithm involves several steps, including the Hilbert transform, phase unwrapping, digital smoothing filter, and normalization. Comparing Fig. 2(c) with Fig. 2(e), we can find that the carrier phases remain unchanged when the phase codes do not change, while the carrier phases will jump when the phase codes change. Therefore, the biphase jumps of the carrier waveform are in perfect agreement with the changes of the retrieved phase information. To validate the performance of the pulse compression, the autocorrelation function (ACF) of the transmitted waveform is provided in Fig. 2(g) and the zoom-in view of the mainlobe peak is shown at the bottom of the ACF. The peak-to-sidelobe ratio (PSR), which is a usual performance metric used in pulse compression, is calculated to be 21.7 dB in power, close to the theoretical value of 22.3 dB. The mainlobe peak has a full-width at half maximum (FWHM) of around 0.24 ns, so that we can obtain that the pulse compression ratio (PCR) and range resolution are 13.54 and 0.036 m, respectively.

 

Fig. 2. (a) and (b) Measured temporal waveforms of the 13-bit and 16-bit biphase coded pulse waveforms at 12 and 24 GHz carrier frequencies; (c) and (d) the zoom-in view for one pulse period; (e) and (f) the retrieved phase information; (g) and (h) the ACF of the waveforms in (c) and (d).

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To demonstrate the frequency tunability of the proposed scheme, the MZM3 is biased at the MATP and the power of the microwave reference signal is increased to 18 dBm for generating the higher second-order harmonics. Figure 2(b) shows the temporal waveforms with a duration of 32 ns at 24 GHz carrier frequency, which are phase-modulated by a 16-bit combined Barker code. In theory, the 16-bit combined Barker code can be generated by calculating the kronecker product of two 4-bit Barker codes $\{{\textrm{ + 1, + }1, - 1,\textrm{ + }1} \}$. Therefore, the resultant 16-bit Barker code is $i(t )= \{{\textrm{ + 1, + }1, - 1,\textrm{ + }1,\textrm{ + }1,\textrm{ + }1, - 1,\textrm{ + 1}, - 1, - 1,\textrm{ + }1, - 1,\textrm{ + }1,\textrm{ + }1, - 1,\textrm{ + }1} \}$, along with 16-bit zeros to achieve the generation of a phase coded pulse signal. Figures 2(d) and 2(f) illustrate the waveforms for one pulse period and the retrieved phase information. Excellent agreement between the measured waveform and the retrieved phase information is again observed, which confirms the frequency tunability of the proposed scheme. As shown in Fig. 2(h), a high sidelobe level can be observed, leading to a PSR of 12.75 dB. The PSR of the 16-bit combined Barker code is much less than that of a 13-bit Barker code. This is due to the fact that the ratio of the sidelobe to mainlobe level no longer satisfies the relation of ${1 / N}$ for the combined Barker code, where N is the code length. The pulse FWHM of around 0.21 ns is obtained, corresponding to a PCR of 18.28 and a range resolution of 0.032 m. The higher value of PCR can probably be ascribed to the presence of the white noise in the generated waveform.

Ambiguity diagram and contour map are used to graphically illustrate the properties of the phase coded pulse compression waveform in terms of the time and doppler frequency. Figure 3 illustrates the normalized 3-D ambiguity diagrams and contour maps of the 13-bit and 16-bit biphase coded pulse waveforms, respectively. As expected, the ambiguity diagrams are akin to an ideal thumbtack-like shape due to the random nature of the Barker code, shown in Fig. 3(a) and 3(b). The responses of the delay-Doppler are symmetric in the vicinity of the peak and the sidelobe levels are relatively small. Nevertheless, it must be noted that the sidelobe level shown in Fig. 3(b) is not as good as that shown in Fig. 3(a), despite the fact that the 16-bit Barker code has a higher PCR. The normalized contour maps are shown in Fig. 3(c) and 3(d). It can be seen that the contour map of the 13-bit Barker code has an X-shaped contour map, while the contour map of the16-bit combined Barker code has a sharp peak at the center of the delay-Doppler plane and the sidelobe levels decrease rapidly at either side of the peak. This implies that the effect of range-Doppler coupling can be generally negligible for the biphase coded pulse signal. However, the biphase coded waveforms have a poor Doppler-tolerance.

 

Fig. 3. (a) and (b) The normalized 3-D ambiguity diagrams of the 13-bit and 16-bit biphase coded pulse waveforms at 12 and 24 GHz carrier frequencies; (c) and (d) the corresponding contour maps.

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The key capability of our proposed scheme to generate a fundamental or frequency-doubled quadriphase coded pulse signal is also demonstrated. To generate a quadriphase coded pulse waveform, a Frank polyphase code of length 16 is employed in our experiment. The Frank polyphase code has a lower sidelobe level and is most commonly used for pulse compression. A 16-bit Frank code is defined as $\{{0,0,0,0,0,{\pi / {2,\pi ,3{\pi / {2,0,\pi ,0,}}}}\pi ,0,{{3\pi } / 2},\pi ,{\pi / 2}} \}$[36]. Figures 4(a) and 4(b) show the quadriphase coded pulse waveforms at 12 and 24 GHz carrier frequencies. For a better observation, the corresponding zoom-in views for one pulse period are presented in Figs. 4(c) and 4(d). According to the mapping rule in Table 1, the 16-bit Frank quadriphase code can be obtained by setting the in-phase and quadrature electrical ternary code sequences $i(t )$ and $q(t )$ to be $\{{\textrm{ + 1, + }1,\textrm{ + }1,\textrm{ + }1,\textrm{ + }1,0, - 1,0,\textrm{ + }1, - 1,\textrm{ + }1, - 1,\textrm{ + }1,\textrm{0}, - 1,\textrm{0}} \}$ and $\{{0,0,0,0,0,\textrm{ + }1,0, - 1,0,0,0,0,0, - 1,0,\textrm{ + }1} \}$, respectively. The following 16 bits of $i(t )$ and $q(t )$ are padded with zeros to achieve the generation of a phase coded pulse signal. The electrical ternary code sequences for in-phase and quadrature components with a bit rate of 2 Gbps are shown in Fig. 4(e) and (f). By performing the phase extracting algorithm to the generated quadriphase coded waveforms, the phase information can be retrieved and are marked on the phase curves, as depicted in Fig. 4(g) and (h). It can be seen that the phase shifts of 0, ${\pi / 2}$, ${{3\pi } / 2}$ and $\pi $ radians are implemented. Moreover, the carrier phase jumps in Fig. 4(c) and 4(d) exactly correspond to the rising and falling edges of the phase curve, indicating that the phase code sequences have been encoded into the RF carrier. The ACFs of the 12 and 24 GHz quadriphase coded waveforms are shown in Fig. 4(j) and 4(k). It can be seen that the calculated ACFs have almost identical shape, and thus the frequency tunability of the proposed scheme is confirmed. For the fundamental quadriphase coded waveform, the PSR is 20.3 dB, which is slightly lower than the theoretical value of 24.1 dB. The FWHM is 0.51 ns, and hence the PCR and range resolution are 15.69 and 0.075m, respectively. For the frequency-doubled quadriphase coded waveform, the PSR, PCR and the range resolution are 21.0 dB, 16.1 and 0.074m, respectively. Therefore, a relatively high PCR can be achieved in a long pulse signal with the help of pulse compression. Furthermore, it should be noted that the quadriphase coded pulse signal has a lower level of sidelobe, as compared to the biphase coded pulse signal. This is crucial for the measurement of the unambiguous range and velocity, due to the fact that a low scatter target may be masked by a higher sidelobe level.

 

Fig. 4. (a) and (b) Measured temporal waveforms of the 16-bit Frank code quadriphase coded pulse waveforms at 12 and 24 GHz carrier frequencies; (c) and (d) the zoom-in views for one pulse period; (e) and (f) the in-phase and quadrature ternary code sequences; (g) and (h) the retrieved phase information; (j) and (k) the ACFs of the waveforms in (c) and (d).

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The normalized 3-D ambiguity diagrams and contour maps for 12 and 24 GHz quadriphase coded waveforms phase-modulated by a 16-bit Frank code are depicted in Fig. 5(a) and 5(b), respectively. Unlike the thumbtack ambiguity diagram of the Barker code, the quadriphase coded pulse waveform modulated by a Frank code exhibits a strong diagonal ridge (i.e, knife-edge) on the delay-Doppler plane. Evidently, the ambiguity diagram of the quadriphse coded waveform features a lower sidelobe and a narrower mainlobe level, as compared to that of the biphase coded waveform. Shown in Fig. 5(c) and 5(d) are the corresponding normalized contour maps. From inspection of the contour maps, we can see that the peaks move diagonally along the delay-Doppler plane. Therefore, the quadriphase coded waveforms have better Doppler tolerance than the waveforms phase-modulated by biphase code sequences.

 

Fig. 5. (a) and (b) The normalized 3-D ambiguity diagrams of the 16-bit Frank code quadriphase coded pulse signals at 12 and 24 GHz carrier frequencies; (c) and (d) the corresponding contour maps.

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4. Conclusion

To summarize, an approach to generating frequency-tunable biphase and quadriphase coded pulse signals without background interference is presented and demonstrated based on a PDM-DPMZM. Leveraging the vector modulation principle of ternary code sequences and balanced detection technique, the phase infromation can be encoded into a pair of orthogonal optical carriers by altering the polarity of the ternary code sequences, while eliminating the background interference in the generated phase coded pulse signals. In addition, the frequency tunability is implemented by properly setting the bias voltage of the modulator. The major advantages of the proposed approach are the amplitude-independent phase shifts, background-free and frequency tunability. A proof-of-principle setup is established and the experimental results confirm the feasibility and effectiveness, achieving the expected precision of the PSR and PCR.