Subcarrier modulation based phase-coded coherent lidar

Anpeng Song; Anpeng Song; Anpeng Song; Kai Jin; Chen Xu; Chen Xu; Jian Li; Jian Li; Jian Li; Youming Guo; Youming Guo; Kai Wei

doi:10.1364/OE.504166

1. Introduction

Lidar is a widely used optical remote sensing technology due to its usefulness and applicability to different fields. Compared to direct-detection lidar, coherent setups are more robust against interference [1], more sensitive to weak signal [2], and can estimate the velocity using the Doppler effect [3]. Therefore, coherent lidar has been applied in multiple fields, including long-distance ranging, micro-Doppler measurement, and synthetic aperture imaging [4–6].

Besides, large time-bandwidth product signals reduce peak power demand in modern coherent lidar applications. An often-used modulation scheme is the frequency-modulated continuous wave (FMCW) [7–11]. In recent years, electronic technology advancements pushed studying phase encoding schemes [12–14]. Compared to traditional FMCW schemes, using phase-coded (PC) signals offers several benefits, such as higher efficiency of power amplifier, lower linearity requirements, multiple-input multiple-output (MIMO) capabilities by orthogonal codes, and a high degree of freedom in the waveform selection [15]. Most importantly, due to laser linewidth, traditional FMCW lidar systems can only operate within the coherent length, significantly limiting their application in long-distance scenarios. In space optical communication technology, the coherent PC lidar can reduce interference and compensate for the carrier phase error, enabling hyper-coherent length sensing.

The PC signal fails to meet the Hilbert transform narrowband requirement [16], hence, current coherent PC lidars mainly use a 90-degree optical hybrid as a quadrature receiver to acquire signal phase information directly [17–19]. The quadrature receiver is widely used in coherent communication due to its ability to reduce the required system bandwidth by half and its high tolerance for phase noise [20]. However, it leads to a more complex system and introduces parasitic imbalances [12]. Furthermore, experiment results in [14] illustrate that the influence of 14km atmospheric transmission channel on PC heterodyne lidar ranging is minimal. In other words, mainstream solutions are unable to offer superior performance benefits for PC lidar applications within kilometer-level range. In this paper, we proposed a subcarrier modulation based PC cohenrent lidar which can extract accurate phase information with a non-quadrature receiver. Leveraging the Doppler properties of periodic autocorrelation of coded sequences, the influence of the spectrum sideband introduced by real sampling can be significantly reduced after range compression, and accurate phase extraction can be achieved with a sampling ratio lower than the Nyquist sampling ratio. Compared to mainstream PC lidar system, the proposed scheme possesses the same requirements for system bandwidth and sampling ratio. This streamlined and efficient structure utilizes fewer devices, maintains lower complexity, and eliminate the issue of parasitic imbalances. In addition, this system has the capability to compensate for the target radial Doppler by modifying the subcarrier frequency in hardware without external components, which allows for more flexible modulation parameter design.

Among the various application of PC lidar, ISAL is quite suitable for validating the effectiveness of the proposed system. The range profile can be used to analyze the spectral properties of the signal, where the impulse response width (IRW) is inversely proportional to the signal’s effective bandwidth. Additionally, phase error can cause the widening of the mainlobe and the rise of sidelobes, reflected as a degradation in peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR). Meanwhile, the azimuth profile is the result of coherent synthesis of pulses, which is also known as Doppler map, can determine the influence of frequency aliasing introduced by real sampling. If not well suppressed, the mirror frequency will generate an image that is symmetrical to the true image relative to the zero Doppler. Therefore, in Section 2, we detail the structural properties of the subcarrier modulation-based PC coherent lidar and develop a full-link signal model for the system from the perspective of ISAL. Section 3 conducts several ISAL experiments on both points and extended targets, and the corresponding results are discussed.

2. System description and signal model

Figure 1 depicts the system structure, which includes a simplified signal model of the proposed system. The model assumes an invariant, one-dimensional polarization of the optical field.

Fig. 1. Blocks of subcarrier modulation-based phase-coded coherent lidar.

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2.1 Modulation and transmission

The optical field of the laser output can be expressed as:

(1)$$e_{0}(t)\propto exp{\left \{ j\omega _{0}t+j\varphi _{0} \right \}}$$

where $\omega _{0}$ and $\varphi _{0}$ are the angular frequency and initial phase of the laser, respectively. The fiber splitter divides the optical laser power into a local oscillator and an unmodulated signal. Additionally, the fiber splitter and coupler divide the optical field as follows [12]:

(2)$$\begin{aligned} \left[\begin{array}{l} E_{1, OUT} \\ E_{2, OUT} \end{array}\right] = \left[\begin{array}{cc} \sqrt{r} & -j \sqrt{1-r} \\ -j \sqrt{1-r} & \sqrt{r} \end{array}\right] \cdot\left[\begin{array}{l} E_{1, I N} \\ E_{2, I N} \end{array}\right] \end{aligned}$$

where $r$ is a split ratio. Since the splitter only has a ingle input, the output signals become:

(3)$$\begin{aligned}&\ e_{l1}(t)\propto exp\left \{ j\omega_{0}t + j\varphi _{0} \right \} \\ &\ e_{l2}(t)\propto exp\left \{ j\omega_{0}t + j\varphi _{0} - j\pi /2\right \} \end{aligned}$$

Unlike traditional phase-coded modulation schemes, we use a DP-MZM rather than a phase modulator. The drive signal can be expressed as:

(4)$$\begin{aligned}V_{I} &= V_{RF}cos\left [ \omega_{RF}t+\phi(t) \right ] \\ V_{Q} &= V_{RF}sin\left [ \omega_{RF}t+\phi(t) \right ] \end{aligned}$$

where $V_{RF}$, $\omega _{RF}$ and $\phi (t)$ are the amplitude, the subcarrier frequency, and the phase-coded sequence of the RF signal, respectively. In general, the coded sequence can be described as the sum of rectangular functions corresponding to:

(5)$$\begin{aligned}\phi(t)&=\sum_{0}^{N-1}rect((t-nT_{s})/T_{s}){\phi_{n}} \\ rect(t/T)&=\left\{\begin{matrix} 1 & for \quad 0\le t\le T\\ 0 & otherwise \end{matrix}\right. \end{aligned}$$

where $\phi _{n}$ is the signal phase state at n, which varies from $\pi /2$ to $3\pi /2$. $N$ corresponds to the length of the code, $T_{s}$ is the single chip duration, $1/F_{s}$ equals to the bandwidth and modulation rate $B$. The modulated signal can be expressed as:

(6)$$e_{s}(t) \propto e_{l1}(t) \cdot exp \left \{ j\omega_{RF}t+j\phi(t)\right \}$$

2.2 Reception and mixture

The modulated signal is emitted by the collimator and reflected by the target comprising $N_{t}$ scattering points, and the reflected signals are superposed additively. Assuming that each scattering point has a distance $d_{i}$ and radial velocity of $v_{i}$, the echo is collected by another collimator and coupled into the fiber, expressed as:

(7)$$e_{R}(t) \propto \sum_{i=1}^{N_{t}}a_{i}e_{s}(t-\tau_{i})exp\left\{ j2v_{i}t/\lambda \right\} $$

(8)$$\propto \sum_{i=1}^{N_{t}}a_{i}e_{l1}(t-\tau_{i})exp\left\{ j\omega_{RF}(t-\tau_{i}) \right\} exp\left\{ j\phi(t-\tau_{i}) \right\}exp\left\{ j\omega_{D,i}t \right\} $$

where $a_{i}$, $\tau _{i}=2d_{i}/c$, $\omega _{D,i}$ corresponds to attenuation, laser time of flight, and Doppler of the echo of $ith$ scattering point. The LO and received signals are mixed by a 3dB coupler, according to Eq. (2), and the output becomes

(9)$$\begin{aligned}&\ e_{1}(t) \propto e^{{-}j\pi/2}\left\{ exp\left\{j(\omega_{0}t+\varphi)\right\} + \sum_{i=1}^{N_{t}}a_{i}exp\left\{j\omega_{RF}(t-\tau_{i})+j\phi(t-\tau_{i})+j\omega_{D,i}t\right\} \right\} \\&\ e_{2}(t) \propto{-}exp\left\{j(\omega_{0}t+\varphi)\right\} + \sum_{i=1}^{N_{t}}a_{i}exp\left\{j\omega_{RF}(t-\tau_{i})+j\phi(t-\tau_{i})+j\omega_{D,i}t\right\} \end{aligned}$$

The output of the 3dB coupler is then detected by an AC-coupled Balanced Photodetector (BPD). The output can be expressed as:

(10)$$\begin{aligned}u(t) &\propto \Re [e_{1}(t)e_{1}^{*}(t)-e_{2}(t)e_{2}^{*}(t)] \\&\propto \sum_{i=1}^{N_{t}}a_{i}cos(\phi(t-\tau_{i})-\omega_{0}\tau_{i}-\omega_{D,i}t-\omega_{RF}(t-\tau_{i}){)} \end{aligned}$$

2.3 Analog-to-digital conversion

As the system operates in continuous wave mode, we use $t=(mN+n)T_{s}$ to discretize the signal model by representing the time of the $nth$ chip in the $mth$ coding sequence. Due to the high-speed modulation rate, the target distance remains nearly constant throughout a coding sequence relative to the system resolution. As a result, $\tau _{i}$ is solely dependent on $m$.

Let $\varphi (n,m)$ be defined as follows, which is exactly the modulation signal of a traditional phase-coded ISAL system:

(11)$$\varphi(n,m)=exp\left\{ j\varphi[(mN+n)T_{s}] \right \}$$

Then the modulation signal of the proposed system can be expressed as:

(12)$$e_{RF}(n)=\varphi(n,0)exp\left\{ j\omega_{RF}nT_{s} \right\}$$

The BPD output signal can be discretized as follows:

(13)$$u(n,m)=\sum_{i=1}^{N_{t}}a_{i}u_{s}(n,m,i)e^{j\theta_{i}(m)}+\sum_{i=1}^{N_{t}}a_{i}u_{s}^{*}(n,m,i)e^{{-}j\theta_{i}(m)}$$

where $u_{s}(n,m,i)=\phi (n,m) \otimes \delta (n-\left \lfloor \tau _{i}(m)/T_{s} \right \rfloor )$, $\theta _{i}(m)=(\omega _{RF}-\omega _{0})\tau _{i}(m)-(\omega _{D,i}+\omega _{RF})mNT_{s}$, $\otimes$ is the circular convolution operator, and $\left \lfloor \cdot \right \rfloor$ indicates the floor operator.

2.4 Range direction compression

The range profile can be extracted from the final received signal by performing periodic cross-correlation using a matched filter. In the proposed system, the matched filter is the modulation signal $e_{RF}(n)$. The resulting signal can be expressed as:

(14)$$\begin{aligned} S_{RC}(n,m) &=u(n,m)\odot e_{RF}(n)\\ &= \sum_{i=1}^{N_{t}}a_{i}u_{s}(n,m,i) \odot e_{RF}(n) \cdot e^{j\theta_{i}(m)}+\sum_{i=1}^{N_{t}}a_{i}u_{s}^{*}(n,m,i) \odot e_{RF}(n) \cdot e^{{-}j\theta_{i}(m)}\\ &= A(n,m) + A^{*}(n,m) \end{aligned}$$

where $\odot$ denotes the periodic correlation operator. Expanding the calculation of $A(u,m)$, provides the following expression:

(15)$$\begin{aligned} A(n,m) &= \sum_{i=1}^{N_{t}}a_{i}\mathbb{F}^{{-}1}\left\{\mathbb{F}\left\{u_{s}(n, m, i)\right\} \times \mathbb{F}^{*}\left\{e_{R F}(n)\right\}\right\} \cdot \exp \{j \theta_{i}(m)\}\\ &= \sum_{i=1}^{N_{t}} a_{i} \mathbb{F}^{{-}1}\left\{\Phi\left(\omega-\omega_{D, i}-\omega_{R F}, m\right) \times \Phi\left(\omega-\omega_{R F}, 0\right)\right\} \cdot \exp \{j \theta_{i}(m)\}\\ &= \sum_{i=1}^{N_{t}} a_{i} R_{s s}\left(n, m, \omega_{D, i}\right) \otimes \delta\left(n-\left\lfloor\tau_{i}(m) / T_{s}\right\rfloor\right) \cdot \exp \{j \theta_{i}(m)\} \end{aligned}$$

where $R_{s s}\left (n, m, \omega _{D, i}\right )=\varphi (n,m)exp\left \{ -j\omega _{D,i}nT_{s} \right \} \odot \varphi (n,0)$. Given that $\varphi (n,m)$ and $\varphi (n,0)$ differ only by a constant phase, $R_{s s}\left (m, \omega _{D, i}\right )$ represents the periodic autocorrelation function of $\varphi (n,0)$ under the doppler condition of $\omega _{D,i}$. Furthermore, it serves as the one-dimensional point spread function of the $ith$ target after pulse compression.

Similarly, $A^{*}(u,m)$ can be calculated as

(16)$$A^{*}(n,m)= \sum_{i=1}^{N_{t}}a_{i} R_{s s}\left(n, m, \omega_{D, i} + 2\omega_{RF}\right) \otimes \delta\left(n-\left\lfloor\tau_{i}(m) / T_{s}\right\rfloor\right) \cdot \exp \{{-}j \theta_{i}(m)\}$$

where $A(n,m)$ is the desired signal, and $A^{*}(n,m)$ represents the interference introduced by real sampling. Note that these terms have the same imaging position with different point spread functions (PSF) in the range direction and conjugate phase in the azimuth direction.

2.5 Azimuth direction compression

Pulse compression in the azimuth direction is achieved by performing a Fourier Transform after aligning the envelope in the range direction between the pulses. Only range gates that correspond to the target are taken into account. Assuming that M-encoded sequences are used for phase synthesis:

(17)$$\begin{aligned} S_{AC}(\left \lfloor \tau_{i}(m) / T_{s} \right \rfloor, \omega_{m}) &= \mathbb{F}\left\{ S_{RC}(\left \lfloor \tau_{i}(m) / T_{s} \right \rfloor, m)\right\}\\ &= \sum_{i=1}^{N_{t}}a_{i}R_{ss}(\left \lfloor \tau_{i}(m) / T_{s} \right \rfloor, m,\omega_{D,i})\mathbb{F}\left\{ exp\left\{ j\theta_{i}(m)\right\} \cdot rect(MNT_{s}) \right\}\\ &+ \sum_{i=1}^{N_{t}}a_{i}R_{ss}(\left \lfloor \tau_{i}(m) / T_{s} \right \rfloor, m,\omega_{D,i}+2\omega_{RF})\mathbb{F}\left\{ exp\left\{{-}j\theta_{i}(m) \right\}\cdot rect(MNT_{s}) \right\} \end{aligned}$$

When it comes to a turntable target, there is $\tau _{i}(m)=2x\omega mNT_{s}$, where $x$ is the coordinate of the scattering point projected onto the azimuth direction and $\omega$ is the angular velocity of the scattering point relative to lidar. Therefore, the following equation can be calculated.

(18)$$\mathbb{F}\left\{ exp\left\{ j\theta_{i}(m)\right\} \cdot rect(MNT_{s})\right\} = \delta(\omega_{m}+\frac{2\omega_{0}x_{i}\omega}{c})\otimes sinc(\frac{\omega_{m}NT_{s}}{2\pi M})$$

Two terms in Eq. (17) have conjugate phase, and according to Eq. (18), the discrepancy in phase will result in a false image that is symmetrical to the true image relative to the zero Doppler in SA imaging result. We define $SL$ to describe the amplitude ratio of conjugate false signal to the desired signal. It can be expressed as

(19)$$\begin{aligned}SL &=R_{ss}(\left \lfloor \tau_{i}(m) / T_{s} \right \rfloor, m,\omega_{D,i}+2\omega_{RF})/R_{ss}(\left \lfloor \tau_{i}(m) / T_{s} \right \rfloor, m,\omega_{D,i}) \\&= \frac{sin[(\omega_{D,i}+2\omega_{RF})NT_{s}/2]}{sin[(\omega_{D,i}+2\omega_{RF})T_{s}/2]} / \frac{sin(\omega_{D,i}NT_{s}/2)}{sin(\omega_{D,i}T_{s}/2)} \end{aligned}$$

By designing the values of $\omega _{RF}$, $N$, and $T_{s}$ to ensure that $SL \ll 1$, the effect of image frequency signal can be ignored, and Eq. (14) can be simplified to:

(20)$$S_{RC}(n,m)=A(u,m)=\sum_{i=1}^{N_{t}} a_{i} R_{s s}\left(m, \omega_{D, i}\right) \otimes \delta\left(n-\left\lfloor\tau_{i}(m) / T_{s}\right\rfloor\right) \cdot \exp \{j \theta_{i}(m)\}$$

Additionally, Eq. (17) can be simplified to:

(21)$$S_{AC}(\left \lfloor \tau_{i}(m) / T_{s} \right \rfloor, \omega_{m}) =\sum_{i=1}^{N_{t}}A_{i}\delta(\omega_{m}+\frac{2\omega_{0}x_{i}\omega}{c})\otimes sinc(\frac{\omega_{m}NT_{s}}{2\pi M})$$

where $A_{i}$ is a constant. Currently, the system sampling ratio requirement is not less than $1/T_{s} + \omega _{RF}$. By increasing the code length, it is possible to simultaneously increase the pulse compression ratio and make $\omega _{RF}<1/T_{s}$, thereby achieving super-Nyquist sampling.

3. Experiment and result

3.1 Experimental setup

The system is entirely developed from commercial off-the-shelf devices based on polarization maintaining fiber components. For convenience, an arbitrary waveform generator (AWG) was used in the system to generate a modulation signal, and a laser output of 20mW was connected to a 99:1 splitter. The modulator was driven by orthogonal signals, which was a pseudo-random bit sequence (PRBS) with a code length $N$ of 16383. The modulation rate was 4GHz, the microwave subcarrier $\omega _{RF}$ was set to 50MHz, and the ADC sampling rate was 5GHz. Additionally, a roll-off filter was used to control the level of spectral sidelobes. Numerical calculations prove that for a target relative Doppler less than 10MHz, the $SL$ remains consistently smaller than $10^{-3}$. In order to prove this theoretical estimation, we conducted two validation experiments. The first verifies the hyper-Nyquist sampling rate, and the second verifies the suppression ability of the mirror frequency introduced by real sampling.

3.2 Hyper-Nyquist sampling rate validation

In this experiment, the EDFA output was directly connected to the receiver after passing through an attenuator to simulate a static point target and avoid interference from external factors. Two ISAL imaging tests were conducted, with group A using a 90-degree hybrid as a quadrature receiver and group B using a 3dB coupler as a non-quadrature receiver. According to Eq. (17) and Eq. (18), and given that the target is relatively stationary, only the range profiles can be used for comparison and phase error analysis, while the azimuth profiles are theoretically the same in both groups.

Based on the PSF, the imaging performance was evaluated using IRW, PSLR, and ISLR. Figure 2 displays the imaging outcomes of both groups, and Table 1 reports the specific parameters. Despite the inclusion of the roll-off filter, there still a small portion of the spectrum signal outside the bandwidth. The equivalent bandwidth of the modulation signal is approximately 4.1GHz. Therefore, the effective signal bandwidth of Group A is 4.1/4 times that of Group B, and the IRW of Group B will also widen at the same ratio compared to Group A, which is consistent with the experimental measurement result. Similarly, spectrum signal outside the sampling bandwidth will result in spectrum aliasing and introduce a small amount of noise, leading to degradation in PSLR and ISLR [21]. In this experiment, both of them decreased by approximately 0.6dB. Furthermore, the azimuth profile of the two groups are essentially identical, which is also consistent with the theory. Overall, it can be considered that the phase information of the desired signal has been effectively obtained with tolerable noise.

Fig. 2. Hyper-Nyquist sampling rate validation result. (a) Contour plot depicting the impulse response of group A. (b) Contour plot depicting the impulse response of group B. (c) Comparison of range profiles. (d) Comparison of azimuth profiles.

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Table 1. Comparison of imaging performance^a

View Table

3.3 Mirror frequency suppression validation

We also conducted indoor imaging experiments on multi-point and extended targets. These experiments are important as the mirror frequency component will result in a false image that is symmetrical to the true image relative to the zero Doppler in the SA imaging result. Based on the ratio of symmetric position in the azimuth profile, the suppression ability of the mirror frequency component can be determined. The targets were positioned approximately 20m from the lidar with a rotation speed of 10 degree/s. Five hundred twelve pulses were employed for imaging. Additionally, we used 8-looking processing to compress speckle noise.

Figure 3(a) shows the multi-point target "IOE", comprising several laser reflective papers, and Fig. 3(b,c,d) represents the extended target "K", "S" and "A" consisting of 3M reflective sheeting. The indoor imaging results are presented in Fig. 4. Due to the laser diameter of 20cm, only a part of the target "IOE" was successfully imaged, while "K", "S", and "A" were imaged effectively. From the azimuth profiles, we conclude that the influence of mirror frequency introduced by real sampling can be ignored in the proposed system.

Fig. 3. Indoor experiment imaging targets. (a) A multi-point target consisting of laser-reflective papers. (b) Extended target ’K’. (c) Extended target ’S’. (d) Extended target’A’.

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Fig. 4. Indoor experiments imaging results. (a) Multi-points target "IOE". (b) Extended target "K". (c) Extended target "S". (d) Extended target "A".

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4. Conclusion

This paper proposes a novel, lean subcarrier modulation-based, phase-coded coherent lidar with a non-quadrature receiver with a single detector. We demonstrate that using a single sideband modulation scheme significantly reduces the influence of the spectrum sideband introduced by real sampling after range compression. This leverages the Doppler properties of periodic autocorrelation of coded sequences and preserves the phase information of the wanted signal. Additionally, by setting the code length and subcarrier frequency, the required sampling rate can be less than or even half of the Nyquist sampling rate. Moreover, a linear frequency modulation lidar can be achieved only by changing the driving signal of the EO modulator, enabling the proposed system to select appropriate modulation methods in different application scenarios.

However, it should be noted that the drawback of low Doppler tolerance in encoding signals remains unresolved, and therefore an accurate Doppler estimation method is still needed. Future work will aim to increase the system’s bit rate under the same bandwidth, using multiple subcarriers to synthesize a large data bandwidth by OFDM.

Acknowledgments

The authors thank Dr. Jinghan Gao of Chinese Academy of Sciences, who gave us useful advice about this paper.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. M. J. Kavaya, S. W. Henderson, J. R. Magee, C. P. Hale, and R. M. Huffaker, “Remote wind profiling with a solid-state nd: Yag coherent lidar system,” Opt. Lett. 14(15), 776–778 (1989). [CrossRef]

2. S. W. Henderson, P. Gatt, D. Rees, and R. M. Huffaker, “Wind lidar,” in Laser Remote Sensing (CRC University, 2005), pp. 487–740.

3. R. Frehlich and L. Cornman, “Estimating spatial velocity statistics with coherent doppler lidar,” J. Atmos. Ocean. Technol. 19(3), 355–366 (2002). [CrossRef]

4. J. B. Abshire, J. A. Rall, and S. S. Manizade, “Altimetry and lidar using algaas lasers modulated with pseudo-random codes,” in Laser Radar Conference (1992), pp. 441–445.

5. N. Satyan, A. Vasilyev, G. Rakuljic, J. O. White, and A. Yariv, “Phase-locking and coherent power combining of broadband linearly chirped optical waves,” Opt. Express 20(23), 25213–25227 (2012). [CrossRef]

6. M. Dobbs, W. Krabill, M. Cisewski, F. W. Harrison, C. Shum, D. McGregor, M. Neal, and S. Stokes, “A multi-functional fiber laser lidar for earth science & exploration,” in International Geoscience and Remote Sensing Symposium, vol. 3 (IEEE, 2008), pp. III–350.

7. X. Zhang, J. Pouls, and M. C. Wu, “Laser frequency sweep linearization by iterative learning pre-distortion for fmcw lidar,” Opt. Express 27(7), 9965–9974 (2019). [CrossRef]

8. X. Cao, P. Song, Z. Pan, and B. Liu, “Correction algorithm of the frequency-modulated continuous-wave lidar ranging system,” Opt. Express 29(21), 34150–34165 (2021). [CrossRef]

9. Z. W. Barber and J. R. Dahl, “Synthetic aperture ladar imaging demonstrations and information at very low return levels,” Appl. Opt. 53(24), 5531–5537 (2014). [CrossRef]

10. S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, “Synthetic-aperture imaging laser radar: laboratory demonstration and signal processing,” Appl. Opt. 44(35), 7621–7629 (2005). [CrossRef]

11. C. Xu, K. Jin, C. Jiang, J. Li, A. Song, K. Wei, and Y. Zhang, “Amplitude compensation using homodyne detection for inverse synthetic aperture ladar,” Appl. Opt. 60(34), 10594–10599 (2021). [CrossRef]

12. S. Banzhaf and C. Waldschmidt, “Phase-code-based modulation for coherent lidar,” IEEE Trans. Veh. Technol. 70(10), 9886–9897 (2021). [CrossRef]

13. Y. Hai, Z. Yan, A. Pang, C. Liu, and A. Dang, “Immunity to mutual interference in coded phase-shift lidar,” J. Lightwave Technol. 41(2), 570–577 (2023). [CrossRef]

14. A. Song, C. Xu, J. Li, K. Jin, and K. Wei, “Single sideband modulation based phase-coded continuous wave inverse synthetic aperture ladar demonstration and outdoor experiment,” in International Applied Computational Electromagnetics Society Symposium (IEEE, 2022), pp. 1–4.

15. L. Giroto de Oliveira, T. Antes, B. Nuss, E. Bekker, A. Bhutani, A. Diewald, M. B. Alabd, Y. Li, M. Pauli, and T. Zwick, “Doppler shift tolerance of typical pseudorandom binary sequences in pmcw radar,” Sensors 22(9), 3212 (2022). [CrossRef]

16. H. Broman, “The instantaneous frequency of a gaussian signal: The one-dimensional density function,” IEEE Trans. Acoust., Speech, Signal Process. 29(1), 108–111 (1981). [CrossRef]

17. X. Xu, S. Gao, and Z. Zhang, “Inverse synthetic aperture ladar demonstration and outdoor experiments,” in China International SAR Symposium (IEEE, 2018), pp. 1–4.

18. A. Cui, D. Li, J. Wu, K. Zhou, J. Gao, M. Qiao, S. Wu, Y. Wang, and Y. Yao, “Moving target imaging of a dual-channel isal with binary phase shift keying signals and large squint angles,” Appl. Opt. 61(18), 5466–5473 (2022). [CrossRef]

19. S. Gao, Z. Zhang, W. Yu, M. Wu, and G. Li, “Inverse synthetic aperture ladar imaging based on modified cubic phase function,” Appl. Opt. 60(7), 2014–2021 (2021). [CrossRef]

20. A. Gover, R. Guenther, D. Steel, and L. Bayvel, “Encyclopedia of modern optics,” (2005).

21. M. Soumekh, Synthetic Aperture Radar Signal Processing, vol. 7 (Wiley, 1999).

	IRW (cm)	PSLR (dB)	ISLR (dB)
RP1	3.53	-15.31	-14.60
RP2	3.61	-14.76	-14.01
AP1	3.39	-13.21	-9.78
AP2	3.39	-13.20	-9.78

Subcarrier modulation based phase-coded coherent lidar

Abstract

1. Introduction

2. System description and signal model

2.1 Modulation and transmission

2.2 Reception and mixture

2.3 Analog-to-digital conversion

2.4 Range direction compression

2.5 Azimuth direction compression

3. Experiment and result

3.1 Experimental setup

3.2 Hyper-Nyquist sampling rate validation

3.3 Mirror frequency suppression validation

4. Conclusion

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (4)

Tables (1)

Equations (21)

Optics Express