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Abstract
We propose an ultra-wideband photonic compressive receiver based on random codes shifting with image-frequency distinction. By shifting the center frequencies of two random codes in large frequency range, the receiving bandwidth is flexibly expanded. Simultaneously, the center frequencies of two random codes are slightly different. This difference is used to distinguish the “fixed” true RF signal from the differently located image-frequency signal. Based on this idea, our system solves the problem of limited receiving bandwidth of existing photonic compressive receivers. In the experiments, with two channels of only 780-MHz outputs, the sensing capability in the range of 11–41 GHz has been demonstrated. A multi-tone spectrum and a sparse radar-communication spectrum, composed of a linear frequency modulated (LFM) signal, a quadrature phase-shift keying (QPSK) signal and a single-tone signal, are both recovered.
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1. Introduction
Compressive sensing (CS) technology can be utilized to reconstruct signals that have been sampled at a much lower sampling rate than the Nyquist rate [1]. It reduces the burden of high bandwidth and high sampling rate on the analog-to-digital converter (ADC), especially when receiving high-frequency signals. In addition, it decreases the requirements of data storage and transmission in practical applications. Recently, CS has been widely used in radar [2], communication [3], biomedical imaging [4], and other areas. However, due to the electronic bottleneck, the traditional electronic compressive receiver has limited receiving bandwidth.
In recent years, photonic-assisted CS receivers have attracted comprehensive interest owing to the intrinsic advantages of high frequency, broad bandwidth, immunity to electromagnetic interference, etc., offered by microwave photonic technology. The existing photonic compressive receiving schemes can be divided into several categories: multi-coset photonic sampling, photonic random demodulation (RD), and photonic modulated wideband conversion (MWC). Multi-coset photonic sampling is implemented based on nonuniform sampling. In [5], a photonic multi-coset sampling system with an instantaneous bandwidth of 5 GHz is realized. However, prior knowledge of which instantaneous segment is required to be provided by an additional physical frontend. The other categories, including photonic RD and photonic MWC, are both implemented through pseudo random code mixing, low-pass filtering, and low-rate sampling [6–8]. In order to guarantee correct sparse recovery, the code rate of the pseudo random code is required to be greater than the Nyquist bandwidth of the signal [6]. The existing pseudo random code mixing approaches for CS include optical spectral control and temporal modulation. The optical spectral-domain control method consists of modulating the signal onto an optical chirped pulse, and then sending the optical pulse to spatial light modulators (SLMs) [9–11] or multi-mode fiber (MMF) [12–15]. The effective pseudo random code is determined by the bit pattern loaded into the SLM, or the speckle pattern of MMF. However, for the method based on SLMs, the maximum code rate of an effective pseudo random code is limited by the far-field condition for frequency-to-time mapping [11]. For the method based on MMF, considering that the signal modulated to the chirped optical pulse carrier can simultaneously change the frequency of the optical pulse, the maximum signal frequency is limited by the granularity of the speckle pattern [14]. Furthermore, a complex photodetector (PD) array is required to receive the compressive output. Another method of pseudo random code mixing is temporal modulation, which is realized by optical mixing [16–22]. However, the receiving bandwidth is limited by the code rate of the pseudo random code generated by an electronic pulse pattern generator (PPG). In [23], a photonic compressive receiver combined with RF channelization based on a bank of extremely narrow-band optical bandpass filters is demonstrated. However, it is only demonstrated by simulation. Pseudo random code mixing can also be realized by optical sampling [24]. In [24], a photonic modulated wideband converter with a receiving bandwidth of 20 GHz is realized. Four channels of optical pulse trains are gated by pseudo random code, respectively, and are nonuniformly interleaved to increase the instantaneous bandwidth [24]. However, further expansion of the receiving bandwidth results in a more complicated system. As can be seen, the present photonic compressive receivers still face challenges in ultra-wideband spectrum sensing.
Here, we propose an ultra-wideband photonic compressive receiver based on random codes shifting. Compared with the existing photonic compressive receivers, our scheme not only has a large operating frequency range, but also can receive signals with large coverage bandwidth without aliasing and has no need for any prior information about the signal’s frequency band. (1) Large operating frequency range is achieved by upconverting the baseband random code to the radio-frequency (RF) band and slide it in a large frequency range. That significantly expands the receiving frequency range of the system. (2) Receiving signals with large coverage bandwidth without aliasing is owing to the filtering ability of the bandpass random codes, which is the key to avoid aliasing between different frequency bands. That also guarantees the system has no need for any prior information of input signal’s frequency band. (3) True signal and image-frequency signal differentiating is achieved by making the center frequencies of two bandpass random codes slightly different. This further ensures the advantage of no need for prior information. In the experiments, with two channels of only 780 MHz outputs, a multi-tone signal spanning in the range of 11–41 GHz was correctly recovered. Further, a sparse radar-communication spectrum, composed of a LFM signal, a QPSK signal, and single-tone signal, was also correctly recovered.
2. Principle
The principle of the proposed ultra-wideband photonic compressive receiving method is shown in Fig. 1. The system is composed of two symmetrical channels. For each channel, a bandpass pseudo random code is used to compressively receive the corresponding segment of the ultra-wideband RF spectrum. The bandpass pseudo random code is realized by simultaneous electronic-optical modulation of the “mirror”, namely, an up-conversion local oscillator, and a bandwidth-limited baseband pseudo random code, as shown in Fig. 2. The center frequencies of the two bandpass pseudo random codes, namely the locations of two “mirrors”, are slightly different. This is critical for the subsequent true signal judgement in digital signal processing (DSP) module shown in Fig. 2. The compressive outputs of the two channels are sampled by an electronic ADC and sent to DSP module. In DSP module, sparse recovery is first performed. The sparse recovered results of two channels are equivalent to down-converted results of the receiving spectrum segment by the corresponding “mirrors”. Digital up-conversion is then performed to acquire the up-converted RF spectra. However, the image-frequency signal comes with the true RF signal. Owing to the differently located “mirrors”, the image-frequency signal also have different locations, while the true signal is always “fixed”. Thus, the true RF signal judgment can be performed. By drastically shifting the two bandpass pseudo random codes, the whole ultra-wideband RF spectrum can be sensed. Next, we introduce the principle in detail.
Fig. 1. Process of random codes shifting to realize ultra-wideband compressive receiving; EADC: electronic analog-to-digital conversion.
Fig. 2. Principle of the proposed photonic compressive receiver. O/E: opto-electronic conversion; LPF: low-pass filter; EADC: electronic analog-to-digital conversion; DSP: digital signal processor.
2.1 Photonic compressive receiving and sparse recovery
We first consider channel 1 as an example. Suppose that the received ultra-wideband RF spectrum is expressed as ${X_r}(f )$. The band-limited baseband pseudo random code ${p_1}^\prime (t )$ has the code rate of ${R_{code}}$ and is acquired through low-pass filtering of a baseband pseudo random code ${p_1}(t )$. Mirror 1 is a local oscillator for photonically up-converting the band-limited baseband pseudo random code ${p_1}^\prime (t )$ to generate the bandpass pseudo random code. Through photonic mixing between the mirror 1, namely $x_{LO1}^i(t )$, and band-limited baseband pseudo random code ${p_1}^\prime (t )$, a bandpass pseudo random code ${p_1}^ \ast (t )$ with a code rate of ${R_{code}}$ is acquired.
Suppose the ith ($i = 1,2, \cdots ,N$) band of ${X_r}(f )$, which is labeled as ${X_i}(f )$, has a bandwidth approximately to that of ${p_1}^ \ast (t )$. Then, the frequency of mirror 1 is set in accordance with the center frequency of ${X_i}(f )$. After photoelectric conversion by the PD, the final compressive output of channel 1 is
Suppose that the frequency of the mirror 1 is $f_{LO1}^i$. Only the down-converted version, namely, the baseband spectrum ${X_i}({f + f_{LO1}^i} )$, is in the spectral coverage of the band-limited baseband pseudo random code ${p_1}^\prime (t )$. Thus, (2) can be simplified as
According to CS theory [7], if the code rate, namely ${R_{code}}$, is larger than the Nyquist bandwidth of ${X_i}({f + f_{LO1}^i} )$, then ${X_i}({f + f_{LO1}^i} )$ can be sparse recovered. It can be seen, the sparse recovered results of band i are the down-conversion of ${X_i}(f )$ by the corresponding “mirrors”. The situation is the same for channel 2.
2.2 Digital up-conversion and true signal judgement
We first consider the situation of single channel. As shown in Fig. 3, suppose that the ith band of ultra-wideband RF spectrum is a single-tone signal whose frequency is ${f_{i0}}$. For channel 1, after sparse recovery, a down-converted baseband signal ${X_i}({f\textrm{ + }f_{LO1}^i} )$ with the frequencies of ${f_{i0}}\textrm{ - }f_{LO1}^i$ and $\textrm{ }f_{LO1}^i\textrm{ - }{f_{i0}}$ is acquired. If digitally up-converted by $f_{LO1}^i$, then the up-converted spectrum is composed of following two frequencies:
The two frequencies are symmetrical about that of mirror 1. However, between these two frequencies, only ${f_{i0}}$ corresponds to the true signal, while $2f_{LO1}^i - {f_{i0}}$ is an image-frequency resulting from the up-conversion process. That is, when only using one channel, the true signal and the image-frequency signal cannot be distinguished. However, it can be seen from Eq. (4) that the image-frequency $2f_{LO1}^i - {f_{i0}}$ is dependent with mirror 1. That is, if providing another differently located mirror, namely mirror 2, the frequency of the true signal remains fixed while the image-frequency changes (as shown in Fig. 3). By comparing the up-converted spectra of the two channels, the true signal can be easily distinguished.
Now, we come to the dual-channel condition. For channel 2, suppose the frequency of mirror 2 for band i is $f_{LO2}^i$ . If digitally up-converting the sparse recovered result of channel 2 by the mirror 2, up-converted spectrum is also composed of two frequencies:
Suppose $\varOmega _{ch1}^i = \{{f_{ch1 - i}^1,f_{ch1 - i}^2} \}$ and $\varOmega _{ch2}^i = \{{f_{ch2 - i}^1,f_{ch2 - i}^2} \}$. Then, the set of true signal frequencies of band i, which is marked as $\varOmega _{true}^i$, can be expressed as
2.3 Ultra-wideband compressive receiving
Based on the abovementioned principle, when further shifting the two bandpass pseudo random codes drastically, the entire ultra-wideband RF spectrum can be compressively sensed as shown in Fig. 4.
3. Experiment
The experimental scheme is shown in Fig. 5(a). The ultra-wideband signal ${x_r}(t )$ is modulated onto a Mach–Zehnder modulator (MZM, PHOTLINE MXAN-LN-40). The output of the MZM is amplified by an erbium-doped fiber amplifier (EDFA) and filtered by an optical bandpass filter (OBPF). The output of the OBPF is sent to an optical coupler to be directed into the following two dual-parallel MZMs (DPMZMs, Fujitsu FTM7938EZ). For channel 1, when receiving the ith band, the mirror 1 $x_{LO1}^i(t )$ and the band-limited baseband pseudo random code ${p_1}^\prime (t )$ are, respectively, modulated onto the two sub-MZMs of DPMZM1. The band-limited baseband pseudo random code ${p_1}^\prime (t )$ is acquired by ∼5 GHz low-pass filtering a baseband pseudo random code ${p_1}(t )$ provided by an arbitrary waveform generator. It has the code rate of 10.95 GHz and repetition rate of 50 MHz. Channel 2 has the same structure as channel 1. The frequencies of the two mirrors are slightly different. After photoelectric conversion by PD (FINISAR XPDV2120RA) and amplification, the electronic signals are respectively low-pass filtered by 780 MHz LPFs, namely LPF1 and LPF2. The hardware implementation is shown in Fig. 5(b).
Fig. 5. (a): Schematic diagram of the proposed photonic compressive receiver;(b): hardware implementation of the proposed photonic compressive receiver.
We first take channel 1 as an example. Assume that the bias of MZM is ${\varphi _r}$, the bias of the sub-MZM modulated by mirror 1 in DPMZM1 is ${\varphi _{LO1}}$, the bias of the sub-MZM modulated by the band-limited baseband pseudo random code ${p_1}^\prime (t )$ in DPMZM1 is ${\varphi _{p1}}$, and the bias between the two sub-MZMs is ${\varphi _1}$. When the ultra-wideband signal ${x_r}(t )$ is connected to the system, the narrowband output of channel 1 is denoted as ${i_1}$. When the input ultra-wideband signal is empty, the narrowband output of channel 1 is denoted as $i_1^0$. Suppose that the minimum frequency of the ultra-wideband spectrum is ${f_{\min }}$ and the bandwidth of the bandpass pseudo random code is ${B_0}$. When ${f_{\min }}$ meet the following requirement:
and when the bias points are set as ${\varphi _r}\textrm{ = }{{\textrm{ - }\pi } / 4}$, ${\varphi _{LO1}}\textrm{ = }{\varphi _{p1}}\textrm{ = }{\pi / 2}$ and ${\varphi _1}\textrm{ = }0$ ; then according to our previous work [25], the final compressive output $i_1^\ast $ can be simplified asSimilarly, for channel 2, the final compressive output is
where ${h_{LPF2}}$ is the impulse response of LPF2. As can be seen, the terms $x_{LO1}^i{p_1}^\prime$ in Eq. (8) and $x_{LO2}^i{p_2}^\prime$ in Eq. (9) play the role of the bandpass pseudo random codes mentioned in Section 2. By shifting the “mirrors”, the entire ultra-wideband signal ${x_r}(t )$ can be compressively sensed.3.1 Multi-tone spectrum receiving
First, we demonstrate the ability of ultra-wideband multi-tone spectrum recovery. The four-tone spectrum obtained by a spectrum analyzer is shown in Fig. 6. It is composed of the frequencies 12.0, 22.83, 27.1, and 39.05 GHz.
We first set the “mirrors” of channels 1 and 2 as 15.983 and 16.017 GHz, respectively, to receive band 1, namely, 11–21 GHz. The sampling rate of EADC is 2GSa/s and spectrum in the vicinity of DC is eliminated. The occupied support size in single-side spectrum ${K_{\textrm{single - side}}}$ is equal to 1 and the reconstruction algorithm is OMP. The sparse recovered results are shown in Fig. 7(a.1)(a.2). After digitally up-converted by 15.983 GHz and 16.017 GHz, respectively, the up-converted RF spectra of the two channels are shown in Fig. 7(b.1)(b.2). The zoomed-in spectra are shown in Fig. 7(c.1)(c.2), with the pair of 12 GHz and 19.966 GHz for channel 1, and the pair of 12 GHz and 20.034 GHz for channel 2. As can be seen, only 12 GHz remains unchanged and is judged as the true signal. The zoomed in spectrum of the true signal is shown in Fig. 7(e). Next, we set the “mirrors” of channels 1 and 2 as 25.983 and 26.017 GHz, respectively, to receive band 2, namely, 21–31 GHz. ${K_{\textrm{single - side}}}$ is equal to 2. The sparse recovered results are shown in Fig. 7(f). After digital up-converting, the up-converted RF spectrum of channel 1 is composed of 22.83, 24.866, 27.1, and 29.136 GHz, as shown in Fig. 7(g.1). The spectrum of channel 2 is composed of 22.83, 24.934, 27.1, and 29.204 GHz, as shown in Fig. 7(g.2). The true signal is judged as 22.83 and 27.1 GHz. The zoomed in spectrum of true signals are shown in Fig. 7(l-m). Finally, we set the “mirrors” as 35.983 and 36.017 GHz to receive band 3, namely, 31–41 GHz. ${K_{\textrm{single - side}}}$ is equal to 1. The sparse recovered results are shown in Fig. 7(n). The up-converted RF spectra are shown in Fig. 7(o). The true signal is judged as 39.05 GHz, and the zoomed in spectrum is shown in Fig. 7(p). By means of the abovementioned “mirrors” shifting process, the entire ultra-wideband multi-tone spectrum is compressively sensed with only the two channels of 780-MHz outputs.
Fig. 7. (a): The sparse recovered results when receiving band 1. (b): The up-converted RF spectra of band 1. (c-d) Zoomed-in spectra of (b). (e): Zoomed in spectrum of true signal when receiving band 1. (f): Sparse recovered results when receiving band 2. (g): Up-converted RF spectra of band 2. (h-k): Zoomed-in spectra of (g). (l-m): Zoomed in spectrum of true signal when receiving band 2. (n): Sparse recovered results when receiving band 3. (o) Up-converted RF spectra of band 3. (p): Zoomed in spectrum of true signal when receiving band 3.
3.2 Receiving frequency range
Further, we verify the receiving frequency range of our system. First, we set the “mirrors” as 15.983 and 16.017 GHz to receive band 1, namely 11–21 GHz. The signal to be received is set as a single tone, with ${K_{\textrm{single - side}}}$ is 1, and its frequency increases every 1 GHz in the range of band 1. Each single-tone signal is compressively received and recovered. The up-converted RF spectra of channel 1 are shown in Fig. 8(a). The true signals are distinguished from the image-frequency signals according to the abovementioned principle and are labeled as asterisks in Fig. 8(a). As can be seen, the single-tone signals in band 1 can all be sensed. Then, the “mirrors” are set as 25.983 and 26.017 GHz to receive band 2, and 35.983 and 36.017 GHz to receive band 3, with the single-tone signal correspondingly varying from 21 GHz to 31 GHz and 31 GHz to 41 GHz. The up-converted RF spectra of channel 1 are shown in Fig. 8(b) for band 2, and Fig. 8(c) for band 3. The distinguished true signals are also labeled as asterisks. As can be seen, the system has the receiving range of 11–41 GHz.
Fig. 8. Up-converted RF spectra of channel 1 when receiving (a) band 1, (b) band 2, and (c) band 3. Zoomed in spectrum of distinguished true signal when receiving (d) 11 GHz,(e) 28 GHz and (f) 41 GHz. Asterisk: the distinguished true signals.
3.3 Radar-communication spectrum receiving
Finally, a sparse radar-communication ultra-wideband spectrum is considered. It is composed of an LFM radar signal in band 1, a QPSK communication signal in band 2, and a single-tone signal in band 3. The spectrum obtained by a spectrum analyzer is shown in Fig. 9(a). The zoomed-in spectrum of the LFM radar signal is shown in Fig. 9(b) (starting frequency: 14.9476 GHz, bandwidth: 50 MHz, pulse width: $100\mathrm{\mu} \mathrm{s}$, ${K_{\textrm{single - side}}}$=2). The zoomed-in spectrum of the QPSK communication signal is shown in Fig. 9(c) (carrier frequency: 24.25 GHz, symbol rate: 5 MHz, ${K_{\textrm{single - side}}}$=1). The communication content is a picture in JPEG compressed format. The zoomed-in spectrum of the single-tone signal of 35.56 GHz is shown in Fig. 9(d), with ${K_{\textrm{single - side}}}$=1.
Fig. 9. (a) The ultra-wideband radar-communication spectrum shown by spectrum analyzer. (b) Zoomed-in spectrum of LFM signal in band 1. (c) Zoomed-in spectrum of QPSK signal in band 2. (d) Zoomed-in spectrum of single-tone signal in band 3.
We first set the “mirrors” of channels 1 and 2 as 15.983 and 16.017 GHz, respectively, to receive band 1. The sparse recovered baseband LFM signals are shown in Fig. 10(a.1) and (a.2). They are then digitally up-converted by frequencies of 15.983 and 16.017 GHz, respectively. The up-converted RF spectra are shown in Fig. 10(b) and the zoomed in versions are shown in Fig. 10 (c-d). Only the LFM component in Fig. 10(c) is common in both two channels. The zoomed in spectrum of distinguished true LFM component is shown in Fig. 10(e) and its time–frequency distribution is shown in Fig. 10(f), which are both in accordance with those of the input signal.
Fig. 10. (a) Sparse recovered results of band 1; (b) up-converted RF spectra; (c-d) zoomed in version of (b); (e) zoomed in spectrum of distinguished true signal; (f) time–frequency distribution of distinguished true signal.
Next, we set the “mirrors” as 25.983 and 26.017 GHz to receive band 2. The sparse recovered baseband QPSK spectra are shown in Fig. 11(a.1) and (a.2). The zoomed in distinguished true signal spectrum is shown in Fig. 11(b), which is consistent with the spectrum in Fig. 9(c). We then directly demodulate the sparse recovered baseband QPSK signal of channel 1 shown in Fig. 11(a.1). The resultant constellation diagram is shown in Fig. 11(c). Further, the bit stream is decompressed, and the resultant image is shown in Fig. 11(d). As a reference, the ideal decompressed JPEG image written to the QPSK signal is shown in Fig. 11(e), which is consistent with the decompressed image acquired from the sparse recovered baseband QPSK signal.
Fig. 11. (a) Sparse recovered results of band 2; (b) zoomed in spectrum of distinguished true QPSK signal; (c) constellation diagram of sparse recovered signal in (a.1); (d) decompressed JPEG image acquired from demodulating sparse recovered signal in (a.1); (e) ideal decompressed JPEG image written to input QPSK signal.
Finally, we set the “mirrors” as 35.983 and 36.017 GHz to receive band 3. The sparse recovered results are shown in Fig. 12(a.1) and (a.2). After the true signal judgement, 35.56 GHz is judged as true signal and its spectrum is shown in Fig. 12(b), which is consistent with the spectrum of input signal in band 3 shown in Fig. 9(d).
Fig. 12. (a) Sparse recovered results of band 3; (b) zoomed in spectrum of distinguished true signal.
It should be noticed that when applied in engineering, the main constraint for the proposed system is the sparsity of the spectrum to be sensed. This is a common constraint that faced by the photonic receivers based on compressive sensing theory. The system is suitable for scenarios with sparse spectrum, which means that the number of signal components is small and the bandwidth of each component is also narrow.
Besides, the use of compressed sensing causes the system to be more sensitive to the measurement noise, which is the noise introduced by the system itself [26]. For our photonic compressive sensing receiver, measurement noise includes RIN noise introduced by laser, ASE noise introduced by EDFA, shot noise introduced by PD, thermal noise introduced by electronic amplifier and so on. The evolution process of measurement noise in photonic compressed sensing system is more complicated than that of the traditional compressed sensing system [26]. In the future, we will further our research on the influence brought by these measurement noise on photonic compressive sensing system.
4. Conclusion
In summary, we have presented an ultra-wideband photonic compressive receiver based on random codes shifting with image-frequency distinguishing. In the experiments, a multi-tone spectrum distributed in the range of 11–41 GHz, and a sparse radar-communication spectrum composed of an LFM signal, a QPSK signal, and a single-tone signal were correctly recovered. Compared with other states-of-art shown in Table 1, our work can receive signals with significantly greater coverage bandwidth, without any prior information about the signal’s frequency band. This makes our system has great potential of being applied in future broadband cognitive radio. The upper limit of input frequency range is restricted by the response of MZM and DPMZMs, which can be improved with further development of high-response modulator.
Table 1. States-of-art photonic compressive receiver
Funding
National Key Research and Development Program of China (2019YFB2203301); National Natural Science Foundation of China (62127805, 61690191).
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.
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