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Abstract
We have proposed an interference and frequency-to-time mapping based high anti-jamming and anti-interception frequency hopping receiving scheme. By changing the delay difference between the interference arms through high-speed switchable delay lines and using electrooptical sampling, fast and large-range frequency hopping signals can be received. Benefited from the high shaping resolution for using the interference as the spectral shaping method, more receiving passbands in high frequency bands can be available to enhance the anti-jamming and anti-interception performance. By fast pulse shaping through switchable delay lines, the bandwidth of the electric end, the sampling rate, and the number of frequencies in the frequency hopping pattern are decoupled, and the bandwidth of the electric end can be reduced to improve the receiving selectivity. In experiments, the signal hopping from 15.2 GHz to 35.4 GHz with the switching time up to that of the used optical switch is received. Utilizing a switchable delay line in the interference arm with the tuning step of 2.5 ps, eight available receiving passbands within 25 GHz to 42 GHz are generated. The receiving selectivity is also improved from 18.3 to 43.7 in terms of Q factor by decreasing the electric end′s bandwidth in experiments.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The frequency hopping receiving is widely used since it increases the anti-jamming and anti-interception ability in communications [1–4]. In order to confront follower jammers [1,2] that have the ability to track and block/intercept the communication frequency channels, and to avoid broadband interference [3,4], a fast and large-range frequency hopping receiving is required. To further improve the anti-jamming performances, besides the increase on the receiving selectivity to suppress the out-of-band jamming, more high-frequency communication bands are also desired since the communication in lower frequency bands is much easier to be intercepted or even completely blocked in contrast to the communication in higher frequency bands [5]. In [6], a frequency hopping receiving method based on the simultaneous photonic filtering and digitizing priciple [7–9] has been proposed to construct a frequency hopping receiver with the assist of digital signal process (DSP). The reception of fast and large-range frequency hopping signals is realized by a verification scheme, where the receiving frequency is rapidly changed by selecting the optical sampling pulses from a set of optical sub-pulses through high-speed optical switch. However, it cannot provide enough high-frequency receiving bands since the receiving frequencies are determined by the shaped optical sub-pulses with a time resolution limited by the spectral resolution of the optical filter and the allowed minimum dispersive value. The selectivity is also limited since the optical sampling rate $f_s$, the bandwidth of the electric end including all the devices from the photodiode (PD) to the analog-to-digital convertor (ADC), $f_E$, and the total number of frequencies within the hopping pattern, $N$, are mutually restricted by
To select one sub-pulse out of all the sub-pulses corresponding to $N$ frequencies in the frequency hopping pattern, the bandwidth of the electric end should be $N$ times larger than the sampling rate. With the increase of the total number of frequencies in the hopping pattern without decreasing the communication code rate according to the Nyquist Law [10], $f_E$ should be increased, so as the bandwidth of the receiving passband. As a result, the receiving selectivity and the anti-jamming performance are degraded as the bandwidth occupied by the signal within the passband remains unchanged.In order to provide high anti-jamming and anti-interception performance in frequency hopping receiving, according to the receiving method in [6], an interference and frequency-to-time mapping based receiving scheme is proposed. It provides more available high-frequency receiving passbands and higher receiving selectivity in fast and large-range frequency hopping receiving. In the proposed scheme, the optical pulse shaping is based on the optical spectral interference and frequency-to-time mapping. Therefore, the receiving frequencies are changed rapidly by tuning the delay difference between the spectral interference arms through the high-speed switchable optical delay lines. Since the optical delay lines have fine resolutions, the proposed scheme can provide more possible receiving frequency bands in high frequencies. Besides, it provides higher receiving selectivity since it decouples the sampling rate, the bandwidth of the electric end and the total number of frequencies in the frequency-hopping pattern. In this case, the bandwidth of the electric end is only restricted to avoid the inter-symbol interference (ISI) during digitizing [7]. Therefore, the bandwidth of the electric end is required to be slightly higher than half of the sampling rate in most cases [11,12]. As a result, the receiving passband is narrowed, and the selectivity is improved.
The principle of the proposed frequency hopping receiving scheme is shown in Section 2. The experimental setup and the frequency hopping reception experiment is illustrated in Section 3. In Section 4, the performance analyses of the proposed scheme and their experimental verifications are proposed. The conclusion is presented in Section 5.
2. Working principle
The schematic of the proposed scheme for fast and large-range frequency hopping receiving is shown in Fig. 1.
Fig. 1. the schematic of the proposed scheme for fast and large-range frequency hopping receiving; MLL: mode-locked laser; PS: power splitter; OS: optical switch; ATT: attenuator; PC: polarization controller; SMF: single mode fiber; MZM: Mach-Zehnder modulator; PD: photodiode; LPF: low-pass filter; ADC: analog-to-digital convertor
The mode-locked laser (MLL)-generated periodic pulses are power split and sent into two arms. The upper arm is fixed, and the lower arm can be adjusted by switchable delay lines. Then after going through different length of fibers, the optical pulses in the two arms are coupled together. The polarization state and power within each arm can be adjusted by attenuators (ATTs) and polarization controllers (PCs). With a transmission time difference between the two arms, the optical pulses are interfered and conducted spectral shaping [13]. The spectral intensity of the optical pulses after interference can be denoted as:
where $2{I_0}$ is the intensity of MLL-generated optical pulses, ${\tau }$ is the time difference between the two arms, and V is the visibility of interference. The visibility of interference is determined by the polarization states and powers of the two arms, as well as the phase fluctuations of the optical source [13,14]. Since the pulse duration of the MLL is less than 1ps, the degradation on V caused by the optical source’s phase noise can be neglected [14]. Then the visibility of the interference reaches its maximum as the polarization states in the two arms are perfectly matched and the optical powers are equal [13]. $G({\omega })$ is the shape of the optical spectrum generated by the MLL. Here we take the optical spectrum centered at $\omega _c$ with the Gaussian shape as an example: Then the spectrally shaped optical pulses are sent to a dispersive medium with the dispersive value of $\ddot {\Phi _{\nu }}$ to conduct frequency-to-time mapping, which maps the spectral shape of the optical pulses into time domain [15]. After spectral shaping and frequency-to-time mapping, the optical pulses are prepared to receive the frequency hopping signals. The intensity of the shaped optical pulses, $p_s(t)$, within one hop of the frequency hopping signals, which is the period that the signals’ carrier frequency remains unchanged, can be denoted as,As illustrated in [6], by changing the angular frequency $\frac {\tau }{\ddot {\Phi _\nu }}$ of the shaped optical pulses, $p_{s,n}(t)$, through the switchable delay lines according to the frequency hopping pattern, the receiving passband of the equivalent system is changed and the frequency hopping signals can be received successfully. The speed to switch the receiving frequency equals the tuning speed of the switchable delay lines, and the frequency hopping range can be as large as the working bandwidth of MZM.
It is worthy to note that in practice, the shaped optical pulse, $p_{s,n}(t)$ is hardly ideal for unideal frequency-to-time mapping. The equivalent system response should be calibrated by measuring the temporal internsity of the shaped optical pulse according to Eq. (6). The impact of the non-ideally shaped optical pulses on the equivalent system response can be further compensated by the DSPs [16] or by pre-distortion in the cooperative frequency hopping transmitter [17].
3. Experimental setup and reception of frequency-hopping signals
An experiment is carried out to verify the reception of frequency hopping signal through the proposed scheme. The experimental setup is shown in Fig. 2.
Fig. 2. The experimental setup for the proposed interference and time-to-frequency mapping based receiving scheme for fast and large-range frequency hopping receiving; OSA: optical spectrum analyzer; SOSC: sampling oscilloscope
In the experiments, as to verify the ability to receive frequency hopping signals, the switchable delay line in the lower interference arm can tune the delay difference between the two arms from 268 ps to 115 ps, which corresponds to the switching between two receiving frequencies. For the frequency hopping signals that hop between more frequencies, they can be received by expanding the scale of the switchable delay lines. The ATTs in interference arms are aiming at optical power control so that the two interference arms have equal optical powers. PCs are also placed in each arm to guarantee the maximum visibility of interference. In the experiment, an MLL with a 1560 nm centered Gaussian-like spectrum whose full-width-at-half-maximum (FWHM) is 12 nm is utilized. The optical spectrum after interference with delay difference of 268ps and 115 ps are captured by an optical spectrum analyzer (OSA), as shown in Fig. 3(a) and (d) respectively. The optical switch in the switchable delay lines has the nominal switching time of less than 1 ms. A $\sim$9km single-mode fiber (SMF) is utilized as the dispersive medium whose dispersive value is $\ddot {\Phi _\nu }=\sim 1.22\times 10^3 ps^2$. After pulse shaping and response frequency tuning, the optical pulses are sent into $\rm {PD_2}$ whose bandwidth is 50 GHz and a sampling oscilloscope (Infiniium DCA-X 86100D) triggered by the electric synchronization output from the MLL to observe the temporal intensity of the shaped optical pulses, as shown in Figs. 3(b) and 3(e). Then the optical pulses are sent into a 40 GHz MZM to be modulated with the test signal, detected by the $\rm {PD_1}$ with the bandwidth of 1 GHz and filtered by a LPF of 167 MHz. An ADC with 1.4 GHz analog bandwidth digitizes the filtered signals with the sampling rate of 250 MS/s, which is synchronized with the MLL, and the digitized outputs are further processed by DSP.
Fig. 3. Experimental results to verify the reception of frequency hopping signals. Optical spectrum after interference with the delay between two arms of 268 ps in (a) and 115 ps in (d); The temporal intensity of the shaped optical pulses within the period of $T_s$ after frequency-to-time mapping with $\tau$ of 268 ps in (b) and 115 ps in (e); (c) and (f): The equivalent system response with $\tau$ of 268 ps and 115 ps; (g) The received frequency hopping signal and (h) its spectrogram.
Before receiving the frequency hopping signals, the equivalent system responses are measured. Stimulated by a single tone radio frequency (RF) signal, the amplitude of the ADC output can be treated as the magnitude of system response at the stimulated frequency. By sweeping the stimulated signal, the system response within the test range can be obtained [7]. The stimulated signal is generated from a RF signal generator (Rohde & Schwarz, SMF100A), and the sweeping range is DC-40 GHz in the experiment. Keeping the delay introduced by the switchable optical delay line unchanged through the RF sweeping procedure, the equivalent system response with a certain delay difference between the two interference arms is obtained. The tested equivalent system responses at delay difference of $\tau =\rm {268}$ ps and 115 ps are shown respectively in Fig. 3(c) and 3(f). The receiving frequency is 15 GHz and 35 GHz respectively.
As Section 2 illustrates, the proposed frequency hopping receiving scheme has the ability to receive frequency hopping signals whose hopping frequency range is within the working bandwidth of MZM, and the hopping speed equals the switching speed of the switchable delay line. To verify the receiving ability, with the current devices in the experimental setup, a signal hopping from 35.4 GHz to 15.2 GHz with the switching time of less than 1 ms is required. However, there is no available equipment that can generate such frequency hopping signals with both high hopping speed and large frequency range. Then, in the experiment, a 15.2 GHz and 35.4 GHz double-tone RF signal generated from two RF signal generators and a broadband RF coupler is used as an approximation of the test frequency hopping signal to verify that the proposed scheme has the ability to receive fast and large-range frequency hopping signals. With the switching of optical switchable delay lines every 20 ms, only one tone is located within the receiving passband at a time, and the switching time between the received frequency is determined by the optical switch. This is identical to the reception of frequency hopping signals whose carrier frequency hops from 15.2 GHz to 35.4 GHz every 20 ms, with a negligible switching time. The test double-tone signal is received as a frequency hopping signal, as illustrated in Fig. 3(g), with the switching time of $\sim \rm {0.8}$ ms, which agrees with the nominal switching time of the optical switch in the switchable delay line. The spectrogram of the received signals is shown in Fig. 3(h) to indicate the frequency components of the received signal in different time windows. It is calculated by the short-time Fourier transform with a 3.2 $\rm {{\mu }s}$ Gaussian time window that overlaps 1.6 $\rm {{\mu }s}$ with the neighboring windows, and the number of points to conduct the Fourier transform is 799. As illustrated in Fig. 3(h), the received signal is a time-various signal and the received frequency hops from 100 MHz to 50 MHz, corresponding to 35.4 GHz and 15.2 GHz respectively. Thus, it proves that the proposed scheme has the ability to receive frequency hopping signals whose hopping speed is equal to the switching speed of the switchable delay lines, which can be faster than 1 ns [18], and the frequency hopping range can be as high as the MZM working bandwidth up to several hundreds of gigahertzes.
4. Performance analysis and experimental verification
Besides the reception of fast and large-range frequency hopping signals, the proposed scheme provides more available receiving passbands in high frequency bands, as well as higher selectivity with a frequency hopping pattern containing more possible frequencies. The performance of the proposed scheme is analyzed and experimentally verified through the setup shown in Fig. 2.
4.1 Number of receiving passbands
In the proposed scheme, the optical pulse shaping is based on spectral shaping and frequency-to-time mapping, and the number of the potential receiving passbands depends on the temporal shaping resolution. With finer temporal shaping resolution, there can be more receiving passbands, especially in higher frequency bands. Different from other proposals utilizing an optical filter to conduct the spectral shaping, the shaping precision through the optical interference in the proposed scheme is not limited by the resolution of optical filters, but by the resolution of the switchable delay lines. Since most optical filters has the resolution of no less than 0.08 nm but switchable delay lines’ resolution can be as high as 1 fs, with the same dispersive medium, there are much more available receiving passbands in the proposed scheme. Take the dispersive value of $\sim 1.22\times 10^3ps^2$ utilized in the experiments as an example, a receiving method based on the optical filter with spectral shaping resolution of 0.08 nm can support only two receiving frequencies (27.77 GHz and 41.66 GHz) within the frequency range of 25 GHz to 42 GHz. Meanwhile, as illustrated by Eq. (6), the interference-based scheme with the switchable delay lines$^{\prime }$ resolution of 2.5 ps can support 8 passbands within the same frequency range.
By tuning the delay between the interference arms with the resolution of 2.5 ps, the equivalent system responses within the range of 6 GHz to 40 GHz have been experimentally obtained once at a time, and depicted together in Fig. 4. There are eight passbands within the frequency range of 25 GHz to 42 GHz, as illustrated above. With the switchable delay line whose resolution is about 1 ps, the 1.35 GHz receiving passband in the experiment can be tuned to cover the entire frequency hopping range of 40 GHz. The decreasing of the receiving gain with the increasing of receiving frequency is caused by the gradual decline of amplitude response of the MZM utilized in the experiment.
4.2 Selectivity of receiving passbands
According to Eq. (6), the bandwidth of the receiving passbands is determined by $G^{\prime }(\omega )$, the Fourier transform of the response of optical filter after frequency-to-time mapping and $H_{E}(\omega )$, the response of the electric end. For $G^{\prime }(\omega )$, it is derived as:
For the bandwidth of $H_E(\omega )$, as illustrated in Section 2, it is required to be larger than half of the sampling rate of ADC to avoid ISI during digitizing [7]. Thus, the requirement on the bandwidth of $H_E(\omega )$ is irrelevant with the total number of frequencies in the frequency hopping pattern. In the proposed scheme, with the increase of total number of possible frequencies in the frequency hopping pattern, the bandwidth of $H_E(\omega )$ does not increase accordingly, neither does the bandwidth of the receiving passband. Compared with the scheme in [6], when receiving signals whose frequency hopping pattern contains more possible frequencies, the passband of the proposed scheme has higher Q factor. Therefore, better reception selectivity and anti-interference performance [19] are provided by the proposed scheme.
A receiving passband is narrowed with the decrease of the electric end$^{\prime }$s bandwidth in the experiment, and the equivalent system responses are depicted in Fig. 5. In the experiment, all devices except the LPF are identical to the devices illustrated in the experimental setup in Section 3. In this experiment, the bandwidth of the electric end is limited by the bandwidth of LPF. The receiving passband$^{\prime }$s 6dB bandwidth is 1.92 GHz for a 1GHz LPF, and 1.35GHz for a 167MHz LPF. The corresponding bandwidths are marked in Fig. (5). By using narrower electric end in this proposed scheme, with the receiving passband at 35 GHz, the 6 dB Q factor increases from 18.3 to 43.7. Then the selectivity and anti-interference performance improve as a result. It is worth noting that in the scheme proposed in [6] with the sampling rate of 250 MS/s, the 1 GHz bandwidth of the electric end supports only two hopping frequencies and the 167 MHz bandwidth of electric end cannot support frequency hopping receiving.
Fig. 5. The experimental result to show the increase on receiving passband$^{\prime }$s selectivity as the bandwidth of electric end’s bandwidth decreases from 1 GHz to 167 MHz.
As the bandwidth of the electric end is decoupled with the total number of possible hopping frequencies in the proposed scheme, with more hopping frequencies available, the bandwidth of the electric end does not have to increase, neither does the receiving passband$^{\prime }$s bandwidth. Therefore, there is no decline on the reception selectivity and anti-interference performance in this scheme with the change of frequency hopping patterns.
5. Conclusion
In conclusion, an interference and frequency-to-time mapping based high anti-jamming and anti-interception frequency hopping receiving scheme is proposed in this article. It can receive frequency hopping signals with hopping speed up to the switching speed of the switchable delay lines. A signal hopping from 15.2 GHz to 35.4 GHz is received with the tuning speed of $\sim \textrm {0.8}$ ms, which is identical to the switching time of the switchable delay line in experiments. Besides, benefited from the interference-based spectral shaping method to improve the spectral shaping resolution, the proposed scheme provides more receiving passbands within the working bandwidth of MZM, especially in high frequency bands. Therefore, the anti-interception performance is enhanced. In the experiment, eight passbands within 25 GHz to 42 GHz with a switchable delay line whose tuning step is 2.5 ps are generated. Moreover, since the receiving frequency is tuned by the rapid change of the switchable delay line in the interference arms, the bandwidth of the electric end can be reduced to the amount that can avoid the ISI during digitizing. As a result, the bandwidth of the receiving passbands is narrowed compared with the verification scheme in [6]. Therefore, the selectivity and anti-jamming performance are improved. In the experiment, the receiving selectivity is improved from a 6 dB Q factor of 18.3 to 43.7 by decreasing the electric end’s bandwidth from 1 GHz to 167 MHz.
Funding
National Natural Science Foundation of China (61627817).
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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