Photonic generation and application of dual-band phase-coded LFM signals

A novel photonic method is proposed to generate dual-band phase encoding linearly frequency modulation (LFM) waveforms. In this scheme, two binary sequences are sent into one dual-polarization Mach–Zehnder modulator (DPol-MZM) to perform phase modulation with the optical carrier, while driving LFM signal is sent into another DPol-MZM to generate second and fourth-order optical sidebands. Then, the generated sidebands and the phase modulated optical carrier are combined together to perform optical to electrical conversion. As a result, bandwidth doubled and quadrupled phase coded LFM signals can be produced. The proposed scheme is verified by simulation, dual-band signals of 6 ~ 10 GHz & 12 ~ 20 GHz, 6 ~ 13 GHz & 12 ~ 26 GHz and 8 ~ 10 GHz & 16 ~ 20 GHz are obtained by using 3 ~ 5 GHz, 3 ~ 6.5 GHz, and 4 ~ 5 GHz driving LFM signals, respectively. Furthermore, the applications of the generated dual-band signals on both radar and communication are demonstrated. For radar detection, optical de-chirping operation for the dual-band signals can be simultaneously realized by using a DPol-MZM, on the other hand, the time bandwidth product of the radar waveform can be improved by phase encoding the LFM signal with M sequence. For wireless communication, each band LFM signal can be modulated with a binary sequence, and the two phase-coded LFM signals can be coherently demodulated in the optical domain. The proposed method features multi-functional operation, which can be potentially employed in radar-communication integrated systems.


Introduction
Linearly frequency modulation (LFM) signal features excellent pulse compression performance, and it is widely used in modern radar systems (Cook 2012;Mark 2014). On the other hand, LFM signal can be applicated in wireless communication through spread spectrum operation to reduce interception probability (Reynders and Pollin 2016). LFM signals Thanks to the polarization controller (PC), the second-order and fourth sidebands can be separated into two polarization states and then combined with phase-modulated optical carriers. After optic-electronic conversion bandwidth doubled and quadrupled, phase encoding LFM waveforms are independently generated. Furthermore, the photonic receiver is also investigated to perform low-speed processing to the received signals. With a local optical signal directly extracted from the generator, optical de-chirping and coherent demodulation can be easily achieved without an independent local oscillator. Figure 1 shows the systematical diagram of the proposed photonic dual-band radar-communication integration system. The system contains two modules, a phonic generator used for dual-band phase-coded LFM signal generation and a photonic receiver to perform dechirping and coherent demodulation to the received signal. The photonic generator consists of a laser diode (LD), two DPol-MZMs, two pulse pattern generators (PPGs), an arbitrary waveform generator, a PC, an optical coupler (OC), two polarization beam splitters (PBSs), two optical filters (OFs), two photodetectors (PDs), two electrical filters, two electrical Fig. 1 Configuration of the proposed generator and receiver. LD laser diode; DPol-MZM dual-polarization Mach-Zehnder modulator; PPG pulse pattern generator; AWG arbitrary waveform generator; PC polarization controller; OC optical coupler; PBS polarization beam splitter; OF optical filter; PD photodetector; BPF bandpass filter amplifiers and two transmitting antennas. While the photonic receiver consists of four receiving antennas, four electrical bandpass filters (BPFs), four electrical amplifiers, a tunable time-delay line (DL), two DPol-MZMs, two PBSs, four PDs, and four electrical low pass filters (LPFs).

Theory and principle
Note that there are two types of DPol-MZM deployed in this scheme, as shown in Fig. 2. In the photonic generator, the DPol-MZM consists of two sub-MZMs, a 90°polarization rotator (PR) and a polarization beam combiner (PBC), as shown in Fig. 2a. Figure 2b shows the structure of another type of the DPol-MZM, it consists of two sub-MZMs, a PBC and a PBS, and it is deployed in the photonic receiver.

Generation of dual-band phase-coded LFM signal
In the photonic generator, the CW laser output from the LD is firstly split into two paths and then applied into the two DPol-MZMs. In DPol-MZM1, the two sub-MZMs are biased at the maximum transmission point (MATP). For each sub-MZM, the input optical carrier is phase modulated by a binary sequence to introduce a phase difference of Δφ, as shown in Fig. 3a. Assume that the light emitted from the LD has an angular frequency of ω c and an amplitude of E in . The i-th symbol of the two binary sequences are respectively N 1i and N 2i . Then the output of DPol-MZM1 in two polarization states can be expressed as, where δ denotes the pulse function, T is the period of each symbol of the binary sequence. M p1 and M p2 are the modulation index of the sub-MZMs in DPol-MZM1. As can be seen in the Eq. 1, the phase difference Δφ is defined by M p1 and M p2 .
The electronic LFM signal is firstly split by a 90°hybrid coupler and then sent into two sub-MZMs of DPol-MZM2. The sub-MZMs are biased at the maximum transmission point (MATP) to generate optical carrier and even-order sidebands in the two polarization states, as shown in Fig. 3b and c. The polarization-multiplexed optical signals are then adjusted by the PC and put into the following PBS. The two principal axes of the PBS have differences of 45° and 135° to one polarization direction of the optical signals. After that, two optical filters (OFs) are used to filter the desired sidebands respectively. As a result, second-order sidebands can be remained in polarization direction y, and fourth-order sidebands in polarization direction x. Assuming the electrical driving signal is a repetitive wave train of s L (t) = V L cos(ω IF t + kt 2 /2), where V L is the amplitude, ω IF is the initial angular frequency, and k is the chirp rate. Then the output of DPol-MZM2 can be given by, where m 2 = πV L /V π is the modulation index of the sub-MZMs in DPol-MZM2, and V π is the switch voltage. Note that the driving signal is synchronized with the binary sequences. By applying the Jacob expansion, Eq. (2) can be rewritten as, In which, J n is the n-th order Bessel function of the first kind. Consequently, the output of OF 1 and OF 2 can be expressed as, Then, E OF1 (t) and E OF2 (t) are respectively combined with E DM1-x (t) and E DM1-y (t) and sent into two PDs. The input signal of PD1 and PD2 can be expressed as, The output signal of PD1 and PD2 can be given by, where η is the responsivity of PD. As shown in Eq. 6, frequency-doubled and quadrupled phase-coded LFM waveforms are generated.

De-chirping of radar detection
In the proposed scheme, de-chirping to the received echo signal with a local optical signal provided by the photonic generator is available. As shown in Fig. 1, the output of DPol-MZM2 is split into two brunches. One is used to generate a dual-band LFM signal. The other is sent into the receiver as a local signal. Echo signal of each band will be sent into one sub-MZM of DPol-MZM4, both the sub-MZMs are biased at MATP to generate second-order optical sidebands, as shown in Fig. 4. Assume that one echo signal has an instantaneous frequency of 4ω IF + 4 k(t−t 0 ), then one of the generated positive second-order sidebands has a frequency of ω c + (4ω IF + 4kt−8kt 0 ). After the PD, the frequency difference between components ω c + (4ω IF + 4kt) and ω c + (4ω IF + 4kt−8kt 0 ) can be extracted through the LPF. The output of the LPF can be expressed as, where t 0 represents the propagation time of the detection signal. The relationship between de-chirp signal and the distance to target can be given by, In which c represents the velocity of light, f LPF is the frequency of the de-chirp signal extracted by LPF. Fig. 4 The optical sidebands modulated by received echo signal

Optical coherent demodulation of communication
One advantage of the proposed scheme is that demodulation to the generated phase-coded LFM signal can be achieved without any electrical devices or independent local oscillator source. As shown in Fig. 1, the output of DPol-MZM2 is sent into DPol-MZM3 through a tunable time-delay line. On the other hand, the frequency quadrupled and doubled communication signals will be respectively received by receiving antennas. After bandpass filtering and power amplifying, the received signals of two bands are sent into the two sub-MZMs of DPol-MZM3, respectively. The sub-MZMs also biased at the MATP. After PD3 and PD4, communication information can be recovered at the output of LPF. Assume that the normalized emitting communication signal is a frequency quadrupled phase-coded LFM waveform train, which can be written as, So, in the receiver end, the corresponding received signal can be given by, where L is the propagation distance from the transceiver end to receiver end.
The local signal sent into DPol-MZM3 on polarization direction x can be expressed as, τ is the time delay introduced by the tunable delay line. In order to ensure the phase synchronization to the received signal, the time delay should be tuned as, where mod represents modulus. Then the output of DPolMZM3 on polarization direction x can be given by, Finally, after the PD and the LPF, the demodulated signal can be expressed as Therefore, the communication information is successfully recovered.

Functional separation in the receiver end
Since the phase-coded LFM waveform generated in a photonic generator can be simultaneously used for target detection and wireless communication, so in the receiver end, the received signal needs to be functionally separated to perform de-chirping and coherent demodulation. In this scheme, we adopt the method proposed by Saddik (2007). In the emitting end, two right-handed circularly polarized (RHCP) antennas working in different wavebands are used. And in the receiver end, two RHCP antennas are used to receive the communication signals, while two left-handed circularly polarized (LHCP) antennas are deployed to receive the echo waves of the radar detection. As shown in Fig. 5, the phase-coded LFM signal transmitted by the photonic generator is a right-handed polarized wave, which can be directly received by RHCP receiving antenna as a communication signal. On the other hand, the polarization direction of the reflected wave will be reversed to be a left-handed polarized wave. Consequently, the echo signal can only be received by an LHCP antenna to perform radar detection. The separation of communication and radar functions can be achieved in the receiver end.

Simulation and discussion
The feasibility of the proposed scheme is verified by a simulation based on the platform Optisystem. The central frequency and optical power of LD are set to be 191.3 THz and 16 dBm. The extinction ratio of all the sub-MZMs is 30 dB.

Application on radar detection
In this section of simulation, an electrical repetitive LFM wave train with a repetitive period of 10 μs is provided. Each basic LFM waveform is chirped from 3 to 5 GHz. Figure 6 shows the DC blocked waveforms and time-frequency diagrams of the generated dual-band signals. As shown in Fig. 6b and d, LFM waveform chirped from 6 to 10 GHz, and 12 to 20 GHz is generated, which means that frequency-doubled and quadrupled dualband radar signals are successfully obtained.
To further verify the tunability of the proposed generator, we change the chirp range of the driving signal to 3 ~ 6.5 GHz and 4 ~ 5 GHz. As shown in Fig. 7b and d, 6 ~ 13 GHz and 12 ~ 26 GHz LFM wave trains are generated. In Fig.7f and h, 8 ~ 10 GHz and 16 ~ 20 GHz, LFM signals are obtained. Since the OFs are only used to extract the positive order sidebands, the passbands don't need to be adjusted to generate the signals  of different chirp range. Consequently, the tunability of the proposed generator will not be influenced by the OFs.
Optical de-chirping to the echo signals is also demonstrated. A time delay of 0.1 μs is introduced to the emitted signal and then sent into the receiving antenna, corresponding an echo signal reflected from a target with distance of 15 m. Figure 8a and b show the electrical spectra of the de-chirp results of each band signal. The peak pulses have frequencies of 79.96 MHz and 160.11 MHz, respectively, which are substantially consistent with the theoretical value 80 MHz and 160 MHz. Besides, the RF spurious sidebands suppression ratios (SSRs) are 42.38 dB and 41.78 dB. Thus, low-speed and realtime radar signal processing of dual-band radar are achieved.
To verify the improvement of the time bandwidth product (TBWP) of this proposed scheme, auto-correlation functions of a 10 ns, 2 GHz bandwidth driving LFM waveform and corresponding generated LFM waveforms are investigated. As can be seen in Fig. 9a, b, and c, the full widths at half maximum (FWHM) of the pulses are 0.6 ns, 0.3 ns, and 0.15 ns. The pulse compression ratios (PCRs) of the driving waveform, the generated bandwidth-doubled and quadrupled waveforms are 16.7(10 ns/0.6 ns), 33.3 (10 ns/0.3 ns) and 66.7(10 ns/0.15 ns), respectively. It indicates that the TBWP of the generated waveforms is improved by twice and four times. Then, two binary sequences are set as two M sequences with lengths of 31 and 63 respectively, the sequences are employed to generate phase-coded dual-band LFM signals. Figure 10a shows the auto-correlation of bandwidth-doubled phase-coded LFM waveform which is modulated by the 31-length M sequence. The PCR is 1033.33 (310 ns/ 0.3 ns), and its TBWP is improved by 62 times. The auto-correlation of the bandwidth-quadrupled LFM waveform which is modulated by the 63-length M sequence is shown in Fig. 10b. The PCR of the pulse is 4200 (630 ns/0.15 ns), verifying that the TBWP is improved by 252 times.

Wireless communication for dual users
In this section, the capability of this scheme to generate dual-band phase-coded LFM signals and perform phase demodulation on the optical domain is demonstrated. A 3 ~ 5 GHz, 10 ns LFM waveform train is generated by the AWG, binary sequences "1,001,011,010" and "0,010,001,011" with identical bit rate of 0.1 Gbit/s are provided by PPG1 and PPG2, respectively. The modulation index of both sub-MZMs in DPol-MZM1 is set as 1.57. of two waveforms with time windows from 0 to 1 ns and 10 to 11 ns is shown in Fig. 11b, a 90°phase shift can be observed. Figure 11d shows the zoom-in and overlapped view of two waveforms for the bandwidth-quadrupled phase-coded signal, a 90° phase shift also exists. Consequently, phase modulation is successfully performed. Figure 12a and c show the normalized binary signals provided by PPG1 and PPG2, while the phase-demodulated waveforms of each band are shown in Fig. 12b and d. Obviously, the phase information is recovered, and optical demodulation is successfully achieved.
As can be seen, the proposed scheme is capable of achieving wireless communication in two bands, which can support independent communication for two users.

Conclusion
A photonic approach to generate a dual-band phase-coded LFM signal is proposed and demonstrated. Bandwidth-doubled and quadrupled LFM waveforms modulated by different binary sequences are simultaneously generated. Optical de-chirping and phase demodulation are also achieved. The proposed scheme is verified by simulation. The results show that 6 ~ 10 GHz and 12 ~ 20 GHz LFM waveforms are generated with a 3 ~ 5 GHz driving signal. Changing the chirp range of the driving signal to 3 ~ 6.5 GHz and 4 ~ 5 GHz, frequency-doubled and quadrupled LFM signals can also be obtained, which shows the good tunability of the proposed generator. For radar detection, optical de-chirping to an echo signal of a target 15 m away is performed, and the de-chirp results in each band are 79.96 MHz and 160.11 MHz, which are consistent with the theoretical values. By setting the binary sequences as 31-length and 63-length M sequences, the TBWPs of the generated dual-band signals are respectively improved by 62 and 252 times. Application on wireless