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Abstract
The measurement accuracy of a Brillouin optical time domain analysis (BOTDA) fiber sensor is determined by the signal-to-noise ratio (SNR) of the received sensing signal. Here, a new hybrid aperiodic coding method is proposed to improve the SNR. In the proposed method, two pre-discovered short seed aperiodic codes (SA-codes) are used to construct a new hybrid aperiodic code (HA-code) in a nested way. The HA-code inherits the good denoising capabilities of the two SA-codes and features a high coding gain. In the proof-of-concept experiment, a SNR improvement up to 8 dB is obtained, which improves the measurement certainty to 1.67 MHz over a 117.46 km sensing range under a spatial resolution of 2.6 m.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Brillouin-based distributed optical fiber sensors have attracted a great deal of attention in the past few decades due to their capabilities to measure physical quantities, such as strain and temperature, along the fiber [1,2]. Among them, Brillouin optical time domain analysis (BOTDA) is intensively investigated and widely applicated due to its superior properties including long sensing distance, high spatial resolution, fast acquisition speed and high accuracy [3–6]. Generally, measurement certainty of a BOTDA is determined by signal-to-noise ratio (SNR) of received sensing signal. Due to inherent fiber loss, the SNR decreases exponentially. As a result, acceptable measurement precision cannot be achieved in ultra-long-distance sensing. Although the improvement of pump and probe power can enhance the SNR, maximal improvement factors are limited by the onsets of nonlinear effects [7,8] and non-local effect [9–11], respectively.
To further improve the SNR, lots of research efforts have been made in recently years. According to the purposes, they can be classified into three kinds: 1) Signal amplification: To boost the degraded pump and probe power, distributed (Brillouin/Raman) and lumped (in-line EDFA) amplification techniques are proposed [12–15]; 2) Noise suppression: Reducing the noise is also an effective way to enhance the SNR. For this goal, optical pulse coding (OPC) [16–22], digital signal processing [23,24] and balanced/coherent detections [25,26] are proposed; 3) Combination of the above methods [27,28]. Particularly, the unipolar unicolor OPC methods are treated to be more promising since they can boost the SNR by a factor $\sqrt {{L_c}} /2$ (Lc is the coding length) with unimpaired spatial resolution by simply replacing the single pulse into the coding sequences [16–21,29]. Moreover, with the discovery and overcoming of detrimental impacts including high-order non-local effect, polarization pulling, EDFA transient effect, optical noise and so on [29–33], the performance of the OPC is further consolidated.
Nevertheless, the current OPC methods (Simplex, Golay and Cyclic codes) [17,19,21] still face many challenges [33,34]: 1) long measurement time due to codeword switching and low real-time capability due to large data volume in the Simplex and Golay coding schemes; 2) intolerance to baseline fluctuations and globally high optical noise in the Cyclic coding [33] and 3) due to the given coding rules, all these coding methods cannot reach arbitrary energy enhancement factor FE (${F_E} = \sum _{n = 1}^{{L_c}}c(n )$, c(n) denotes the coding sequence, Lc is the coding length) according to the need of system configurations and sensing tasks. Fortunately, a favorable turn has been appeared as the proposal of a new genetic-optimized aperiodic coding (GO-code) technique [34]. In this technique, dedicatedly selected aperiodic code with deconvolution process enables the decoding to be achieved in one-shot measurement. As a result, the codeword switching time and data volume are minimized, and fast acquisition speed and high real-time capability can be reached. Meanwhile, as the duration of aperiodic code is shorter than the fiber length, probe baseline fluctuations can be eliminated by trace normalization [29] and the optical noise is highly suppressed at the far end of the fiber [33]. More importantly, the aperiodic codes with arbitrary energy enhancement factors (FE) can be flexibly achieved, which enables the coding scheme to be adaptable for various applications and systems. Besides the impressive improvements, the results are also exciting: 0.63 MHz measurement certainty is experimentally demonstrated over 100 km sensing range [34].
However, not all aperiodic codes can be adopted for denoising. Only few of the codes can reach satisfactory denoising capabilities (i.e., coding gains). In order to find these denoising aperiodic codes, distributed genetic optimization (DGA) searching algorithm is adopted in Ref. [34]. Although the DGA searching is found to be more efficient than brute-force searching, the searching process is still time-consuming (∼135 minutes for the code with energy enhancement factor of 40). The searching time would be longer with the increase of energy enhancement factors and coding lengths. Meanwhile, the DGA searching efficiency and quality depend on various factors including 1) the selection of population number, crossover probability, number of alternating segments, mutation probability and so on, 2) the quality of initial populations (random and uncontrollable) and 3) target energy enhancement factors and coding lengths. High-quality searching is a complex process which needs professional knowledge. As such, it is highly desirable to find a new method that capable to directly generate the denoising aperiodic codes with high coding gains.
In this paper, we propose and demonstrate a simple method for direct generation of high coding gain aperiodic codes. This method includes 1) rapid generation of short seed aperiodic codes (SA-codes) through a simple and efficient acquired-learning (AL) algorithm and 2) direct generation of long hybrid aperiodic code (HA-code) through the combination of two existing SA-codes. The HA-code inherits good denoising capabilities of the two SA-codes and features a coding gain of Gc1•Gc2 (Gc1 and Gc2 are coding gains of the two SA-codes). In this way, target coding gain can be directly achieved by properly selecting the SA-codes and the laborious searching process is not needed. Experimental results reveal that a ∼8 dB SNR enhancement together with a ∼1.67 MHz measurement certainty over a 117.46 km sensing range with a spatial resolution of 2.6 m are achieved by using a HA-code with FE of 100.
2. Principle
The proposed method aims to directly generate a long hybrid aperiodic code (HA-code) with a high coding gain through the hybrid of two pre-discovered short seed aperiodic codes (SA-codes). Firstly, to generate the SA-codes rapidly, we present an acquired-learning (AL) algorithm. As mentioned in Ref. [34], randomly generated aperiodic sequences can hardly reach acceptable coding gains. The reason is that any defective distribution of the code will change the flatness of its frequency spectrum and result in the coding gain reduction. Thus, to enhance the coding gain, the key is to correct these defective coding distributions. Here, the AL algorithm is proposed for aperiodic code correction and obtaining the SA-codes with high coding gains.
Figure 1(a) shows the flow chart of the AL algorithm. The AL correction process contains the following main phases: 1) Replacing i-th bit of initial aperiodic code (c0) into the inversed one (0→1, 1→0) and becoming a new coding sequence c1; 2) Checking if the coding gain difference Gc1-Gc0 (in dB) is larger than the threshold value Vth. If so, assigning c1 to c0. Here, the coding gain (Gc=$\sqrt {1/Q} $) is calculated via noise scaling factor Q [34]. The Vth=(Gr1-Gr0)/R. The Gr1 and Gr0 are reference coding gains (in dB) of c1 and c0, respectively. The reference coding gain (Gr=$\sqrt {{F_E}/2} $, ${F_E} = \sum _{n = 1}^{{L_c}}c(n )$) is a numerical reference that denotes the coding gain offered by other traditional codes (such as Golay and Simplex) under the same energy enhancement factor FE [34]. R is an adjustment factor which is set as 0.8 to 1. The comparison between Gc1-Gc0 and Vth is extremely important since it guarantees a small difference between the Gc and Gr of the corrected code; 3) After replacing and checking each bit, one learning period completes. The last Gc0 will be compared with the initial coding gain Gc00. If the Gc0 is different from the Gc00, the above procedure will be repeated to see if the Gc0 can be further enhanced. On the other hand, if the Gc0 is equal to the Gc00, ending the correction process and outputting the denoising aperiodic code (i.e., seed code).
Fig. 1. (a) Flow chart of AL algorithm for aperiodic code correction. (b) Coding gain evolution during the AL. (c) Coding gain distributions of initial and corrected aperiodic codes. (d) Coding gain differences (Gc/Gr) in 10 repeated correction/searching processes. Lc: coding length.
It is worth noting that, 1) to avoid the picket fence effect-induced fake coding gain, the number of FFT points should be set as at least 8 times larger than the coding length (the more FFT points are used, the higher correction precision will be obtained) and 2) the only one parameter that needs to be adjusted in the AL algorithm is the R (0.8 ∼ 1). For higher FE, the lower R is more likely to reach better correction performance. Generally, by setting the R as 0.8, most of the aperiodic codes (FE from 10 to 100) can be corrected with desired performance, which makes the AL algorithm free from parameter adjustment.
Figure 1(b) illustrates the evolution of coding gain during the AL correction of an aperiodic code with a coding length Lc=240 and a FE=80 (Gr=8.0103 dB). Obviously, significant coding gain enhancements occur in the 1st and 2nd learning periods since the initial aperiodic code has the most defective distributions. After 10 learning periods, the denoising aperiodic code with the Gc=7.806 dB is reached. Furthermore, 10000 randomly generated aperiodic codes (with the same coding length and FE) are generated and corrected through the AL. The resulting coding gain distributions for both cases are shown in Fig. 1(c). It can be seen that the coding gains are averagely enhanced by ∼2.2 dB after the AL correction. Meanwhile, ∼0.2% of the corrected codes can reach the coding gains that are nearly the same as the reference coding gains (Gr-Gc < 0.25dB). This means that at least 500 initial aperiodic codes are needed for obtaining one or more corrected codes with high coding gains. Here, 3500 initial aperiodic codes are adopted for the SA-code generation. Finally, the stabilities of the AL and DGA are compared through 10 times repeated correction/searching processes. The number of FFT points for both cases is 4096. The R in AL is set as 0.8. The DGA and parameters are the same as that in Ref. [34] (EDFA fading = 0). Figure 1(d) illustrates the ratios between Gc and Gr in the two cases. The higher Gc/Gr means the smaller gap between them. It can be seen that the AL can obtain higher coding gains and stability than the DGA. Meanwhile, the processing time of the AL is ∼14 minutes which is averagely 7 times shorter than that of the DGA, indicating a higher efficiency.
Higher FE will bring higher coding gains. However, with the increase of FE and coding lengths, the correction time will increase accordingly, due to larger data volume and correction number. It is still a challenge to obtain the high coding gain aperiodic codes with the FE ranging from hundreds to thousands. To overcome this problem, our strategy is to obtain the short SA-codes rapidly through the AL, and then further generate long HA-code with a high coding gain directly through the combination of two existing SA-codes. This enables the target coding gain and FE to be achieved by properly selecting the two SA-codes. In the following, the generation and denoising-capability of the HA-code will be introduced.
The key of the hybrid process is the convolution between two SA-codes. This eventually enables the noise to be suppressed by the two SA-codes simultaneously. The schematic diagram of the HA-code generation and denoising is shown in Fig. 2. The two SA-codes are represented by N1- and N2-points discrete-time signals cSA-1(n) and cSA-2(n), respectively. The hybrid process includes two steps: 1) The SA-code1 is zeros-padded (inter-codeword) into the sequence with a length of N1•N2 (The zeros-padding will not affect the coding gain of SA-code1 and is an important procedure to generate the HA-code with a flat amplitude). The resulting coding sequence is represented by $c_{SA - 1}^{IC - ZP}(n)$; 2) The $c_{SA - 1}^{IC - ZP}(n)$ is then convoluted with SA-code2. After that, the HA-code is generated and given as follows
where cHA(n) is a N1•N2-points sequence and represents the generated HA-code. The resulting energy enhancement factor FE-HA= FE-SA1•FE-SA2. The HA-code is then converted into the optical pulse sequence with a specific pulse width and duty cycle. After pump-probe SBS interaction in the sensing fiber, the coded Brillouin signal can be expressed as where r(n) is the coded signal, pHA(n) is the HA-coded pulse sequence, h(n) is the fiber impulse response, e(n) is zero-mean additive white noise. ${p_{HA}}(n) = c_{HA}^{IC - ZP}(n) \otimes p(n)$, where $c_{HA}^{IC - ZP}(n)$ is inter-codeword zeros-padded cHA(n) (the zeros-padding in this case is used for the coded pulse sequence generation [34]), p(n) is a single pulse.Fig. 2. Schematic diagram of hybrid aperiodic code generation and denoising. cSA-1/-2(n): seed aperiodic code 1 or 2; cHA(n): hybrid aperiodic code; GSA-1/-2: coding gains of SA-code 1 or 2.
The decoding process completes in one-shot measurement, which bases on the deconvolution between the r(n) and cHA(n). The deconvolution is executed in frequency domain through fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) [34,35]. Before the decoding, logarithmic normalization should be implemented to eliminate the probe baseline fluctuation and extract the linear cumulated Brillouin gain signal [29]. Meanwhile, the cHA(n) should be 1) inter-codeword zeros-padded according to the pulse interval and data acquisition (DAQ) sample rate [34] and 2) tail zeros-padded according to the total length of the coded signal. After that, the deconvolution can be adopted to retrieve the single-pulse response s(n)=p(n)⊗h(n) and suppress the additive white noise as below
Figure 3 illustrates the coding gains corresponding to different FE. The SA-codes with FE ranging from 10 to 80 are obtained by using the AL. Then, the HA-codes with FE ranging from 90 to 200 are directly generated by properly combining the SA-codes with FE ranging from 9 to 20. Moreover, the acquired SA- and HA-codes are retested through numerical simulation. It can be seen that 1) the coding gains in simulation (Gc-sim) match well with the theorical gains (Gc-th); 2) From FE=10 to 200, the coding gains gradually increase from 4.14 to 9.54 dB with the mean value 0.24 dB lower than the reference coding gain. The results above indicate that the HA-codes can reach high coding gains. Moreover, the HA-codes with higher coding gains can be reached by using the SA-codes with higher FE.
3. Experimental setup
The experimental setup of the HA-coded BOTDA is shown in Fig. 4. The CW light is emitted from a narrow linewidth (∼100 kHz) external cavity laser (ECL) and then split into two branches by a 50:50 coupler. In the upper branch, the light wave is frequency up-/down-converted by an electric-optic modulator (EOM) working at a carrier-suppressed double-sideband modulation mode. The EOM is driven by radiofrequency (RF, sweeping from 10.78 GHz to 10.98 GHz with 2 MHz step) signals. After being frequency up-converted (200 MHz) by an acousto-optic frequency shifter (AOFS), the probe wave is injected into a fiber-under-test (FUT). The probe input power is around −17 dBm/sideband. The FUT is a 117.46-km standard single-mode fiber with the transmission attenuation of 0.2 dB/km. In the lower branch, the CW light is firstly amplified by a high-power erbium-ytterbium co-doped fiber amplifier (EYDFA) and then gated to an acousto-optic modulator (AOM, 200-MHz frequency up-conversion) to generate the HA-coded pump pulse sequence. The AOM is driven by an arbitrary function generator (AFG). By changing the single pulse and coded sequences in the AFG, the single-pulse and HA-coded BOTDA schemes can be easily switched. The extinction ratio of the AOM is 60 dB. The optical pulse width and duty cycle are 26 ns and 10.83%, respectively. The corresponding spatial resolution is 2.6 m. The pulse width of 26 ns is carefully chosen after comprehensively considering the Brillouin gain at the fiber far-end and spatial resolution. The duty cycle is set as low as 10.83% to avoid acoustic-wave crosstalk between adjacent pulses [16]. It is worth noting that, by using the AOFS to compensate the frequency shift introduced by the AOM, the system is a dual-sideband BOTDA which is robust to the pump depletion effect [9]. Then, to eliminate the impacts of polarization fading and polarization pulling, the state of polarization of pump pulse sequence is randomized by a polarization scrambler (PS) [29]. After that, the pump wave is sent to the receiver side by a circulator. The pump peak power is around 20 dBm (limited by the onset of MI [7,8]).
Fig. 4. Experimental setup of the HA-coded BOTDA. ECL: external cavity laser; PC: polarization controller; EOM: electric-optic modulator; MG: microwave generator; AOFS: acousto-optic frequency shifter; FUT: fiber-under-test; EYDFA: erbium-ytterbium co-doped fiber amplifier; AOM: acousto-optic modulator; AFG: arbitrary function generator; PS: polarization scrambler; EDFA: erbium-doped fiber amplifier; FBG: fiber Bragg grating; PD: photodiode; OSC: oscilloscope.
After propagated through the FUT and interacted with the pump, the probe wave is sent to the receiver by a circulator. In the receiver side, the probe wave is firstly pre-amplified by an erbium-doped fiber amplifier (EDFA) to compensate the transmission loss. Then, a narrowband fiber Bragg grating (FBG) is adopted to select the probe Stokes component (Brillouin gain configuration) and filter the out-of-band amplified spontaneous emission (ASE) noise. After that, the light wave is detected by a photodetector (PD). Finally, the detected electric signal is A/D converted by an oscilloscope (OSC) with a 100 MSa/s sample rate. To avoid PD saturation, the peak receiving power is properly adjusted by controlling the pulse width, duty cycle, energy enhancement factor and probe baseline power. It is worth noting that, due to large cumulated Brillouin gain, the coding scheme requires a large vertical range in the OSC (1.7 V for pulse-coding and 0.3 V for single-pulse) for overall coded Brillouin signal acquisition. While the vertical resolution of the OSC in our experiment is only 8-bit. This leads the decoded overall intrinsic Brillouin signal to be affected by digital quantization noise. To suppress the quantization noise for a fair SNR comparison between the single-pulse and pulse-coding schemes, the vertical range in the OSC is decreased to 0.3 V (the same as that in the single-pulse case). In this situation, the coded Brillouin signal from 8 to 38 km (cumulated Brillouin gain > 70%) is interrupted. Only the coded Brillouin signal after 58 km (38 km + Ls, Ls is the length of coded pulse sequence ≈ 20 km) has complete coding information. Accordingly, only the intrinsic Brillouin signal after 58 km can be correctly extracted (decoded) via the deconvolution. Notably, the quantization noise can be suppressed drastically and becomes negligible if a data-acquisition (DAQ) equipment with 12-bit (or higher) vertical resolution is used. In this case, the vertical range reduction is not needed.
4. Experimental results
In this section, the sensing performance of the HA-coded BOTDA is experimentally investigated. Considering the sensing range, spatial resolution, Brillouin gain, PD dynamic range and OSC vertical range/resolution in our system, the HA-code with FE=100 (SNR enhancement=8.05 dB) is chosen for experimental demonstration. The averaging number for the HA-code is 4096. To validate the coding gain obtained by the HA-code, the gain trace in the single-pulse BOTDA is averaged by 168000-times (compared with 4096-times averaging, the SNR is enhanced by ∼8.05 dB) for comparison. Figure 5(a) shows the linear cumulated Brillouin gain trace around the BFS (10.878 GHz). It can be seen that the peak linear cumulated Brillouin gain is ∼170%. After the decoding process, the decoded Brillouin gain trace at 10.878 GHz (around the BFS) is shown in Fig. 5(b). The detail from 18 to 22 km is depicted in Fig. 5(c). It can be seen that the decoded Brillouin signal matches well with the intrinsic Brillouin signal in the single-pulse case. This means that the HA-code can preserve the detail information well and owns a high decoding fidelity. Meanwhile, Fig. 5(d) shows the detail from 80 to 125 km, it can be observed that 1) the SNRs in both cases are the same. This means that the coding gain of ∼8.05 dB is totally achieved by the HA-code with FE of 100; 2) Thanks to the high noise suppression, the Brillouin signal at the far end of the fiber can be clearly discerned even though the Brillouin gain is only 0.01%.
Fig. 5. (a) Measured accumulated Brillouin gain trace in the HA-coding. (b) Measured intrinsic Brillouin gain trace in the single pulse case and decoded Brillouin gain trace in the HA-coding. Details from (c) 18 to 22 km and (d) 80 to 125 km. GB: Brillouin gain. The OSC vertical ranges for cases of single-pulse and HA-coding in 1) Fig. 5(a)–5(c) are 0.3 and 1.7 V, respectively, and 2) Fig. 5(d) are both 0.3 V.
Then, the measurement certainty of the HA-coded BOTDA is investigated. Here, the BGS distributions along the fiber are consecutively measured by 10 times. The BFS distributions corresponding to the 10 BGS distributions are estimated through Lorentz curve fitting, as illustrated in Fig. 6(a). The 117.46 km FUT is composed by three fiber segments with different properties (the length of each fiber segment is ∼40 km). As a result, the measured BFS distribution divides into three parts with different patterns. It can be observed that the 10 BFS distributions are totally aligned, which means that the HA-coded BOTDA owns a high sensing stability. By calculating the standard deviation value of the 10 BFSs at each location, the measurement uncertainty along the fiber is confirmed, as shown in Fig. 6(b). It can be found that, 1) from 0 to 117.46 km, the BFS uncertainty gradually increases from 0.09 to 1.65 MHz, due to inherent fiber loss; 2) Compared with the traditional codes (such as Golay [30,32]), the sensing stability at the fiber near-end is relatively high in the HA-coding, indicating a higher robustness to the polarization noise. This phenomenon results from that, in the HA-coding, the intrinsic Brillouin signal can be extracted after injecting only one coding sequence into the fiber. Thus, for a given total averaging number, the averaging number for each HA-coded trace is much larger than that in the traditional codes, which makes the coded signal get higher ergodicity of polarization scrambling and thus obtain a higher robustness to the polarization noise.
Fig. 6. (a) The 10 estimated BFS distributions along the fiber. (b) BFS uncertainty along the fiber. The BGSs before and after 60 km are acquired under the OSC vertical ranges of 1.7 and 0.3 V, respectively.
5. Conclusion
In conclusion, we have theoretically proposed and experimentally demonstrated a new HA-coding method for SNR improvement in the BOTDA. By combining two short SA-codes with good denoising capabilities, high coding gain denoising aperiodic codes (i.e., HA-codes) can be directly generated. Experimental results show the effectiveness of this approach. A ∼8 dB SNR improvement and ∼1.65 MHz measurement certainty over a 117.46 km sensing range with a spatial resolution of 2.6 m are achieved. The proposed method is expected to offer a higher level of sensing performance for other distributed fiber sensors. For instance, Rayleigh scattering-based sensors (such as OTDR [36] and φ-OTDR [37]) are expected to be boosted by the HA-codes with higher FE, since they do not need acoustic wave excitation and are not affected by some of the detrimental impacts occurred in the coded-BOTDA, such as optical noise and high-order non-local effect [29,33]. More investigations about the improvements of the HA-coding are expected in the near future. For instance, by using the SA-codes with higher coding gains or exploring other hybrid structures, the HA-codes with stronger denoising capabilities can be constructed. The HA-coding can be incorporated with other SNR enhancement techniques [11–15,23–26] to further improve the sensing accuracy and distance.
Funding
National Natural Science Foundation of China (61735015); Cultivation Program for the Excellent Doctoral Dissertation of Southwest Jiaotong University (2020YBPY05).
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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