Narrowband Signals Research Articles

Robust Wideband Adaptive Beamforming by Convolutional Neural Network Structures in an Array System

The structure of arrays capable of receiving wideband signals differs from arrays which can only receive narrowband signals. These arrays should be capable of receiving several GHz instant bandwidth signals over the entire operating frequency, like High Resolution Radars or Terahertz in 6G communication systems. In these arrays, the number of beamformer coefficients increase due to using a time delay line structure, hence leading to a high computational complexity. This is one of the challenges of beamforming in wideband systems. Additionally, there are other factors in classic Wideband beamformers. These factors include poor performance against input DOA (direction of arrival) error, array calibration error, and too many snapshots to reach the steady state of the beamformer. Therefore, this paper focuses on the robustness of beamforming using deep learning technique, which has not been discussed before. The basis of network design is convolutional layers. Two different proposed approaches have been proposed to obtain optimal structure. In the first approach, appropriate values of hyperparameters are estimated, whereas the network model is selected in the second approach. Also, the network training method is done to become more robust against the mentioned factors. In the proposed structures, the constraints of the previous methods have been evaluated. The proposed structure is shown to have a superior performance when compared with other existing algorithms. In addition, the matrix of signal samples is replaced with the covariance matrix at the network's input, so the calculation time is significantly improved compared to the previous methods.

A Search for Technosignatures Around 11,680 Stars with the Green Bank Telescope at 1.15–1.73 GHz

We conducted a search for narrowband radio signals over four observing sessions in 2020–2023 with the L-band receiver (1.15–1.73 GHz) of the 100 m diameter Green Bank Telescope. We pointed the telescope in the directions of 62 TESS Objects of Interest, capturing radio emissions from a total of ∼11,680 stars and planetary systems in the ∼9′ beam of the telescope. All detections were either automatically rejected or visually inspected and confirmed to be of anthropogenic nature. We also quantified the end-to-end efficiency of radio SETI pipelines with a signal injection and recovery analysis. The UCLA SETI pipeline recovers 94.0% of the injected signals over the usable frequency range of the receiver and 98.7% of the injections when regions of dense radio frequency interference are excluded. In another pipeline that uses incoherent sums of 51 consecutive spectra, the recovery rate is ∼15 times smaller at ∼6%. The pipeline efficiency affects calculations of transmitter prevalence and SETI search volume. Accordingly, we developed an improved Drake figure of merit and a formalism to place upper limits on transmitter prevalence that take the pipeline efficiency and transmitter duty cycle into account. Based on our observations, we can state at the 95% confidence level that fewer than 6.6% of stars within 100 pc host a transmitter that is continuously transmitting a narrowband signal with an equivalent isotropic radiated power (EIRP) > 1013 W. For stars within 20,000 ly, the fraction of stars with detectable transmitters (EIRP > 5 × 1016 W) is at most 3 × 10−4. Finally, we showed that the UCLA SETI pipeline natively detects the signals detected with AI techniques by Ma et al.

The Effectiveness of Least Mean Squared-Based Adaptive Algorithms for Active Noise Control System in a Small Confined Space

Active noise control (ANC) is a technique applied to eliminate an unwanted sound by superposing a signal of equal amplitude and opposite phase, sometimes defined as an anti-noise signal, computed through an adaptive algorithm. The study described herein aims to evaluate and compare the performance of some of the most popular algorithms based on the least mean squares (LMS) approach applied to a multichannel active noise control system in a small, enclosed space. The comparison is conducted through an experimental evaluation of the ANC algorithms’ performance, carried out on a tractor cabin in a hemi-anechoic chamber, generating the unwanted sound field using a dodecahedron sound source placed outside the enclosure, emitting narrowband and broadband signals. The experimental analysis and the comparison with the results obtained in a free field condition have made it possible to show certain practical limitations when implementing the algorithms. The results show that the feed-forward systems allow for greater stability, avoiding the acoustic feedback from the control loudspeakers to the reference microphone when this is outside the cabin, while the feedback system is the slowest configuration to converge, requiring an internal modeling of the reference signal. With random signals, the feed-forward systems concentrate their performance in the range above 500 Hz, while the feedback system becomes ineffective.

The Most Sensitive SETI Observations Toward Barnard's Star with FAST

Search for extraterrestrial intelligence (SETI) has been mainly focused on nearby stars and their planets in recent years. Barnard’s star is the second closest star system to the Sun and the closest star in the Five-hundred-meter Aperture Spherical radio Telescope (FAST) observable sky which makes the minimum Equivalent Isotropic Radiated Power required for a hypothetical radio transmitter from Barnard’s star to be detected by FAST telescope a mere 4.36 × 108 W. In this paper, we present the FAST telescope as the most sensitive instrument for radio SETI observations toward nearby star systems and conduct a series of observations to Barnard’s star (GJ 699). By applying the multibeam coincidence matching strategy on the FAST telescope, we search for narrow-band signals (∼Hz) in the frequency range of 1.05–1.45 GHz, and two orthogonal linear polarization directions are recorded. Despite finding no evidence of radio technosignatures in our series of observations, we have developed predictions regarding the hypothetical extraterrestrial intelligence signal originating from Barnard’s star. These predictions are based on the star’s physical properties and our observation strategy.

Direction-of-arrival and power spectral density estimation using a single directional microphone and group-sparse optimization

In this paper, two approaches are proposed for estimating the direction of arrival (DOA) and power spectral density (PSD) of stationary point sources by using a single, rotating, directional microphone. These approaches are based on a method previously presented by the authors, in which point source DOAs were estimated by using a broadband signal model and solving a group-sparse optimization problem, where the number of observations made by the rotating directional microphone can be lower than the number of candidate DOAs in an angular grid. The DOA estimation is followed by the estimation of the sources’ PSDs through the solution of an overdetermined least squares problem. The first approach proposed in this paper includes the use of an additional nonnegativity constraint on the residual noise term when solving the group-sparse optimization problem and is referred to as the Group Lasso Least Squares (GL-LS) approach. The second proposed approach, in addition to the new nonnegativity constraint, employs a narrowband signal model when building the linear system of equations used for formulating the group-sparse optimization problem, where the DOAs and PSDs can be jointly estimated by iterative, group-wise reweighting. This is referred to as the Group-Lasso with l_1-reweighting (GL-L1) approach. Both proposed approaches are implemented using the alternating direction method of multipliers (ADMM), and their performance is evaluated through simulations in which different setup conditions are considered, ranging from different types of model mismatch to variations in the acoustic scene and microphone directivity pattern. The results obtained show that in a scenario involving a microphone response mismatch between observed data and the signal model used, having the additional nonnegativity constraint on the residual noise can improve the DOA estimation for the case of GL-LS and the PSD estimation for the case of GL-L1. Moreover, the GL-L1 approach can present an advantage over GL-LS in terms of DOA estimation performance in scenarios with low SNR or where multiple sources are closely located to each other. Finally, it is shown that having the least squares PSD re-estimation step is beneficial in most scenarios, such that GL-LS outperformed GL-L1 in terms of PSD estimation errors.

3D Localization With a Single Partially-Connected Receiving RIS: Positioning Error Analysis and Algorithmic Design

In this paper, we introduce the concept of partially-connected receiving reconfigurable intelligent surfaces (R-RISs), which refers to metasurfaces designed to efficiently sense electromagnetic waveforms impinging on them, and perform localization of the users emitting them. The presented R-RIS hardware architecture comprises subarrays of meta-atoms, with each of them incorporating a waveguide assigned to direct the waveforms reaching its meta-atoms to a reception radio-frequency (RF) chain, enabling signal/channel parameter estimation. We particularly focus on the scenarios where the user is located in the far-field of all the R-RIS subarrays, and present a three-dimensional (3D) localization method which is based on narrowband signaling and angle of arrival (AoA) estimates of the impinging signals at each single-receive-RF R-RIS subarray. For the AoA estimation, which relies on spatially sampled versions of the received signals via each subarray's phase configuration of meta-atoms, we devise an off-grid atomic norm minimization approach, which is followed by subspace-based root multiple signal classification (MUSIC). The AoA estimates are finally combined via a least-squared line intersection method to obtain the position coordinates of a user emitting synchronized localization pilots. Our derived theoretical Cramér Rao lower bounds (CRLBs) on the estimation parameters, which are compared with extensive computer simulation results of our localization approach, verify the effectiveness of the proposed R-RIS-empowered 3D localization system, which is showcased to offer cm-level positioning accuracy. Our comprehensive performance evaluations also demonstrate the impact of various system parameters on the localization performance, namely the training overhead and the distance between the R-RIS and the user, as well as the spacing among the R-RIS's subarrays and its partitioning patterns.

A Re-configurable Body Channel Transceiver towards Wearable and Flexible Biomedical Sensor Networks.

Body channel communication (BCC) has become a promising candidate in wireless body area networks (WBAN) due to its advantages in energy efficiency and security. However, BCC transceivers face two challenges: diverse application requirements and varying channel conditions. To overcome these challenges, this paper proposes a re-configurable architecture for BCC transceivers (TRXs), whose key parameters and communication protocols can be software-defined (SD) according to the requirements. In the proposed TRX, the programmable direct-sampling receiver (RX) is a combination of a programmable low-noise amplifier (LNA) and a fast-convergent successive approaching register analog-to-digital converter (SAR ADC), to achieve simple but energy-efficient data reception. The programmable digital transmitter (TX) is essentially implemented by a 2-bit DAC array to transmit either wide-band carrier-free signals like 4-level pulse amplitude modulation (PAM-4) or non-return-to-zero (NRZ) or narrow-band carrier-based signals like on-off keying (OOK) or frequency shift keying (FSK). The proposed BCC TRX is fabricated in a 180-nm CMOS process. Through an in-vivo experiment, it achieves up to 10-Mbps data rate and 119.2 pJ/bit energy efficiency. Moreover, the TRX is able to communicate under long-distance (1.5 m) and body-shielding conditions by switching its protocols, which shows the potential to be deployed in all categories of WBAN applications.

High-resolution on-chip spatial heterodyne Fourier transform spectrometer based on artificial neural network and PCSBL reconstruction algorithm.

A novel compact on-chip Fourier transform (FT) spectrometer has been proposed based on the silicon-on-insulator (SOI) platform with wide operating bandwidth and high resolution. The spectrometer consists of a 16-channel power splitter and a Mach-Zehnder interferometer (MZI) array of 16 MZIs with linearly increasing optical path length (OPL) difference. We have also developed a spectral retrieval algorithm based on the pattern-coupled sparse Bayesian learning (PCSBL) algorithm and artificial neural network (ANN). The experimental results show that the designed spectrometer has a flat transmission characteristic in the wavelength range between 1500 nm and 1600 nm, indicating that the device has a wide operating bandwidth of 100 nm. In addition, with the assistance of the spectral retrieval algorithm, our spectrometer has the ability to reconstruct narrowband signals with full width at half maximum (FWHM) of 0.5 nm and a triple-peaked signal separated by a 3-nm distance.

Coherent stepped-frequency waveform generation based on recirculating microwave photonic frequency conversion.

We propose a novel method for generating coherent and wideband stepped-frequency waveforms using recirculating microwave photonic frequency conversion (MWP-FC). By injecting a narrowband signal into an MWP-FC loop utilizing a dual-parallel Mach-Zehnder modulator (DPMZM), the signal frequency is continuously converted to produce a stepped-frequency waveform with a wide bandwidth. Within the MWP-FC loop, photo-electric conversion is achieved based on self-mixing detection, where the optical phase noise can be suppressed, guaranteeing stability and coherence of the generated signal. In a proof-of-concept experiment, a stepped-frequency signal with a frequency interval of 2 GHz and a bandwidth of about 16 GHz and a stepped-frequency chirp signal with a frequency interval of 3 GHz and a bandwidth of about 15 GHz are generated. In addition, coherence of the generated signals is verified by coherent integration and de-chirping.

An all-pass based internal model principle controller for galvanometer mirror steering

Galvanometer is a critical component for beam steering in additive manufacturing, profilometry, and medical imaging. In these applications, the quality of the process relies on the precision motion control of the galvanometer to either track or reject narrow-band signals. From the internal model principle, this can be accomplished by incorporating the dynamic model of the reference or disturbance signal in the feedback loop. This paper proposes an innovative internal model principle controller based on numerically robust all-pass filters. The main concept revolves around converting the controller design into a phase response design problem with all-pass filters. For the proposed approach, the targeted frequencies of the internal model can be arbitrarily placed without sacrificing the performance. Further, it produces lower-order controller and is robust against quantization effect. When combining with frequency estimation algorithm and adaptive filter, it can be readily applied to unknown and time-varying disturbance rejection. The advantages of the proposed method are demonstrated by comparing with conventional approaches through analysis, simulation, and experimentation.

Real-time low latency estimation of brain rhythms with deep neural networks

Objective. Neurofeedback and brain-computer interfacing technology open the exciting opportunity for establishing interactive closed-loop real-time communication with the human brain. This requires interpreting brain’s rhythmic activity and generating timely feedback to the brain. Lower delay between neuronal events and the appropriate feedback increases the efficacy of such interaction. Novel more efficient approaches capable of tracking brain rhythm’s phase and envelope are needed for scenarios that entail instantaneous interaction with the brain circuits. Approach. Isolating narrow-band signals incurs fundamental delays. To some extent they can be compensated using forecasting models. Given the high quality of modern time series forecasting neural networks we explored their utility for low-latency extraction of brain rhythm parameters. We tested five neural networks with conceptually distinct architectures in forecasting synthetic EEG rhythms. The strongest architecture was then trained to simultaneously filter and forecast EEG data. We compared it against the state-of-the-art techniques using synthetic and real data from 25 subjects. Main results. The temporal convolutional network (TCN) remained the strongest forecasting model that achieved in the majority of testing scenarios 90% rhythm’s envelope correlation with 10 ms effective delay and circular standard deviation of phase estimates. It also remained stable enough to noise level perturbations. Trained to filter and predict the TCN outperformed the cFIR, the Kalman filter based state-space estimation technique and remained on par with the larger Conv-TasNet architecture. Significance. Here we have for the first time demonstrated the utility of the neural network approach for low-latency narrow-band filtering of brain activity signals. Our proposed approach coupled with efficient implementation enhances the effectiveness of brain-state dependent paradigms across various applications. Moreover, our framework for forecasting EEG signals holds promise for investigating the predictability of brain activity, providing valuable insights into the fundamental questions surrounding the functional organization and hierarchical information processing properties of the brain.

Underwater Sound Detection Thresholds (0.031-80 kHz) of Two California Sea Lions (Zalophus californianus) and a Revised Generic Audiogram for the Species

Unmasked behavioral audiograms of two California sea lions (Zalophus californianus), an adult female (F01) and a subadult male (M02), were recorded using narrow-band frequency-modulated hearing test signals. Signals had a duration of 1 s and center frequencies ranging from 0.031 to 80 kHz. Hearing thresholds were measured by varying test signal amplitude according to the up-down staircase method. The resulting underwater audiograms (50% detection thresholds) of the two sea lions were similar and showed the typical mammalian U-shape. Maximum hearing sensitivity (58 and 57 dB re 1 mPa) occurred at 11.3 kHz for F01 and at 8 kHz for M02, respectively. The range of best hearing (defined as < 10 dB from the maximum sensitivity) was from 1 to 16 kHz (four octaves). The detection thresholds for hearing test signal frequencies 0.031, 0.040, and 0.050 kHz were lower than expected, possibly caused by a shift in perceptional modality from auditory to vibrotactile, or due to the difficulty in measuring accurate SPLs of such low frequencies in a pool. Measurements of particle motion deemed detection of these very low frequencies via the vibrissae unlikely. The present study extends the frequency range for which the hearing of California sea lions has been tested. Based on the two audiograms of the present study and audiograms reported by Reichmuth et al. (2013) and Cunningham & Reichmuth (2016), a revised generic audiogram for California sea lions is proposed.

Classification of Motor Imagery Using Trial Extension in Spatial Domain with Rhythmic Components of EEG

Electrical activities of the human brain can be recorded with electroencephalography (EEG). To characterize motor imagery (MI) tasks for brain–computer interface (BCI) implementation is an easy and cost-effective tool. The MI task is represented by a short-time trial of multichannel EEG. In this paper, the signal of each channel of raw EEG is decomposed into a finite set of narrowband signals using a Fourier-transformation-based bandpass filter. Rhythmic components of EEG are represented by each of the narrowband signals that characterize the brain activities related to MI tasks. The subband signals are arranged to extend the dimension of the EEG trial in the spatial domain. The spatial features are extracted from the set of extended trials using a common spatial pattern (CSP). An optimum number of features are employed to classify the motor imagery tasks using an artificial neural network. An integrated approach with full-band and narrowband signals is implemented to derive discriminative features for MI classification. In addition, the subject-dependent parameter optimization scheme enhances the performance of the proposed method. The performance evaluation of the proposed method is obtained using two publicly available benchmark datasets (Dataset I and Dataset II). The experimental results in terms of classification accuracy (93.88% with Dataset I and 91.55% with Dataset II) show that it performs better than the recently developed algorithms. The enhanced MI classification accuracy is very much applicable in BCI implementation.

Integrated Microring Spectrometer with In‐Hardware Compressed Sensing to Break the Resolution‐Bandwidth Limit for General Continuous Spectrum Analysis

AbstractMicrospectrometers have numerous applications in mobile optical sensing due to their dramatic advantages of compact size, light weight, and low power consumption. Reconstructive spectrometers, based on computational algorithms, have garnered considerable interest as they exhibit superior resolution or spectral bandwidth. However, existing reconstructive spectrometer designs face challenges in spectral applicability, algorithm robustness, and the resolution‐bandwidth limit. Here, a reconstructive spectrometer that utilizes a microring resonator (MRR) is proposed to achieve compressed sensing in hardware by decomposing an arbitrary continuous spectrum into a series of simple comb spectra. Owing to the presparse operation of the MRR, one needs to construct the comb spectra with a known line shape, only leaving the amplitude to be solved. Consequent random gratings measure the comb spectra, which are reconstructed with high robustness. Thanks to the independent engineering of spectral resolution and bandwidth, the approach breaks the traditional resolution‐bandwidth limit. A narrowband signal of a dual peak at 0.2 nm and a broadband spectrum with a large spectral bandwidth of 60 nm and 300 spectral channels using only eight physical channels is retrieved, achieving an ultrahigh reconstructive compression ratio of 37.5. This work opens up the possibility of on‐site spectral spectroscopy applications for the lab‐on‐a‐chip system.

Machine-Learning-Assisted Cyclostationary Spectral Analysis for Joint Signal Classification and Jammer Detection at the Physical Layer of Cognitive Radio.

Cognitive radio technology was introduced as a possible solution for spectrum scarcity by exploiting dynamic spectrum access. In the last two decades, most researchers focused on enabling cognitive radios for managing the spectrum. However, due to their intelligent nature, cognitive radios can scan the radio frequency environment and change their transmission parameters accordingly on-the-fly. Such capabilities make it suitable for the design of both advanced jamming and anti-jamming systems. In this context, our work presents a novel, robust algorithm for spectrum characterisation in wideband radios. The proposed algorithm considers that a wideband spectrum is sensed by a cognitive radio terminal. The wideband is constituted of different narrowband signals that could either be licit signals or signals jammed by stealthy jammers. Cyclostationary feature detection is adopted to measure the spectral correlation density function of each narrowband signal. Then, cyclic and angular frequency profiles are obtained from the spectral correlation density function, concatenated, and used as the feature sets for the artificial neural network, which characterise each narrowband signal as a licit signal with a particular modulation scheme or a signal jammed by a specific stealthy jammer. The algorithm is tested under both multi-tone and modulated stealthy jamming attacks. Results show that the classification accuracy of our novel algorithm is superior when compared with recently proposed signal classifications and jamming detection algorithms. The applications of the algorithm can be found in both commercial and military communication systems.

Vulnerability of Smart Grid-enabled Protection Relays to IEMI

Abstract. The electricity sector has been undergoing transformations towards the smart grid concept, which aims to improve the robustness, efficiency, and flexibility of the power system. This transition has been achieved by the introduction of smart electronic devices (SEDs) and advanced automatic control and communication systems. Despite the benefits of such modernization, safety issues have emerged with significant concern by experts and entities worldwide. One of these issues is known as Intentional Electromagnetic Interference (IEMI), where offenders employ high-power electromagnetic sources to maliciously disrupt or damage electronic devices. One of the possible gateways for IEMI attacks targeting the smart grids is the microprocessor-based protection relays. On the one hand, the malfunctioning of these devices can lead to equipment damage, including high-voltage equipment (e.g., power transformers), which represent one of the most high-cost items of energy infrastructure. On the other hand, a possible misleading triggering of these devices could cause cascading effects along the various nodes of the power system, resulting in widespread blackouts. Thus, this study presents the possible recurring effects of IEMI exposure of a typical protection relay used in smart grid substations as part of the SCADA (Supervisory Control and Data Acquisition) system. For this purpose, a test setup containing a smart grid protective unit, a monitoring box, and the device's wiring harness is exposed to radiated IEMI threats with high-power narrowband signals using a TEM waveguide and horn antennas. The effects during the test campaigns are observed by means of an IEMI-hardened camera system and a software developed to real-time monitor the device's fibre optic communication link, which is established according to the IEC 60870-5-105 protocol. The results revealed failures ranging from display deviation to various types of protection relay shutdown. Moreover, the consequences of the identified failures in a power substation are discussed to feed into a risk analysis regarding the threat of IEMI to power infrastructures.

Multi-transversal mode pumping of narrow-bandwidth backward wave optical parametric oscillator.

A stable, narrow-bandwidth (274 MHz) backward wave optical parametric oscillator (BWOPO) generating mJ-level backward signal at 1885nm and forward idler at 2495 nm is presented. The BWOPO was pumped by a single-longitudinal mode, Q-switched Nd:YAG high-energy laser at 1064 nm. We show that multi-transversal mode pumping leads to the spectral broadening of the BWOPO backward signal and the generation of nanosecond pulses 2.7 times above the Fourier transform limit. We demonstrate over 100 GHz continuous tuning of the parametric output by adjusting the temperature of the BWOPO crystal, showcasing the significant role of thermal expansion in tuning performance. The BWOPO signal was used as a seed for a single-stage PPRKTP optical parametric amplifier (OPA) to boost the narrowband signal and idler energies to 20 mJ. This combination of mJ-level BWOPO seed with a single-stage PPRKTP OPA comprises a simple concept that would benefit long-range differential absorption lidar (DIAL) in the near and mid-infrared regions.

On Detecting Interstellar Scintillation in Narrowband Radio SETI

To date, the search for radio technosignatures has focused on sky location as a primary discriminant between technosignature candidates and anthropogenic radio frequency interference (RFI). In this work, we investigate the possibility of searching for technosignatures by identifying the presence and nature of intensity scintillations arising from the turbulent, ionized plasma of the interstellar medium. Past works have detailed how interstellar scattering can both enhance and diminish the detectability of narrowband radio signals. We use the NE2001 Galactic free electron density model to estimate scintillation timescales to which narrowband signal searches would be sensitive, and discuss ways in which we might practically detect strong intensity scintillations in detected signals. We further analyze the RFI environment of the Robert C. Byrd Green Bank Telescope with the proposed methodology and comment on the feasibility of using scintillation as a filter for technosignature candidates.

Passive Tone Detection for Moving Targets Based on Long-Time Coherent Integration

The detection of sinusoidal signals embedded in noise is an important topic in passive sonar signal processing. The performance of existing tone detection techniques is limited by the Doppler frequency shift, which is caused by the relative motion between moving targets and the receiver. In this study, an algorithm based on long-time coherent integration is proposed to achieve robust tonal signal detection under the influence of a Doppler frequency shift. First, the received narrowband signals radiated by moving targets are split into multiple segments through a window-length constraint. The results obtained by applying a discrete Fourier transform (DFT) to the data segments are modeled as a polynomial phase signal in the frequency domain. Then, the polynomial Radon-polynomial Fourier transform (PRPFT) is applied to simultaneously compensate the time-variant frequency drift and phase difference. To avoid the gain loss due to the discretization of the phase difference compensation in PRPFT, a phase compensation factor searching algorithm is proposed. The simulation results show that the proposed algorithm can provide higher frequency resolution and higher coherent integration gain even in the case of a severe Doppler shift. Furthermore, the results of sea trials demonstrate that the proposed method can perfectly achieve coherent integration for signals with a duration of several hundred seconds under different experimental conditions.

Passive depth estimation for a narrowband source using a single vector sensor in deep water.

For a narrowband signal, an oscillating interference pattern is formed with a target's moving when receiving at the bottom of the sea. In this Letter, the interference pattern of a narrowband source is observed using a single vector sensor (SVS). A passive depth estimation method employing a SVS is proposed. This approach processes the signals after the adaptive line enhancing and extracts the vector intensity, which oscillates periodically with the vertical azimuth. The passive estimation is achieved based on the Fourier-transform relationship between the depth and interference period. The simulation and sea experiment verify this method.