Orthogonal Waveforms Research Articles

Orthogonal Waveform Design for MIMO Radar Using Deep Learning

Abstract This paper explores the design of orthogonal waveforms for multiple-input multiple-output (MIMO) radar. We combine the peak sidelobe level (PSL) with the omnidirectional beampattern matching as the optimization objective. To address this challenging non-linear and non-convex problem, we propose an unsupervised optimization network based on residual network and attention mechanism. This approach harnesses the potent nonlinear fitting capabilities of neural networks to address the complex optimization problem. Simulation results indicate that the waveforms designed by the algorithm proposed in this paper exhibit better orthogonality than those designed by the traditional algorithm.

Experimental study on identifying anomaly azimuth based on acoustic vector array of borehole acoustic reflection imaging

Accurate anomaly azimuth identification is a major challenge in borehole acoustic reflection imaging. We propose an azimuth estimation method using an acoustic vector array to address this issue. This method was rigorously tested through a physical simulation experiment in a water-filled tank using a monopole acoustic source and an acoustic receiver station comprised of eight azimuthal elements. The proposed method involves the synthesis of multiazimuth acoustic pressure waveforms recorded by the receiver into multicomponent particle velocity waveforms. These waveforms are paired and subjected to coordinate conversion, yielding multiple groups of orthogonal component particle velocity waveforms. Each group underwent polarization analysis to obtain the direction of particle polarization on the horizontal plane and isolate the principal component particle velocity waveform. Using the particle polarization direction, the amplitude of the multiazimuth acoustic pressure waveform, and the type of echo mode, we accurately determined the azimuth of the anomaly, facilitating the creation of a spatial distribution image of the anomaly. Further validation of this method was conducted through a large-scale physical simulation experiment in a deep-water lake using a borehole acoustic reflection imaging instrument. The obtained experimental data were used to validate the effectiveness of this method. Finally, considering an actual logging environment, the feasibility of this method in a borehole environment was verified using numerical simulations and field data of acoustic detection of nearby wells. The present findings demonstrate that this novel method considerably enhances the accuracy and stability of the measurement of anomaly azimuth based on the particle polarization direction. In addition, this method effectively harnesses both acoustic pressure and particle velocity in borehole acoustic reflection imaging, exhibiting superior noise robustness, mitigating noise, and improving the signal-to-noise ratio of the echoes.

Orthogonal waveform design with fractional programming on the ambiguity suppression of SAR systems

Orthogonal waveform design with fractional programming on the ambiguity suppression of SAR systems

Spatial–Temporal Joint Design and Optimization of Phase-Coded Waveform for MIMO Radar

By simultaneously transmitting multiple different waveform signals, a multiple-input multiple-output (MIMO) radar possesses higher degrees of freedom and potential in many aspects compared to a traditional phased-array radar. The spatial–temporal characteristics of waveforms are the key to determining their performance. In this paper, a transmitting waveform design method based on spatial–temporal joint (STJ) optimization for a MIMO radar is proposed, where waveforms are designed not only for beam-pattern matching (BPM) but also for minimizing the autocorrelation sidelobes (ACSLs) of the spatial synthesis signals (SSSs) in the directions of interest. Firstly, the STJ model is established, where the two-step strategy and least squares method are utilized for BPM, and the L2p-Norm of the ACSL is constructed as the criterion for temporal characteristics optimization. Secondly, by transforming it into an unconstrained optimization problem about the waveform phase and using the gradient descent (GD) algorithm, the hard, non-convex, high-dimensional, nonlinear optimization problem is solved efficiently. Finally, the method’s effectiveness is verified through numerical simulation. The results show that our method is suitable for both orthogonal and partial-correlation MIMO waveform designs and efficiently achieves better spatial–temporal characteristic performances simultaneously in comparison with existing methods.

Orthogonal waveform-based backscattering interference suppression technique for underwater optical wireless communication

The backscattering effects degrade the detection performance in a full-duplex underwater optical wireless communication (UOWC) system when the power of received backscattering interference is comparable to that of a target signal. In this paper, the orthogonal waveforms with the Hermite–Gaussian function and prolate spheroidal wave function are first introduced for a pulse position modulation based dynamic UOWC system to alleviate the backscattering effects. Then, a joint maximum likelihood detection scheme is proposed accordingly. Experimental results verify the superiority of the proposed method with orthogonal waveforms over the scheme without orthogonal pulse shaping in a dynamic underwater bubbly channel.

Optimal Design of Group Orthogonal Phase-Coded Waveforms for MIMO Radar

Digital radio frequency memory (DRFM) has emerged as an advanced technique to achieve a range of jamming signals, due to its capability to intercept waveforms within a short time. multiple-input multiple-output (MIMO) radars can transmit agile orthogonal waveform sets for different pulses to combat DRFM-based jamming, where any two groups of waveform sets are also orthogonal. In this article, a group orthogonal waveform optimal design model is formulated in order to combat DRFM-based jamming by flexibly designing waveforms for MIMO radars. Aiming at balancing the intra- and intergroup orthogonal performances, the objective function is defined as the weighted sum of the intra- and intergroup orthogonal performance metrics. To solve the formulated model, in this article, a group orthogonal waveform design algorithm is proposed. Based on a primal-dual-type method and proper relaxations, the proposed algorithm transforms the original problem into a series of simple subproblems. Numerical results demonstrate that the obtained group orthogonal waveforms have the ability to flexibly suppress DRFM-based deceptive jamming, which is not achievable using p-majorization–minimization (p-MM) and primal-dual, two of the most advanced orthogonal waveform design algorithms.

A High-Resolution Imaging Method for Multiple-Input Multiple-Output Sonar Based on Deterministic Compressed Sensing.

Differences between conventional sonar and Multiple-Input Multiple-Output (MIMO) sonar systems arise in achieving high angular and range resolution. MIMO sonar uses Matched Filtering (MF) with well-correlated transmitted signals to enhance spatial resolution by obtaining virtual arrays. However, imperfect correlation characteristics yield high sidelobe values, which hinder accurate target localization in underwater imagery. To address this, a Compressed Sensing (CS) method is proposed by reconstructing echo signals to suppress correlation noise between orthogonal waveforms. A shifted dictionary matrix and a deterministic Discrete Fourier Transform (DFT) measurement matrix are used to multiply received echo signals to yield compressed measurements. A sparse recovery algorithm is applied to optimize signal reconstruction before joint transmit-receive beamforming forms a 2D sonar image in the angle-range domain. Numerical simulations and lake experimental results confirm the effectiveness of the proposed method, by obtaining a lower sidelobe sonar image under sub-Nyquist sampling rates as compared with other approaches.

Simultaneous measurement of orthogonal terahertz fields via an emission multiplexing scheme.

We propose a polarization sensitive terahertz time-domain spectrometer that can record orthogonally polarized terahertz fields simultaneously, using fibre-coupled photoconductive antennas and a scheme that modulated the emitter's polarization. The s and p channels of the multi-pixel terahertz emitter were modulated at different frequencies, thereby allowing orthogonal waveforms to be demultiplexed from the recorded signal in post-processing. The performance of the multi-pixel emitter used in this multiplexing scheme was comparable to that of a commercial single-polarization H-dipole antenna. The approach allowed two orthogonally polarized terahertz pulses to be recorded with good signal to noise (>1000:1) within half a second. We verified the capability of the spectrometer by characterizing a birefringent crystal and by imaging a polarization-sensitive metamaterial. This work has significant potential to improve the speed of terahertz polarization sensitive applications, such as ellipsometry and imaging.

A Novel MIMO Radar Orthogonal Waveform Design Algorithm Based on the Multi-Objective Improved Archimedes Optimization Algorithm

Realization and enhancement of detection techniques for multiple-input–multiple-output (MIMO) radar systems require polyphase code sequences with excellent orthogonality characteristics. Therefore, orthogonal waveform design is the key to realizing MIMO radar. Conventional orthogonal waveform design methods fail to ensure acceptable orthogonal characteristics by individually optimizing the autocorrelation sidelobe peak level and the cross-correlation sidelobe peak level. In this basis, the multi-objective Archimedes optimization algorithm (MOIAOA) is proposed for orthogonal waveform optimization while simultaneously minimizing the total autocorrelation sidelobe peak energy and total cross-correlation peak energy. A novel optimal individual selection method is proposed to select those individuals that best match the weight vectors and lead the evolution of these individuals to their respective neighborhoods. Then, new exploration and development phases are introduced to improve the algorithm’s ability to increase its convergence speed and accuracy. Subsequently, novel incentive functions are formulated based on distinct evolutionary phases, followed by the introduction of a novel environmental selection method aimed at comprehensively enhancing the algorithm’s convergence and distribution. Finally, a weight updating method based on the shape of the frontier surface is proposed to dynamically correct the shape of the overall frontier, further enhancing the overall distribution. The results of experiments on the orthogonal waveform design show that the multi-objective improved Archimedes optimization algorithm (MOIAOA) achieves superior orthogonality, yielding lower total autocorrelation sidelobe peak energy and total cross-correlation peak energy than three established methods.

A Space–Time–Range Joint Adaptive Focusing and Detection Method for Multiple Input Multiple Output Radar

The Multiple Input Multiple Output (MIMO) radar, as a new type of radar, emits orthogonal waveforms, which provide it with waveform diversity characteristics, leading to increased degrees of freedom and improved target detection performance. However, it also poses challenges such as difficulty in meeting higher data demand, separating waveforms, and suppressing the multidimensional sidelobes (range sidelobes, Doppler sidelobes, and angle sidelobes) of targets. Phase-coded signals are frequently employed as orthogonal transmission signals in the MIMO radar. However, these signals exhibit poor Doppler sensitivity, and the intra-pulse Doppler frequency shift can have an impact on the effectiveness of the matching filtering process. To address the aforementioned concerns, this paper presents a novel approach called the Space–Time–Range Joint Adaptive Focusing and Detection (STRJAFD) method. The proposed method utilizes the Mean Square Error (MSE) criterion and integrates spatial, temporal, and waveform dimensions to achieve efficient adaptive focusing and detection of targets. The experimental results demonstrate that the proposed method outperforms conventional cascaded adaptive methods in effectively addressing the matching mismatch issue caused by Doppler frequency shift, achieving super-resolution focusing, possessing better suppression effects on three-dimensional sidelobes and clutter, and exhibiting better detection performance in low signal-to-clutter ratio and low signal-to-noise ratio environments. Furthermore, STRJAFD is unaffected by coherent sources and demands less data.

Design of Orthogonal Pulse Waveforms With Tunable Frequency and Bandwidth for Carrier-Free THz Communications

Carrier-free pulse-based waveforms are desired in terahertz (THz) communications since pulse-based systems have simpler transceiver architectures than carrier-based systems. For such a pulse-based THz communication system, there still lacks pulse waveforms that can support high-order modulation and flexible multiple access. In this paper, a pulse-based waveform with continuously tunable center frequencies and bandwidths is designed for carrier-free THz communications. More specifically, a Gaussian pulse is utilized as the basic pulse, and then the weighted sum of its high-order derivatives is used to generate waveforms with tunable frequencies and bandwidths according to the probability density function of Rice distribution. Such a pulse-based waveform is called frequency and bandwidth continuously tunable (FBCT) pulse. By making the derivative orders of all weighted terms odd or even, a pair of orthogonal FBCT pulses can be generated. Based on the pair of orthogonal FBCT pulses, a basic pulse-based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary quadrature amplitude modulation (P <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> QAM) scheme can be readily achieved. Moreover, with frequency and bandwidth tunability, FBCT pulse can support pulse division multiple access (PDMA) with tunable bandwidth, through which frequencies with high molecular absorption loss can be avoided. Numerical results demonstrate that FBCT pulse is significantly effective and flexible in supporting carrier-free THz communications.

Integrated Waveform Design Based on UAV MIMO Joint Radar Communication

The problem of orthogonal waveform construction in multiple input/multiple output (MIMO) radar communication integration greatly limits the realization of integration technology. In the unmanned aerial vehicle (UAV) MIMO antenna scenario, an orthogonal integrated waveform suitable for a MIMO antenna is designed using a sub−LFM−BPSK waveform combined with a chaotic spread spectrum code. After spread spectrum processing, each MIMO antenna transmits different communication data for orthogonal spread spectrum processing, which is suitable for the omnidirectional detection of MIMO application scenarios; moreover, the closed-form expressions of the integrated orthogonal waveform under certain constraints are derived. Finally, the simulation proves that the integrated orthogonal waveform set in the UAV MIMO scenario has excellent radar detection and communication capabilities.

Joint Design of Complementary Sequence and Receiving Filter with High Doppler Tolerance for Simultaneously Polarimetric Radar

Simultaneously polarimetric radar (SPR) realizes the rapid measurement of a target’s polarimetric scattering matrix by transmitting orthogonal radar waveforms of good ambiguity function (AF) properties and receiving their echoes via two orthogonal polarimetric channels at the same time, e.g., horizontal (H) and vertical (V) channels (antennas) sharing the same phase center. The orthogonality of the transmitted waveforms can be realized using low-correlated phase-coded sequences in the H and V channels. However, the Doppler tolerances of the waveforms composed by such coded sequences are usually quite low, and it is hard to meet the requirement of accurate measurement regarding moving targets. In this paper, a joint design approach for unimodular orthogonal complementary sequences along with the optimal receiving filter is proposed based on the majorization–minimization (MM) method via alternate iteration for obtaining simultaneously polarimetric waveforms (SPWs) of good orthogonality and of the desired AF. During design, the objective function used for minimizing the sum of the complementary integration sidelobe level (CISL) and the complementary integration isolation level (CIIL) is constructed under the mismatch constraint of signal-to-noise ratio (SNR) loss. Different SPW examples are given to show the superior performance of our design in comparison with other designs. Finally, practical experiments implemented with different SPWs are conducted to show our advantages more realistically.

Research on an Intra-Pulse Orthogonal Waveform and Methods Resisting Interrupted-Sampling Repeater Jamming within the Same Frequency Band

Interrupted-sampling repeater jamming (ISRJ) is a kind of intra-pulse coherent deception jamming that can generate false target peaks in the range profile and interfere with the detection and tracking of real targets. In this paper, an anti-ISRJ method based on the intra-pulse orthogonal waveform is proposed, which can recognize common interference signals by comparing sub-signal matched filtering results. For some special scenes where real targets cannot be directly differentiated from false targets, a new recognition method based on the energy discontinuity of the interference signal in the time domain is proposed in this paper. The method proposed in this paper can recognize real and false targets in all ISRJ modes without any prior information, such as jammer parameters, with a small amount of calculation, which is suitable for actual radar systems. Simulation experiments using different interference parameters show that although this method has a 3 dB loss of pulse compression gain, it can completely suppress different kinds of ISRJ interference when the SNR before pulse compression is higher than −20 dB, with 100% target detection probability.

Space time adaptive processing for airborne MIMO radar based on space time sampling matrix

Different from the traditional airborne single-input multi-output (SIMO) radar, each array element of airborne multiple-input multiple-output (MIMO) radar transmits mutually orthogonal waveforms, and multiple array elements receive at the same time. A set of matched filters are used to separate the transmitted waveforms in the echo signal. When the elements of the transmitting antenna are close to each other, the airborne MIMO radar can gain the benefit of waveform diversity and produce a large spatial virtual receiving array. It has certain advantages in signal-to-noise ratio, spatial degree of freedom (DoF) and spatial resolution. In this paper, the clutter DoF estimation formula of airborne MIMO radar is given and can accurately estimate the clutter DoF values under different parameters. On this basis, this paper proposes a space-time adaptive processing (STAP) method based on space-time sampling matrix. This method utilizes the low rank characteristic of clutter covariance matrix, constructs the clutter covariance matrix based on space-time sampling matrix, and estimates the clutter power through subaperture smoothing. In the non-homogeneous clutter background, the method only needs a single sample to effectively suppress clutter. In the homogeneous clutter background, as the space-time equivalent array is a dense non-uniform array, the robustness of the method is further improved by adding a small amount of training sample information.

Phase response similarity based waveform design for FDA-MIMO radar

The transmit degrees-of-freedom (DOFs) of multiple-input multiple-output (MIMO) radar depend on the orthogonality of transmit waveforms. However, ideal orthogonal waveforms are unrealistic because existing waveforms cannot avoid influence of cross-correlation sidelobes. In this paper, a waveform design algorithm is proposed by introducing the phase response similarity (PRS) concept. The PRS enables consistency of spatial steering vectors for different time instance. In this case, the spatial power spectrum of signal in the transmit spatial domain will be well-focused, which is the desired property for the jammer suppression application. Moreover, we further explore the combination of correlation amplitude and phase response as the objective function, which improves the anti-jammer performance. Simulation examples are conducted to verify the effectiveness and performance gains of the proposed method.

Nonorthogonal waveform assisted DOA estimation for joint MIMO sensing and communication

Conventional direction-of-arrival (DOA) estimation methods for multiple-input multiple-output (MIMO) joint sensing and communication system normally pursue high estimation accuracy and resolution by imposing orthogonal waveforms. However, such operation results in a deterioration of communication performance. In this paper, we propose a nonorthogonal waveform assisted DOA estimation algorithm, where an augmented virtual array is derived by exploiting the nonorthogonal MIMO communication waveforms, while a high communication rate can still be maintained. To estimate the round-trip sensing channels of each subcarrier, we utilize the transmitted symbols as pilot symbols, and obtain all the channel coefficients with a minimum mean square error solver. A virtual channel matrix can be formulated with these channel coefficients, which can be regarded as the samples of an augmented virtual array. Based on that, the subspace processing can be conducted for DOA estimation with fully nonorthogonal waveforms. Furthermore, the rank deficiency property of the equivalent signal matrix of the virtual array is analyzed when the distance of targets are identical. To address the problem, a Toeplitz reconstruction method is proposed to restore the rank of the rank-deficient equivalent signal matrix for DOA estimation. Simulations show that the proposed nonorthogonal waveform assisted DOA estimation algorithm outperforms the conventional methods in terms of resolution and accuracy, while maintaining a satisfactory computational efficiency.

Transmitted-Signal-Free Target Information Extraction for OFDM-Based Passive Radar With Time-Varying Sparse Model

Compressive sensing theory have been proposed in the field of radar for target detection. The challenge of compressive sensing applied to passive bistatic radar lies in the high computational complexity aggravated by the transmitted signal dependent time-varying sparse model. So, we propose a transmitted-signal-free and time-invariant sparse model for passive radar based on orthogonal frequency division multiplexing waveforms. We first generate the sparse model by using the surveillance signal and pilot information only, and exploiting the sparsity of scene including only a few targets and clutter. Then, range-Doppler profile for target detection can be implemented based on our proposed sparse model. Finally, simulation and experimental results illustrate that our proposed sparse model has high detection performance.

Target Detection for Distributed MIMO Radar With Non-Orthogonal Waveforms in Cluttered Environments

Orthogonal radar waveforms originating from spatially distributed transmitters (TXs) usually arrive at a receiver (RX) in non-orthogonal forms, as they propagate through different paths with distinct delays and Doppler frequencies in distributed multi-input multi-output (MIMO) radar. Non-orthogonal waveforms complicate the composition of the target and clutter returns, making it more challenging to separate one from the other. In this paper, we consider joint target detection and clutter mitigation in distributed MIMO radar. We first present a general signal model for distributed MIMO radar in cluttered environments. Next, we propose three families of detection solutions, including non-coherent detectors that require no phase estimation and are relatively simple to implement, coherent detectors that offer enhanced detection performance given accurate phase information, and hybrid detectors that are a compromise of the former two, requiring only local phase coherence but no explicit phase estimation. In addition, approximate solutions are proposed in each category with further complexity reduction, using high clutter-to-noise (CNR) approximation or convex relaxation. Simulation results are presented to demonstrate the performance of the proposed detectors, which outperform their earlier counterparts that neglect the presence of clutter.

DDMA-MIMO Observations With the MU Radar: Validation by Measuring a Beam Broadening Effect

The phased-array radar, basically developed with the defense systems, has mainly utilized for the atmospheric radar and the wind profiling radar in the field of meteorological remote sensing, and recently it has also applied to the weather radar for research purposes. As a further development of phased-array technology, the “Multiple-Input Multiple-Output (MIMO) technique,” which has been developed in the field of communication systems, has been applied to radars. With the MIMO radar, it is possible to create a virtual antenna aperture plane beyond the actual antenna and to reduce the actual antenna size compared to that of the conventional antenna while maintaining the angular resolution. This effect is expected to reduce costs, which is one of the major hurdles in expanding phased array radars instead of parabolic antenna systems. In order to confirm the effect, an experimental observation was performed using the MU radar which is a VHF-band phased array atmospheric radar with multi-channel receivers. The MIMO technique requires orthogonal waveforms on each transmitter to identify the transmitted signals with multiple receivers, and various methods are known to realize orthogonality. In this paper, we focus on the “ Doppler Division Multiple Access (DDMA)” MIMO technique, with which slightly different frequencies are selected as transmit waveforms to separate in each receiver in the Doppler frequency domain. The observation results by measuring a beam broadening effect with the MU radar indicate that it will be a key technique for the atmospheric radar in the near future.