Waveform Diversity Research Articles

A New Waveform Design Method for Multi-Target Inverse Synthetic Aperture Radar Imaging Based on Orthogonal Frequency Division Multiplexing Chirp

With the increasing use of the strategy and group target attack method in the modern battlefield, multi-target inverse synthetic aperture radar (ISAR) imaging simultaneously with high efficiency draws more and more attention, which gives a promising prospect for aerospace target detection and recognition in the multi-target scenario. To overcome the shortcomings of traditional multi-target imaging with one beam at one pulse repetition time (PRT) based on phase array radar (PAR), this paper proposes a novel multi-target imaging waveform design method based on the newly full digital array radar (DAR). Firstly, we propose using radar waveform diversity with 2D orthogonality to realize multi-target ISAR imaging with high imaging quality and efficiency. Then, to meet the constant modulus requirement for maximizing the transmitting power, orthogonal frequency division multiplexing (OFDM) chirp theory is proposed to directly generate the transmit waveform instead of the traditional optimization method with the nonconvex problem for waveform design. Based on time-variant weighted and time diversity technology, a of group transmit waveforms is designed, which can form multiple beams simultaneously and make the signals arriving at different targets approximately orthogonal. Finally, simulations and experiments are carried out to demonstrate the effectiveness of the proposed method.

A fully digital transmitting-receiving platform for MIMO radar waveform diversity experiment

A fully digital transmitting-receiving platform for MIMO radar waveform diversity experiment

A Novel Intrapulse Beamsteering SAR Imaging Mode Based on OFDM-Chirp Signals

The multiple-input multiple-output synthetic aperture radar (MIMO SAR) system has developed rapidly since its discovery. At the same time, the low-disturbance and high-gain requirements of the MIMO system are continuing to increase. Through the application of digital beamforming (DBF) techniques, the multidimensional waveform encoding (MWE) technique can play a key role in MIMO systems, which can greatly improve the system’s performance, especially the multi-mission capability of radar. Intrapulse beamsteering in elevation is a typical form of multi-dimensional waveform encoding which can greatly improve the transmitting efficiency and multi-mission performance of radar. However, because of the high sensitivity of the DBF technique to height, there is significant deterioration in performance in the presence of terrain undulations. The OFDM (Orthogonal Frequency Division Multiplexing) technique is widely used in communication. Due to the similarity of radar and communication systems and the great waveform diversity of OFDM signals, the OFDM radar has recently begun to emerge as a new radar system, simultaneously, the orthogonality of OFDM signals is in the time and frequency domains, and is not affected by terrain undulation. So, this paper proposes a novel radar mode combining intrapulse beamsteering in elevation and OFDM-Chirp signals, that is, the combination of “beam orthogonality” and “waveform orthogonality”, which can greatly improve the performance and fault tolerance to interference signals. In this manuscript, the system working mode and signal processing flow are introduced in detail, and simulations for both point targets and distributed targets are carried out to verify the feasibility of the proposed mode. Simultaneously, a comparison experiment is carried out, which shows the high level of fault tolerance to terrain undulation and the high potential of the proposed radar mode in Earth observation.

Fast Antenna Array Calibration Using One External Receiver.

In multiple array communication or radar systems, waveform diversity can be utilized for beampattern design. However, one of the critical issues for such systems is the presence of mutual coupling, which degrades the beampattern design's quality. We address the calibration of the mutual coupling of transmit arrays by developing a new matrix-inversion-free algorithm that requires only a single antenna receiver. It has a very low computational complexity for accelerating the mutual coupling calibration compared to previous methods; therefore, it can be utilized for large array systems such as massive multiple-input-single-output (MISO) systems. The key idea here revolves around utilizing fast Fourier transform (FFT). This approach simplifies matrix calculations and reduces the number of multiplications required to compute the inverse of FFT. Moreover, the algorithm is applicable for high-power active radar calibration, since it incorporates a constant modulus training sequence. The application of the algorithm in MISO systems, including massive MISO, offers the potential for calibrating mutual coupling. It enables the precise measurement and compensation of mutual coupling effects, improving the signal quality and system performance in areas such as radars, mobile communications and more. We evaluated the proposed algorithm under various scenarios, compared it with the ground truth and showed that it achieves excellent performance with few computations.

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.

Range ambiguity suppression under high-resolution estimation using the MUSIC-AP algorithm for pulse-Doppler radar

Range ambiguity is a significant challenge in conventional pulse-Doppler radar systems with medium or high pulse repetition frequencies, greatly impacting radar detection and imaging capabilities. The classic approaches such as waveform diversity and compressed sensing are based on the isolation between pulses. However, these methods encounter issues like residual ambiguity and grid mismatch, resulting in poor range ambiguity suppression performance. In this paper, the multiple signal classification-alternating projection (MUSIC-AP) method is proposed to address these challenges and achieve high-resolution estimation. The proposed method converts the range-velocity estimate into a spectrum estimate, enabling the utilization of the MUSIC algorithm to solve the grid mismatch problem and improve echo reconstruction. Then, to mitigate the effect of ambiguous energy on reconstruction, the MUSIC reconstruction subprocess is embedded into the AP framework. Through iterative approximation, the method gradually suppresses ambiguous and noise energy, thereby further enhancing the echo reconstruction accuracy and range ambiguity suppression performance. Simulations demonstrate the effectiveness of the proposed method. Moreover, algorithm analysis is conducted, considering aspects such as resolution, robustness, and sparsity, which provides a basis for parameter selection and applicability conditions.

An Advanced Non-Interrupted Internal Calibration Model Based on Azimuth Modulation and Waveform Diversity for SAR Systems

Internal calibration, designed for obtaining the gain and phase errors introduced by the fluctuations of the electronic instruments, is an essential operation to guarantee the imaging performance of modern synthetic aperture radar (SAR) systems. However, in most of the current internal calibration schemes, the internal calibration processes interrupt the normal SAR data acquisition, which results in a loss of azimuth samples and degradation of the SAR image quality. To this end, an advanced non-interrupted internal calibration model is proposed, performing the internal calibration during nominal data acquisitions. The calibration signals and echoes are orthogonal and are received simultaneously. Then, they can be separated by postprocessing via the waveform diversity concept. Two schemes based on the proposed model are demonstrated via theoretical analysis and simulation experiments. The proposed model can achieve a considerable signal-to-noise ratio (SNR) and reduce the influence of calibration signals on echoes, which have some potential applications for future SAR missions.

Orbital Angular Momentum Imaging Based on Waveform Diversity and Rotational Array

Orbital Angular Momentum Imaging Based on Waveform Diversity and Rotational Array

Joint Design of Horizontal and Vertical Polarization Waveforms for Polarimetric Radar via SINR Maximization

For an extended target with different polarimetric response, one way of improving the detection performance is to exploit waveform diversity on the dimension of polarization. In this paper, we focus on joint design of transmit signal and receive filter for polarimetric radars with local waveform constraints. Considering the signal-to-interference-plus-noise ratio (SINR) as the figure of merit to optimize, where the average Target-Impulse-Response Matrix (TIRM) within a certain Target-Aspect-Angle (TAA) interval is employed as the target response, the waveform is decomposed and then designed for both horizontal and vertical polarization segments, subject to energy and similarity constraints. An iterative algorithm is proposed based on the majorization-minimization (MM) method to solve the formulated problem. The developed algorithm guarantees the convergence to a B-stationary point, where in each iteration, optimal horizontal and vertical transmit waveforms are respectively solved by using the feasible point pursuit and successive convex approximation (FPP-SCA) technique. Experiment results show the effectiveness of the proposed algorithm, the robustness of the output SINR against the TAA change, and the advantages of polarization diversity and local design.

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.

Colocated MIMO Radar Waveform-Array Joint Optimization for Sparse Array.

Colocated multiple-input multiple-output (MIMO) radar can transmit a group of distinct waveforms via its colocated transmit antennas and the waveform diversity leads to several advantages in contrast to conventional phased-array radar. The performance depends highly on the degrees available, and element spacing can be deemed as another source of degrees of freedom. In this paper, we study the joint waveform and element spacing optimization problem. A joint waveform and array optimization criterion is proposed to match the transmit beampattern, the suppression range, and the angular sidelobes, under the constraints of minimal element spacing and total array aperture. Meanwhile, the effect of receive beamforming on suppressing mutual correlation between returns from different spatial directions is also incorporated into the optimization criterion. The optimization problem is solved by the sequential quadratic programming algorithm. Numerical results indicate that with more degrees of freedom from array spacings, colocated MIMO radar achieves a better transmit beampattern matching performance and a lower sidelobe level, compared with a fixed half-wavelength spaced array, but the benefits from additional degrees of freedom from array spacing optimization have a limit.

Precise Ambiguity Performance Evaluation for Spaceborne SAR with Diverse Waveforms

The ambiguity suppression is a technical challenge for the present generation of spaceborne synthetic aperture radar (SAR) systems since this kind of suppression does not take the high spatial resolution and wide coverage into account simultaneously. The transmitting scheme based on the waveform diversity technique is a promising candidate for the conventional (one transmit, one receive channel) SAR systems and has been widely discussed, because it has almost no extra system costs and the ambiguity suppression performance is not closely related to pulse repetition frequency (PRF). However, the accurate method to evaluate the ratio of the intensities of the ambiguities to that of the signal is still a gap. To this end, starting from the precise signal model formulated in this paper, the ambiguity evaluation for spaceborne SAR with waveform diversity has been analyzed in detail. Particularly, the modified azimuth ambiguity-to-signal ratio (AASR) and range ambiguity-to-signal ratio (RASR) formulas are given for the single polarization SARs and quadrature-polarimetric (quad-pol) SARs, which contributes a lot, for the system designer, to precisely evaluating the ambiguity performance. Finally, detailed simulation experiments exploiting the system parameters of the LuTan (LT-1) system are carried out to corroborate the theoretical developments.

Information embedding in DFRC networks through chirp waveform diversity

We consider a dual function radar communications network and propose a waveform diversity-based approach to embed both target and scheduling data in the transmitter pulses. The scheduling data of radar signal bandwidth, carrier frequency, and waveform along with the information on target detection, range, and Doppler are shared among the network radar nodes without a need for designated communication links. Scheduling and target information are encoded to bits and transmitted over the radar coherent processing interval using up- and down-chirps. We derive exact expressions of probability of bit error and false alarm rate for sharing scheduling and target information data between two radar nodes. The effect of different parameters and data sharing on the radar performance is analyzed and validated by computer simulations. Using the cross-ambiguity function, we show the capability of the up- and down- chirp sequence transmission scheme in reducing range sidelobes compared to the conventional transmission of only the up- (or down-) chirps. To overcome the limited data rate associated with only using two chirp waveforms, we consider orthogonal chirp division multiplexing and derive its CAF. We demonstrate the suitability of OCDM for high data rate radar operations by examining the mainlobe width and sidelobe levels of the zero-Doppler and zero-delay cuts of the CAF.

Forward-Looking Super-Resolution Imaging of MIMO Radar via Sparse and Double Low-Rank Constraints

Multiple-input multiple-output (MIMO) radar uses waveform diversity technology to form a virtual aperture to improve the azimuth resolution of forward-looking imaging. However, the super-resolution imaging capability of MIMO radar is limited, and the resolution can only be doubled compared with the real aperture. In the radar forward-looking image, compared with the whole imaging scene, the target only occupies a small part. This sparsity of the target distribution provides the feasibility of applying the compressed sensing (CS) method to MIMO radar to further improve the forward-looking imaging resolution. At the same time, the forward-looking imaging method for a MIMO radar based on CS has the ability to perform single snapshot imaging, which avoids the problem of a motion supplement. However, the strong noise in the radar echo poses a challenge to the imaging method based on CS. Inspired by the low-rank properties of the received radar echoes and the generated images, and considering the existing information about sparse target distribution, a forward-looking super-resolution imaging model of a MIMO radar that combines sparse and double low-rank constraints is established to overcome strong noise and achieve robust forward-looking super-resolution imaging. In order to solve the multiple optimization problem, a forward-looking image reconstruction method based on the augmented Lagrangian multiplier (ALM) is proposed within the framework of the alternating direction multiplier method (ADMM). Finally, the results of the simulation and the measurement data show that the proposed method is quite effective at improving the azimuth resolution and robustness of forward-looking radar imaging compared with other existing methods.

High-stable and reconfigurable photonic generation of radio-frequency arbitrary waveforms with multi-tone inputs

Conventional temporal pulse shaping (TPS) for radio frequency (RF) arbitrary waveform generation (RF AWG) based on the Fourier transform relation between the input–output waveform pair requires the electronic AWG to generate RF input signal, which greatly limits the output waveform diversity due to the relative low sampling rate and bit resolution of electronic AWG, i.e., high-fidelity square waveforms are hard to be achieved since high-resolution broadband Sinc input signals are difficult to be generated by current commercial electronic AWGs. The approaches based on TPS with phase modulation incorporating with iterative algorithms can relatively improve the waveform diversity by applying the optimal phase information. However, time-consuming iterative algorithms significantly restrict the waveform reconfigurability, i.e., desired RF waveforms cannot be generated in real-time. We propose a novel high-stable and reconfigurable RF AWG scheme with multi-tone inputs, which aims to improve the output waveform diversity with simple manipulation and high stability. In our design, any desired RF waveform can be achieved in real-time by simply adjusting the power values of multi-tone inputs. A proof-of-concept experiment was implemented, which fully verified the feasibility of the approach. The system performance in terms of output waveform stability was investigated in detail. As no electronic AWG is employed and no iterative algorithms are required, the proposed design provides a promising solution for high-performance reconfigurable photonic-based RF arbitrary waveforms generation.

Array Scheduling With Power and Bandwidth Allocation for Simultaneous Multibeam Tracking Low-Angle Targets in a VHF-MIMO Radar

The very high frequency (VHF) radar suffers from the multipath interference and false alarms when tracking low-angle targets. The co-located multiple-input multiple-output (MIMO) radar technique can mitigate these adverse effects with waveform diversity. However, the limited resources restrict the potential of the VHF-MIMO radar. In this paper, an array scheduling with power and bandwidth allocation (ASPBA) strategy is proposed for the VHF-MIMO radar tracking low-angle targets. The predicted posterior Cramér-Rao lower bound (PCRLB) under the multipath interference and measurement origin uncertainty (MOU) effects is derived to serve as the optimization metric. The measurement amplitude information (AI) is incorporated into the PCRLB to facilitate target detection and tracking. It is shown that the ASPBA problem is a mixed integer programming and NP-hard problem, where the array, power, and bandwidth allocation variables are both coupled in the objective and constraints. An efficient three-stage-based solution is proposed for problem-solving. The approximated relationship among three variables is derived using Hölder's inequality, and an auxiliary variable is introduced to describe the array contribution. Thereby, the array scheduling is determined by a heuristic rounding algorithm, and the power and bandwidth allocation are achieved using the approximated relationship. Simulation results confirm the effectiveness and efficiency of the proposed ASPBA strategy, compared with state-of-the-art algorithms. It is also shown that the target height is a main factor that influences the resource allocation results in the low-angle tracking scenario.

Open-Metric for Unknown Signal Inference

The closed-set assumption that only known classes can be classified during testing is usually adopted in traditional signal recognition missions. It has been thoroughly explored and made huge progress in the past decade. However, it cannot cope with the unknown categories coming from the changing environment. As waveform diversity technology evolves by leaps and bounds, the existence of novel unknown classes is inevitable in the open-world environment, imposing a huge challenge to the non-cooperative electronic support system. To further satisfy the demands of modern electronic intelligence systems and sense new threats, it is urgent to find an approach that can tackle unknown signals. An Open-Metric strategy is proposed in this article to deduce the unknown classes from the intercepted signals. By virtue of metric learning methods, a plain backbone can be trained to offer more discriminative representations and a consistent proxy for each class. According to extreme value analysis, information about known classes can be converted into an estimated score of unknown classes, creating an open decision layer. The investigated Open-Metric approach demonstrates its superiority in unknown signal inference tasks, facilitating improvements in the intelligence and smartness of the electronic reconnaissance agents to cope with future cognitive electronic warfare.

A 2-D Method Based on Nonlinear Frequency Modulation Waveform and Phase Coding for Range Ambiguity Suppression

Range ambiguity suppression is a key technical challenge for synthetic aperture radar (SAR) systems. Waveform diversity technology is a potential solution due to its low system complexity. In this letter, a 2-D method based on orthogonal nonlinear frequency modulation (NLFM) waveform and azimuth phase coding (APC) for range ambiguity suppression is proposed. This approach not only suppresses range ambiguity energies instead of dispersing them, but also works for multiple consecutive orders of range ambiguity energies. The imaging processing and range ambiguity suppression performance are described in detail. In addition, the range-ambiguity-to-signal radio (RASR) is analyzed, and the simulation results for the point target and distribution scenarios are given to verify the effectiveness and practicality of the proposed scheme.

Directional modulation based on dual-function radar-communication system

Dual-function radar-communication (DFRC) system has recently been proposed to enable the co-design of radar and wireless communications, which in turn alleviates the increased spectrum congestion crisis. DFRC system exploits the transmit beamforming technique and waveform diversity, the combination of which enables the system to embed information in radar emission. In this paper, directional modulation (DM) based on dual-function radar communication system is proposed. To achieve the security of information transmission, a beam weight vector set is established. The reference beam weight vector is initially designed and the remaining weight vectors are derived from it, by minimizing the differences between them. The transmitting beams shaped by the designed weight vectors are almost the same in radar main lobe, but differ in the amplitudes and phases towards the direction of intended communication receivers. The communication receivers decode the data based on its radiated beam. The proposed communication process is secure against intercept from directions other than the pre-assigned communication directions. Simulation results are provided for performance evaluation and to demonstrate the effectiveness of the proposed scheme.

Beampattern synthesis with nulling for sub-arrayed MIMO radar under constant modulus constraints

Sub-arrayed multiple-input multiple-output (MIMO) radar holds the benefits of waveform diversity and coherent processing gain jointly. Based on prior knowledge, we exploit the sub-arrayed MIMO radar to form multiple beams in the desired directions and null the power toward the interference or clutter. Meanwhile, to maximize the radiation efficiency of nonlinear amplifiers in radar systems, the transmit weight vectors are required to have constant modulus properties, which leads to a complicated nonconvex problem. To that end, an iteration method with high calculation efficiency based on the alternating direction penalty method (ADPM) framework is presented to resolve this problem. The original problem is transformed into a general bi-convex problem with bi-affine constraints via introducing auxiliary variables. A high convergence rate can be achieved by selectively increasing the penalty parameters in each iteration. For any initialization, the ADPM-based method is proved to converge. And the obtained convergent solution fulfills the Karush-Kuhn-Tucker (KKT) conditions. Finally, the effectiveness of the proposed method is demonstrated by simulation results.