Ambiguity Function Research Articles

Range and Velocity Resolution of Linear- Frequency-Modulated Signals on Subarray-Mimo Radar

The most important radar system performance is determining the range-velocity of the detected target. This performance is obtained from processing an ambiguity-function (AF) between signals from target reflections and radar radiation signals. Selection of the appropriate waveform transmitted by the radar is a key factor in supporting high resolution radar performance in the AF. There are many waveforms that have been studied in radar systems, especially for multi-antenna radars, i.e., subarray-MIMO (SMIMO) radar which can form phased array (PA) and MIMO radars simultaneously, in the form of linear-frequency-modulated (LFM) signals. In this paper, we examine the use of LFM waveforms combined with SMIMO radar to produce plots of three-dimensional AF as a function of time delay and Doppler shift. The results of the comparison with the Hadamard signal determine the effectiveness of the observed AF performance on parameters such as magnitude, range-velocity resolution, peak sidelobe level ratio, and integrated sidelobe ratio by taking into account the factors of the number of Tx antennas on the PA radar and the number of Tx subarrays on the MIMO radar. The evaluation results of the SMIMO radar configuration (M = 6) with the number of Tx-Rx antenna elements the being 8 provide the best mainlobe magnitude, sidelobe magnitude, range resolution, velocity resolution, PSLR, and ISLR of AF LFM signals compared to conventional radars are 235.2dB, 7.54dB, 37.5m, 75km/s, 29.89dB, and 29.8dB, respectively. Meanwhile, the LFM signal is far superior to the Hadamard signal which has PSLR and ISLR 1.16dB and -3.36dB, respectively.

The short-time Wigner–Ville distribution

The Wigner–Ville distribution (WD) and ambiguity function (AF) are serviceable tools for the global analysis of non-stationary signals. However, when dealing with time-varying signals that exhibit changing characteristics and require real-time signal processing, they have high limitations due to the existence of cross-items. In this paper, we propose the short-time Wigner–Ville distribution (STWD) as a novel approach that effectively analyzes time-varying signals with changing characteristics. First, the definition of STWD and short-time ambiguity function (STAF) and their properties are advanced. Next, three uncertainty principles that define the lower bound for the product of signal spread and its bandwidth are derived. Then, the discrete STWD (DSTWD) and the process of computerization are also proposed which can be used more widely in practice. Finally, the optimization of window functions based on Rényi entropy is discussed. Simulation experiments show that the STWD can be effectively applied for the analysis of local change characteristics and real-time processing of signals with valid and accurate results.

Optimal investment in ambiguous financial markets with learning

We consider the classical multi-asset Merton investment problem under drift uncertainty, i.e. the asset price dynamics are given by geometric Brownian motions with constant but unknown drift coefficients. The investor assumes a prior drift distribution and is able to learn by observing the asset prize realizations during the investment horizon. While the solution of an expected utility maximizing investor with constant relative risk aversion (CRRA) is well known, we consider the optimization problem under risk and ambiguity preferences by means of the KMM (Klibanoff et al., 2005) approach. Here, the investor maximizes a double certainty equivalent. The inner certainty equivalent is for given drift coefficient, the outer is based on a drift distribution. Assuming also a CRRA type ambiguity function, it turns out that the optimal strategy can be stated in terms of the solution without ambiguity preferences but an adjusted drift distribution. To the best of our knowledge an explicit solution method in this setting is new. We rely on some duality theorems to prove our statements.Based on our theoretical results, we are able to shed light on the impact of the prior drift distribution as well as the consequences of ambiguity preferences via the transfer to an adjusted drift distribution, i.e. we are able to explain the interaction of risk and ambiguity preferences. We compare our results with the ones in a pre-commitment setup where the investor is restricted to deterministic strategies. It turns out that (under risk and ambiguity aversion) an infinite investment horizon implies in both cases a maximin decision rule, i.e. the investor follows the worst (best) Merton fraction (over all realizations of it) if she is more (less) risk averse than a log-investor. We illustrate our findings with an extensive numerical study.

Application of Quasi-Continuous Waveform Coding in Spaceborne Synthetic Aperture Radar

Quasi-continuous wave radar is an attempt to give consideration to the performance of pulse and continuous wave radar signals. However, it also has the shortcomings of both. This paper aims to add a new quasi-continuous-wave coding method to the spaceborne synthetic aperture radar (SAR) system. The technology of improving spaceborne SAR imaging performance by coding quasi-continuous-wave pulses is studied, and some shortcomings of this algorithm are improved. Firstly, the application of quasi-continuous-wave radar in the SAR system is studied, and the coding and reconstruction scheme is provided so that this technology can be successfully applied in spaceborne SAR. Secondly, the effects of different quasi-continuous-wave coding methods on SAR imaging performance are evaluated, including signal-to-noise ratio, resolution, and integration time. Then, several coding schemes are given, and the characteristic changes of the signal after quasi-continuous-wave coding are analyzed. The transmit–receive conversion loss function and azimuth Doppler ambiguity function of the design scheme are analyzed, which proves the advantages of the scheme. Finally, we design the hardware implementation scheme and carry out the practical test.

Exosomes: the next frontier in vaccine development and delivery.

Exosomes are small disk-shaped extracellular vesicles (EVs) that are naturally released into the environment by different types of cells. Exosomes range from 30-150 nm in size and contain complex RNA and proteins. They are widely found in body fluids such as blood, saliva, urine and breast milk and participate in cell communication by functioning as cell messengers. Almost all cell types can transmit information and exchange substances through the production and release of exosomes to regulate proliferation, differentiation, apoptosis, the immune response, inflammation, and other biological functions. Because exosomes exist widely in various body fluids, they are easy to obtain and detect and have the potential for use in disease diagnosis and prognosis detection. Exosomes can be genetically fused with targeted proteins, enhancing their biocompatibility and immunogenicity. Therefore, exosomes are the preferred vector tools for vaccines. In this review, we describe the characteristics of exosomes and discuss their unique and ambiguous functions in the immune microenvironment after infection. In this regard, we explored the ability of exosomes to carry immunogenic virus antigens and to establish adaptive immune responses. Exosomes can provide an interesting platform for antigen presentation and since vaccines are a powerful method for the prevention of infectious diseases, we further review the advantages and disadvantages of the use of exosomes in vaccine preparation. Overall, exosomes are emerging as a promising avenue for vaccine development.

OTFS Based Joint Radar and Communication: Signal Analysis Using the Ambiguity Function

OTFS Based Joint Radar and Communication: Signal Analysis Using the Ambiguity Function

Radar Ambiguity Functions of Binary-Coded and Frequency-Hopped Waveforms Designed Based on the Permutations of Sudoku Matrix

Radar Ambiguity Functions of Binary-Coded and Frequency-Hopped Waveforms Designed Based on the Permutations of Sudoku Matrix

Ambiguity Function Analysis and Optimization of Coherent FDA Radar

Ambiguity Function Analysis and Optimization of Coherent FDA Radar

Cross Ambiguity Function Shaping of Cognitive MIMO Radar: A Synergistic Approach to Antenna Placement and Waveform Design

Cross Ambiguity Function Shaping of Cognitive MIMO Radar: A Synergistic Approach to Antenna Placement and Waveform Design

Pulse Diversity Phase Coded Waveform and Mismatched Filter Bank Design via Periodic Ambiguity Function Shaping

Pulse Diversity Phase Coded Waveform and Mismatched Filter Bank Design via Periodic Ambiguity Function Shaping

Joint Optimization of Transmit Waveforms Design and Antenna Positions Selection Based on MIMO Ambiguity Function

Joint Optimization of Transmit Waveforms Design and Antenna Positions Selection Based on MIMO Ambiguity Function

Transmit Waveform Design Based on Ambiguity Function Shaping for Distributed Coherent Aperture Radar in MIMO Mode

Transmit Waveform Design Based on Ambiguity Function Shaping for Distributed Coherent Aperture Radar in MIMO Mode

Sensing Matrix Optimization for Random Stepped-Frequency Signal Based on Two-Dimensional Ambiguity Function

Sensing Matrix Optimization for Random Stepped-Frequency Signal Based on Two-Dimensional Ambiguity Function

Algorithm design of a combinatorial mathematical model for computer random signals.

To improve the processing effect of computer random signals, the manuscript employs the intelligent signal recognition algorithm to design a combinatorial mathematical model for computer random signals, and studies the parameter estimation of conventional frequency hopping signal (FHS) based on optimizing kernel function (KF). First, the mathematical form and graphical representation of the ambiguity function of the conventional FHS are explored. Furthermore, a new KF is presented according to its fuzzy function (FF) and the parameters of conventional FHSs are estimated according to the time-frequency distribution corresponding to the KF. Then, simulation experiments are carried out in different types of interference noise environments. The proposed combinatorial mathematical model for computer random signals shows a practical impact, and can effectively improve the effect of random signal combination.

Enhanced Micro-Doppler Feature Extraction Using Adaptive Short-Time Kernel-Based Sparse Time-Frequency Distribution

The extraction of the micro-Doppler (m-D) feature based on time-frequency distribution (TFD) is of great significance for target detection and identification. To improve the feature extraction performance, numerous TFDs have been developed, with the majority falling under Cohen’s class. Nevertheless, these TFDs basically face a trade-off between artifact suppression and energy concentration. The main reason is that each Cohen’s class TFD is constructed by applying the two-dimensional Fourier transform to a kerneled ambiguity function directly, while existing kernels generally attenuate artifacts at the expense of losing valuable information. In this paper, a TFD reconstruction method employing an adaptive short-time kernel (ASTK) is developed in the framework of sparse representation (SR) theory to overcome this trade-off and enhance the m-D feature. Firstly, the task of the optimal kernel is explained from the viewpoint of the instantaneous auto-correlation function (IAF). Secondly, based on the quasi-linear frequency modulation feature of most m-D signals during short-time periods, the distribution rule of the short-time IAF (STIAF) in the ambiguity plane is concluded. Guided by this rule, an ASTK that can effectively remove unwanted artifacts with the least information loss is designed. Finally, an SR-based reconstruction procedure is conducted on the kerneled STIAF to generate an artifact-free TFD with high energy concentration, which can effectively enhance the m-D feature. Experiments using both simulated and real-world m-D signals demonstrate the effectiveness of the proposed method.

Joint design of transmit precoding and antenna selection for multi-user multi-target MIMO DFRC

Dual-function radar and communications (DFRC) systems based on multiple-input multiple-output (MIMO) arrays have received considerable attention in recent years due to their excellent ability to alleviate spectrum congestion. The MIMO DFRC systems enable high-resolution detection of multiple targets while communicating with multiple users simultaneously. However, MIMO arrays require numerous radio frequency (RF) units and suffer a strong mutual coupling among antennas, resulting in significant system overhead and performance degradation, respectively. In light of this, this paper investigates the joint optimization of transmit precoding and antenna selection for MIMO DFRC systems, aiming to improve the angular ambiguity function with a guaranteed communication quality of service (QoS) using a small number of antennas. To address the resultant non-convex optimization problem, both the indirect and direct precoding methods are proposed. In the former, the waveform covariance and antenna selection vector are first jointly optimized via a promoted sparsity along the covariance diagonal, followed by the precoding matrix indirectly derived from the optimal covariance. In the latter, the precoding matrix is directly optimized via an imposed group sparsity under the communication QoS and power constraints. Simulation results demonstrate that the proposed sparse MIMO DFRC system with fewer active antennas can achieve comparable dual-functional performance to that of the full array system.

Synthetic Meta-Signal Observations: The Beidou Case.

A Global Navigation Satellite System (GNSS) meta-signal is obtained when two or more side-band components from different frequencies are jointly processed as a single entity. This requires advanced signal processing techniques able to cope with the subcarrier, generated by the interaction of the side-band components, and handle possibly multi-peaked ambiguous correlation functions. An alternative approach to meta-signal processing is to reconstruct meta-signal observations using side-band measurements. Meta-signal high-accuracy pseudoranges can be reconstructed from the side-band code and carrier observations. The success of the reconstruction depends on several factors, including the frequency separation of the side-band components and the presence of measurement biases. The Beidou Navigation Satellite System (BDS), with its second- and third-generation signals, provides a wide range of components with various frequency separations. In this paper, we experimentally investigate the performance and limitations of the measurement reconstruction approach using Beidou observations. When the B1I and B1C components are considered, their reduced frequency separation leads to unambiguous measurements fully exploiting the potential of meta-signals. For larger frequency separations, jumps and discontinuities are observed in the position domain, which is a major limiting factor of this type of approach.

Robust conjugate ambiguity functions and application for strictly noncircular signals in correlated impulsive noise

Robust conjugate ambiguity functions and application for strictly noncircular signals in correlated impulsive noise

Wigner-Ville distribution and ambiguity function of QPFT signals

The quadratic phase Fourier transform(QPFT) has received my attention in recent years because of its applications in signal processing. At the same time the applications of Wigner-Ville distribution (WVD) and ambiguity function (AF) in signal analysis and image processing can not be excluded. In this paper we investigated the Wigner-Ville Distribution (WVD) and ambiguity function (AF) associated with quadratic phase Fourier transform (WVD-QPFT/AF-QPFT). Firstly, we propose the definition of the WVD-QPFT, and then several important properties of newly defined WVD-QPFT, such as nonlinearity, boundedness, reconstruction formula, orthogonality relation and Plancherel formula are derived. Secondly, we propose the definition of the AF-QPFT, and its with classical AF, then several important properties of newly defined AF-QPFT, such as non-linearity, the reconstruction formula, the time-delay marginal property, the quadratic-phase marginal property and orthogonal relation are studied. Further, a novel quadratic convolution operator and a related correlation operator for WVD-QPFT are proposed. Based on the proposed operators, the corresponding generalized convolution, correlation theorems are studied. Finally, a novel algorithm for the detection of linear frequency-modulated(LFM) signal is presented by using the proposed WVD-QPFT and AF-QPFT.

Integrated Sensing and Communication With Delay Alignment Modulation: Performance Analysis and Beamforming Optimization

Delay alignment modulation (DAM) has been recently proposed to enable manipulable channel delay spread for efficient single- or multi-carrier communications. In particular, with perfect delay alignment, inter-symbol interference (ISI) can be eliminated even with single-carrier (SC) transmission, without relying on sophisticated channel equalization. The key ideas of DAM are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">delay pre-compensation</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">path-based beamforming</i> , so that all multi-path signal components may arrive at the receiver simultaneously and be superimposed constructively, rather than causing the detrimental ISI. Compared to the classic orthogonal frequency division multiplexing (OFDM) transmission, DAM-enabled SC communication has several appealing advantages, including low peak-to-average-power ratio (PAPR) and high tolerance for Doppler frequency shift, which renders DAM also appealing for radar sensing. Therefore, in this paper, DAM is investigated for integrated sensing and communication (ISAC) systems. We first study the output signal-to-noise ratios (SNRs) for ISI-free SC communication and radar sensing, respectively, and then derive the closed-form expressions for DAM-based sensing in terms of the ambiguity function (AF) and integrated sidelobe ratio (ISR). Furthermore, we study the beamforming design problem for DAM-based ISAC to maximize the communication SNR while guaranteeing the sensing performance in terms of the sensing SNR and ISR. Finally, we provide performance comparison between DAM and OFDM for ISAC, and it is revealed that DAM signal may achieve better communication and sensing performance, thanks to its low PAPR, reduced guard interval overhead, as well as higher tolerance for Doppler frequency shift. Simulation results are provided to show the great potential of DAM for ISAC.