Joint Delay and Doppler Shift Estimation for Multiple Targets Using Exponential Ambiguity Function

In this paper, we investigate the impact of Doppler shift on bit error rate (BER) in OFDM-based transform domain communication system (TDCS) and propose a novel Doppler shift estimation algorithm to recover the system performance. The Doppler shift estimation algorithm in OFDM systems is robustly designed and can be applied in OFDM-based TDCS. However, the accuracy of these existing estimation algorithms will degrade seriously when the signal to noise ratio (SNR) is low. An attractive feature of the proposed algorithm is that it can utilize characteristics of OFDM-based TDCS to estimate Doppler shift accurately with SNR as low as -10dB. Simulation results demonstrate that the proposed algorithm can eliminate the effects of additive noise to estimation accuracy. Furthermore, we show that the system performance improved significantly after Doppler shift compensation.

According to the characteristics of non-cooperative bistatic pulse radar systems and the issue that the doppler mismatched loss of the cross-correlation detection of moving targets is serious, two fast methods for joint time delay and doppler shift estimation of moving targets, based on segment correlation-FFT processing and modified partial segment correlation-FFT processing, are proposed, after analyzing the common methods for cross-ambiguity function processing such as direct calculation, FFT, Zoom-FFT method. The processing performance of direct calculation and partial segment correlation-FFT processing of LFM pulse-series is analyzed in theory and by simulation. And the simulation shows that the weak moving target can be detected effectively and the time delay and doppler shift can be fast estimated by the methods presented in this paper.

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.

Resolution probability is the most important indicator for signal parameter estimator, including estimating time delay, and joint Doppler shift and time delay. In order to get high-resolution probability, some procedures have been suggested such as compressed sensing. Based on the signal’s sparsity, compressed sensing has been used to estimate signal parameters in recent research. After solving ℓ0 norm Optimization problem, the methods would achieve high resolution. These methods all require high SNR. In order to improve the performance in low SNR, a novel implementation is proposed in this paper. We give a sparsity representation for the generalized matched filter output, or ambiguity function, while the former methods utilized the sparsity representation for channel response in time domain. By deconvolving the generalized matched filter output, 2-dimension estimation for Doppler shift and time delay would be gotten by greedy method, optimization method based on relaxation, or Bayesian method. Simulation demonstrates our method has better performance in low SNR than the method by the channel sparsity representation.

Physical wavelets are acoustic or electromagnetic waves resulting from the emission of a time signal by an acoustic or electromagnetic source moving along an arbitrary trajectory in space. Thus they are localized solutions of the wave equation or Maxwell's equations. In this paper we model the emission, reflection, and reception of such wavelets and propose their application to sonar and radar. The concept of ambiguity functions is extended to ambiguity functionals, which apply in a very general setting: The transmitter, the target, and the receiver can all execute arbitrary and independent motions. In the monostatic case, when the transmitter and the receiver are identical and at rest and the target moves with a constant, radial velocity, the ambiguity functional reduces to the wideband ambiguity function, which depends on time delay and Doppler scale factor and amounts to a wavelet transform of the return. In the narrowband approximation, it reduces further to the usual ambiguity function depending on time delay and Doppler frequency shift, which amounts to a windowed Fourier transform of the return. Thus, in the setting of ambiguity functions, time-frequency analysis is a narrowband approximation to wavelet analysis, which is in turn a linear approximation to the new physical wavelet analysis.

Ambiguity function(AF) modeling of radar signals is a powerful approach to feature extraction and recognition of radar emitters.An AF subspace based optimization framework is proposed to identify radar emitters by exploring unintentional modulation on pulse(UMOP) features.First,near-zero Doppler cuts of AF were extracted as a preliminary feature subset.Then,two kinds of cut-concatenation schemes were designed to construct two different pairs of feature vectors with complementary information respectively,which will facilitate the subsequent feature fusion via canonical correlation analysis(CCA) or discriminative canonical correlation analysis(DCCA).Theoretical analysis and experimental results show that the proposed algorithms not only alleviate the calculation problem in the existing AF based method,but also improve the recognition performance considerably,due to the successful information fusion and redundancy reduction conducted in the AF subset.

OF THE DISSERTATION Adaptive OFDM Radar for Target Detection and Tracking by Satyabrata Sen Doctor of Philosophy in Electrical Engineering Washington University in St. Louis, December 2010 Research Advisor: Dr. Arye Nehorai We develop algorithms to detect and track targets by employing a wideband orthogonal frequency division multiplexing (OFDM) radar signal. The frequency diversity of the OFDM signal improves the sensing performance since the scattering centers of a target resonate variably at different frequencies. In addition, being a wideband signal, OFDM improves the range resolution and provides spectral efficiency. We first design the spectrum of the OFDM signal to improve the radar’s wideband ambiguity function. Our designed waveform enhances the range resolution and motivates us to use adaptive OFDM waveform in specific problems, such as the detection and tracking of targets. We develop methods for detecting a moving target in the presence of multipath, which exist, for example, in urban environments. We exploit the multipath reflections by utilizing different Doppler shifts. We analytically evaluate the asymptotic performance of the detector and adaptively design the OFDM waveform, by maximizing the noncentrality-parameter expression, to further improve the detection performance. ii Next, we transform the detection problem into the task of a sparse-signal estimation by making use of the sparsity of multiple paths. We propose an efficient sparse-recovery algorithm by employing a collection of multiple small Dantzig selectors, and analytically compute the reconstruction performance in terms of the `1-constrained minimal singular value. We solve a constrained multi-objective optimization algorithm to design the OFDM waveform and infer that the resultant signal-energy distribution is in proportion to the distribution of the target energy across different subcarriers. Then, we develop tracking methods for both a single and multiple targets. We propose a tracking method for a low-grazing angle target by realistically modeling different physical and statistical effects, such as the meteorological conditions in the troposphere, curved surface of the earth, and roughness of the sea-surface. To further enhance the tracking performance, we integrate a maximum mutual information based waveform design technique into the tracker. To track multiple targets, we exploit the inherent sparsity on the delay-Doppler plane to develop an computationally efficient procedure. For computational efficiency, we use more prior information to dynamically partition a small portion of the delay-Doppler plane. We utilize the block-sparsity property to propose a block version of the CoSaMP algorithm in the tracking filter.

Linear frequency modulation (LFM) signal is widely used in pulse compression radars, whereas faced with the time delay bias caused by Doppler shift of radar echoes, which must be accounted for in some applicative occasions where the linear frequency modulation ratio is very low or Doppler shift is very large. The method of time delay estimation based on cross-ambiguity function (CAF) could solve the problem but need two-dimensional search around the entire time delay and Doppler shift plane, which increases computational complexity heavily and brings great challenge to real-time processing. An effective time delay estimation method is proposed in this paper based on the relationship of time delay and Doppler shift, which can reduce two-dimensional search to one-dimensional search along LFM signal energy line, and diminish the computation complexity greatly with the same performance of parameters estimation. Simulations proved the validity of the method proposed.

A computationally efficient algorithm for estimating time delay between signals received at two spatially separated sensors is proposed. The delay estimate is adapted directly to maximise the mean product of the first sensor output and the filtered output of the second received signal. The convergence behaviour and variance of the delay estimate are derived. It is shown that the proposed algorithm outperforms the explicit time delay estimator at a low signal-to-noise ratio.

ABSTRACTOptimizing waveforms in radar and sonar systems is crucial for enhancing spectral efficiency and target detection capabilities, yet this process often faces challenges like computational complexity and convergence issues. This research introduces a novel method that leverages the frequency‐domain exponential cross ambiguity function (FECAF) within multi‐tone sinusoidal frequency modulated (MTSFM) waveforms, combined with the Conjugate Gradient Method with Efficient Line Search (CGM‐ELS) for optimization. The optimization of MTSFM waveforms is achieved by combining the generalized integrated sidelobe level (GISL) and peak‐to‐mean power envelope ratio (PMEPR) metrics. The GISL metric controls the main lobe and sidelobe structure of the waveform's autocorrelation function (ACF), quantifying unwanted energy in sidelobes to find an optimal compromise. PMEPR ensures efficient operation of radar or sonar transmitters by minimizing energy variations in the waveform's envelope, which is crucial for peak power‐limited systems. To optimize these metrics, the CGM‐ELS algorithm is employed, ensuring efficient convergence through iterative adjustment of waveform parameters based on gradient information and penalty functions. The proposed method transforms the optimization problem into an unconstrained format, reducing computational complexity and improving convergence rates. Experimental results have shown significant enhancements in computational efficiency and convergence rate, demonstrating the effectiveness of the CGM‐ELS algorithm in synthesizing waveforms with optimal ambiguity function characteristics for radar and sonar applications.

In this paper, a new Doppler shift estimator is proposed for Time Division-Synchronous Code Division Multiple Access (TD-SCDMA) over Rician channels. Different from other existing methods, the proposed estimator is developed based on the training sequence, i.e., midamble and the statistical properties of demodulation signal. By the help of a training sequence, the received line-of-sight (LOS) signal is first demodulated. Afterwards, its second-order and fourth-order statistics are calculated. Then, by exploiting these statistical results, the Doppler shift estimator is obtained. The proposed estimator employs a smoothing function with corrective factor. By optimizing the corrective factor, an accuracy solution is acquired within the Doppler shift range of possibilities. Simulation results indicate that the proposed estimator is greatly reliable and effective to estimate Doppler shift up to 400 Hz.

The ambiguity function (AF) is a critical tool in radar waveform design, representing the two-dimensional correlation between a transmitted signal and its time-delayed, frequency-shifted version. Obtaining a radar signal to match a specified AF magnitude is a bi-variate variant of the well-known phase retrieval problem. Prior approaches to this problem were either limited to a few classes of waveforms or lacked a computable procedure to estimate the signal. Our recent work provided a framework for solving this problem for both band-and time-limited signals using non-convex optimization. In this paper, we introduce a novel approach <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WaveMax</i> that formulates waveform recovery as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">convex</i> optimization problem by relying on the fractional Fourier transform (FrFT)-based AF. We exploit the fact that AF of the FrFT of the original signal is equivalent to a rotation of the original AF. In particular, we reconstruct the radar signal by solving a low-rank minimization problem, which approximates the waveform using the leading eigenvector of a matrix derived from the AF. Our theoretical analysis shows that unique waveform reconstruction is achievable with a sample size no more than three times the signal frequencies or time samples. Numerical experiments validate the efficacy of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WaveMax</i> in recovering signals from noiseless and noisy AF, including scenarios with randomly and uniformly sampled sparse data.

Design of the sounding waveform is an important consideration in both remote sounding of environmental targets and characterization of communication channels since it is this waveform that determines, to a large extent, the sensitivity and resolution capabilities of the sounder. It is highly desirable to be able to compare the different possible waveforms and sounding techniques with regard to sensitivity or output signal-to-noise ratio, and resolution in time delay and frequency shift. A straight-forward quantitative method of comparing the sensitivity of dissimilar sounders is developed and illustrated by an example comparing a microwave sounder and an acoustic sounder. The comparison of resolution capability is made by using the ambiguity function or delay-doppler weighting function for that waveform. This presentation covers properties of the ambiguity function and examples for the four principle types of sounder waveforms; pulse, coherent pulse sequence, linear FM and coded. A distinct advantage to these comparison methods is that they are easy to apply and can be used in the planning stage of a project since neither experimental results nor detailed design data are needed. The presentation is directed to scientists and engineers not familiar with recent developments in radar.

In this work, we study the problem of Doppler shift and channel estimation for wireless communication systems on high-speed railways (HSRs). We focus on tunnel scenario, one of the classical scenarios of HSRs. We first build up the mathematical system model, design a joint Doppler shift and channel estimator, and compare its performance with the typical Moose algorithm. We show that our estimator outperforms the Moose algorithm in Doppler estimation. Besides, since wireless channels in tunnel scenarios often contain several or multiple taps, we suggest an adaptive frame structure to improve transmission efficiency. Simulations are then provided to corroborate our proposed studies.

A multi-frame space-time coding method for the phase-coded signal in MIMO radars