Two-dimensional Frequency Estimation Research Articles

Time-Frequency Domain Channel Estimation for OTFS Systems

Orthogonal-time-frequency-space (OTFS) has been developed as a promising modulation scheme for high Doppler channels. In OTFS systems, channel estimation (CE) plays a key role. Most existing CE schemes put pilots in delay-Doppler (DD)-domain, often resulting in low spectrum efficiency and high peak-to-average-power-ratio (PAPR). In this paper, we propose three schemes to solve the problems. Proposed methods have distinct features being able to estimate fractional delays and fractional Dopplers. Different from existing methods, our approach places pilots in time-frequency (TF)-domain. The first scheme overlaps pilots and data in both TF- and DD-domain, while Scheme II overlaps them in TF- but not in DD-domain. To further enhance the performance, the third scheme makes pilots and data non-overlapped in both TF- and DD-domain. To conduct CE, time-domain pilot signals are extracted with a filtering operation and a two-dimensional frequency estimation problem is formulated consequently. Delays are first estimated with root-MUSIC. Then, Dopplers are estimated using a simple line-fitting method. Finally, channel gains are estimated by a least-squares method. To solve the interference between pilots and data, successive-interference-cancellation (SIC) is also applied. With the estimated channel, a minimum-mean-square-error (MMSE) equalizer is used for the compensation of channel effect. Simulation results show that the bit-error-rate (BER) performance with the channel estimated by proposed CE methods can approach to that with known channel. Also, spectrum efficiency can be improved by at most 25% and PAPR can be reduced by at least 19 dB.

Fast Rank-Revealing QR Factorization for Two-Dimensional Frequency Estimation

It is well known that the singular value decomposition (SVD), as the best rank-revealing factorization, furnishes the best rank- $k$ approximation to a dense matrix with expensive computational cost of $\mathcal O(M^{2}N+N^{2}M+\min (M,N)^{3})$ . Moreover, it is hard to implement in parallel, which challenges the memory storage in wireless communications data-driven system. In this letter, a fast rank-revealing technique, namely, bilateral random projections (BRP) with $\mathcal O(MN)$ operations, is exploited for two-dimensional (2-D) frequency estimation of a complex sinusoid in noisy environment. Based on the resulting data matrix, whereafter, two-stage QR factorization frequency estimation method with the weighted least squares (WLS) as solver, is proposed to reduce the computational complexity of those SVD-based frequency estimators. Simulation results demonstrate the efficiency of the proposed algorithm in comparison with several frequency estimation approaches and the Cramer-Rao lower bound (CRLB) as benchmark.

Second order multi-synchrosqueezing transform for rub-impact detection of rotor systems

Rub-impact fault is one of the most common and severe failure modes for rotating machinery. Disclosing the changing dynamic in rub-impact fault signal could provide a basic foundation for rub-impact detection of rotor systems. In this study, a dynamic model of a flexible rotor system is established to simulate the rub-impact fault signal to help us understand the dynamic characteristics of rub-impact fault signal. Meanwhile, considering that an advanced time-frequency analysis method is of vital importance in an effective rub-impact fault detection method. A new time-frequency analysis algorithm termed as second order multi-synchrosqueezing transform is also proposed in this study, in which a second order two-dimensional instantaneous frequency estimation is embedded into a multi-synchrosqueezing framework. It is shown that the proposed method could produce a time-frequency representation result with a high time-frequency resolution. Assisted by the proposed method, the impulse shaped amplitude modulated phenomenon in high frequency band and the fast varying frequency modulated phenomenon around the rotation frequency and its fractional or super harmonics are clearly revealed through the analysis of rub-impact fault signals from both dynamical simulation and experimental cases.

FMCW MIMO 레이다를 이용한 거리-각도 동시 추정 기법

Frequency-modulated continuous wave(FMCW) radars with array antennas are widely used because of their light weight and relatively high resolution. A usual approach for the joint range and angle estimation of a target using an array FMCW radar is to create a range-angle matrix with the deramped received signal, and subsequently apply two-dimensional(2D) frequency estimation methods such as 2D fast Fourier transform on the range-angle matrix. However, such frequency estimation approaches cause bias errors since the frequencies in the range-angle matrix are not independent. Therefore, we propose a new maximum likelihood-based algorithm for joint range and angle estimation of targets using array FMCW radar, and demonstrate that the proposed algorithm achieves the Cramér-Rao bounds, both for range as well as angle estimation.

Joint Two-Dimensional DOA and Frequency Estimation for L-Shaped Array via Compressed Sensing PARAFAC Method

In this paper, we combine the compressed sensing theory with the parallel factor (PARAFAC) model to present a 2-D direction of arrival (2D-DOA) and a frequency estimation algorithm for an L-shaped array. We first build the multi-delay outputs data as the PARAFAC model, then compress it with partitioning and perform the PARAFAC decomposition through a trilinear alternating least square algorithm. Finally, we reconstruct the received data with sparsity to obtain the automatically paired 2D-DOA and frequency. The proposed algorithm is effective for both uniform and non-uniform L-shaped array, and owing to the compression process, it holds the properties of lower computational complexity and smaller capacity for data storage, compared with a traditional PARAFAC algorithm. The angle and frequency estimation performance of the proposed algorithm is close to the traditional PARAFAC method, and outperforms the estimating signal parameters via a rotational invariance techniques algorithm and a propagator method. Simulation results verify the effectiveness and superiority of our approach.

Unitary PUMA Algorithm for Estimating the Frequency of a Complex Sinusoid

One-dimensional (1-D) and two-dimensional (2-D) frequency estimation for a single complex sinusoid in white Gaussian noise is a classic signal processing problem with numerous applications. It is revisited here through a new unitary principal-singular-vector utilization modal analysis (PUMA) approach, which is realized in terms of real-valued computations. The 2-D unitary PUMA is first formulated as an iteratively weighted least squares optimization problem. Recognizing that only one iteration is sufficient when 2-D unitary PUMA is initialized using least squares, a computationally attractive closed-form solution is then obtained. A variant of 2-D unitary PUMA is also developed for the 1-D case. Due to the real-valued computations and closed-form expression for the frequency estimate, the unitary PUMA is more computationally efficient than a number of state-of-the-art methods. Furthermore, the asymptotic variances of 1-D and 2-D unitary PUMA estimators are theoretically derived, and numerical results are included to demonstrate the effectiveness of the proposed methods.

Modified two-stage separated virtual steering vector-based algorithm for high resolution inverse synthetic aperture radar imaging

A computationally efficient propagator and two-stage separated virtual steering vector based algorithm (SVSV) is recently developed by D. Liu and J. Liang for two-dimensional (2D) frequency estimation. SVSV has introduced a novel electric angle z to jointly estimate the 2D components (frequencies or scatterers' locations) and to avoid the incorrect mismatch. However, SVSV cannot resolve the multiple 2D components having equivalent value of z. This problem limits the use of SVSV in ISAR imaging application. Hence, in this paper, we have proposed a new modified SVSV method called MSVSV for 2D ISAR imaging. Main contributions of our work are: (a) use of the propagator based subspace methods (SVSV and MSVSV) for 2D high resolution ISAR imaging. (b) We have suggested a technique to estimate the number of unknown 2D components prior to calculating the propagator operator from the covariance matrix. (c) We have incorporated a technique, due to which MSVSV can successfully resolve the multiple scatterers sharing the same electric angles, where SVSV fails. Radar images are generated for simulated and experimental target data (collected at AERO, Pakistan) by using SVSV, MSVSV and conventional Fourier Transform methods.

Two-dimensional frequency estimation using non-unitary joint diagonalisation

Joint diagonalisation (JD) is an effective tool in many signal processing applications. A non-unitary JD method is proposed to estimate the two-dimensional (2D) frequencies. Experiments show that the proposed algorithm achieves good performance and the estimated 2D frequencies can be paired automatically.

Estimation of Two-Dimensional Frequencies Using Modified Matrix Pencil Method

The problem of multiple two-dimensional (2-D) sinusoidal frequency estimation is considered. A modified matrix pencil method is proposed to simultaneously estimate the frequency pairs in the signal, thereby bypassing the computationally expensive pairing operation as seen in the literature. Simulation results show that the accuracy of the estimates for each frequency from our technique is better than or comparable to that of existing methods and the variance of the estimates are close to the Crameacuter-Rao bound. Simulation results also show that our method provides accurate and consistent frequency estimation results that other methods cannot provide with less or comparable computational complexity

An Eigenvector-Based Approach for Multidimensional Frequency Estimation With Improved Identifiability

This paper presents an algebraic method for two-dimensional (2-D) and multidimensional frequency estimation by exploiting eigenvector structure. The algorithm is based on multidimensional smoothing and data folding, and offers significantly improved identifiability (ID) over existing algebraic approaches, thus is termed the improved multidimensional folding (IMDF) algorithm. The ID, performance, and computational complexity of the proposed algorithm are analyzed in detail. In the 2-D case, it is shown that with the IMDF algorithm, up to approximately 0.34M1(M2+1) 2-D frequencies can be uniquely resolved with probability one from an M1 by M2 data mixture (assuming M1gesM2), while the most relaxed ID bound offered by existing algebraic approaches is approximately M1M2/4. Unlike most eigenvalue techniques that usually require an extra frequency association step, the IMDF algorithm achieves automatic frequency pairing once an eigenvalue decomposition problem is solved because frequencies are estimated from the eigenvectors instead of the eigenvalues. Theoretical analysis and simulation results demonstrate its competitive performance compared to the Crameacuter-Rao bound (CRB)

A novel algorithm for two-dimensional frequency estimation

This paper addresses the two-dimensional (2-D) frequency estimation embedded in additive Gaussian noise. By use of the biorthogonality of matrices and rotational invariance property, we construct an interesting cost function and propose a novel iterative algorithm for 2-D frequency estimation, which obtains one column of the Vandermonde matrix containing 1-D frequencies and the corresponding column of the Vandermonde matrix containing the other 1-D frequencies at each stage. Therefore, the proposed algorithm can pair the 2-D frequencies automatically. The convergence of the proposed iterative algorithm is also proven. Moreover, all the columns of the frequency matrices can be obtained by systematically multistage decomposition and multistage reconstruction. Simulation results are provided to show the good performance of the proposed algorithm.

A novel method for two-dimensional frequency estimation

This paper proposes a novel solution to two-dimensional (2-D) frequency estimation problems. The solution is applicable to the cases where the data length is much larger in one dimension than the other. The method estimates 2-D frequencies based on several one-dimensional (1-D) frequency estimation processes and hence has a low computational complexity. To avoid resolving close frequencies in 1-D processing, we construct matrices to estimate the linear combinations of the 2-D frequencies. Performance evaluation of this method is presented based on the comparison of the Crame/spl acute/r-Rao bound (CRB) and numerical simulations.

Performance comparison of two methods for 2-D frequency estimation in both medium and high SNR cases

This paper further analyses the asymptotical estimation variances of the MUSIC and MP (matrix pencil) methods for two-dimensional (2-D) frequency estimation, assuming a number of 2-D snap-shots and each snap-shot is a large 2-D array of data. The new expressions obtained for the asymptotic variances are valid for both medium and high SNR cases. For the single 2-D frequency case, the new expressions are not only most explicit but also general enough to incorporate the previous existing results as special cases.

An efficient algorithm for two-dimensional frequency estimation

This paper presents a computationally efficient eigenstructure-based 2D-MODE algorithm for two-dimensional frequency estimation. We derive the theoretical performance of the 2D-MODE estimator and show that it is asymptotically statistically efficient under either the assumption that the number of temporal snapshots is large or the signal-to-noise ratio is high. Numerical examples showing the performance of this algorithm and comparing it with the computationally efficient subspace rotation algorithms are also given. We show that the statistical performance of the 2D-MODE algorithm is better than that of the subspace rotation methods. The amount of computations required by the former is no more than a few times of that needed by the latter for either small numbers of spatial measurements or a single temporal snapshot, which are the cases of interest herein.

Statistical analysis of an eigendecomposition based method for 2-D frequency estimation

An eigendecomposition based method for two-dimensional frequency estimation is analyzed in this paper. This method, to be referred to as matrix pencil (MP) method, computes a smoothed data covariance matrix, then its eigendecomposition, and then the two-dimensional frequencies via a MP approach. The MP method is now known to be more efficient in computation than many other methods and able to provide a near optimum performance for relatively large signal-to-noise ratio (SNR). The aim of this paper is to provide a further analysis of the MP method assuming a moderate SNR. To make the problem tractable, a large two-dimensional data set is considered. In this paper, a number of fundamental relations inherent in the MP method are revealed which lead to a general expression of the large-sample covariances of the estimated two-dimensional frequencies. The large-sample covariances are reduced to a very simple form for the single two-dimensional frequency case. The theoretical covariances are verified by the simulation results.

An efficient two-dimensional frequency estimator

The problem of two-dimensional frequency estimation of a sinusoid embedded in complex white Gaussian noise is addressed. A frequency estimator and its statistical performance are derived. The estimator is demonstrated to be an efficient estimator (it achieves the Cramer-Rao bound) for high signal-to-noise ratios. The results of a computer simulator which compares the variance with that of the maximum likelihood estimator and the theoretical two-dimensional Cramer-Rao bound are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>