Time-frequency MUSIC Research Articles

Polarimetric Direction of Arrival Estimations Based on Adaptive Linear Time-Frequency Transforms

A spatially polarized time-frequency distribution (SPTFD) based on dual-polarized double-fed antenna arrays is adapted to deal with polarization-unstable signals. A linear time-frequency (TF) representation was used for an instantaneous frequency (IF) estimate, primarily due to its simplicity and immunity to cross-interference. Using a set of linear TF transformations using Gaussian windows and Fourier oscillation kernels, the IF estimated window widths of multiple unstable signals are obtained. This paper introduces a new method for estimating the direction of arrival (DOA) of polarized waves using adaptive linear time-frequency transforms. In this paper, a narrowband far-field point source on the receiving array is analyzed. The source signal is split into two orthogonally polarized components. The optimal window is determined by the first derivative of the IF; for this purpose, we take a simple algorithm for solving the derivative and optimize it. In developing TF-adaptive and fully automatic TF display technology, the first method is to use the time-adaptive window for minimizing the IF estimate mean square error (MSE) sum at each moment, while the second procedure is to adjust according to time and frequency and minimize estimate MSE sum at each position in the TF region. Due to its combination with signal polarization, the spatial time-frequency distribution (STFD) gains more freedom and thus perfects the phonon space estimation of noise and signal. On the SPTFD platform, polarized time-frequency multiple signal classification (PTF-MUSIC) is used for the estimation of signal direction of arrival, which outperforms conventional time-frequency MUSIC. Using the example of a synthesized signal, this method outperforms conventional techniques in DOA estimation.

Spatially Smoothed TF-Root-MUSIC for DOA Estimation of Coherent and Non-Stationary Sources Under Noisy Conditions

This paper proposes a method for efficient Direction-of-Arrival (DOA) estimation of coherent and non-stationary sources under adverse noise conditions. The method consists of three main parts: 1) derivation of Spatial Time-Frequency Distribution (STFD) matrix; 2) application of the forward-backward spatial smoothing technique; 3) estimating the angles of arrival by solving for the roots of the polynomial. The key significance of the proposed method is that the combination of existing methods and techniques allows an estimation of DOA angles for both coherent and non-stationary source signals under noise. Whereas the individual use of the existing methods does not show adequate performance under these conditions. The experiments allow studying the performance of the proposed method for 1) both coherent and non-coherent clean sinusoidal signals; 2) noisy non-stationary chirp signals; 3) coherent and non-stationary signals under noise. Furthermore, extensive simulations have been carried out to compute the root mean square error (RMSE) performance of the proposed method in comparison with the existing ones. The experiments have been designed for varying number of microphones, level of noise, and value of the time-frequency threshold. As a result of the experiments, we observe the efficacy of the proposed method in comparison with the conventional Root-MUSIC and Time-Frequency MUSIC (TF-MUSIC) methods.

Spatial polarimetric time-frequency distribution based DOA estimation: combining ESPRIT with MUSIC

Spatial spectrum estimation technology has always been the focused research project in an array signal processing of High Frequency Surface Wave Radar (HFSWR). This paper takes the polarization sensitive array for the model and combines with time-frequency analysis method for DOA estimation of HFSWR echo signals, which can make full use of the spatial, time-frequency, and polarized domain information of signals. The time-frequency MUSIC and ESPRIT algorithms of integrated polarization information are studied, and the improved algorithm is proposed based on the advantages and disadvantages of both algorithms. The improved algorithm first estimates the azimuth angles of signals roughly with the polarized time-frequency ESPRIT algorithm and then determines a small scope centered on each azimuth. Within the scope, a more accurate DOA-estimated value is got by spectral peak search with MUSIC algorithm, so it can save computation time on the basis of accuracy of the DOA estimation, and their performance is analyzed by computer simulations.

Time–frequency beamforming for nondestructive evaluations of plate using ultrasonic Lamb wave

The objective of this study is to detect structural defect locations in a plate by exciting the plate with a specific ultrasonic Lamb wave and recording reflective wave signals using a piezoelectric transducer array. For the purpose of eliminating the effects of the direct excitation signals as well as the boundary-reflected wave signals, it is proposed to improve a conventional MUSIC beamforming procedure by processing the measured signals in the time–frequency domain. In addition, a normalized, damped, cylindrical 2-D steering vector is proposed to increase the spatial resolution of time–frequency MUSIC power results. A cross-shaped array is selected to further improve the spatial resolution and to avoid mirrored virtual image effects. Here, it is experimentally demonstrated that the proposed time–frequency MUSIC beamforming procedure can be used to identify structural defect locations on an aluminum plate by distinguishing the defect-induced waves from the excitation-generated and boundary-reflected waves.

High-resolution direction finding of non-stationary signals using matching pursuit

One of the main goals of time–frequency (TF) signal representations in non-stationary array processing is to equip multi-antenna receivers with the ability to separate sources in the TF domain prior to direction finding. This permits high-resolution direction-of-arrival (DOA) estimation of individual sources and of more sources than sensors. In this paper, we use linear decomposition of sensor data based on matching pursuit (MP). The leading atoms of the MP, which capture most of the source TF signatures, can be different for different sources and, as such, provide the desired source discrimination. The MP coefficients with high signal-to-noise ratio (SNR) and corresponding to the leading decomposition atoms are used to develop the MP-MUSIC DOA estimation for non-stationary source signals. We demonstrate the source discriminatory capability of the proposed technique using linear FM, nonlinear FM, and other non-stationary signals. Further, we compare MP-MUSIC performance with conventional MUSIC and the time–frequency MUSIC, which incorporates bilinear transforms.

Spatial polarimetric time-frequency distributions for direction-of-arrival estimations

Time-frequency distributions (TFDs) are traditionally applied to a single antenna receiver with a single polarization. Recently, spatial time-frequency distributions (STFDs) have been developed for receivers with multiple single-polarized antennas and successfully applied for direction-of-arrival (DOA) estimation of nonstationary signals. In this paper, we consider dual-polarized antenna arrays and extend the STFD to utilize the source polarization properties. The spatial polarimetric time-frequency distributions (SPTFDs) are introduced as a platform for processing polarized nonstationary signals, which are received by an array of dual-polarized double-feed antennas. This paper deals with narrow-band far-field point sources that lie in the plane of the receiver array. The source signals are decomposed into two orthogonal polarization components, such as vertical and horizontal. The ability to incorporate signal polarization empowers the STFDs with an additional degree of freedom, leading to improved signal and noise subspace estimates for direction finding. The polarimetric time-frequency MUSIC (PTF-MUSIC) method for DOA estimation based on the SPTFD platform is developed and shown to outperform the time-frequency, polarimetric, and conventional MUSIC techniques, when applied separately.

Time–frequency maximum likelihood methods for direction finding

This paper proposes a novel time–frequency maximum likelihood ( t– f ML) method for direction-of-arrival (DOA) estimation for nonstationary signals impinging on a multi-sensor array receiver, and compares this method with conventional maximum likelihood DOA estimation techniques. Time–frequency distributions localize the signal power in the time–frequency domain, and as such enhance the effective SNR, leading to improved DOA estimation. The localization of signals with different time–frequency signatures permits the division of the time–frequency domain into smaller regions, each containing fewer signals than those incident on the array. The reduction of the number of signals within different time–frequency regions not only reduces the required number of sensors, but also decreases the computational load in multidimensional optimizations. Compared to the recently proposed time–frequency MUSIC ( t– f MUSIC), the proposed t– f ML method can be applied to coherent environments, without the need to perform any type of preprocessing that is subject to both array geometry and array aperture.

Estimating neural sources from each time-frequency component of magnetoencephalographic data.

We have developed a method that incorporates the time-frequency characteristics of neural sources into magnetoencephalographic (MEG) source estimation. This method, referred to as the time-frequency multiple-signal-classification algorithm, allows the locations of neural sources to be estimated from any time-frequency region of interest. In this paper, we formulate the method based on the most general form of the quadratic time-frequency representations. We then apply it to two kinds of nonstationary MEG data: gamma-band (frequency range between 30-100 Hz) auditory activity data and spontaneous MEG data. Our method successfully detected the gamma-band source slightly medial to the N1m source location. The method was able to selectively localize sources for alpha-rhythm bursts at different locations. It also detected the mu-rhythm source from the alpha-rhythm-dominant MEG data that was measured with the subject's eyes closed. The results of these applications validate the effectiveness of the time-frequency MUSIC algorithm for selectively localizing sources having different time-frequency signatures.

Iterative algorithm for direction of arrival estimation with wideband chirp signals

A time–frequency MUSIC algorithm with narrowband models for the estimation of direction of arrival (DOA) when the source signals are chirps has been developed by Amin et al. (1998, 1999). The present authors consider wideband models. The joint time–frequency analysis is first used to estimate the chirp rates of the source signals, and then the DOA is estimated by the MUSIC algorithm with an interative approach.