Joint Angle-frequency Estimation Research Articles

Frequency-Angle Spectrum Hole Detection with Taylor Expansion Based Focusing Transformation

In cognitive radio (CR), the problem of spectrum hole detection has been extensively studied in single dimension, such as frequency domain, spatial domain, and so on. Recently, a class of two dimension spectrum hole detection methods, named as joint angle-frequency estimation (JAFE), has attracted much attention. Nevertheless, most of the existing approaches are only suitable for the scenario with matching frequency-angle pairs, rather than the non-matching scenario between the two parameters, like space division multiple access (SDMA) or frequency division multiplexing access (FDMA) communication mode which allows the same frequency band (or angle) to be reused in different angles (or frequencies). For the above two cases, including matching and non-matching scenarios, this paper develops an effective frequency-angle spectrum hole detection algorithm with Taylor expansion based focusing transformation (TFT-FASHD), on the basis of signal sparse representation by extending the array manifold from angle domain to frequency-angle domain. In the proposed method, for Fourier transform representation of the sparse model, a focusing transformation based on Taylor expansion is first performed to focus the signal subspaces at different frequencies to a single frequency, so as to carry out dimension reduction of dictionary in angular domain. TFT is derived by decomposing the array manifold with Taylor expansion, and further the optimum focusing frequency of focusing transform is discussed theoretically. Second, atoms with high representative performance are chosen by the presented TFT and compressed sensing (CS). Third, according to the low dimension dictionary, the TFT-FASHD is implemented by CS under multiple measurement vector (MMV) circumstances. The accuracy of the algorithm in non-matching scenario is verified by simulation results. For the matching scenario, compared with the related JAFE methods, the proposed algorithm has a lower computational complexity, smaller detection error, and higher energy efficiency, which are validated through simulation.

Joint Angle–Frequency Estimation Using Nested Sampling with One-Bit Quantization

The problem of joint angle and frequency estimation is considered in this paper. An algorithm using spatial–temporal nested sampling and one-bit quantization is developed. It is shown that under moderate condition when the signal-to-noise ratio is low enough, the defined one-bit correlation matrix has linear relationship with the unquantized one, and therefore, subspace-based algorithms can be applied to this one-bit correlation matrix directly. The enhanced identification performance, offered by the nested sampling, can also be provided when one-bit quantization is used. Simulation results are provided to verify the performance of the presented algorithm.

Joint angle–frequency estimation with spatiotemporal nested sampling

In this study, the authors propose a new method for joint estimation of angle and frequency parameters in pulsed Doppler radar systems. Unlike many existing methods, in which uniform sampling with Nyquist rate are used for spatiotemporal data acquisition, the presented method is based on the non-uniform nested sampling. The basic idea of is to use the radar cross-sections diversity in multiple coherent processing intervals to construct a virtual spatial–temporal manifold with extended degree of freedom. Through theoretical analysis and computer simulations, they show that the proposed method can offer better identifiability performance and higher parameter estimation accuracy, as compared with existing methods.

Unitary-JAFE algorithm for joint angle–frequency estimation based on Frame–Newton method

The joint angle–frequency estimation (JAFE) based on the multidimensional ESPRIT is recently developed high-resolution parameter estimation technique for determining the directions of arrival (DOAs) and center frequencies of a number of narrow-band sources in a band of interest impinging on the far field of a planar array. In this paper, we present a simple and efficient joint angle–frequency estimation method via the unitary transformation, named as Unitary-JAFE algorithm. In the final stage of Unitary-JAFE, the matrix required to eigendecomposition is a complex unsymmetric matrix. For the eigendecomposition of a complex unsymmetric matrix, we will develop an effective algorithm based on Frame method and Newton iteration method, referred as Frame–Newton algorithm. The proposed method offers a number of advantages over other recently proposed ESPRIT-based techniques by taking advantage of the temporal smoothing, spatial smoothing, and forward–backward averaging techniques. Firstly, except for the final eigenvalue decomposition of dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Secondly, in the final stage of the proposed algorithm, the real and imaginary parts of the i th eigenvalue of a matrix are one-to-one related to the frequency and direction of arrival (DOA) of the i th source. That is, the pairing of the estimated frequency and DOA is automatically determined. Thirdly, the proposed method avoids the joint diagonalization processing, which reduces the computation complexity. Finally, simulation results are presented verifying the efficacy of the proposed algorithm.

Analysis of joint angle-frequency estimation using ESPRIT

High-resolution parameter estimation techniques have been applied to jointly estimate multiple signal parameters. we consider the problem of determining the directions and center frequencies of a number of narrowband sources in a band of interest. We present a joint angle-frequency estimation method, based on the multidimensional ESPRIT algorithm. A perturbation error analysis gives bounds on the parameter estimates and provides optimal values for the temporal and spatial smoothing parameters. The analysis is shown to be consistent with simulation results.

Forward–backward spatio-temporal smoothing for joint angle-frequency estimation in multipath environment

A new method is proposed for joint angle-frequency estimation (JAFE) in the presence of coherent signals. This method is based on constructing a forward–backward smoothed spatio-temporal array data matrix by using the proposed forward-backward spatio-temporal smoothing method before performing the JAFE algorithm. The simulation results show that the proposed method is superior to the published spatio-temporal smoothing method.