Multidimensional Sinusoidal Frequency Estimation Using Subspace and Projection Separation Approaches

Abstract

In this correspondence, a computationally efficient method that combines the subspace and projection separation approaches is developed for R-dimensional (R-D) frequency estimation of multiple sinusoids, where R ≥ 3, in the presence of white Gaussian noise. Through extracting a 2-D slice matrix set from the multidimensional data, we devise a covariance matrix associated with one dimension, from which the corresponding frequencies are estimated using the root-MUSIC method. With the use of the frequency estimates in this dimension, a set of projection separation matrices is then constructed to separate all frequencies in the remaining dimensions. Root-MUSIC method is again applied to estimate these singletone frequencies while multidimensional frequency pairing is automatically attained. Moreover, the mean square error of the frequency estimator is derived and confirmed by computer simulations. It is shown that the proposed approach is superior to two state-of-the-art frequency estimators in terms of accuracy and computational complexity. Index TermsMultidimensional frequency estimation, subspace method, projection separation.

Computationally efficient estimation of multi-dimensional spectral lines

“…To avoid cluttering the figure, the FFT-based periodogram estimates are not shown as it is well known that these will also yield statistically efficient estimates for this setting, if using a sufficiently large zero-padding; here, in order to do so, it would require a total grid size of at least 2 48 , for the 3-D FFT at SNR= 10. Similarly, it is well-known that several parametric estimators, such as the FB-Root-MUSIC algorithm presented in [9], will also achieve the CRB, if given full knowledge of the model order.…”

“…In particular, the two-dimensional (2-D) case has been investigated in several works, such as [3][4][5], wherein the authors examine algorithms based on the problem's eigenvector structure, exploit a sparsity framework, as well as a subspace framework, respectively. Further works include [6], which examined the 3-D case, [7,8], wherein different compressed sensing methods are compared for high dimensional NMR signals, and [8,9], which examined high-dimensional subspace based estimators. Several works also focus on one of the computationally most efficient ways of forming multidimensional sinusoidal paramThis work was supported in part by the Swedish Research Council and the Crafoord's and Carl Trygger's foundations.…”

“…Finally, the full data set is utilized to refine the initial estimate. Numerical examples illustrate the statistically efficient performance of the proposed estimator, as well as the required computational complexity as compared to both the multi-dimensional periodogram and the commonly used efficient parametric estimator FB-Root-MUSIC proposed in [9].…”

Joint Range‐Doppler‐Angle Estimation for OFDM‐Based RadCom System via Tensor Decomposition

“…TPM initialized by the results of SeROAP is also considered. In addition, the subspace-based forward-backward root-MUSIC (FB-RootMUSIC) method [20] incorporating the inherent signal structures is selected for comparison.…”

“…The number of random initializations is selected in the collection I = {1, 5,10,15,20,25,30,35,40,45,50,75, 100}. Figure 3 shows the detection probability versus the number of random initializations for SNR = -30, -31, and -32 dB, respectively.…”