Pilot Decontamination over Time Frequency and Space Domains in Multi-Cell Massive MIMO System

In this article, we show that Pilot contamination problem can be seen as a source separation problem using time, frequency, and space domains. Our method capitalizes on a nonunitary joint diagonalization of spatial quadratic time-frequency (STFD) signal representation to identify the desired and interfering users. We first compute the noise subspace from the STFD matrices selected appropriately. Secondly, we use the noise subspace obtained to estimate the Elevation (El) and the Azimuth (Az) angles for which the MUSIC cost function is maximized. Numerical simulations are provided to illustrate the effectiveness and the behavior of the proposed approach

Joint 2D Direction-of-Arrival and Range Estimation for Nonstationary Sources

Passive localization of nonstationary sources in the spherical coordinates (azimuth, elevation, and range) is considered, and a parallel factor analysis based method is addressed for the near-field parameter estimation problem. In this scheme, a parallel factor analysis model is firstly constructed by computing five time-frequency distribution matrices of the properly chosen observation data. In addition, the uniqueness of the constructed model is proved, and both the two-dimensional (2D) direction-of-arrival (DOA) and range can be jointly obtained via trilinear alternating least squares regression (TALS). The investigated algorithm is well suitable for near-field nonstationary source localization and does not require parameter-pairing or multidimensional search. Several simulation examples confirm the effectiveness of the proposed algorithm

An Improved Multiple-Toeplitz Matrices Reconstruction Algorithm for DOA Estimation of Coherent Signals

The Toeplitz matrix reconstruction algorithms exploit the row vector of an array output covariance matrix to reconstruct Toeplitz matrix, which provide the direction-of-arrival (DOA) estimation of coherent signals. However, the Toeplitz matrix reconstruction method based on any row vector of the array output covariance matrix suffers from signal correlation, it results in poor robustness. The methods based on multi-row vectors suffer serious performance degradation when in the low signal-to-noise ratio (SNR) owing to the noise energy is the square of the input noise energy. To solve the above problems, we propose an improved method that exploits all rows of the time-space correlation matrix to reconstruct the Toeplitz matrix, namely TS-MTOEP. This method firstly uses the coherence of the narrowband signal and the uncorrelated noise at different snapshots to construct the time-space correlation matrix, it effectively eliminates the influence of noise. Then, the Toeplitz matrix is reconstructed via all rows of the time-space correlation matrix, which effectively improves the energy of the signal, and further results in the improvement of the SNR. Finally, the DOAs can be obtained by combining it with the subspace-based methods. The theoretical analysis and simulation results indicate that compared with the existing Toeplitz and spatial smoothing methods, the proposed method in this paper provides good performance on estimation and resolution in cases with low input signal-to-noise due to time-space correlation matrix processing. Furthermore, in cases where the DOAs between the coherent sources are closely spaced and the snapshot number is low, our proposed method significantly improves the performance of the DOA estimation. We also provide the code to realize the reproducibility of the proposed method

Subspace Analysis of Spatial Time-Frequency Distribution Matrices

Spatial time--frequency distributions (STFDs) have been recently introduced as the natural means to deal with source signals that are localizable in the time--frequency domain. Previous work in the area has not provided the eigenanalysis of STFD matrices, which is key to understanding their role in solving direction finding and blind source separation problems in multisensor array receivers. The aim of this paper is to examine the eigenstructure of the STFDs matrices. We develop the analysis and statistical properties of the subspace estimates based on STFDs for frequency modulated (FM) sources. It is shown that improved estimates are achieved by constructing the subspaces from the time--frequency signatures of the signal arrivals rather than from the data covariance matrices, which are commonly used in conventional subspace estimation methods. This improvement is evident in a low signal-tonoise ratio (SNR) environment and in the cases of closely spaced sources. The paper considers the MUSIC technique to demonstrate the advantages of STFDs and uses it as grounds for comparison between time--frequency and conventional subspace estimates