Improved Coarray Interpolation Algorithms with Additional Orthogonal Constraint for Cyclostationary Signals

Abstract

Many modulated signals exhibit a cyclostationarity property, which can be exploited in direction-of-arrival (DOA) estimation to effectively eliminate interference and noise. In this paper, our aim is to integrate the cyclostationarity with the spatial domain and enable the algorithm to estimate more sources than sensors. However, DOA estimation with a sparse array is performed in the coarray domain and the holes within the coarray limit the usage of the complete coarray information. In order to use the complete coarray information to increase the degrees-of-freedom (DOFs), sparsity-aware-based methods and the difference coarray interpolation methods have been proposed. In this paper, the coarray interpolation technique is further explored with cyclostationary signals. Besides the difference coarray model and its corresponding Toeplitz completion formulation, we build up a sum coarray model and formulate a Hankel completion problem. In order to further improve the performance of the structured matrix completion, we define the spatial spectrum sampling operations and the derivative (conjugate) correlation subspaces, which can be exploited to construct orthogonal constraints for the autocorrelation vectors in the coarray interpolation problem. Prior knowledge of the source interval can also be incorporated into the problem. Simulation results demonstrate that the additional constraints contribute to a remarkable performance improvement.

Sparse Array Design Exploiting the Augmented Conjugate Correlation Statistics for DOA Estimation

“…The sources can be noncircular signals or cyclostationary signals. The way to construct the coarrays with cyclostationary signals can be found in [24]. In this paper, we assume K narrowband far-field noncircular signals s k (t)(k = 1, .…”

“…The other is utilizing the specific non-zero conjugate correlation statistics such as the pseudo covariance or the conjugate cyclic correlation, which characterize two kinds of modulating signals, viz the noncircular signals and the cyclostationary signals. Some literatures have reported that by exploiting this statistic property, the virtual array aperture is extended by constructing the additional sum coarray with the pseudo covariance of noncircular signals [22] or with the conjugate cyclic correlation of cyclostationary signals [23], [24].…”

“…Two obvious issues are emerged in the aforementioned methods [22]- [24]. The additional sum coarrays are usually inconsecutive and irregular distributed, owning to that the majority of sparse arrays are designed to form consecutive difference coarrays regardless of the structure of the sum coarrays.…”

A Novel Nested Configuration Based on the Difference and Sum Co-Array Concept

“…As the degree of freedom (DOF) is limited by the array aperture, such estimators can detect no more than sources by using R physical sensors. In order to enhance the detection ability, many novel methods, such as the spatial smoothing based MUSIC (SS MUSIC) method [ 13 ], apply the concept of the Khatri–Rao (KR) product to sparse arrays for constructing the difference co-array (DCa) [ 13 , 14 , 15 , 16 , 17 , 18 ]. The combination of sparse arrays and the DCa concept can improve the DOF capacity and detect as many as sources.…”

DOA Estimation for Coprime Linear Array Based on MI-ESPRIT and Lookup Table

“…For the coprime linear array (CLA), two mainstream DOA estimation methods exist: the virtualization array sensor method [ 16 , 17 , 18 , 19 , 20 ] and the solving-ambiguity-based method [ 21 , 22 , 23 , 24 , 25 , 26 ]. In the solving-ambiguity-based method, CLA can be decomposed into two uniform linear subarrays, and then DOA can be achieved according to conventional DOA estimation algorithms [ 7 , 8 , 9 ].…”