Abstract
In recent years, much attention has been focused on difference co-array perspective in DOA estimation field due to its ability to increase the degrees of freedom and to detect more sources than sensors. In this article, a fractional difference co-array perspective (FrDCA) is proposed by vectorizing structured second-order statistics matrices instead of conventional zero-lag covariance matrix. As a result, not only conventional virtual sensors but also the fractional ones can be utilized to further increase the degrees of freedom. In a sense, the proposed perspective can be viewed as an extended structured model to generate virtual sensors. Then, as a case study, four DOA estimation algorithms for wideband signal based on the FrDCA perspective are specifically presented. The fractional virtual sensors can be generated by dividing the wideband signal into many sub-band signals. Accordingly, the degree of freedom and the maximum number of resolvable sources are increased. The corresponding numerical simulation results validate the advantages and the effectiveness of the proposed perspective.
Highlights
Direction of arrival (DOA) estimation is a critical problem in phased-array radar signal processing field [1]
2.2 Fractional difference co-array perspective According to the above data model, we propose the perspective and definition of fractional difference co-array perspective (FrDCA)
Any desired virtual sensor position can be generated by choosing an appropriate operation frequency fk. In a sense, such FrDCA generated by multi-frequencies operation has been utilized in [16, 17] to fill the missing co-array elements, thereby enabling the co-prime array to effectively utilize all of the offered DOFs. 3. β = 0, α = 0; The pair-wise element positions can be expressed as ci,j = β(ai + aj) = cj,i, which indicates that the redundancy of any virtual sensor position is no less than two
Summary
Direction of arrival (DOA) estimation is a critical problem in phased-array radar signal processing field [1]. The founder of the DCA model, proposed an auto-focusing based method in [20] to extend the co-array concept into wideband signal case. As an extension, the fractional difference co-array (FrDCA) perspective is proposed by introducing two fractional factors, which can generate either fractional difference sensor position or conventional integral difference ones. Such an extension would bring some advantages for the wideband signal DOA estimation: the sub-bands with different center frequencies would be converted into a set of signal received from the fractional virtual sensors. The symbol and ⊗ denote the Khatri-Rao product and Kronecker product, respectively. |A| denotes the cardinality of set A, which is a measure of the number of elements of the set A
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