Ambiguity Analysis and Design of Sparse Arrays via Generalized Vandermonde Rank Conditions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911735019995136 |
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| author | Pesavento, Marius |
| author_facet | Pesavento, Marius |
| contents | Sparse linear arrays obtained by thinning a uniform linear array (ULA) achieve large effective apertures with a reduced number of physical sensors and have become a key enabling technology across radar, sonar, communications, and integrated sensing and communications. The price of thinning, however, is the emergence of ambiguities in the array manifold: distinct sets of directions of arrival that produce identical sensor measurements, precluding unique identification of multiple sources. Conventional sparse-array design criteria, based on beampattern shaping or estimation-performance optimization, do not fully capture how multiple steering vectors interact jointly to produce such ambiguities. This paper develops a scalable algebraic framework for the multi-source identifiability analysis of thinned ULAs. By relating the rank deficiency of the generalized Vandermonde matrix associated with the sparse steering matrix to that of a thinned Toeplitz matrix, and further to a rank condition on an augmented full-ULA steering matrix with prescribed generators, we obtain a systematic characterization of the ambiguity sets in large sparse arrays together with constructive design guidelines for ambiguity-free geometries. Algebraic and numerical examples demonstrate that the proposed framework characterizes ambiguity sets at scales well beyond the practical reach of previous sparse-array design and synthesis methods |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00360 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ambiguity Analysis and Design of Sparse Arrays via Generalized Vandermonde Rank Conditions Pesavento, Marius Signal Processing Sparse linear arrays obtained by thinning a uniform linear array (ULA) achieve large effective apertures with a reduced number of physical sensors and have become a key enabling technology across radar, sonar, communications, and integrated sensing and communications. The price of thinning, however, is the emergence of ambiguities in the array manifold: distinct sets of directions of arrival that produce identical sensor measurements, precluding unique identification of multiple sources. Conventional sparse-array design criteria, based on beampattern shaping or estimation-performance optimization, do not fully capture how multiple steering vectors interact jointly to produce such ambiguities. This paper develops a scalable algebraic framework for the multi-source identifiability analysis of thinned ULAs. By relating the rank deficiency of the generalized Vandermonde matrix associated with the sparse steering matrix to that of a thinned Toeplitz matrix, and further to a rank condition on an augmented full-ULA steering matrix with prescribed generators, we obtain a systematic characterization of the ambiguity sets in large sparse arrays together with constructive design guidelines for ambiguity-free geometries. Algebraic and numerical examples demonstrate that the proposed framework characterizes ambiguity sets at scales well beyond the practical reach of previous sparse-array design and synthesis methods |
| title | Ambiguity Analysis and Design of Sparse Arrays via Generalized Vandermonde Rank Conditions |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2606.00360 |