{"ID":2900948,"CreatedAt":"2026-06-01T05:51:17.9442275Z","UpdatedAt":"2026-06-01T06:23:29.641557848Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2605.31059","arxiv_id":"2605.31059","title":"CRB-Optimal Arrays and Waveforms in Active Sensing: Role of Redundancy and Spatial Covariance of Array Geometry","abstract":"This paper characterizes the performance limits of optimal array designs using orthogonal and coherent waveforms for both linear and planar arrays. For orthogonal waveforms, we show that the single-target Cramér-Rao Bound (CRB) depends on the sum of the so-called spatial variances of the transmit (Tx) and receive (Rx) arrays, or equivalently, the spatial variance of the sum co-array weighted by the multiplicities of the virtual sensors. This reveals that CRB-optimal geometries are inherently redundant, highlighting a fundamental trade-off between mean squared error (MSE) and identifiability in parameter estimation. Moreover, we derive optimal Tx-Rx sensor allocations given a total sensor budget and show that unequal allocation (favoring the Rx) is optimal even for nonredundant arrays, questioning conventional designs. We extend our results to planar arrays, providing a new general condition that the spatial covariances of the Tx and Rx arrays should satisfy for the optimal waveforms to direct power in the target direction. Additionally, we establish a connection between Diophantine equations and array geometries with equal CRB, along with a constructive method for designing such arrays. Our work provides new guidelines for and insights into optimal array and waveform design with relevance in emerging active sensing multiple-input multiple-output systems.","short_abstract":"This paper characterizes the performance limits of optimal array designs using orthogonal and coherent waveforms for both linear and planar arrays. For orthogonal waveforms, we show that the single-target Cramér-Rao Bound (CRB) depends on the sum of the so-called spatial variances of the transmit (Tx) and receive (Rx)...","url_abs":"https://arxiv.org/abs/2605.31059","url_pdf":"https://arxiv.org/pdf/2605.31059v1","authors":"[\"Ids van der Werf\",\"Robin Rajamäki\",\"Geert Leus\"]","published":"2026-05-29T09:29:33Z","proceeding":"eess.SP","tasks":"[\"eess.SP\",\"cs.IT\"]","methods":"[]","has_code":false}