BlockMFRAs: Block-Wise Multiple-Fold Redundancy Arrays for Joint Optimization of Radiometric Sensitivity and Angular Resolution in Interferometric Radiometers

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Radiometric sensitivity and angular resolution are two of the most important performances for microwave and millimeter-wave interferometric radiometers. These two performance metrics are mutually constrained. Generally, low-degradation arrays (LDAs) or low-redundancy arrays (LRAs) are employed to individually optimize radiometric sensitivity or angular resolution in interferometric array synthesis tasks. In this article, we propose a novel kind of array configuration, named block-wise multiple-fold redundancy arrays (BlockMFRAs), to achieve joint optimization of radiometric sensitivity and angular resolution for interferometric radiometers. The BlockMFRA with any number of elements can be efficiently constructed by exploiting combinatorial natures of three number sequences, that is, a difference basis (DB), a cyclic difference set (CDS), and a bunched pattern (BP). In more detail, we introduce a set of new analytical DBs, corresponding to multiple-fold redundancy arrays (MFRAs) with <tex-math notation="LaTeX">β </tex-math> -fold redundant baselines for <tex-math notation="LaTeX">β ∈ N⁺ </tex-math> , to determine layout positions of normal blocks in the BlockMFRA. Each normal block shares an identical subarray configuration with elements located by a suitable CDS. Then, a specific BP, used as a supplementary block, is properly combined with the above normal blocks. The generated block-wise structure enables the BlockMFRA to possess a relatively uniform distribution of baseline redundancy for attaining satisfactory radiometric sensitivity. Meanwhile, for a given baseline redundancy’s fold <tex-math notation="LaTeX">β </tex-math> , the BlockMFRA can achieve a better angular resolution than arrays designed by traditional methods. Several important properties of BlockMFRAs are proved theoretically, and numerical analyses are conducted to demonstrate BlockMFRAs’ superior performances.