Sparse near-field arrays have limited interference suppression per sub-array
Effective DoF Collapse in Sparse Near-Field Beamforming: A Block-Rank-1 Mechanism
Information Theory
Summary
Sparse near-field arrays combine many small antenna groups spread out over a large area to send and receive signals. The authors found that the ability to reduce interference in a certain region mainly depends on each small antenna group's internal coherence, not on the total size of the whole array. This means there are fewer effective spatial channels than expected, simplifying design. They used mathematical tools to prove this and showed their ideas work with a simulation of eight satellites.
What this means in practice
- •For satellite communication engineers: Design interference suppression schemes for satellite arrays by focusing on per-sub-array coherence limits rather than the entire formation size.
- •For wireless network designers: Optimize distributed MIMO systems by accounting for effective spatial degrees of freedom collapsing to simplify beamforming strategies.
Authors
Changhao He, Xiaojuan Zhang, Francois Chin Po Shin
Abstract
Sparse near-field arrays phase-cohere $M$ widely separated sub-arrays of $N$ elements and underpin distributed MIMO, satellite formations, and integrated sensing and communication. We show that their interference suppression over a protected region is set by coherence within a single sub-array rather than by the span of the formation: the effective rank of the region covariance can collapse from $MN$ to $M$. Two independent arguments establish this. For canonical line and disk regions each diagonal covariance block is exactly a classical concentration operator, which supplies sharp per-block rank thresholds and makes fewer than one spatial degree of freedom per sub-array a conservative design rule; an orthogonal decomposition with eigenvalue interlacing gives a nonasymptotic sufficient condition that assumes nothing about the coupling between platforms. The consequences are covariance-side and beamformer-independent: the unloaded Capon functional upper-bounds worst-case signal-to-interference ratio, while its regularized counterpart scales very differently for angularly separated and for in-cone targets. An eight-satellite LEO study validates the theory, including realized worst-case SIR.