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.

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