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The rapid progress in radar and communication places increasing demands on low-latency and energy-efficiency array signal processing methods. There is an emerging direction of constructing analog computing processors for directly processing electromagnetic (EM) waves. However, the existing methods are constrained by 2D physical aperture and imprecise design process with inefficient computing architecture, resulting in limited sensing resolution and number of separated sources. Here, we present a fully-analog array signal processor (FASP) using 3D aperture engineering framework to perform super-resolution direction-of-arrival estimation, source number estimation, and multi-channel source separation in parallel for both coherent and incoherent sources. 3D aperture engineering is realized by constructing deep cascaded metasurface layers so that the diffractive propagation from oblique incident fields can be layer-wise modulated and piecewise encoded for perceiving EM fields far exceeding physical aperture limits. The multi-dimensional synthetic aperture (MSA) training is developed to characterize the metasurface modulation and optimize the neuro-augmented physical model for extending system aperture and generating high-order nonlinear angular response. FASP orthogonalizes the array response vectors of communication channels to map them into antenna detectors in the analog domain. The $N$-layer FASP has the capability to achieve ~N times higher angular resolution than the Rayleigh diffraction limit. Experiments further validate the source number estimation and independent channel separation of 10-target that can suppress radar jamming signals by ~20 dB and enhance channel communication capacity by 13.5 times at 36~41 GHz. FASP heralds a paradigm shift in signal processing for super-resolution optics, advanced radar, and 6G communications.