Apparent Direction-of-Arrival Synthesis via Near-Field Transmit Beamforming: Feasibility, Limits, and a Spatial-Index Modulation Application

Direction-of-arrival (DOA) estimation is normally treated as a passive, trustworthy measurement of a transmitter's physical bearing. This paper asks whether a transmit array can defeat that assumption by design: given two facing uniform linear arrays (ULAs) whose broadsides are mechanically aligned along the true line of sight (boresight, θ = 0°), can transmit-side beamforming at ULA #1 make a standard beamscan/MUSIC-style DOA estimator at the fixed, unmoved ULA #2 report an arbitrary synthesized angle θd ≠ 0° ? We show, through an exact spherical-wave channel model and a feasibility metric derived from the channel's singular value decomposition, that this "apparent-DOA synthesis" is physically real and controllable, but only within the near-to-moderate field of the array pair; it becomes fundamentally impossible once the link enters the deep far field, where the line-of-sight channel matrix collapses to rank one. We quantify the governing scaling laws — Fraunhofer range RFF ∝ N², achievable synthesis fidelity versus range and frequency — for both a generic RF/microwave array and, as a detailed case study, an underwater acoustic link (Thorp absorption, spherical spreading, sonar-equation link budget). We further introduce a defensible, pairwise-correlation-verified metric for the number of mutually distinguishable synthesized-angle "index states," and use it to determine when encoding data bits through the choice of θd yields real throughput gain on top of conventional space-time block coding (STBC) and spatial multiplexing (SMX). We find that SMX at QPSK and above already extracts more bits per spatial mode than index selection can, so the technique adds essentially nothing there; but for diversity-oriented (STBC-like) links and for RF-chain-constrained hybrid-beamforming hardware, the method adds a robust, physically bounded throughput gain, which we bracket with two complementary honest bounds — a fixed-modulation bound and a Shannon-capacity bound. We further validate the core DOA claim with an actual MUSIC pseudospectrum, not just beamscan, and run a synthetic multipath robustness sweep showing the geometric feasibility boundary itself is not fragile to multipath under full channel knowledge, but that delivered fidelity is highly sensitive to channel-model mismatch at the transmitter — the more likely practical failure mode. All numerical results were cross-validated between independent Python and MATLAB implementations, including a 60-decimal-digit arbitrary-precision check that rules out floating-point artifacts in the reported near-field "plateau" behavior