Causal Dispersive Plasma-Inversion Point-Ahead Tracking and Doubly-Stochastic Cox–Bessel Demodulation for Interplanetary Optical–RF Satellite Communications

Abstract

Near Superior Solar Conjunction (α_SEP ≤ 5°), interplanetary 1550 nm Pulse-Position Modulation (M-PPM) links fail across both pointing and photon-counting layers. Transverse solar coronal electron-density wedges (∇_⊥ STEC) and temporal boiling (dSTEC/dt) bias radiometric orbit-determination (ΔDOR and Doppler) point-ahead vectors, while the 1517 s Round-Trip Light Time (RTLT = 2D/c at D = 1.52 AU) renders Earth-to-spacecraft pointing feedback non-causal. Simultaneously, sub-solar scintillation, residual beam jitter, and fractional slot clock drift trigger doubly-stochastic Cox photon bunching and inter-slot spill that saturate standard Consultative Committee for Space Data Systems (CCSDS) homogeneous Poisson log-likelihood ratios (LLRs). A strictly causal, two-node optical–RF transceiver architecture (DP-RPAT + CB-VLLR) closes the conjunction link without ground laser beacons. Onboard the spacecraft (DP-RPAT-TX, Proposition 1), K = 16 epochs of the Deep Space Network (DSN) dual-band regenerative PN X/Ka (7.18/34.35 GHz) uplink are inverted via Lorentz–Appleton–Hartree group–phase duality (L_AH = 0.5[τ_g + τ_φ] = D/c), balanced Gauss–Markov Best Linear Unbiased Estimation (BLUE, w_BLUE = 0.74, 0.26), and spacecraft-vertex Euler–Beta Abel advection across ΔR_{0,PAA} = |D − s_closest|θ_PAA to strip coronal refraction from the relativistic point-ahead angle θ_PAA = 2v_⊥/c + θ_PN with zero Earth feedback. At the Earth receiver (DP-RPAT-RX ↔ CB-VLLR, Theorem 1), a closed sub-block loop pairs a Cox-posterior Early–Late Timing Error Detector (Cox-TED) and 1D scalar Kalman Riccati tracker with a 3-slot Gamma–Gamma modified Bessel K_{α−β}(2√(αβu*(k))) variational saddle-point and Negative-Binomial Pochhammer soft demodulator (Δℓ > 0, Δ²ℓ ≤ −0.055 < 0). Across an 8-seed Common-Random-Number (CRN) campaign at D = 1.52 AU, α_SEP = 2.5° (64-PPM, 32-pixel WSi SNSPD array, blind Rate-1/2 [16,8,d_min=5] shortened QR decoding), DP-RPAT + CB-VLLR reduces pointing RMSE from 3.409 to 0.763 µrad (0.19 dB loss) and compresses slot timing drift by 11.4× (0.1545 → 0.0135 slots). Coded Frame Error Rate (FER) drops by 9.3× over DP-RPAT Only (0.2167 → 0.0233, BER = 9.85 × 10⁻⁴), sustaining 36.97 Mbps (+24.4% over DP-RPAT Only, 1.97× over active 5 kW beacon PAT, and 105.6× over CCSDS static Poisson) within 23.83 µs per codeword.