🤖 AI Summary
This work addresses the high computational complexity of message-passing detectors in massive MIMO systems by proposing a low-complexity receiver framework based on orbital priors. By relaxing discrete symbol priors into mixed discrete–continuous densities and leveraging an orbital prior decomposition, the symbol distribution is compressed into 3L real-valued scalars, yielding three closed-form denoisers—OBD, OGD, and OPD—that reduce per-iteration complexity to O(1). Combining the Jacobi–Anger expansion, state evolution analysis, and optimal transport theory, the proposed method asymptotically achieves capacity (log₂M), eliminates error floors, attains an MMSE dimension of d = 1/2, and establishes a Wasserstein-distance bound linking constellation ring geometry to achievable rates.
📝 Abstract
We introduce orbital detection (OD), a framework for designing asymptotically optimal, low-complexity message passing (MP) receivers for digitally modulated multiple-input multiple-output (MIMO) systems, based on relaxing the discrete symbol prior into a mixed discrete-continuous density. The resulting orbital prior factors each symbol's distribution into a discrete radial component, supported on only the \(L << M\) amplitude rings of an arbitrary constellation \(\mathcal{M}\) of cardinality \(M = |\mathcal{M}|\), and a continuous, maximum-entropy phase density on each ring. This compresses the propagated posterior mean and variance losslessly into \(3L\) real scalars, and collapses the optimal \(\mathcal{O}(M)\)-complexity denoiser into a closed-form hierarchy whose per-symbol cost falls to \(\mathcal{O}(L)\) and ultimately \(\mathcal{O}(1)\): the orbital Bessel denoiser (OBD), its Bessel-free variant the orbital Gaussian denoiser (OGD), and the orbital phase denoiser (OPD), proved irreducible on the ring manifold. A Jacobi-Anger ladder recovers the exact detector with geometrically vanishing error. Five information-theoretic results follow. First, the OBD, OGD, and OPD share an identical leading-order state evolution (SE) fixed point. Second, the sole price is a change in the high-SNR error-decay law, from exponential to linear, which never hardens into an error floor. Third, for any underloaded system the induced rate loss vanishes exponentially in SNR, so every level is asymptotically capacity-achieving in the constellation-constrained sense, attaining \(\log_2 M\). Fourth, OD attains a minimum mean square error (MMSE) dimension \(d=1/2\), halfway between the \(d=0\) Bayes-optimal denoiser (BOD) and the \(d=1\) linear receiver. Fifth, a non-asymptotic optimal-transport bound in Wasserstein distance links constellation ring geometry directly to the achievable rate.