Orbital Detection: On Maximum-Entropy Priors
Abstract
Soft-input detection over a discrete constellation ℳ of cardinality M requires computing a posterior whose mean and mode are respectively given by the minimum mean square error (MMSE) and maximum a posteriori (MAP) estimates, both of which incur a computational cost of order 𝒪(M) per symbol. We show that this cost is reduced to 𝒪(L), where L ≤ M is the number of distinct amplitudes (rings), once the discrete prior is replaced by its maximum-entropy counterpart subject to the same radial marginal. This orbital prior, which is a mixture of uniform circular shells, is obtained by maximizing a mixed discrete-continuous entropy. We prove in this paper that such a distribution is the only distribution on ℂ that preserves the amplitude statistics of ℳ exactly while remaining maximally noncommittal in phase. Under the additive white Gaussian noise (AWGN) channel, the orbital prior induces a closed-form posterior that factors into a softmax over the L rings and a von Mises phase distribution whose concentration is supplied entirely by the observation, yielding closed-form orbital MMSE and MAP detectors of the discrete symbol at 𝒪(L) cost. The resulting hierarchical rule selects the ring by posterior mass and the phase by conditional mode. We compare the pairwise ring boundary with that of the joint posterior-density and quantify the leading-order outward shift at high signal-to-noise ratio (SNR). Numerical results using standard constellations confirm that the orbital detectors maintain similar symbol error rate (SER) performance to optimal detectors, at a fraction of the complexity.
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BibTeX
@misc{ranasinghe2026orbital,
title = {{Orbital Detection: On Maximum-Entropy Priors}},
author = {Kuranage Roche Rayan Ranasinghe and Takumi Takahashi and Giuseppe Thadeu Freitas de Abreu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21466},
eprint = {2609.21466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21466},
}
RIS
TY - UNPB
TI - Orbital Detection: On Maximum-Entropy Priors
AU - Kuranage Roche Rayan Ranasinghe
AU - Takumi Takahashi
AU - Giuseppe Thadeu Freitas de Abreu
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21466
UR - https://arxiv.org/abs/2609.21466
AB - Soft-input detection over a discrete constellation ℳ of cardinality M requires computing a posterior whose mean and mode are respectively given by the minimum mean square error (MMSE) and maximum a posteriori (MAP) estimates, both of which incur a computational cost of order 𝒪(M) per symbol. We show that this cost is reduced to 𝒪(L), where L ≤ M is the number of distinct amplitudes (rings), once the discrete prior is replaced by its maximum-entropy counterpart subject to the same radial marginal. This orbital prior, which is a mixture of uniform circular shells, is obtained by maximizing a mixed discrete-continuous entropy. We prove in this paper that such a distribution is the only distribution on ℂ that preserves the amplitude statistics of ℳ exactly while remaining maximally noncommittal in phase. Under the additive white Gaussian noise (AWGN) channel, the orbital prior induces a closed-form posterior that factors into a softmax over the L rings and a von Mises phase distribution whose concentration is supplied entirely by the observation, yielding closed-form orbital MMSE and MAP detectors of the discrete symbol at 𝒪(L) cost. The resulting hierarchical rule selects the ring by posterior mass and the phase by conditional mode. We compare the pairwise ring boundary with that of the joint posterior-density and quantify the leading-order outward shift at high signal-to-noise ratio (SNR). Numerical results using standard constellations confirm that the orbital detectors maintain similar symbol error rate (SER) performance to optimal detectors, at a fraction of the complexity.
ER -