轨道检测：关于最大熵先验
Orbital Detection: On Maximum-Entropy Priors
- School of Computer Science and Engineering, Constructor University（Constructor大学计算机科学与工程学）
- Graduate School of Engineering, Osaka University（大阪大学工学研究科）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对离散星座软输入检测计算成本高的问题，提出最大熵轨道先验，将每符号复杂度从O(M)降至O(L)，并导出闭式MMSE和MAP检测器，在保持相似SER性能下大幅降低复杂度。
AI中文摘要：
在基数为\\(M\\)的离散星座\\(\mathcal{M}\\)上进行软输入检测需要计算一个后验，其均值和众数分别由最小均方误差（MMSE）和最大后验（MAP）估计给出，两者每个符号的计算成本均为\\(\mathcal{O}(M)\\)阶。我们证明，一旦将离散先验替换为其在相同径向边缘约束下的最大熵对应物，该成本可降至\\(\mathcal{O}(L)\\)，其中\\(L \le M\\)是不同幅度（环）的数量。这种轨道先验是均匀圆形壳的混合，通过最大化混合离散-连续熵获得。我们在本文中证明，该分布是\\(\mathbb{C}\\)上唯一精确保持\\(\mathcal{M}\\)的幅度统计量且在相位上保持最大非承诺性的分布。在加性高斯白噪声（AWGN）信道下，轨道先验导出一个闭式后验，该后验分解为\\(L\\)个环上的softmax和冯·米塞斯相位分布，其浓度完全由观测提供，从而以\\(\mathcal{O}(L)\\)成本得到离散符号的闭式轨道MMSE和MAP检测器。由此产生的分层规则通过后验质量选择环，并通过条件众数选择相位。我们将成对环边界与联合后验密度的边界进行比较，并量化高信噪比（SNR）下的前导阶向外偏移。使用标准星座的数值结果证实，轨道检测器在保持与最优检测器相似的符号错误率（SER）性能的同时，复杂度仅为其一小部分。
英文摘要：
Soft-input detection over a discrete constellation \(\mathcal{M}\) 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 \(\mathcal{O}(M)\) per symbol. We show that this cost is reduced to \(\mathcal{O}(L)\), where \(L \le M\) 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 \(\mathbb{C}\) that preserves the amplitude statistics of \(\mathcal{M}\) 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 \(\mathcal{O}(L)\) 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.
