AI 中文总结
提出轨道检测框架，将离散符号先验松弛为混合密度，设计出低复杂度的轨道贝塞尔、高斯、相位去噪器，获五个信息论结果，实现渐近容量与特定MMSE维度。
AI 中文摘要
我们提出了轨道检测（OD）框架，用于为数字调制多输入多输出（MIMO）系统设计渐近最优、低复杂度的消息传递（MP）接收机，该框架基于将离散符号先验松弛为混合离散-连续密度。所得的轨道先验将每个符号的分布分解为离散径向分量（仅支撑于基数为\boldsymbol{M = |\boldsymbol{M}|}的任意星座\boldsymbol{\boldsymbol{M}}的\boldsymbol{L << M}个振幅环上）和每个环上的连续最大熵相位密度。这将传播的后验均值和方差无损压缩为\boldsymbol{3L}个实标量，并将复杂度为\boldsymbol{\boldsymbol{O}(M)}的最优去噪器折叠为闭式层次结构，其每个符号的成本降至\boldsymbol{\boldsymbol{O}(L)}，最终降至\boldsymbol{\boldsymbol{O}(1)}：包括轨道贝塞尔去噪器（OBD）、其无贝塞尔变体轨道高斯去噪器（OGD），以及轨道相位去噪器（OPD），后三者在环流形上被证明不可约。雅可比-安格尔阶梯以几何级消失误差恢复精确检测器。随后得到五个信息论结果：第一，OBD、OGD和OPD共享相同的领先阶状态演化（SE）不动点；第二，唯一代价是高信噪比（SNR）误差衰减规律的改变，从指数衰减变为线性衰减，且永远不会形成误差下限；第三，对于任何欠载系统，诱导的速率损失随SNR指数消失，因此每个层级在星座约束意义上渐近达到容量，实现\boldsymbol{\boldsymbol{\text{log}_2 M}}；第四，OD达到最小均方误差（MMSE）维度\boldsymbol{\boldsymbol{d=1/2}}，介于\boldsymbol{\boldsymbol{d=0}}的贝塞尔最优去噪器（BOD）和\boldsymbol{\boldsymbol{d=1}}的线性接收机之间；第五，瓦瑟斯坦距离中的非渐近最优传输边界将星座环几何与可达速率直接关联。
英文摘要
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.
CommentsSubmitted to an IEEE journal
