As wireless communication applications evolve from traditional multipath environments to high-mobility scenarios like unmanned aerial vehicles, multiplexing techniques have advanced accordingly. Traditional single-carrier frequency-domain equalization (SC-FDE) and orthogonal frequency-division multiplexing (OFDM) have given way to emerging orthogonal time-frequency space (OTFS) and affine frequency-division multiplexing (AFDM). These approaches exploit specific channel structures to diagonalize or sparsify the effective channel, thereby enabling low-complexity detection. However, their reliance on these structures significantly limits their robustness in dynamic, real-world environments. To address these challenges, this paper studies a random multiplexing technique that is decoupled from the physical channels, enabling its application to arbitrary norm-bounded and spectrally convergent channel matrices. Random multiplexing achieves statistical fading-channel ergodicity for transmitted signals by constructing an equivalent input-isotropic channel matrix in the random transform domain. It guarantees the asymptotic replica MAP bit-error rate (BER) optimality of AMP-type detectors for linear systems with arbitrary norm-bounded, spectrally convergent channel matrices and signaling configurations, under the unique fixed point assumption. A low-complexity cross-domain memory AMP (CD-MAMP) detector is considered, leveraging the sparsity of the time-domain channel and the randomness of the equivalent channel. Optimal power allocations are derived to minimize the replica MAP BER and maximize the replica constrained capacity of random multiplexing systems. The optimal coding principle and replica constrained-capacity optimality of CD-MAMP detector are investigated for random multiplexing systems. Additionally, the versatility of random multiplexing in diverse wireless applications is explored.

翻译：随着无线通信应用从传统的多径环境演进至无人机等高移动性场景，复用技术也相应发展。传统的单载波频域均衡（SC-FDE）和正交频分复用（OFDM）已逐渐被新兴的正交时频空间（OTFS）和仿射频分复用（AFDM）所取代。这些方法通过利用特定的信道结构来对角化或稀疏化有效信道，从而实现低复杂度检测。然而，它们对这些结构的依赖严重限制了其在动态现实环境中的鲁棒性。为应对这些挑战，本文研究了一种与物理信道解耦的随机复用技术，使其能够应用于任意范数有界且谱收敛的信道矩阵。随机复用通过在随机变换域中构建等效的输入各向同性信道矩阵，实现了传输信号的统计衰落信道遍历性。在唯一不动点假设下，该方法保证了对于具有任意范数有界、谱收敛信道矩阵和信号配置的线性系统，AMP类检测器能够渐近达到副本MAP误码率（BER）最优性。本文考虑了一种低复杂度的跨域记忆AMP（CD-MAMP）检测器，其利用了时域信道的稀疏性和等效信道的随机性。推导了最优功率分配方案，以最小化副本MAP误码率并最大化随机复用系统的副本约束容量。针对随机复用系统，研究了CD-MAMP检测器的最优编码原理及副本约束容量最优性。此外，还探讨了随机复用技术在多样化无线应用中的普适性。