随机调制：在任意范数受限且频谱收敛的信道矩阵上实现渐近副本最优
Random Modulation: Achieving Asymptotic Replica Optimality over Arbitrary Norm-Bounded and Spectrally Convergent Channel Matrices
AI总结：
本文提出随机调制技术，通过构造等效随机信道矩阵，实现线性系统在任意范数受限且频谱收敛信道下的渐近副本最优检测性能。
摘要：
本文介绍了一种随机调制技术，该技术与信道矩阵解耦，使其能够应用于任意范数受限且频谱收敛的信道矩阵。所提出的随机调制构造了一个等效的密集且随机的信道矩阵，确保信号经历足够的统计信道衰落。它还保证了当其状态演化具有唯一固定点时，近似消息传递（AMP）型检测器在具有任意范数受限且频谱收敛的信道矩阵的线性系统中实现渐近副本最大后验（MAP）比特错误率（BER）最优。然后，提出了一种低复杂度的跨域内存近似消息传递（CD-MAMP）检测器，利用时域信道的稀疏性和随机变换域信道的随机性。此外，推导出最优功率分配方案，以最小化副本MAP BER并最大化随机调制线性系统的副本受限容量，假设收发端具有信道状态信息（CSI）。数值结果表明，所提出的随机调制在平均和优化功率分配下，相比现有OFDM/OTFS/AFDM与5G-NR LDPC码的BER和块错误率（BLER）性能提升可达2-3 dB。
英文摘要：
This paper introduces a random modulation technique that is decoupled from the channel matrix, allowing it to be applied to arbitrary norm-bounded and spectrally convergent channel matrices. The proposed random modulation constructs an equivalent dense and random channel matrix, ensuring that the signals undergo sufficient statistical channel fading. It also guarantees the asymptotic replica maximum a posteriori (MAP) bit-error rate (BER) optimality of approximate message passing (AMP)-type detectors for linear systems with arbitrary norm-bounded and spectrally convergent channel matrices when their state evolution has a unique fixed point. Then, a low-complexity cross-domain memory approximate message passing (CD-MAMP) detector is proposed for random modulation, leveraging the sparsity of the time-domain channel and the randomness of the random transform-domain channel. Furthermore, the optimal power allocation schemes are derived to minimize the replica MAP BER and maximize the replica constrained capacity of random-modulated linear systems, assuming the availability of channel state information (CSI) at the transceiver. Numerical results show that the proposed random modulation can achieve BER and block-error rate (BLER) performance gains of up to 2 - 3 dB compared to existing OFDM/OTFS/AFDM with 5G-NR LDPC codes, under both average and optimized power allocation.
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