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In order to maximize the spectral efficiency (SE) in multicarrier-division duplex (MDD) enabled cell-free massive MIMO (CF-mMIMO), a heterogeneous graph neural network (HGNN), referred to as CF-HGNN, is specifically introduced to optimize the power allocation (PA). To efficiently manage the interference invoked, a meta-path based mechanism is applied in CF-HGNN to enable individual access point (AP) and mobile station (MS) nodes to aggregate information from the interfering and communication paths with different priorities during message passing. Moreover, the proposed CF-HGNN employs the adaptive node embedding layer and adaptive output layer to make it scalable to the various numbers of APs, MSs and subcarriers. For comparison, a quadratic transform and successive convex approximation (QT-SCA) algorithm is proposed to solve the PA problem in classic way. Numerical results show that CF-HGNN is capable of achieving 99% of the SE achievable by QT-SCA but using only 10−4 times of its operation time, and it can outperform the conventional learning-based and greedy unfair methods in terms of SE performance. Furthermore, CF-HGNN exhibits good scalability to the CF networks with various numbers of nodes and subcarriers, and also to the large-scale CF networks when assisted by user-centric clustering.

In orthogonal time sequency multiplexing (OTSM) modulation, the information symbols are conveyed in the delay-sequency domain upon exploiting the inverse Walsh Hadamard transform (IWHT). It has been shown that OTSM is capable of attaining a bit error ratio (BER) similar to that of orthogonal time-frequency space (OTFS) modulation at a lower complexity, since the saving of multiplication operations in the IWHT. Hence we provide its BER performance analysis and characterize its detection complexity. We commence by deriving its generalized input-output relationship and its unconditional pairwise error probability (UPEP). Then, its BER upper bound is derived in closed form under both ideal and imperfect channel estimation conditions, which is shown to be tight at moderate to high signal-to-noise ratios (SNRs). Moreover, a novel approximate message passing (AMP) aided OTSM detection framework is proposed. Specifically, to circumvent the high residual BER of the conventional AMP detector, we proposed a vector AMP-based expectation-maximization (VAMP-EM) detector for performing joint data detection and noise variance estimation. The variance auto-tuning algorithm based on the EM algorithm is designed for the VAMP-EM detector to further improve the convergence performance. The simulation results illustrate that the VAMP-EM detector is capable of striking an attractive BER vs. complexity trade-off than the state-of-the-art schemes as well as providing a better convergence. Finally, we propose AMP and VAMP-EM turbo receivers for low-density parity-check (LDPC)-coded OTSM systems. It is demonstrated that our proposed VAMP-EM turbo receiver is capable of providing both BER and convergence performance improvements over the conventional AMP solution.