In this paper, we investigate joint user (UE) scheduling, base station (BS) clustering and beamforming design in a dense network. To reduce the computation burden, we propose a deep unfolding UE scheduling, BS clustering and beamforming (DU-USBCB) method based on the iterative weighted minimum mean square error (WMMSE) algorithm, where the UE scheduling and BS clustering are represented by the group sparsity of the transmit beamforming vectors. The proposed DU-USBCB neural network layer comprises receive coefficient, weight and transmit beamforming vector modules, the former two of which have closed-form expressions. For the third module, the group sparse transmit beamforming vectors are obtained by multiple steps of projected gradient descent and nonlinear sparsification, where the step-sizes are learned through unsupervised learning. We also propose a distributed UE selection (DUS) algorithm, which helps reduce the computation workload. Simulation results verify the effectiveness of the proposed DU-USBCB and DUS methods. The learned step-sizes are directly applied in the testing scenarios with different numbers of UEs, BSs and antennas as well as incomplete channel state information. Besides, our proposed methods can achieve comparable performance but with about 53% and 89% computation reduction compared to the RSRP-WMMSE and SWMMSE methods respectively.

Differential spatial modulation (DSM) is a novel multiple-input-multiple-output (MIMO) transmission technology that uses the transmit antenna index matrices to carry part of the information in non-coherent communication scenarios. However, when high-order modulation should be used for spectral efficiency considerations, the conventional use of constant modulus Phase Shift Keying (PSK) constellations in DSM would result in significant performance loss, whereas using non-constant modulus constellations such as Quadrature Amplitude Modulation (QAM) in DSM is very challenging because the peak signal power may grow without bound through the differential iterative processing. In this work, a generalized transmission scheme that uses non-constant modulus constellations for DSM signaling is investigated. By normalizing the power of all symbols in the previous transmit matrix when performing differential transmission, the Precoding Normalized DSM (PN-DSM) scheme which can adopt non-constant modulus constellations is proposed. In addition to the legacy QAM, another two non-constant modulus constellations in the literature, Amplitude Phase Shift Keying (APSK) and star-QAM, are considered for PN-DSM transmissions. It is revealed by numerical studies that, compared with the legacy QAM, APSK and star-QAM are more robust to the error propagation issue of the proposed PN-DSM scheme. In addition, because of the increased minimum distance in the constellation, the star-QAM slightly outperforms the APSK in terms of the average error rate performance.

Spatial modulation orthogonal frequency division multiplexing with subcarrier index modulation (ISM-OFDM) is a novel OFDM technique that conveys additional information bits by active antenna indices and grouped subcarrier indices. However, it takes a huge amount of resources to acquire the channel state information (CSI) at the receiver. In this paper, we propose two differential spatial frequency modulation with orthogonal frequency division multiplexing (DSFM-OFDM) systems, termed DSFM-OFDM-single (DSFM-OFDM-S) and DSFM-OFDM- multiple (DSFM-OFDM-M) over space-time-frequency, which completely avoid the need for CSI at the transmitter and receiver. In DSFM-OFDM, the transmitted symbols are modulated through ordinary signal modulation. And then part of some additional information bits are transmitted by selecting a permutation of the active antennas, whereas another part of it are employed to determine the subcarrier index matrices. Simulation results show that at low spectral efficiency, the performance of the proposed two schemes are better than differential spatial modulation (DSM) with the high SNR. Besides, the performance degradation of DSFM-OFDM-M and DSFM- OFDM-S over ISM-OFDM can be less than 6dB. And that the loss decreases as the number of receive antennas decreases.