1.
Lu, Zhou; El-Hajjar, Mohammed; Yang, Lie-Liang
Wavelet Transform Aided Single-Carrier FDMA With Index Modulation Journal Article
In: IEEE Open Journal of Vehicular Technology, vol. 6, pp. 1524–1538, 2025, ISSN: 2644-1330.
Abstract | Links | BibTeX | Tags: detection, Frequency division multiaccess, Frequency-domain analysis, index modulation, Indexes, Maximum likelihood detection, Modulation, OFDM, Peak to average power ratio, peak-to-average power ratio, single carrier-frequency division multiple access (SC-FDMA), spatial modulation, Symbols, Time-domain analysis, Vectors, Wavelet, Wireless communication
@article{lu_wavelet_2025,
title = {Wavelet Transform Aided Single-Carrier FDMA With Index Modulation},
author = {Zhou Lu and Mohammed El-Hajjar and Lie-Liang Yang},
url = {https://ieeexplore.ieee.org/document/11021437},
doi = {10.1109/OJVT.2025.3576062},
issn = {2644-1330},
year = {2025},
date = {2025-01-01},
urldate = {2025-10-08},
journal = {IEEE Open Journal of Vehicular Technology},
volume = {6},
pages = {1524–1538},
abstract = {Single-carrier frequency-division multiple access (SC-FDMA) is a well-known multiuser transmission method for uplink communications owing to its low peak-to-average power ratio (PAPR) characteristics. Simultaneously, index modulation (IM) has been widely studied owing to its flexibility for spectral-efficiency versus energy-efficiency trade-off. However, applying conventional IM schemes with SC-FDMA may affect the desirable characteristics of SC-FDMA signals, resulting in the increase of PAPR, for example. On the other side, Wavelet Transform (WT) has been shown to provide an improved performance over the fast Fourier transform (FFT)-based SC-FDMA, owing to WT's local focusing capability in both time and frequency domains. In this paper, we propose three IM schemes, namely Symbol Position Index Modulation (SPIM), Spreading Matrix Index Modulation (SMIM) and Joint Matrix-Symbol Index Modulation (JMSIM) schemes, which perform IM at the symbol vector level, spreading matrix level, or a combination of both. These IM schemes are implemented with the WT-based SC-FDMA for data transmission. We consider two spreading matrix design schemes, namely random dispersion matrix design and Gram-Schmidt (GS) orthogonalization matrix design. Correspondingly, we propose different detection schemes, including Maximum Likelihood Detection (MLD), Simplified Maximum Likelihood Detection (SMLD), and the Two Stage Index-QAM Detection (TSD). The performance of the proposed schemes is evaluated by simulations. Our studies and results show that all the three schemes can effectively reduce the PAPR encountered by the conventional IM-assisted SC-FDMA signals. Moreover, the method of GS matrices can provide a gain upto 20 dB compared with the method of random dispersion matrices. Furthermore, the GS-based system can employ the proposed low-complexity TSD, allowing to achieve a similar bit error rate (BER) performance as MLD, while requiring significantly low complexity.},
keywords = {detection, Frequency division multiaccess, Frequency-domain analysis, index modulation, Indexes, Maximum likelihood detection, Modulation, OFDM, Peak to average power ratio, peak-to-average power ratio, single carrier-frequency division multiple access (SC-FDMA), spatial modulation, Symbols, Time-domain analysis, Vectors, Wavelet, Wireless communication},
pubstate = {published},
tppubtype = {article}
}
Single-carrier frequency-division multiple access (SC-FDMA) is a well-known multiuser transmission method for uplink communications owing to its low peak-to-average power ratio (PAPR) characteristics. Simultaneously, index modulation (IM) has been widely studied owing to its flexibility for spectral-efficiency versus energy-efficiency trade-off. However, applying conventional IM schemes with SC-FDMA may affect the desirable characteristics of SC-FDMA signals, resulting in the increase of PAPR, for example. On the other side, Wavelet Transform (WT) has been shown to provide an improved performance over the fast Fourier transform (FFT)-based SC-FDMA, owing to WT's local focusing capability in both time and frequency domains. In this paper, we propose three IM schemes, namely Symbol Position Index Modulation (SPIM), Spreading Matrix Index Modulation (SMIM) and Joint Matrix-Symbol Index Modulation (JMSIM) schemes, which perform IM at the symbol vector level, spreading matrix level, or a combination of both. These IM schemes are implemented with the WT-based SC-FDMA for data transmission. We consider two spreading matrix design schemes, namely random dispersion matrix design and Gram-Schmidt (GS) orthogonalization matrix design. Correspondingly, we propose different detection schemes, including Maximum Likelihood Detection (MLD), Simplified Maximum Likelihood Detection (SMLD), and the Two Stage Index-QAM Detection (TSD). The performance of the proposed schemes is evaluated by simulations. Our studies and results show that all the three schemes can effectively reduce the PAPR encountered by the conventional IM-assisted SC-FDMA signals. Moreover, the method of GS matrices can provide a gain upto 20 dB compared with the method of random dispersion matrices. Furthermore, the GS-based system can employ the proposed low-complexity TSD, allowing to achieve a similar bit error rate (BER) performance as MLD, while requiring significantly low complexity.
2.
Feng, Xinyu; El-Hajjar, Mohammed; Xu, Chao; Hanzo, Lajos
Graph Neural Network Aided Detection for the Multi-User Multi-Dimensional Index Modulated Uplink Journal Article
In: IEEE Open Journal of Vehicular Technology, vol. 6, pp. 1593–1612, 2025, ISSN: 2644-1330.
Abstract | Links | BibTeX | Tags: Artificial neural networks, Detectors, graph factor, graph neural network (GNN), Graph neural networks, Index modulation (IM), Indexes, machine learning, Message passing, message passing (MP), multi-user, Next generation networking, Peak to average power ratio, Symbols, Uplink, Vectors
@article{feng_graph_2025,
title = {Graph Neural Network Aided Detection for the Multi-User Multi-Dimensional Index Modulated Uplink},
author = {Xinyu Feng and Mohammed El-Hajjar and Chao Xu and Lajos Hanzo},
url = {https://ieeexplore.ieee.org/document/11017516},
doi = {10.1109/OJVT.2025.3574934},
issn = {2644-1330},
year = {2025},
date = {2025-01-01},
urldate = {2025-10-08},
journal = {IEEE Open Journal of Vehicular Technology},
volume = {6},
pages = {1593–1612},
abstract = {The concept of Compressed Sensing-aided Space-Frequency Index Modulation (CS-SFIM) is conceived for the Large-Scale Multi-User Multiple-Input Multiple-Output Uplink (LS-MU-MIMO-UL) of Next-Generation (NG) networks. Explicitly, in CS-SFIM, the information bits are mapped to both spatial- and frequency-domain indices, where we treat the activation patterns of the transmit antennas and of the subcarriers separately. Serving a large number of users in an MU-MIMO-UL system leads to substantial Multi-User Interference (MUI). Hence, we design the Space-Frequency (SF) domain matrix as a joint factor graph, where the Approximate Message Passing (AMP) and Expectation Propagation (EP) based MU detectors can be utilized. In the LS-MU-MIMO-UL scenario considered, the proposed system uses optimal Maximum Likelihood (ML) and Minimum Mean Square Error (MMSE) detectors as benchmarks for comparison with the proposed MP-based detectors. These MP-based detectors significantly reduce the detection complexity compared to ML detection, making the design eminently suitable for LS-MU scenarios. To further reduce the detection complexity and improve the detection performance, we propose a pair of Graph Neural Network (GNN) based detectors, which rely on the orthogonal AMP (OAMP) and on the EP algorithm, which we refer to as the GNN-AMP and GEPNet detectors, respectively. The GEPNet detector maximizes the detection performance, while the GNN-AMP detector strikes a performance versus complexity trade-off. The GNN is trained for a single system configuration and yet it can be used for any number of users in the system. The simulation results show that the GNN-based detector approaches the ML performance in various configurations.},
keywords = {Artificial neural networks, Detectors, graph factor, graph neural network (GNN), Graph neural networks, Index modulation (IM), Indexes, machine learning, Message passing, message passing (MP), multi-user, Next generation networking, Peak to average power ratio, Symbols, Uplink, Vectors},
pubstate = {published},
tppubtype = {article}
}
The concept of Compressed Sensing-aided Space-Frequency Index Modulation (CS-SFIM) is conceived for the Large-Scale Multi-User Multiple-Input Multiple-Output Uplink (LS-MU-MIMO-UL) of Next-Generation (NG) networks. Explicitly, in CS-SFIM, the information bits are mapped to both spatial- and frequency-domain indices, where we treat the activation patterns of the transmit antennas and of the subcarriers separately. Serving a large number of users in an MU-MIMO-UL system leads to substantial Multi-User Interference (MUI). Hence, we design the Space-Frequency (SF) domain matrix as a joint factor graph, where the Approximate Message Passing (AMP) and Expectation Propagation (EP) based MU detectors can be utilized. In the LS-MU-MIMO-UL scenario considered, the proposed system uses optimal Maximum Likelihood (ML) and Minimum Mean Square Error (MMSE) detectors as benchmarks for comparison with the proposed MP-based detectors. These MP-based detectors significantly reduce the detection complexity compared to ML detection, making the design eminently suitable for LS-MU scenarios. To further reduce the detection complexity and improve the detection performance, we propose a pair of Graph Neural Network (GNN) based detectors, which rely on the orthogonal AMP (OAMP) and on the EP algorithm, which we refer to as the GNN-AMP and GEPNet detectors, respectively. The GEPNet detector maximizes the detection performance, while the GNN-AMP detector strikes a performance versus complexity trade-off. The GNN is trained for a single system configuration and yet it can be used for any number of users in the system. The simulation results show that the GNN-based detector approaches the ML performance in various configurations.