Massive multiple-input multiple-output low-Earth-orbit communication channels are highly time-varying due to severe Doppler shifts and propagation delays. While satellite-mobility-induced Doppler shifts can be compensated using known ephemeris data, those caused by user mobility require accurate user positioning information; the absence of such information contributes to amplified channel aging in conventional channel estimators. To address this challenge, we propose a data-aided channel estimator based on the expectation–maximization (EM) algorithm, combined with a discrete Legendre polynomial basis expansion model (DLP-BEM), to estimate the channel under imperfect Doppler compensation. The EM algorithm iteratively exploits hidden data symbols for improved channel estimation, while DLP-BEM regularizes the process by projecting the channel estimate onto a lower-dimensional subspace that mitigates estimation errors. Simulation results demonstrate the superiority of the proposed framework over existing methods in terms of normalized mean square error and symbol error rate.

ABSTRACT Generalized Frequency Division Multiplexing (GFDM) is a flexible multi-carrier scheme and has a potential to overcome some of the limitations of orthogonal frequency division multiplexing (OFDM) specifically for diverse use cases of beyond 5G (B5G)/ 6G systems. However, as a non-orthogonal waveform, GFDM suffers from intrinsic self-interference, such as inter-subsymbol interference (ISSI) and inter-subcarrier interference (ISCI). To mitigate self-interference, a low-complexity modified eigenvalue decomposition-based GFDM system deploying a triangular-raised cosine (TRC) filter is proposed. Self-interference elimination is achieved through pre-processing and post-processing techniques. A sufficient condition for ISCI elimination is derived, and the impact of filter roll-off on ISCI-free transmission is examined. In addition to it, an analytical expression for the symbol error rate (SER) in κ − μ fading channels with M -PSK and M -QAM modulations is derived. Simulations confirm the superiority of the proposed GFDM system over Conventional GFDM (CGFDM).

DD-OCQAM: A spectrally efficient modulation scheme for in-vivo ultrasonic sensors

Abstract In the context of smart grids and the Internet of Things (IoT) for power systems, power line communication (PLC) and power wireless private network (VPC) channels exhibit complex hybrid characteristics such as strong nonlinearity, multipath fading, and impulse noise, leading to a sharp deterioration in the performance of traditional MQAM demodulators. Traditional methods, relying on accurate channel estimation and rigid mathematical models, are ill-suited to the dynamic interference environment of power systems. This paper proposes a deep learning-based MQAM demodulation algorithm. It utilizes a symmetric fully-connected deep neural network (DNN) to learn the nonlinear characteristics and joint statistical properties of signals in hybrid power channels, constructing complex decision boundaries to achieve intelligent compensation for signal impairments in an end-to-end manner. It utilizes deep neural networks to learn the nonlinear characteristics and joint statistical properties of signals in hybrid power channels, constructing complex decision boundaries to achieve intelligent compensation for signal impairments in an end-to-end manner. Simulation results show that, compared with traditional demodulation algorithms based on signal space and decision boundaries, the proposed algorithm exhibits superior performance under time-varying and non-ideal power channel conditions, and is particularly suitable for high-order modulation and complex power communication scenarios.The system achieves a 1.5 to 3 times reduction in Symbol Error Rate (SER) for 16QAM, 64QAM, and 128QAM configurations,providing an effective solution for improving the reliability and adaptability of power system communication.

This paper proposes a method for determining the minimum required power for the weak user in a two-user power-domain non-orthogonal multiple access (PD-NOMA) system employing quadrature amplitude modulation (QAM), such that a given symbol error rate (SER) constraint is satisfied under known channel conditions. Most existing methods rely on the Shannon model with idealized signals and a number of simplifying assumptions. Such models make it possible to assess the theoretical potential of the system; however, the corresponding methods are inapplicable under practical transmission conditions. For models with QAM constellations, an analytical solution to the problem is not available due to the complex structure of signal superposition and the dependence of the error probability on inter-user interference; therefore, the suboptimal and computationally expensive exhaustive search method is widely used. In contrast to such approaches, this paper formulates an equation based on an analytical expression for SER, whose solution is obtained using the Newton method. The proposed approach provides fast convergence and significantly reduces the computational complexity. It constitutes a part of the power allocation procedure on the “weak” user side and specifies a lower bound on the required power. Simulation results confirm the correctness and robustness of the method over a wide range of PD-NOMA parameters.

As sixth-generation (6G) network development progresses, research continues to explore various technologies and new waveforms to meet the demands of future communications. Generalized frequency division multiplexing (GFDM) is considered as a promising waveform due to its adaptable structure, reduced latency, and efficient use of the spectrum. Nevertheless, nonorthogonal subcarriers of GFDM induce severe inter-symbol interference (ISI) and inter-carrier interference (ICI), leading to slow convergence and elevated symbol error rate (SER) floors. This study introduces a blind equalization strategy that integrates the multimodulus algorithm (MMA) with discrete Fourier transform (DFT)-based channel estimation. The simulation results show that a GFDM system employing the proposed MMA-DFT blind equalizer with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i>=128 subcarriers and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>=5 subsymbols over the long-term evolution extended pedestrian A (LTE-EPA) channel closely approaches the theoretical bound within 20 GFDM-block iterations. Moreover, the mean square error (MSE) of MMA-DFT converges within approximately 15–20 GFDM blocks, enabling near-optimal detection performance with a limited number of adaptation iterations. Furthermore, as a result of the higher effective signal-to-noise ratio (SNR) enabled by the reduced cyclic prefix (CP) overhead of GFDM, the MMA-DFT equalizer applied to GFDM achieves a 0.89-dB SER gain compared to the same MMA-DFT equalizer applied to orthogonal frequency division multiplexing (OFDM) under identical parameter settings. A theoretical SER expression incorporating misadjustment, channel frequency response (CFR)-estimation error, and residual ICI is derived and shown to closely match the simulation. The proposed method reduces pilot overhead, improves spectral efficiency, and supports scalable massive multiple-input multiple-output (mMIMO) scenarios, contributing to energy-efficient future networks.

This paper proposes two quadrature amplitude modulation (QAM) constellation integration schemes for recon figurable intelligent surface (RIS)-enabled symbiotic backscatter systems termed Schemes I and II, where the primary and backscatter signals merge into a standard 16-QAM constellation by offsetting the amplitude-phase coupling effects of a practically measured RIS, Specifically, the primary and backscatter signals adopt: (a) a binary phase-shift keying and a symbol subset of eight symbols selected from a 16-QAM constellation for Scheme I; (b) a quadrature phase-shift keying and a symbol subset of four symbols selected from a 16-QAM constellation for Scheme II. On this basis, we design the corresponding detector and derive closed-form expressions of the symbol error rate (SER) and throughput of the primary signal, the backscatter signal, and the whole system for the underlying schemes. Our theoretical and numerical results show that the SER and throughput of Scheme II outperform those of Scheme I at low and medium transmit signal-to-noise-ratios (SNRs), and tend to be the same at high transmit SNR.

The use of non-orthogonal signals has several benefits over orthogonal signals in multi-coded communications. We provide a novel, theoretical study of non-orthogonal signaling to expand the applicability of these schemes. Motivated by a class of multi-carrier spread spectrum systems, this paper presents a thorough symbol error rate analysis of the broad class of multi-code signaling methods when they make use of codes which are not necessarily orthogonal. Our analysis is also extended to the case where the code set includes the negative of each code vector, i.e., an extension to biorthogonal signaling. Moreover, it is shown that the symbol error rate results derived in this paper reduce to those available in the literature when the multi-codes are orthogonal or have equal correlation between vectors. Additionally, we show how Monte Carlo integration can be used to evaluate the integrals in the error probability calculation and derive low complexity upper bounds on the error probabilities. We show that by combining these techniques, the error probability can be efficiently computed across the full SNR regime. Finally, we use the upper bound of the error probability to develop some analytical insights about the impacts of non-orthogonality among the code vectors on the symbol error probability.

We present a new analytical framework for the uplink data detection in massive multiple-input multiple-output systems with 1-bit analog-to-digital converters (ADCs). We first characterize the expected values of the soft-estimated symbols (after the linear receiver and prior to the data detection), which are affected by 1-bit quantization during both the channel estimation and the uplink data transmission. In our analysis, we consider conventional receivers such as maximum ratio combining (MRC), zero forcing, and minimum mean squared error (MMSE), with multiple user equipments (UEs) and correlated Rayleigh fading. Additionally, we design a linear minimum mean dispersion (LMMD) receiver tailored for data detection with 1-bit ADCs, which exploits the expected values of the soft-estimated symbols previously derived. Then, we propose a joint data detection (JD) strategy that exploits the interdependence among the soft-estimated symbols of the interfering UEs, analyzing its symbol error rate (SER), and subsequently introduce a low-complexity variant. These strategies are compared with robust maximum likelihood data detection with 1-bit ADCs. Numerical results examining the SER show that MMSE exhibits considerable performance gains over MRC, whereas the proposed LMMD receiver significantly outperforms the conventional receivers. Lastly, the proposed JD and its low-complexity variant provide a significant boost in comparison with the UE-specific data detection.

Fluid antenna multiple access (FAMA) has recently emerged as a user-centric approach to massive connectivity. By exposing many reconfigurable “ports” on an antenna aperture, they exploit local spatial fading fluctuations at each user terminal (UT) to mitigate multiuser interference (MUI) without the need for precoding. While both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">turbo</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fast</i> FAMA promise ultra-massive access, its practicality is limited by the need to observe, at symbol rate, the complete set of per-port channel gains and received signals. This letter addresses this bottleneck with a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">plug-and-play attentional-copula extrapolator</i> that reconstructs the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">joint</i> per-symbol field of channel gains and received signals from a small subset of ports. The module couples monotone normalizing-flow marginals with a Transformer-based copula to capture both intra-port (channel-signal) and inter-port (spatial) dependencies, yielding drop-in estimates for existing turbo FAMA pipelines without retraining. Simulation results reveal that even with an extremely small port subset, the normalized mean-square error (NMSE) rapidly converges and the symbol error rate (SER) after turbo FAMA remains within a few percent of the full-channel state information (CSI) oracle across aperture sizes. By replacing exhaustive sampling with accurate learned extrapolation, the proposed scheme preserves turbo FAMA’s scalability while <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unlocking practical, low-overhead deployment</i>—a viable pathway to extreme massive access.

Terahertz (THz) communication, a key enabler for 6 G networks, suffers from high path loss and limited coverage. To address these challenges, this paper proposes a RIS-assisted hybrid THz/RF architecture that integrates RIS with THz and radio frequency (RF) links, aiming to combine the high-capacity advantage of THz with the reliability of RF. To this end, a dynamic threshold switching (DTS) scheme is introduced, enabling real-time selection between THz and RF links based on the instantaneous signal-to-noise ratio. A complete analytical framework is developed, incorporating hardware impairments, pointing errors, and generalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha -\mu$</tex-math></inline-formula> fading in both RF and THz domains. The model incorporates deterministic RIS gains and frequency-dependent THz absorption, offering practical insights into the joint impact of RIS geometry, beam width, and switching thresholds. Closed-form expressions for outage probability, symbol error rate, ergodic capacity, and energy efficiency are derived. Simulation results confirm the accuracy of the proposed model and demonstrate that the hybrid system outperforms single-band THz or RF links and traditional diversity combining schemes. Additionally, increasing RIS elements improves performance and reduces transmit power requirements, with energy efficiency trends identifying optimal RIS configurations for practical deployment. These findings establish RIS-assisted hybrid THz/RF systems as a key enabler of reliable, high-capacity 6G communication for autonomous vehicles and smart factories.

Terahertz (THz) communication is envisioned as a key technology for 6G and beyond wireless systems owing to its multi-GHz bandwidth. To maintain the same aperture area and the same link budget as the lower frequencies, ultra-massive multi-input and multi-output (UM-MIMO) with hybrid beamforming is promising. Nevertheless, the hardware imperfections particularly at THz frequencies, can degrade spectral efficiency and lead to a high symbol error rate (SER), which is often overlooked yet imperative to address in practical THz communication systems. In this paper, the hybrid beamforming is investigated for THz UM-MIMO systems accounting for comprehensive hardware imperfections, including DAC and ADC quantization errors, in-phase and quadrature imbalance (IQ imbalance), phase noise, amplitude and phase error of imperfect phase shifters and power amplifier (PA) nonlinearity. Then, a two-stage hardware imperfection compensation algorithm is proposed. In the first stage, a deep neural network (DNN) based unified hardware imperfection model is developed to represent the combined hardware imperfections. Furthermore, to balance the performance and model complexity, a tailored network slimming framework is proposed using three slimming methods including pruning, parameter sharing, and power-aware scheme to slim the network in the first stage. In the second stage, the digital precoder in the transmitter (Tx) or the combiner in the receiver (Rx) is designed using neural network (NN) to effectively compensate for these imperfections. Numerical results show that the Tx compensation can perform better than the Rx compensation. Additionally, using the combined slimming methods can reduce parameters by 97.2% and running time by 39.2% while maintaining nearly the same performance in both uncoded and coded systems.

This paper proposes a unified analytical framework for reconfigurable intelligent surface (RIS)-assisted two-way full-duplex (TW-FD) communication systems in 6G Internet of Things (IoT) scenarios. The proposed framework specifically addresses RISs with N reflective elements, facilitating efficient bidirectional communication. A novel unified moment-based analytical approach is developed, accommodating diverse fading models including Rayleigh, Nakagami-n, Weibull, Nakagami-m, and κ-μ, thereby significantly enhancing the versatility and practicality for complex 6G IoT environments. To comprehensively validate the applicability of our analysis, both independently identically distributed (i.i.d.) and independently non-identically distributed (i.n.i.d.) fading channel scenarios are investigated. By employing the Edgeworth expansion method, we derive analytical expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the end-to-end signal-to-interference-plus-noise ratio (SINR). Additionally, closed-form expressions for probability, average symbol error rate (SER) for various modulation schemes, and end-to-end ergodic rate are provided. Monte Carlo simulations demonstrate the accuracy and robustness of the theoretical models proposed. The results presented in this work not only contribute substantially to the analytical methodologies for RIS-assisted communication but also offer practical guidance for the design and optimization of future 6G IoT systems.

In this letter, we propose to implement an index modulation (IM) scheme in a reconfigurable intelligent surface (RIS) assisted downlink non-orthogonal multiple access (DL-NOMA) system. Specifically, by allocating different numbers of RIS elements per user during each transmission, we can convey additional information bits. The proposed scheme improves the channel quality while simultaneously increasing the spectral efficiency (SE). We use a simple two-user communication model with PSK modulation to explain the concepts and derive new expressions for the PSK NOMA symbol error rate (SER). Simulations show that as the number of RIS elements increases, the improvement in transmission rate is at the cost of only a small degradation in the error rate performance.

Observing the evolution of mobile communication networks across successive generations, frequency band allocation has progressively expanded both in quantity and frequency. The relative simplicity of generating high-frequency signals via heterodyning of optical carriers in analog radio-over-fiber systems demonstrates considerable potential for enabling millimeter-wave and even terahertz-range wireless communication systems. Nevertheless, the prospective utilization of sub-terahertz or higher frequency bands in future wireless networks may introduce significant phase fluctuations in the received signal due to degraded phase coherence, a consequence of the large frequency separation between optical carriers. This degradation underscores the necessity of implementing phase correction techniques at the receiver. This paper reexamines the heterodyne-based detection approach as a potential phase noise correction method at the receiver, incorporating machine learning techniques. This study primarily addresses the inherent limitation of the conventional heterodyne-based detection method, which requires a minimum frequency spacing between the reference tone and the wireless signal to prevent signal-to-signal beating interference. The implementation of a machine learning algorithm aims to suppress signal-to-signal beating interference without relying on additional bandpass filters or previously proposed machine learning-based solutions, which often involve more complex configurations. The objective is to preserve the simplicity of conventional heterodyne-based receivers, while eliminating the need for high-frequency oscillators for frequency downconversion. Our results indicate that integrating a machine learning algorithm into the heterodyne-based detection approach can effectively suppress signal-to-signal beating interference, leading to improved detection accuracy. This enhancement surpasses the performance of conventional heterodyne-based detection, reducing the symbol error rate from 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> to 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−6</sup>.

Precoding techniques, particularly linear precoding, are widely employed in multiple-input multiple-output (MIMO) systems. Although well-studied in the literature, linear precoding design still faces two fundamental challenges: high computational complexity and the lack of a general design approach. This paper presents an efficient and unified framework for linear precoding design in downlink multiuser systems that accommodates diverse criteria, such as weighted sum rate (WSR) maximization and weighted symbol error rate (WSER) minimization, while ensuring quality of service (QoS) requirements. The proposed framework achieves an order-of-magnitude reduction in per-iteration computational complexity compared to existing methods. In particular, by accurately characterizing the feasible signal-to-interference-plus-noise ratio (SINR) region, we transform the high-dimensional precoding design problem into a more manageable, low-dimensional SINR allocation problem. We propose an efficient SINR-based precoding (SBP) framework that employs a water-filling solution at each iteration, without the need for matrix inversion. The proposed framework can be extended to broadcast and interference channels with multi-antenna users under pre-fixed receivers. Simulation results demonstrate that our method achieves near-optimal performance while significantly reducing computational complexity compared to existing methods, such as the weighted minimum mean square error (WMMSE) method.

As 6G standardization continues, Orthogonal Frequency Division Multiplexing (OFDM) continues to be the preferred waveform due to its spectral efficiency and robustness against multipath fading. However, high Peak to Average Power Ratio (PAPR) of OFDM severely degrades power amplifier efficiency, creating a critical bottleneck for energy constrained uplink devices. This manuscript proposes an hybrid forward error correction (FEC) assisted PAPR reduction procedure that combines Reed Solomon (RS) coding, Zadoff-chu (ZC) matrix precoding, and nonlinear companding to reduce the PAPR of OFDM system. Comprehensive system level simulations in nakagami-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> channel demonstrate that the proposed method suppresses the PAPR to 5 to 9 dB at a complimentary cumulative distribution function (CCDF) of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup>, while also preserving reliable symbol detection. This reduction in PAPR translates into a substantial improvement in theoretical power amplifier efficiency, increasing it from a baseline value of approximately 3% for conventional OFDM to values ranging from 6.5% to 17% depending on the selected companding profile. The proposed procedure maintains a robust Average Symbol Error Rate (ASER) across 16 QAM, 64 QAM, and 256 QAM modulation modes, achieving error levels as low as 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−8</sup>. Independent monte-carlo trials are utilized to obtain the system level performance.

This paper presents a noncoherent massive multiple-input multiple-output (MIMO) uplink scheme designed for low-complexity Internet of Things (IoT) devices. We consider a scenario where a single device equipped with two antennas transmits short packets to a base station with a large antenna array. To minimize latency and avoid pilot overhead, we introduce a structured space-time constellation design. Our key innovation is a parametric constellation framework that jointly encodes information in amplitude, mixing angle, and phase within an Alamouti structure. By optimizing the Kullback-Leibler (KL) divergence, we formulate the design as a tractable problem of selecting parameters for geometric and arithmetic sequences, rather than a complex search over all possible constellations. This results in a scheme specified by a few parameters, enabling both minimal storage and a low-complexity sequential maximum likelihood detector. Theoretical and numerical results demonstrate that our design achieves a larger minimum KL divergence and a superior symbol error rate compared to benchmarks, including Riemannian distance-based codes, KL-optimized single-input multiple-output schemes, and noncoherent pulse amplitude modulation, particularly in the high-SNR regime, where it eliminates error floors.

This paper introduces two comprehensive composite fading models: the α-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> Mixture and the α-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> Mixture. These models unify a broad spectrum of previously reported composite fading distributions and enable the systematic construction of hundreds of new ones. Their first-order statistics (namely, probability density function (PDF), cumulative distribution function (CDF), moment-generating function, and higher-order moments) are derived in compact, tractable forms that, for specific cases, yield singularity-free expressions improving upon existing state-of-the-art solutions. By consolidating a wide range of multiplicative shadow (MS) and LOS shadow (LOSS) fading families into a single parameterized framework, they provide a unified analytical basis for obtaining the key statistics of numerous composite fading scenarios. Serving as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">plug-and-play</i> base models, they enable direct evaluation of metrics such as outage probability (OP) and average symbol error rate (ASER) for both established and new composite fading models without rederiving channel statistics. Their unified structure and flexible parameterization also support systematic analysis of fading and shadowing in emerging scenarios, providing practical and extensible tools for next-generation wireless channel characterization.

LoRa is a widely recognized modulation technology in the field of low power wide area networks (LPWANs). However, the data rate of LoRa is too low to satisfy the requirements of Internet of Things applications. To address this issue, we propose a novel high-data-rate LoRa scheme based on the spreading factor index (SFI). In the proposed SFI-LoRa scheme, the starting frequency bin of a chirp signal is used to transmit information bits, while the combinations of spreading factors are exploited as a set of indices to convey additional information bits. Moreover, the theoretical symbol error rate, data rate, transmission throughput, complexity and energy efficiency of the proposed SFI-LoRa scheme are carefully analyzed. Simulation results not only verify the accuracy of our theoretical analysis, but also demonstrate that the proposed SFI-LoRa scheme can improve the transmission throughput of existing LoRa schemes without sacrificing the BER performance over additive white Gaussian noise, Rayleigh fading, and multipath flat-fading channels. Therefore, the proposed SFI-LoRa scheme is a potential solution for applications requiring a high data rate in the LPWAN domain.