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Multiple-Input Multiple-Output (MIMO) architectures are now widely adopted in wireless systems, providing substantial capacity benefits by harnessing spatial diversity and spatial multiplexing. Nonetheless, the large Peak-to-Average Power Ratio (PAPR) associated with common pre-processing techniques, like Singular Value Decomposition (SVD), increases the system’s susceptibility to nonlinear distortion. Conventional receiver designs that mitigate this distortion often neglect the fact that it has useful information on the transmitted data. Maximum Likelihood (ML) detection offers the capability to take advantage of the nonlinear distortion, but its inherent complexity is prohibitively high. This paper introduces a new MIMO receiver design aimed at exploiting the diversity introduced by the transmitter nonlinearities. It also provides an approximate bound on the achievable ML Bit Error Rate (BER) performance. Our results indicate that the proposed receiver can have a performance close to the ML receiver with just a few iterations.

As wireless networks advance toward the Sixth Generation (6G), which will support highly heterogeneous scenarios and massive data traffic, conventional computing methods may struggle to meet the immense processing demands in a resource-efficient manner. This paper explores the potential of quantum computing (QC) to address these challenges, specifically by enhancing the efficiency of Maximum-Likelihood detection in Multiple-Input Multiple-Output (MIMO) Non-Orthogonal Multiple Access (NOMA) communication systems, an essential technology anticipated for 6G. The study proposes the use of the Quantum Approximate Optimization Algorithm (QAOA), a variational quantum algorithm known for providing quantum advantages in certain combinatorial optimization problems. While current quantum systems are not yet capable of managing millions of physical qubits or performing high-fidelity, long gate sequences, the results indicate that QAOA is a promising QC approach for radio signal processing tasks. This research provides valuable insights into the potential transformative impact of QC on future wireless networks. This sets the stage for discussions on practical implementation challenges, such as constrained problem sizes and sensitivity to noise, and opens pathways for future research aimed at fully harnessing the potential of QC for 6G and beyond.

Abstract For wireless communications, the multiple‐input multiple‐output (MIMO) system efficiently makes use of the spectrum and enhances the transmission throughput. In this work, the maximum‐likelihood (ML) detection for the MIMO system is studied, and two ML detection algorithms are first considered for the MIMO system, including the sphere decoding (SD) algorithm and an algorithm based on differential metrics (DMs). Each of the two algorithms has its advantages and disadvantages. The two algorithms are first modified such that they are based on the same signal model. Then, a new ML detection algorithm is proposed for the MIMO system based on the hybrid operation of the two modified algorithms on the tree search process, in which both the branch‐and‐bound principle and indicative functions are applied to remove unnecessary searches. The proposed algorithm can attain the ML detection with lower average complexity over low and high ranges of signal‐to‐noise ratio (SNR), as the authors verify by simulations. The proposed ML detection can also generate soft output, and anti‐phase sequences are exploited to further reduce the complexity.

Abstract The design of an optimal non‐orthogonal multiple access (NOMA) transmission scheme with finite alphabet inputs for a typical two‐user uplink wireless communication system is investigated in which each terminal is equipped with a single antenna. Each of the two users utilises a four quadrature amplitude modulation (4‐QAM) constellation to transmit information data to a common base station, and the receiver employs a maximum likelihood (ML) detector to jointly estimate both transmitted signals. Assuming the availability of channel state information at both the transmitters and the receiver, it is aimed to design a pair of scalar beamformers for the two users such that the minimum Euclidean distance between elements of the received sum‐constellation is maximised subject to the power constraints on the users. A thorough consideration of all the different conditions results in the derivation of a closed‐form optimal beamformer design. As well, examination of the construction of sum‐constellation resulted from the optimum design directly leads to the unique decoding of the original transmitted signal of each user. To facilitate practical implementation, a fast decoding procedure of the optimum NOMA scheme is further developed. The corresponding theoretic probability of ML detection error is also derived. The theoretical development of an optimum sum‐constellation for the basic 2‐user 4‐QAM system provides a solid platform for the derivation of an optimum sum‐constellation for a K‐user and/or M‐QAM system. Indeed, a simple development of the basic sum‐constellation map facilitates such extensions. Numerical simulations not only demonstrate that the performance of the fast decoder agrees closely with the theoretical analysis, but also verify that it is superior in performance to other existing NOMA designs for the same system under high signal‐to‐noise ratio.

Unmanned aerial vehicles (UAVs) have been widely utilized for their various advantages. However, UAVs exhibit high mobility and energy storage restrictions in some applications, which can compromise the quality and reliability of communication links. This is a challenge that future aircraft and low-orbit aircraft will inevitably encounter. To effectively address the issue of dynamic Doppler spread in air-to-ground communication, this paper creatively introduces four-dimensional spherical code modulation into the orthogonal time–frequency space with an index modulation (OTFS-IM) system. The fundamental concept of the four-dimensional spherical code is elaborated in detail. Multiple resource symbols can be jointly used to increase the modulation dimension, thereby achieving a larger minimum Euclidean distance between constellation points. Furthermore, detailed analysis is conducted on the bit error rate (BER) and the peak-to-average-power ratio (PAPR) expressions of the proposed system to evaluate its performance and provide theoretical guidance. The proposed scheme not only adapts well to high-speed scenarios but also achieves better power consumption efficiency. The simulation results demonstrate that our proposed scheme outperforms conventional methods. Its robustness and generalization ability are also validated.

Synchronization is a challenging issue in vehicle-to-everything (V2X) cellular communication, especially when V2X devices need to directly communicate with each other outside the network coverage area. By adopting the maximum likelihood principle, we propose joint detection of the sidelink secondary synchronization signal (SL-SSS) and carrier frequency offset (CFO) in a V2X system using 5G new radio sidelink. We formulate an effective joint coherent synchronization scheme for cellular V2X applications by decoupling the estimation of the sidelink identity and CFO, which requires a priori knowledge of channel state information. To verify the feasibility of the proposed detection scheme, we derive a simplified implementation of the proposed SL-SSS detector and a closed-form expression for the detection probability. Simulation results demonstrate that the proposed SL-SSS detector exhibits either comparable performance in terms of detection probability or reduced complexity when compared with conventional SL-SSS detectors. Using the proposed method in the cellular V2X system enables V2X devices to achieve robust synchronization with reduced power consumption during the initial synchronization procedure, while also offering valuable insights for designing a simple, efficient sidelink synchronization receiver.

The Golden code is a full-rate space-time block code (STBC), which achieves a diversity order of $2N_{r}$ , where $N_{r}$ is the number of receive antennas. The multiple complex symbol Golden code (MCS-Golden code) is a generalized Golden code. The MCS-Golden code not only achieves full-rate but also achieves a diversity order of $2^{n}{N_{r}}$ , $n$ , $n\ge {1}$ , is an integer, and $2^{n}$ is the number of multiple complex symbols in the MCS-Golden code system. In this paper, we apply the labelling diversity technique to the MCS-Golden code to form a new type of STBC, named as multiple complex symbol Golden space-time labelling diversity (MCS-GSTLD). The proposed MCS-GSTLD achieves a diversity order of $2\times {2^{n}}{N_{r}}$ , and further improves error performance compared to the MCS-Golden code. We also formulate the theoretical average bit error probability (ABEP) for the proposed MCS-GSTLD system. Furthermore, we apply sphere decoding with sorted detection subset (SD-SDS) to detect the transmitted symbols in the MCS-GSTLD system. Simulation results show that the SD-SDS scheme achieves the theoretical ABEP for $N_{r}>2$ . Both theoretical and simulation results demonstrate that with the same spectral efficiency and four receive antennas, the 2CS-GSTLD achieves at least 1.3 dB signal-to-noise ratio (SNR) gain compared to the 2CS-Golden code at a BER of $3\times {10^{-6}}$ , while the 4CS-GSTLD achieves at least 0.7 dB SNR gain compared to the 4CS-Golden code.

As industrial plants increase the number of wirelessly connected sensors for fault detection, a key problem is to identify and obtain data from the sensors. Due to the large number of sensors, random access protocols exploiting non-orthogonal multiple access (NOMA) are a natural approach. In this paper, we develop new algorithms based on approximate message passing for sensor identification and channel estimation accounting for correlation in the activity probability of each sensor and observations of physical variables (e.g., temperature) by the access point. These algorithms form the basis for data decoding, while also identifying faulty machines and estimating local values of the temperature, which can lead to a reduction in the amount of data required to be transmitted. Numerical results show that for an expected activity probability of 0.35, our algorithms improve the normalized mean-square error of the channel estimate by up to 5dB and reduce the rate of sensor identification errors by a factor of four.

For the first time, the recently proposed “talkative power” paradigm combining power electronics and communication engineering is extended by channel coding and advanced receiver design aspects. In this concept, the pulses that control the duty cycle of switched-mode power converters are simultaneously used for data transmission by modifying the pulse phase, pulse frequency, pulse position or pulse width. The data sequence is embedded into the switching signal, similar to random modulation. The data can be used for example in point-to-point links, inside multi-port power converters, and for communication in networked power grids. As an application example a buck converter is studied. Its output voltage is numerically calculated for arbitrary two-level switching signals. The corresponding system model serves as a common framework for switching waveform design, receiver design, and performance analysis. The data sequence is represented by a small deterministic output voltage ripple. Various techniques to improve the data rate and the robustness of the communication are introduced, including line coding, a derivation of the optimum receiver in the sense of maximum-likelihood detection, and forward error correction coding as an option. Although emphasis is on a buck converter, the concept is applicable to other power converter topologies as well.

The Golden code is a full-rate full-diversity (FRFD) space-time block code (STBC). The conventional Golden code takes four complex symbols and generates two pairs of Golden codewords. Each pair of Golden codewords contains two complex symbols. In this paper, a new type of Golden code is proposed, where we extend the two complex symbols in each pair of Golden codewords into multiple complex symbols. The scheme hereinafter referred to as the multiple complex symbol Golden code (MCS-Golden code) preserves the FRFD property but achieves a diversity order of 2nNr compared to the conventional Golden code, where Nr is the number of receive antennas, n, n ≥ 1, is an integer, and 2n is the number of multiple complex symbols in the MCS-Golden code system. An equivalent model of the MCS-Golden code is constructed, then used to derive a closed-form bound on the average bit error probability (ABEP) for the MCS-Golden code system. We further propose a low complexity detection scheme, sphere decoding with sorted detection subset (SD-SDS) for the MCS-Golden code. Finally, we discuss the detection complexity for the proposed SD-SDS. Both simulation and theoretical results show that the MCS-Golden code significantly improves error performance compared to the conventional Golden code. For example, at an average bit error rate of 3 × 10-6, a four complex symbol Golden code system with three receive antennas achieves approximately 2.5 dB signal-to-noise ratio (SNR) gain compared to the conventional Golden code.

Non-orthogonal multiple access (NOMA) is a technique which allows multiple users to share the same radio access resources. However, there exist interferences among these users in the NOMA system. These interferences need to be taken into account in the signal detection and error performance analysis. In the downlink NOMA system, the far user detects its signal by treating the near user's signal as interference, while the near user employs successive interference cancellation (SIC) to detect its signal. Based on the conventional signal detection, it is not straightforward to derive the error performance for both the far user and near user. By analyzing the constellation relationships between the far user's signal and superposition coded (SC) signal, and the near user's signal and SC signal, in this article, a simple threshold based detection algorithm is proposed to detect both the far user's signal and near user's signal. Furthermore, by aid of the constellation relationships, in this article, simple expressions of the average symbol error probability (ASEP) with squared M -ary quadrature amplitude modulation for both the far user and near user are easily derived in Rayleigh fading channels. Simulation results validate the derived theoretical ASEP results.

Orthogonal frequency division multiplexing (OFDM-IM) is a multicarrier transmission technology that modulates information bits not just onto subcarriers by means of M-ary constellation mapping but also onto selected (active) subcarrier indices. Consequently, errors can occur in OFDM-IM systems indices in addition to the errors of M-ary symbols. This paper analyzes the error scenarios and derives mathematical expressions for the error performance based on the maximum likelihood (ML) detection. In evaluating the bit error rate (BER) in the additive white Gaussian noise (AWGN) channel, some assumptions are made and our analytical result show that the BER of OFDM-IM system is a weighted sum of exponential functions and Q-functions. Our general BER expression has been shown to be in excellent agreement with numerical simulation and proven to be accurate and can serve as a reference for the design and evaluation of any arbitrary size and configuration of OFDM-IM systems.

To meet the requirements of beyond 5G networks, the significant amount of unused spectrum in sub-TeraHertz frequencies is contemplated for high-rate wireless communications. Yet, the performance of sub-TeraHertz systems is severely degraded by strong oscillator phase noise. We investigate in this paper the design of digital communications robust to phase noise. This problem is addressed in three steps: the characterization of the phase noise channel, the design of the optimum receiver, and the optimization of the modulation scheme. This paper proposes a joint performance and implementation optimization. First, we address the design of the demodulation scheme for phase noise channels and propose the polar metric, a soft-decision rule for symbol detection. It is shown that performance gains are achieved for coded and uncoded systems with valuable complexity reductions of the receiver. Second, we investigate the optimization of the modulation scheme for phase noise. We demonstrate that using a constellation defined upon a lattice in the amplitude-phase domain leads to significant performance gains and a low-complexity implementation. Thereupon, we propose the Polar-QAM scheme with efficient binary labeling and demodulation. Numerical simulation results show that the proposed modulation and demodulation schemes offer valuable solutions to achieve high-rate communications on systems strongly impaired by phase noise.

Ubiquitous light-emitting diodes provide natural infrastructures for multiuser visible light communications (VLCs). However, the current available works for multiuser VLC systems mainly focus on broadcast scenarios and beamforming techniques. In this paper, we consider a multiuser multi-access VLC system with finite-alphabet inputs. Intended for two-user multi-access VLC systems, we propose an energy-efficient time-collaborative constellation design to manage the nonnegative multiuser interference and we develop a joint maximum-likelihood demodulation and successive interference cancellation decoding algorithm for signal detection. Simulation results indicate that our proposed time-collaborative constellation design outperforms time-uncollaborative scheme in error performance perspective.

Ubiquitous light emitting dioxides provide natural infrastructures for multiuser visible light communications (VLC). The current available works mainly focus on a potential assumption of the continuous signaling. In this paper, we consider a two-user multiaccess VLC system with finite-alphabet inputs. To manage the nonnegative finite-alphabet multiuser interference, we adaptively adjust the power of each user's transmitted signals to maximize the received minimum Euclidean distance. By applying the properties of Farey sequence in number theory to solve the finite-alphabet optimization, it is proved that the optimal received signal constitutes an equally spaced pulse amplitude modulation constellation, which admits a low-complexity maximum likelihood detection. Both analytical results and computer simulations demonstrate that our proposed design has substantial performance advantage over time division multiple access, especially for significant channel strength difference.

Serial Concatenation of Two Dimensional Soft Output Viterbi Algorithm (2D-SOVA) and regular Viterbi Algorithm (VA) for 2D equalisation and detection of Shingled Magnetic Recording (SMR) media provides excellent performance as compared to the use of 1 Dimensional (1D) maximum likelihood detector. In this paper, we implement and evaluate the performances of two versions of it. The first version performs 2D SOVA along the tracks to eliminate the effect of inter-symbol interference (ISI) and then the Viterbi detector across the tracks to remove inter-track interference (ITI). The second version carries out 2D-SOVA across the tracks and VA along the tracks. The results for high ITI and ISI show a better performance when using 2D-SOVA across the track with a small difference in computational complexity in favour of 2D-SOVA across the tracks.

Index modulation has become a promising technique in the context of orthogonal frequency division multiplexing (OFDM), whereby the specific activation of the frequency domain subcarriers is used for implicitly conveying extra information, hence improving the achievable throughput at a given bit error ratio (BER) performance. In this paper, a dual-mode OFDM technique (DM-OFDM) is proposed, which is combined with index modulation and enhances the attainable throughput of conventional index-modulation-based OFDM. In particular, the subcarriers are divided into several subblocks, and in each subblock, all the subcarriers are partitioned into two groups, modulated by a pair of distinguishable modem-mode constellations, respectively. Hence, the information bits are conveyed not only by the classic constellation symbols, but also implicitly by the specific activated subcarrier indices, representing the subcarriers' constellation mode. At the receiver, a maximum likelihood (ML) detector and a reduced-complexity near optimal log-likelihood ratio-based detector are invoked for demodulation. The minimum distance between the different legitimate realizations of the OFDM subblocks is calculated for characterizing the performance of DM-OFDM. Then, the associated theoretical analysis based on the pairwise error probability is carried out for estimating the BER of DM-OFDM. Furthermore, the simulation results confirm that at a given throughput, DM-OFDM achieves a considerably better BER performance than other OFDM systems using index modulation, while imposing the same or lower computational complexity. The results also demonstrate that the performance of the proposed low-complexity detector is indistinguishable from that of the ML detector, provided that the system's signal to noise ratio is sufficiently high.

In wideband wireless communication systems the RAKE receiver is commonly used to collect the resolvable multipath energy and counter the effects of fading through diversity. However, in channels with large delay and energy spread, its high complexity still remains a major issue. This motivates the study and application of computationally efficient finger placement algorithms that significantly reduce the receiver complexity with a reasonable performance loss. In this paper, a low–complexity maximum likelihood RAKE receiver, the Suboptimum – Maximum Power Minimum Correlation (S–MPMC) RAKE is proposed. The allocation of its first two fingers is based on the received signal correlation properties. Their positions determine also the placement of the rest of the fingers. Simulation results are provided to show the operation of the receiver and demonstrate its performance. Comparisons with relevant methods are performed to corroborate the merits of the proposal. The balance on the performance and the complexity of the technique makes it suitable for use in commercial wideband communication systems.