Optimal Maximum Likelihood Detection Research Articles

Vector Approximate Message Passing Based OFDM-IM Detection for Underwater Acoustic Communications.

Orthogonal frequency division multiplexing with index modulation (OFDM-IM) has great potential for the implementation of high spectral-efficiency underwater acoustic (UWA) communications. However, general receivers consisting of the optimal maximum likelihood detection suffer from high computational load, which prohibits real-time data transmissions in underwater scenarios. In this paper, we propose a detection based on a vector approximate message passing (VAMP) algorithm for UWA OFDM-IM communications. Firstly, a VAMP framework with a non-loopy factor graph for index detection is formulated. Secondly, by utilizing the sparsity inherently existing in OFDM-IM symbols, a novel shrinkage function is derived based on the minimum mean square error criterion, which guarantees better posterior estimation. To reduce the errors from estimated non-existing indices, one trick is utilized to search the elements from the look-up table with the minimal Euclidean distance for the replacement of erroneously estimated indices. Experiments verify the advantages of the proposed detector in terms of low complexity, robustness and effectiveness compared with the state-of-art benchmarks.

Relay‐assisted multiuser MIMO‐DQSM system for correlated fading channels

AbstractThis paper presents the performance evaluation of an amplify‐and‐forward (AF) relay‐assisted multiuser multiple input–multiple output (MU–MIMO) downlink transmission system for correlated fading channels. The overall system performance was improved by incorporating a double‐quadrature spatial modulation (DQSM) scheme. The bit error rate (BER) performance and detection complexity of the AF–MU–MIMO–DQSM system were analyzed and compared with those of a conventional AF–MU–MIMO system under the same conditions and parameters. The results showed that the correlated fading channel severely affected the performance of systems with higher spectral efficiency (SE). Considering an SE of 12 bpcu/user, the AF–MU–MIMO–DQSM system yielded a gain of up to 3 dB in BER performance compared with that of its conventional counterpart for the analyzed cases. In terms of detection complexity, the AF–MU–MIMO–DQSM system showed a reduction of up to 56 % compared with that of the conventional system for the optimal maximum likelihood detection criterion.

Beamforming and data detection in intelligent reflecting surfaces‐assisted communication using deep learning

SummaryIn this article, we propose two deep neural network (DNN) architectures for an intelligent reflecting surface (IRS)‐assisted network with a single transmitter and multiple receivers. The first DNN is designed to obtain an optimal beamforming weight vector that maximizes the achievable sum rate over the IRS‐aided network. The beamforming vector is designed based on a pilot‐based channel estimation procedure, which requires only a small fraction of the available number of reflecting surfaces on the IRS to be active. The obtained vector is fed to the second DNN, which is designed for detecting information symbols from the transmitter. Our simulation study shows that the achievable rate obtained using the designed beamforming vector approaches the maximum achievable rate quickly, as the number of active elements increases. The impact of the number of active elements and the beamforming vector on the performance of the detector is also studied, in terms of the bit error rate (BER). We show that the BER performance of the second DNN is close to that of the optimal maximum likelihood detector. Further, we study the effect of the channel estimation errors on the performance of the DNNs. Moreover, we study the effect of the hyperparameters of the architectures on the training time and performance, in terms of root mean squared error and accuracy.

Error probability analysis for ultra-massive MIMO system and near-optimal signal detection

In this paper, average bit error probability (ABEP) bound of optimal maximum likelihood (ML) detector is first derived for ultra massive (UM) multiple-input-multiple-output (MIMO) system with generalized amplitude phase modulation (APM), which is confirmed by simulation results. Furthermore, a minimum residual criterion (MRC) based low-complexity near-optimal ML detector is proposed for UM-MIMO system. Specifically, we first obtain an initial estimated signal by a conventional detector, i.e., matched filter (MF), or minimum mean square error (MMSE) and so on. Furthermore, MRC based error correction mechanism (ECM) is proposed to correct the erroneous symbol encountered in the initial result. Simulation results are shown that the performance of the proposed MRC-ECM based detector is capable of approaching theoretical ABEP of ML, despite only imposing a slightly higher complexity than that of the initial detector.

Performance analysis for orthogonal time frequency space modulation systems with generalized waveform

Orthogonal time-frequency space (OTFS), which exhibits beneficial advantages in high-mobility scenarios, has been considered as a promising technology in future wireless communication systems. In this paper, a universal model for OTFS systems with generalized waveform has been developed. Furthermore, the average bit error probability (ABEP) upper bounds of the optimal maximum likelihood (ML) detector are first derived for OTFS systems with generalized waveforms. Specifically, for OTFS systems with the ideal waveform, we elicit the ABEP bound by recombining the transmitted signal and the received signal. For OTFS systems with practical waveforms, a universal ABEP upper bound expression is derived using moment-generating function (MGF), which is further extended to MIMO-OTFS systems. Numerical results validate that our theoretical ABEP upper bounds are concur with the simulation performance achieved by ML detectors.

Joint RIS Grouping Design Assisted Generalized Quadrature Reflection Modulation

In this paper, a novel joint reconfigurable intelligent surface (RIS) grouping design assisted generalized quadrature reflection modulation (JGD-GQRM) scheme is proposed for a single radio frequency (RF) multiple-input multiple-output (MIMO) system. In JGD-GQRM, a limited number of RIS elements are spatially grouped, and the remaining reflection patterns are utilized for joint mapping to improve the reliability of the transmission. Moreover, it maps additional information bits by full reflection passive beamforming to improve the system's spectral efficiency (SE). In addition to the optimal maximum likelihood (ML) detector that has high computational complexity, a low-complexity sequential greedy detection (SGD) for JGD-GQRM is proposed. Simulation results show that the proposed scheme can achieve better bit error rate (BER) performance than the existing reflection modulation.

RIS-Aided Joint Transceiver Space Shift Keying Reflection Modulation

In this letter, a reconfigurable intelligent surface-aided joint transceiver space shift keying reflection modulation (RIS-JTSSK-RM) scheme is proposed. The RIS aids the transceiver SSK modulation and inserts additional bits into the reflected phase shift of the radio frequency (RF) signal simultaneously. The design of reflection modulation constellation points and the joint mapping of transceiver antennas enhance the system’s reliability. To reduce the RIS-JTSSK-RM required computational complexity, a practical non-coherent greedy detector is proposed. In addition, we analyze the proposed system’s bit error rate (BER) performance under the optimal maximum likelihood detector. The theoretical and simulation results show that the proposed system has better BER performance.

Learning From Noisy Labels for MIMO Detection With One-Bit ADCs

This letter presents a data detection method for multiple-input multiple-output systems with one-bit analog-to-digital converters. The basic idea is to learn the likelihood function of the system from training samples. To this end, a training data generation strategy is first proposed, which labels a one-bit received signal with a symbol index determined by channel-based data detection. This strategy requires no extra training overhead beyond pilot symbols for channel estimation, but leads to noisy labels due to data detection errors. For accurate learning from the noisy labels, an expectation-maximization algorithm is also developed. This algorithm learns both the likelihood function and the transition probability from each noisy label to a true label. Numerical results demonstrate that the presented method performs similar to the optimal maximum likelihood detection.

Maximum Likelihood Detection in Single-Input Double-Output Non-Gaussian Barrage-Jammed Systems

We derive the likelihood functions and the maximum likelihood (ML) detectors for four classes of single-input double-output (SIDO) communication systems, i.e., systems with one transmit and two receive antennas. For all classes, the received signals are contaminated by a Gaussian noise component and a non-Gaussian component induced by the Gaussian transmissions of a proactive continuous single-antenna jammer over an unknown complex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\times 1$</tex-math></inline-formula> Gaussian vector channel. The considered classes correspond to whether full channel distribution information (CDI), or partial CDI about the transmitter channel and the jammer channel is available at the receiver. Unlike their scalar counterparts, the vector channels considered herein interweave the components of the received signal, rendering the derivation of the likelihood function a daunting task for more than two receive antennas. Furthermore, the interweaving of the received signal components in the vector channel case prevents the optimal ML detector for unit-norm constellations from reducing to the corresponding Gaussian approximation-based detector. This is in sharp contrast with the scalar case, wherein the two detectors are equivalent for unit-norm constellations. Confirming our analytical findings, experimental results show that the difference between the two detectors can be significant, especially when the transmitter-receiver and jammer-receiver channels have substantial line-of-sight components. Although the computational cost of performing optimal ML detection in the presence of non-Gaussian jamming is higher in the case of two receive antennas, the performance advantage over the single antenna case justifies it.

Combined Radar and Communications With Phase-Modulated Frequency Permutations

This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using M-ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has a negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on a modified Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM. Extensive numerical examples are provided to illustrate the accuracy of our results.

Deep Learning-Based Signal Detection for Rate-Splitting Multiple Access Under Generalized Gaussian Noise

In this paper, we propose a long short-term memory-based deep learning (DL) architecture for signal detection in uplink and downlink rate-splitting multiple access systems with multi-carrier modulation, over Nakagami-m fading and generalized Gaussian noise (GGN). The proposed DL detector completely eliminates the need for the use of successive interference cancellation (SIC), which suffers from disadvantages such as error propagation. In an orthogonal frequency division multiplexing setting, we show that the proposed DL detector outperforms the standard SIC receivers such as the least squares detector and the minimum mean-squared error receiver, and attains the performance of the optimal maximum likelihood detector, in terms of the symbol error rate (SER). Furthermore, we study the effects of the shaping parameter of GGN, hyperparameters of the DL network such as batch size and learning rate on the SER performance.

Frequency Permutations for Joint Radar and Communications

This paper presents a new joint radar and communication technique based on the classical stepped frequency radar waveform. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. A new signaling scheme is proposed in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. Considering the optimum maximum likelihood detection, the union bound and the nearest neighbour approximation on the communication block error probability is derived for communication in an additive white Gaussian noise channel. The results are further extended to incorporate the Rician fading channel model, of which the Rayleigh fading channel is presented as a special case. Furthermore, an efficient communication receiver implementation is discussed based on the Hungarian algorithm which achieves optimum performance with much less operational complexity when compared to an exhaustive search. From the radar perspective, two key analytical tools, namely, the ambiguity function and the Fisher information matrix are derived. Furthermore, accurate approximations to the Cramer-Rao lower bounds on the delay and Doppler estimation errors are derived based on which the range and velocity estimation accuracy of the waveform is analysed.

Reordered Amplitude Phase Shift Keying Aided Differential Spatial Modulation: DFDD-Based Low-Complexity Detector and Performance Analysis Over Fading Channels

Differential spatial modulation (DSM) is a multiple input multiple output (MIMO) wireless transmission technique that achieves additional data bit transmission by utilizing antenna activation indexes. Combined with amplitude phase shift keying (APSK) constellations, the spectrum efficiency of DSM system can be further improved. However, the theoretically optimal maximum likelihood (ML) detection suffers from a high complexity that grows exponentially with the number of transmit antennas (TAs). Besides, the imperfect channel state information in fast fading channels leads to a severe deterioration of the detection performance. To address these problems, we propose a novel transmission scheme named reordered amplitude phase shift keying aided differential spatial modulation (RAPSK-DSM) and its low-complexity decision-feedback differential detection (DFDD) based detection algorithm. The proposed RAPSK-DSM scheme provides a better solution for addressing the error propagation problem and its detector utilizes the preceding channel gain vectors from previous detection results to mitigate the performance loss caused by time-selective channel fading. Furthermore, by decomposing and pre-computing the detection process, the complexity of proposed detector is effectively reduced due to the avoidance of redundant computations. Numerical analyses and simulation results show that the proposed RAPSK-DSM system is able to achieve substantial bit error rate (BER) performance improvement under fast fading channel conditions at the expense of low complexity.

Low complexity deep neural network based transmit antenna selection and signal detection in SM-MIMO system

In this paper, with the investigation of the conventional Euclidean distance based transmit antenna selection (ED-AS) and the maximum likelihood detection (MLD) in spatial modulation (SM) multiple-input multiple-output (MIMO) system, we propose the deep neural network (DNN) based transmit antenna selection (DNN-AS) and signal detection (DNN-SD), respectively, to effectively balance the system performance and the complexity. For the proposed DNN-AS, we transform the existing problem of AS into a prediction problem and design a low dimension multi-output classifier to achieve the low complexity solution of AS. For the DNN-SD, we present two sub-DNNs to recover the transmitted SM signal. Numerical results reveal that the proposed DNN-AS scheme gets a better average bit error rate (ABER) performance than the typical AS schemes in SM-MIMO system with lower complexity. In contrast to the ED-AS approach, it attains the optimal and suboptimal ABER performance at low-and-moderate signal-to-noise ratio (SNR) region and high SNR region, respectively. The proposed DNN-AS scheme achieves obvious SNR gains compared with the conventional SM system and gets about 3.5 dB gains over the typical maximum-norm based AS (Norm-AS) algorithm. Furthermore, the proposed DNN-SD scheme obtains a superior detection performance compared with the conventional linear detection methods and provides the same ABER performance as the optimum MLD scheme in the presence of correlated noise.

Envelope Distribution of Two Correlated Complex Gaussian Random Variables and Application to the Performance Evaluation of RIS-Assisted Communications

The operation of point-to-point communication assisted with reconfigurable intelligent surface, where the multi-hop channels between the source and the destination are subject to Rician fading but are not necessarily independent, is investigated. Considering binary phase-shift keying signaling for the data transmission and optimal maximum-likelihood detection at the receiver, a system performance evaluation is conducted in terms of reliability and capacity. For such, the distributions of the magnitude of the product of the complex channel gains are first obtained for both, the case when the channel gains are independent and the case when they are correlated. Subsequently, expressions of the system’s error rate and the upper-bounds on the average capacity are obtained for the said correlated and uncorrelated channel cases. Numerical results corroborating the analysis are also presented. In particular, it is revealed that correlation between the channels has negligible effect on the error rate when the fading is Rayleigh distributed, and that an increase in the value of the Rician parameter pertaining to the channel between the receiver pair has reduced impact on the reduction of the error rate, which provides practical guidelines for system deployments with high reliability.

Defeating Super-Reactive Jammers With Deception Strategy: Modeling, Signal Detection, and Performance Analysis

This paper develops a novel framework to defeat a super-reactive jammer, one of the most difficult jamming attacks to deal with in practice. Specifically, the jammer has an unlimited power budget and is equipped with the self-interference suppression capability to simultaneously attack and listen to the transmitter’s activities. Consequently, dealing with super-reactive jammers is very challenging. Thus, we introduce a smart deception mechanism to attract the jammer to continuously attack the channel and then leverage jamming signals to transmit data based on the ambient backscatter communication technology. To detect the backscattered signals, the maximum likelihood detector can be adopted. However, this method is notorious for its high computational complexity and requires the model of the current propagation environment as well as channel state information. Hence, we propose a deep learning-based detector that can dynamically adapt to any channels and noise distributions. With a Long Short-Term Memory network, our detector can learn the received signals’ dependencies to achieve a performance close to that of the optimal maximum likelihood detector. Through simulation and theoretical results, we demonstrate that with our approaches, the more power the jammer uses to attack the channel, the better bit error rate performance the transmitter can achieve.

Successive Interference Cancellation on Frequency-Selective Channels With Mode-Dependent Gain

In ultra-long-haul optical communication systems, polarization-dependent gain from single-mode semiconductor optical amplifiers or mode-dependent gain from multi-mode erbium-doped fiber amplifiers causes a channel’s achievable information rate (AIR) using linear minimum-mean-square error (MMSE) detection to become substantially lower than the capacity of optimal maximum likelihood detection owing to loss of orthogonality between modes. However, such capacity loss can be mitigated using techniques that retain reasonable complexity, such as successive interference cancellation (SIC). In wireless systems, multicarrier transmission with many subcarriers transforms the frequency-selective channel into a set of uncoupled memoryless subchannels, and it is possible to obtain good performance using SIC on each subchannel independently. Multicarrier transmission in optical fibers, however, is susceptible to performance loss caused by Kerr nonlinearity. Therefore, we study methods for applying SIC on frequency-selective optical fiber channels using single-carrier transmission. We compare the theoretical performance of MMSE and SIC equalizers on frequency-selective optical fiber channels operating at 64 Gbaud with transmission distances up to 15,000 km and evaluate the penalties of SIC implementation. We consider single-mode fiber links with random artificial polarization-mode dispersion inserted along the link to enhance frequency diversity, as well as multi-core fiber links supporting 14 spatial and polarization modes. We show that SIC can increase outage capacity by 19%, but the AIR increase is reduced by almost half if error correction coding is not performed across modes. We confirm that SIC can adapt to fast channel perturbations with only a 3% decrease in AIR.

A Novel Average Autoencoder-Based Amplify-and-Forward Relay Networks With Hardware Impairments

In this paper, we propose a novel Average autoencoder (AE)-based amplify-and-forward (AF) relay networks impacted by the I/Q imbalance (IQI) and additional hardware impairments (AHI), where the source and destination nodes are equipped with neural network (NN)-based encoder and decoder, while a conventional AF relay node assists the transmission. The average AE employs multiple small NN-based decoders at the destination node, each decoding a soft probabilistic output that is averaged to obtain the final soft probabilistic output at the destination node. By considering multiple small NN decoders, we reduce the implementation complexity significantly while improving the performance compared to the AE with a single large but NN-based decoder. Within this Average AE framework, we propose a coded modulation design (CMD) with zero-forcing-based IQI compensation that considers the availability of the channel state information (CSI) and IQI knowledge. However, the IQI and CSI need to be estimated separately. Thus, we also propose a CMD with no IQI compensation that requires only the CSI knowledge. Finally, we propose a differential CMD that removes the necessity of both the CSI and IQI knowledge. Under low signal-to-interference-and-noise-ratio regimes, we show that the proposed Average AE outperforms the optimal maximum likelihood detector by considerable margin.

Low-Complexity GSM Detection Based on Maximum Ratio Combining

Generalized spatial modulation (GSM) technology is an extension of spatial modulation (SM) technology, and one of its main advantages is to further improve band efficiency. However, the multiple active antennas for transmission also brings the demodulation difficulties at the receiver. To solve the problem of high computational complexity of the optimal maximum likelihood (ML) detection, two sub-optimal detection algorithms are proposed through reducing the number of transmit antenna combinations (TACs) detected at the receiver. One is the maximum ratio combining detection algorithm based on repetitive sorting strategy, termed as (MRC-RS), which uses MRC repetitive sorting strategy to select the most likely TACs in detection. The other is the maximum ratio combining detection algorithm, which is based on the iterative idea of the orthogonal matching pursuit, termed the MRC-MP algorithm. The MRC-MP algorithm reduces the number of TACs through finite iterations to reduce the computational complexity. For M-QAM constellation, a hard-limited maximum likelihood (HLML) detection algorithm is introduced to calculate the modulation symbol. For the M-PSK constellation, a low-complexity maximum likelihood (LCML) algorithm is introduced to calculate the modulation symbol. The computational complexity of these two algorithms for calculating the modulation symbol are independent of modulation order. The simulation results show that for GSM systems with a large number of TACs, the proposed two algorithms not only achieve almost the same bit error rate (BER) performance as the ML algorithm, but also can greatly reduce the computational complexity.

Efficient jamming attack against MIMO transceiver

This work addresses the issue of point-to-point intelligent jamming against MIMO architecture-based systems. The receiver uses an optimal Maximum Likelihood (ML) detector to extract the data stream from the received signal. Analyzing the receiver performance in the presence of a jamming signal, optimal attack strategies based on the pairwise error probability parameter as an objective function are designed, enabling the achievement of maximum degradation of the service quality. To perform the worst-case jamming of a legitimate transceiver, we assume that the jammer can eavesdrop on the Channel State Information (CSI). Depending on the jamming power budget constraint and the potential of jamming systems to estimate the CSI, different scenarios are envisaged, including imperfect CSI estimation cases. By minimizing the trace of Positive Semi-Definite (PSD) matrix products, the optimal jamming approaches that ensure maximum degradation of the legitimate link are designed. The disruption efficiency of the proposed approaches is comparable to the employment of the brute-force attack, but with a higher power level that is proportional to the number of jamming antennas in the case of partial knowledge of CSI, and inversely to the statistical expectation of the square root of the Wishart matrix's eigenvalues in the case of complete knowledge of CSI. To justify the relevance of the suggested policy, extensive simulations of the effect of these interventions are presented.