Maximum Likelihood Receiver Research Articles

Terminological features of the concept of signal-to-noise ratio when processing ultra-wideband signals

Currently, when processing various signals and studying various types of receivers, there are many definitions for one of the basic characteristics of radio systems – signal-to-noise ratio (SNR). At the same time, the terminological feature of the SNR concept is that any definition within the framework of a locally solvable signal processing problem is correct. However, difficulties arise when comparing the effectiveness of one algorithm with another, when studying different signal models, or when measuring the SNR in different parts of the receiving system. Some researchers ignore this fact due to the apparent absolute clarity of this issue, which leads to incorrect comparison of various processing algorithms or the formation of obviously unrealizable requirements for the designed equipment. In each locally solved problem, the determination of SNR will be individual, and comparison of efficiency at a fixed SNR must be carried out with mandatory scaling of signal energies depending on the formulation of the problem. This paper systematizes the terminological features of the SNR concept in order to ensure uniformity of its application by researchers and engineers. The purpose of the work is to systematize the definition of SNR for various signal models and conditions for measuring this characteristic, to specify the results in terms of terminological features of UWB signal processing and to propose a model for recalculating the SNR depending on the stage of the signal transmission and reception process. The paper examines the determination of SNR at the input and output of optimal and matched filters, at the output of optimal receivers operating under conditions of various a priori uncertainties, as well as when processing various classes of signals. By determining the SNR at the output of the matched filter and the SNR at the output of the maximum likelihood receiver for a rectangular video pulse, the discrepancy between the signal energies, all other things being equal, is clearly demonstrated. A connection has been established between the SNR when processing ultra-wideband signals at the output of the optimal receiver with similar devices for processing other types of signals, as well as with the SNR at the input of the receiving system. Systematization of the terminological features of the SNR concept will allow theoretical researchers to choose SNR definitions that are as close as possible to practical applications when analyzing the effectiveness of synthesized algorithms, and will allow practicing engineers to correctly interpret the results of theoretical calculations when developing or testing radio engineering systems.

A novel iterative detection method based on a lattice reduction-aided algorithm for MIMO OFDM systems

The lattice reduction-aided algorithm has received broad attention from researchers since it operates as a maximum likelihood receiver with better system performance for multiple-input multiple-output orthogonal frequency division multiplexing systems and contains a full diversity. A novel iterative detection algorithm canceling parallel iterations that employ the lattice reduction-aided approach is proposed. Soft information is exchanged through the detector itself. Its iteration occurs inside the detector, which reduces much of the exchange cost between the multiple-input multiple-output orthogonal frequency division multiplexing detector and the turbo decoder. Since the parallel interference cancellation algorithm is constrained by the accuracy of the initial value of the detection, it is easy to form error propagation after several iterations. Due to the lattice reduction-aided algorithm, its performance is approximated with the maximum likelihood algorithm. Therefore, the lattice reduction-aided algorithm is introduced into the parallel interference cancellation algorithm to make its detection algorithm more accurate and overcome the effect of error propagation in the manuscript. Simulation results indicate that the proposed algorithm leads to an improvement of 0.8–2 dB when the bit error rate is set to 10–4 when compared to other algorithms.

An improved deep learning-based end-to-end autoencoder for UAV-to-ground free space optical communication

In this paper, an improved deep learning-based end-to-end autoencoder is proposed for unmanned aerial vehicle (UAV) to ground free space optical communication to mitigate atmospheric turbulence. Deep neural network (DNN) is applied to the intensity modulation/direct detection (IM/DD) autoencoder, including transmitter, receiver as well as channel model. The performance is improved by two-stage deep learning training because the minimum Hamming distance between the codewords is increased through pre-training. Simulation results show that the bit error rate of our proposed scheme can reach the 7% hard-decision forward error correction (HD-FEC) threshold at signal-to-noise ratio of approximately 22 dB and in strong atmospheric turbulence where the maximum Rytov variance is 3.5. Our proposed scheme can outperform the state-of-the-art IM/DD system with PPM transmitter and maximum likelihood receiver by achieving approximately 12 dB improvement and reducing ∼51.3% of the decoder's running time without the need for accurate channel state information.

Impact of channel imperfections on variant SMTs MIMO systems over revised Nakagami-[formula omitted] channel model

Recently, a revised model for the Nakagami-m multiple-input multiple-output (MIMO) channel has been proposed, yielding distinct results and conclusions compared to the existing model. This article focuses on evaluating and discussing the performance of MIMO space modulation techniques (SMTs) transmission schemes, namely space shift keying (SSK), quadrature space shift keying (QSSK), spatial modulation (SM), and quadrature spatial modulation (QSM), over the revised channel model. The evaluation considers spatial correlation, imperfect channel state information (CSI), and examines various performance metrics such as average bit error rate (ABER), mutual information, and capacity. Specifically, a closed-form expression for the ABER is derived under the assumption of a maximum-likelihood (ML) receiver. Additionally, formulas for mutual information and capacity are derived and thoroughly discussed. To validate the derived formulas, extensive Monte Carlo simulations are performed. Furthermore, the impact of system parameters on the ABER, mutual information, and capacity is investigated, providing a comprehensive analysis of their variations. A comparative study is conducted between different transmission schemes using the revised model, elucidating their relative performance. Moreover, a comparison is made between the reported results of the revised model and the existing Nakagami-m model, as well as other channel distributions such as Rayleigh and Rice fading channels. The findings clearly demonstrate the disparities between the existing and revised models, with the revised model exhibiting superior performance. Notably, when comparing the scenario of m=1 with a Rayleigh fading channel, an exact match is observed for the revised channel model, while some differences are detected for the existing model.

A machine learning-based concentration-encoded molecular communication system

Molecular communication (MC) is a recent novel communication paradigm, which could enable revolutionary applications in the fields of medicine, military, and environment. Inspired by nature, MC uses molecules as information carriers to transmit and receive data. Concentration-encoded molecular communication (CEMC) is an information encoding approach, where the information is encoded in the concentration of the transmitted molecules. In this paper, we propose a machine learning (ML)-based CEMC system. In particular, we propose a modulation scheme named concentration position-shift keying (CPSK), which encodes information as the position of the transmitted molecular concentration. After passing through a diffusion-based channel, the molecules are captured via a ligand–receptor binding process (LRBP) at the nanoreceiver. Then, a ML-based approach is employed to decode the data bits. From numerical simulations, it has been shown that increasing the transmission time and using 4-ary CPSK would enhance the communication performance of the proposed ML-based CEMC system. In addition, we found that the ML receiver mitigates the bias effect and reduces inter-symbol interference (ISI) of the diffusion-based molecular channel. As a result, the proposed ML-based receiver shows better performance than the conventional maximum-likelihood (MLE) receiver.

Generalized BER of MCIK-OFDM with imperfect CSI: selection combining GD versus ML receivers

This paper analyzes the bit error rate (BER) of multicarrier index keying—orthogonal frequency division multiplexing (MCIK-OFDM) with selection combining (SC) diversity reception. Particularly, we propose a generalized framework to derive the BER for both the low-complexity greedy detector (GD) and maximum likelihood (ML) detector. Based on this, closed-form expressions for the BERs of MCIK-OFDM with the SC using either the ML or the GD are derived in presence of the channel state information (CSI) imperfection. The asymptotic analysis is presented to gain helpful insights into effects of different CSI conditions on the BERs of these two detectors. More importantly, we theoretically provide opportunities for using the GD instead of the ML under each specific CSI uncertainty, which depend on the number of receiver antennas and the M-ary modulation size. Finally, extensive simulation results are provided in order to validate our theoretical expressions and analysis.

NOMA Joint Channel Estimation and Signal Detection Using Rotational Invariant Codes and GMM-Based Clustering

This letter studies the joint channel estimation and signal detection for the uplink power-domain non-orthogonal multiple access. The proposed technique performs both detection and estimation without the need of pilot symbols by using a clustering technique. We apply rotational-invariant coding to assist signal detection at the receiver without sending pilot symbols. We utilize Gaussian mixture model (GMM) to automatically cluster the received signals without supervision and optimize decision boundaries to improve the bit error rate (BER) performance. Simulation results show that the proposed scheme without using any pilot symbol achieves almost the same BER performance as that for the conventional maximum likelihood receiver with full channel state information.

Exploiting User Diversity in OTFS Transmission for Beyond 5G Wireless Systems

Orthogonal time frequency space (OTFS) modulation is a recent technology that offers a significant advantage on link reliability due to its strong delay-Doppler resilience. In classical cellular technology, overall system performance is limited by the fading and interference experienced by particular user equipment (UE) over its radio resources (RR). Besides, OTFS performance depends on the channel diversity of the UEs. Therefore, this letter examines the potential of multi-user diversity for OTFS systems considering practical scenarios. Specifically, we introduce a novel scheduling algorithm that proposes the assignment of the available RR of OTFS frame to the UE with the largest number of channel taps, resulting in enhanced channel diversity. It is shown via both mathematical analysis and simulation results that the proposed scheduling technique outperforms the scheme with random access to delay-Doppler RR in terms of system bit error rate (BER) with maximum likelihood (ML) receiver. The BER results validate the accuracy of the proposed technique for OTFS transmission with minimum mean square error (MMSE) detector considering various system configurations.

Theoretical and Experimental Analysis of Asymmetrically Clipped-FSK VLC System

In this article, energy efficient asymmetrically clipped frequency-shift keying (AC-FSK) based visible light communication (VLC) system is theoretically and experimentally demonstrated. In order to facilitate straightforward comparison with the experimental results, theoretical expression for bit error probability, based on the Euclidean distance analysis of AC-FSK symbols, is provided. The VLC setup is based on commercial off-the-shelf components and software defined radio. The bit error rate (BER) performance of AC-FSK is evaluated considering maximum likelihood (ML) receiver, 1-tap discrete cosine transform (DCT) based receiver and frequency-domain harmonic receiver. Simulation and experimental results reveal that the performance of harmonic and ML receivers is almost identical. On the other hand, considering harmonic receiver for both AC-FSK and state-of-the-art unipolar (U)-FSK, we also gather that the BER performance of both schemes is almost the same. However, the harmonic receiver complexity of AC-FSK is 41.6% and 33.3% less compared to that of U-FSK for modulation order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M = 16$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M = 128$</tex-math></inline-formula> , respectively. This is because unlike U-FSK, AC-FSK requires limited number of harmonics for its optimal operation.

Non-Coherent Multi-Level Index Modulation

This paper develops a non-coherent index modulation (IM) system in which activation patterns are characterized by multi-level block codes. We analyze performance of such a system under the maximum-likelihood (ML) receiver and when the set of activation patterns follows a multi-level code generated from asymptotically optimal alphabets. An asymptotic analysis of the pair-wise error probability (PEP) shows that the system can exploit a diversity order that is determined by the distance of the worst codeword pair in the <inline-formula> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> metric, known as the Manhattan norm. We then explore the rate-diversity tradeoff for the developed non-coherent IM system as a function of the code length. Specifically, Gilbert-style bounds on the data rates for systems based on binary and ternary codes are obtained that can ensure a given diversity order. We approach the problem of packing in the <inline-formula> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> metric by partitioning codes into permutation modulation codes (PMCs) and obtaining Gilbert-style bounds on PMCs. Several achievable rates for non-coherent binary and ternary IM systems, as well as a tradeoff between the information rate and codeword error probability (CEP) are also derived. Finally, simulation results are provided to corroborate the theoretical analysis.

A Tutorial on Decoding Techniques of Sparse Code Multiple Access

Sparse Code Multiple Access (SCMA) is a disruptive code-domain non-orthogonal multiple access (NOMA) scheme to enable future massive machine-type communication networks. As an evolved variant of code division multiple access (CDMA), multiple users in SCMA are separated by assigning distinctive sparse codebooks (CBs). Efficient multiuser detection is carried out at the receiver by employing the message passing algorithm (MPA) that exploits the sparsity of CBs to achieve error performance approaching to that of the maximum likelihood receiver. In spite of numerous research efforts in recent years, a comprehensive one-stop tutorial of SCMA covering the background, the basic principles, and new advances, is still missing, to the best of our knowledge. To fill this gap and to stimulate more forthcoming research, we provide a holistic introduction to the principles of SCMA encoding, CB design, and MPA based decoding in a self-contained manner. As an ambitious paper aiming to push the limits of SCMA, we present a survey of advanced decoding techniques with brief algorithmic descriptions as well as several promising directions.

Identifying youth at high risk for sexually transmitted infections in community-based settings using a risk prediction tool: a validation study

Background Chlamydia trachomatis (CT) and Neisseria gonorrhoeae (NG) are the most common bacterial sexually transmitted infections (STIs) worldwide. In the absence of affordable point-of-care STI tests, WHO recommends STI testing based on risk factors. This study aimed to develop a prediction tool with a sensitivity of > 90% and efficiency (defined as the percentage of individuals that are eligible for diagnostic testing) of < 60%.Methods This study offered CT/NG testing as part of a cluster-randomised trial of community-based delivery of sexual and reproductive health services to youth aged 16–24 years in Zimbabwe. All individuals accepting STI testing completed an STI risk factor questionnaire. The outcome was positivity for either CT or NG. Backwards-stepwise logistic regression was performed with p ≥ 0.05 as criteria for exclusion. Coefficients of variables included in the final multivariable model were multiplied by 10 to generate weights for a STI risk prediction tool. A maximum likelihood Receiver Operating Characteristics (ROC) model was fitted, with the continuous variable score divided into 15 categories of equal size. Sensitivity, efficiency and number needed to screen were calculated for different cut-points.ResultsFrom 3 December 2019 to 5 February 2020, 1007 individuals opted for STI testing, of whom 1003 (99.6%) completed the questionnaire. CT/NG prevalence was 17.5% (95% CI 15.1, 19.8) (n = 175). CT/NG positivity was independently associated with being female, number of lifetime sexual partners, relationship status, HIV status, self-assessed STI risk and past or current pregnancy. The STI risk prediction score including those variables ranged from 2 to 46 with an area under the ROC curve of 0.72 (95% CI 0.68, 0.76). Two cut-points were chosen: (i) 23 for optimised sensitivity (75.9%) and specificity (59.3%) and (ii) 19 to maximise sensitivity (82.4%) while keeping efficiency at < 60% (59.4%).ConclusionsThe high prevalence of STIs among youth, even in those with no or one reported risk factor, may preclude the use of risk prediction tools for selective STI testing. At a cut-point of 19 one in six young people with STIs would be missed.

Generalized Mutual Information Analysis for BICM-8QAM With Residual Phase Noise

Generalized mutual information (GMI) has become a key metric for bit-interleaved coded modulation (BICM) system design and performance analysis. As residual phase noise (RPN) normally exists after imperfect phase estimation, the mostly used mismatched Gaussian receiver is suboptimal for GMI analysis in phase noise. This letter thus analyzes the GMI of BICM systems using 8-ary quadrature-amplitude-modulations (QAM) in the presence of both RPN and additive white Gaussian noise (AWGN). We will use the maximum-likelihood receiver derived in our earlier work to calculate the GMI of Star-8QAM, Circular-8QAM, Rect-8QAM and 8PSK. The explicit symbol and bit log-likelihood ratios are specifically expressed in amplitude-phase form with RPN considered. Numerical results are given in details to show the GMI comparison in phase noise and the GMI loss compared to the pure AWGN case. It is shown that Star-8QAM is much more tolerant to large RPN. Moreover, the ratio parameters of Rect-8QAM and Star-8QAM are optimized to maximize the GMI as the RPN variance increases. We also optimize the bit mapping for non-Gray 8QAM.

Layered Molecular Shift Keying for Molecular Communication via Diffusion

Molecular communication (MC) is a promising communication paradigm for realizing nano-networks, where molecules are employed as an information carrier. In this letter, based on diffusive MC we propose a novel modulation scheme, called layered molecular shift keying (LMoSK), where several types of molecule form different layers to encode information bits, which can not only improve the data rate but also reduce the effect of inter-symbol interference (ISI). For detection of LMoSK, we formulate an ideal maximum likelihood (ML) receiver assuming knowledge of the ISI. Considering the limited capability of the receiver, we further propose a practical ML detection, enjoying both reduced computational complexity and memory of the receiver. The error performance of the LMoSK with practical ML receiver is analyzed and compared with that of molecular shift keying modulation and molecular type permutation shift keying modulation. Simulation results demonstrate that the proposed LMoSK outperforms benchmark schemes.

Near-Optimal Low-Complexity Harmonic Receiver for Unipolar-FSK

In this letter, we propose a near-optimal low-complexity frequency-domain (FD) harmonic receiver for visible light communication based unipolar frequency-shift keying (U-FSK). The time-domain (TD) maximum-likelihood (ML) receiver for U-FSK is computationally complex, while the sub-optimal receiver increases the noise variance. The proposed harmonic receiver determines the transmitted frequency from the cross-correlations between the FD received waveform and the FD dictionary waveforms reduced to their strongest harmonics. The results shall demonstrate that besides affording a linerarithmic complexity, the performance of the harmonic receiver closely approaches that of TD ML receiver which exhibits quadratic complexity.

Performance Analysis of Typical Telemetry Modulation Methods Under Downlink Integrated Channel of Hypersonic Vehicles

Due to the severe impact of dynamic plasma sheath on electromagnetic (EM) waves, the communication quality of hypersonic vehicles deteriorates, even resulting in communication blackouts during the reentry process. In this article, the hypersonic vehicle downlink integrated channels that cascade the plasma sheath channel and Rice fading channel, i.e., the downlink telemetry channels, are first established, and then the demodulation method and performance of typical telemetry modulations including the M-ary phase shift keying (MPSK), M-ary amplitude shift keying (MASK), and M-ary frequency shift keying (MFSK) are studied. Considering the high dynamics of the plasma sheath, the pilot signals are used to detect the signal correctly for MPSK, and the non-coherent demodulation is adopted for MASK and MFSK. Especially, an adaptive maximum likelihood (ML) receiver for ASK is proposed based on a reduced reversible jump Markov chain Monte Carlo (RRJ-MCMC) algorithm to estimate the probability density function (pdf) of the received signal. The simulation results show that the communication performance of PSK and ASK is improved with the modulation order $M$ decreasing; the performance of non-coherent FSK is improved with the modulation order $M$ increasing. Meanwhile, the performance follows the order of NC-MFSK (M ≥ 8) > BPSK > NC-4FSK > NC-2FSK > 2ASK. For NC-8FSK, when the electron density peak value ${Ne}_{\mathrm {peak}}$ = {2, 4, 6, 8, 10} $\times 10^{18}\,\,\text{m}^{-3}$ , the signal to noise ratio (SNR) required to reduce the bit error rate (BER) to 10−6 are 17, 18, 19, 21, and 34 dB, respectively.

Space-Frequency Coded Quadrature Index Modulation With Linear Maximum Likelihood Detection

This paper focuses on the issue of achieving transmit diversity for the multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system working with quadrature index modulation (QIM). Inspired by the ideas of quadrature spatial modulation (QSM) and quadrature space-frequency index modulation (QSF-IM), parts of the space-frequency resource units in each resource block (RB) of the MIMO-OFDM system are activated twice independently to send the in-phase and quadrature components of a space-frequency code, respectively, to achieve the second order transmit diversity. Thus the proposed scheme is called space-frequency coded QIM (SFC-QIM). The SFC-QIM scheme allows for a linear-complexity maximum likelihood (ML) receiver, which benefits from the orthogonality between the real and imaginary parts of the symbols in the SFC codewords. Owing to obtaining higher diversity order, simulation results of bit error rate (BER) performance demonstrate that the new SFC-QIM scheme outperforms some existing IM schemes in both independent and identically distributed (i.i.d.) and correlated Rayleigh fading channels.

Adaptive Switching Hybrid Blast-STBC MIMO System

Fading in a wireless channel has negative effects on the performance of communication systems. Bell Laboratories layered space-time (BLAST) has been used to get a high data rate while space-time block codes (STBC) have been used to get a low bit error rate (BER) performance. Under deep faded channels, hybrid BLAST-STBC systems are considered as a trade-off between BLAST and STBC systems. By exploiting the benefits of both systems, a new method to represent a 4 × 4 multiple-input and multiple-output (MIMO) system is proposed and studied, in which the transmission process is carried out adaptively between both 4 × 4 VBLAST, Quasi-Orthogonal STBC (QOSTBC) and Hybrid systems according to the transmit links state. The proposed adaptive switching hybrid system (ASHS) reduces the total transmitted power, achieves the maximum throughput by obtaining the best BER. An adaptive switching transmission scheme using the strategy of measuring the transmit links fading is investigated as well. The simulated results are obtained in an environment of a 4 × 4 MIMO system using MATLAB platform where the total transmitting power is normalized to unity. The detections are done using the maximum likelihood (ML) receiver. The proposed ASHS system shows a lot of advantages such as maximum throughput is obtained in bad channel states, no additional transmit power is needed and no additional bandwidth is needed. Finally, under deep fading condition, the proposed ASHS transmission scheme obtains the best BER, reduces wasting the total transmitted power, achieves the maximum throughput and obtains the best BER.

Improved Pair-Wise Detections of Differential Quasi-Orthogonal Space-Time Modulation with Four Transmit Antennas

In this paper, we propose new complex and real pair-wise detection for conventional differential space–time modulations based on quasi-orthogonal design with four transmit antennas for general QAM. Since the new complex and real pair-wise detections allow the independent joint ML detection of two complex and real symbol pairs, respectively, the decoding complexity is the same as or lower than conventional differential detections. Simulation results show that the proposed detections exhibit almost identical performance with an optimum maximum-likelihood receiver, as well as improved performance compared with conventional pair-wise detections, especially for higher modulation order.

Modulation, Detection, and Performance for Noncoherent Massive SIMO Systems for Hypersonic Vehicle Downlink Integrated Channel

For hypersonic flight, high-dynamic plasma sheaths surrounding vehicles deteriorate communication quality. In this work, hypersonic vehicle downlink integrated channels that cascade the plasma sheath channel and Rice fading channel are first established, and the probability density functions (PDFs) of the integrated channel amplitude and phase are derived theoretically. Then, a downlink SIMO system over the integrated channel is considered, including a single antenna transmitter and a single ground receiver equipped with a large number of antennas. For this system, a noncoherent telemetry scheme is proposed, a transmitter that modulates information only in the power of the symbols, and an adaptive maximum likelihood (ML) receiver which demodulates symbols using the PDF of the average received power (ARP) across the antennas. Motivated by the efficient power utilization, an asymptotically optimal constellation design in terms of symbol error rate (SER) with an increasing number of antennas is proposed, under an assumption that CSI statistics are available. The PDF of ARP is well estimated by a reduced reversible jump markov chain monte carlo (RRJ-MCMC) algorithm and used for symbol demodulation and achievable rate derivation. The numerical results demonstrate that the optimal constellation scheme outperforms the amplitude shift keying (ASK) constellation scheme and is robust against the plasma sheath attenuation with moderate antennas or a large line-of-sight (LOS) component.