Low-complexity Maximum Likelihood Research Articles

Performance enhancement of multiple-mode FBMC-IM VLC systems with group-interleaved precoding

In this paper, we introduce the application of multiple-mode index modulation (MMIM) to filter bank multi-carrier (FBMC) for the first time in visible light communication (VLC) systems. Additionally, we propose a group-interleaved precoding (GIP) technique to enhance the performance of MM-FBMC-IM-based VLC systems. The GIP technique reduces complexity in precoding by grouping and achieves equalization of the signal-to-noise ratio (SNR) through subcarrier interleaving. Furthermore, we develop a robust low-complexity maximum likelihood (LCML) detector, which can maintain the same computational complexity as a conventional LCML detector and achieve similar performance as an ML detector. The effectiveness and superiority of the proposed MM-FBMC-IM-based VLC system with GIP are demonstrated through comprehensive validation by both simulation and experimental results.

Probabilistic Constellation Shaping for Molecular Communications

Molecular communication (MC) is an emerging field aiming at realizing information exchange via chemical signals between nanomachines in nanonetworks. Information transmission that is energy-efficient and relies on relatively low-complexity transceiver techniques is of practical importance for MC systems. Based on the fact that constellation shaping can improve energy efficiency, in this paper, we propose a molecular shell mapping (MSM) scheme to implement the probabilistic constellation shaping for MC. The MSM method is designed to exploit the concentration sequences with the lowest sum sequence weight, which results in an energy-efficient signal constellation. Furthermore, we propose an algorithm for selecting and sorting the concentration sequences to mitigate inter-symbol interference. For information detection, we design a genie-aided maximum-likelihood (ML) detector and a realistic ML detector to leverage the constructive effect of intra-sequence interference, as well as derive their bit error rates and achievable rates. Additionally, for the applications using large blocklength sequences, a low-complexity ML detection method is proposed. Numerical simulation results confirm that the shaped signaling using the MSM method is more energy-efficient than the conventional equiprobable signaling, achieving shaping gains of up to 1.5 dB at an ultra-short blocklength of 4.

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.

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.

Spatial Modulation: An Attractive Secure Solution to Future Wireless Networks

As a green and secure wireless transmission method, secure spatial modulation is becoming a hot research area. Its basic idea is to exploit both the index of activated transmit antenna and amplitude phase modulation signal to carry messages, improve security, and save energy. In this article, we review its crucial challenges: transmit antenna selection, artificial noise projection, power allocation (PA), and joint detection at the desired receiver. We proposed a low-complexity maximum likelihood (ML) detector, which efficiently reduces the complexity of detection. Meanwhile, for the sake of improving further secrecy rate (SR) performance, a PA strategy is designed on the basis of a deep neural-network (DNN). Simulation results show that the proposed low-complexity ML detector achieves lower complexity but the same bit error rate performance, compared to the traditional ML method, while the proposed DNN method strikes a good balance between complexity and SR performance.

Low-complexity soft ML detection for generalized spatial modulation

Generalized Spatial Modulation (GSM) is a recent Multiple-Input Multiple-Output (MIMO) scheme, which achieves high spectral and energy efficiencies. Specifically, soft-output detectors have a key role in achieving the highest coding gain when an error-correcting code (ECC) is used. Nowadays, soft-output Maximum Likelihood (ML) detection in MIMO-GSM systems leads to a computational complexity that is unfeasible for real applications; however, it is important to develop low-complexity decoding algorithms that provide a reasonable computational simulation time in order to make a performance benchmark available in MIMO-GSM systems. This paper presents three algorithms that achieve ML performance. In the first algorithm, different strategies are implemented, such as a preprocessing sorting step in order to avoid an exhaustive search. In addition, clipping of the extrinsic log-likelihood ratios (LLRs) can be incorporating to this algorithm to give a lower cost version. The other two proposed algorithms can only be used with clipping and the results show a significant saving in computational cost. Furthermore clipping allows a wide-trade-off between performance and complexity by only adjusting the clipping parameter.

Filter Bank Orthogonal Frequency Division Multiplexing With Index Modulation

Filter bank orthogonal frequency division multiplexing(FB-OFDM) is a promising multicarrier technique due to its ability to significantly reduce out-of–band (OOB) emission. In this letter, a combined application of FB-OFDM and index modulation (IM) (FB-OFDM-IM) is proposed to improve bit error rate (BER) performance. Firstly, the average bit error probability (ABEP) upper bound is derived over multipath fading channel. Then, a low-complexity maximum likelihood (ML) detection method is designed at receiver. Simulation results verify the superiority of FB-OFDM-IM system in terms of BER performance. Furthermore, the proposed detection scheme is proven to be ML-optimal with much lower complexity.

Low complexity maximum likelihood decoding for orthogonal space-time block codes using non-square and rotated quadrature amplitude modulation

ABSTRACT High diversity gain can be achieved for orthogonal space-time block codes (OSTBCs) using rotated QAM constellations at a cost of high Maximum Likelihood (ML) decoding complexity. Thus far, low complexity ML decoding algorithms were proposed only for OSTBCs with square QAM constellations. In this paper, an algorithm has been proposed to reduce the ML decoding complexity of OSTBCs with non-square and rotated QAM constellations. The ML formulation using real-valued lattice representations is modified in such a way that the complexity depends upon the number of real values required to construct the alphabet of any constellation. Arithmetic progression and symmetry are the two elementary characteristics observed in the real numbers of the alphabets. Based on these characteristics, a new approach called Add and accumulate method has been proposed which drastically reduces the complexity to and without sacrificing the performance.

Low Complexity Maximum Likelihood FBMC QAM for Improved Performance in Longer Delay Channels

Filter bank multi-carrier (FBMC) is an emerging 5G technology due to its finer spectral characteristics than its counterpart orthogonal frequency-division multiplexing (OFDM). In most cases, FBMC is united with an Offset Quadrature Amplitude modulation (OQAM) for individual sub-carrier to maximize the spectrum efficiency and Nyquist rate. But it is achieved at the cost of an inherent accumulative imaginary interference called intrinsic interference. When a channel is highly selective, the FBMC system undergoes inter-symbol-interference (ISI) and co-channel interference (CCI). In this research, we consider FBMC QAM as a solution to intrinsic interference and mitigates both ISI and CCI by incorporating ML equivalent signal detection. In this paper, some of the prominent issues related to the existing FBMC–OQAM are explored and its potential integrity constraints with existing MIMO and signal detection techniques are studied. In addition to that, a lightweight optimized ML which constitutes parallel sub-detectors with the least hardware complexity overhead is proposed. It also achieved a near-optimal performance that matches the CP-OFDM system. In this research, the experimental results proved that the proposed suboptimal ML detector offered significant complexity reduction with improved quality of services. Thus evidently shows the proposed system is attractive from both BER performance and hardware complexity reduction perspectives for 5G communications.

Low-Complexity Maximum-Likelihood Detector for IoT BLE Devices

Internet of Things (IoT) is a technology that has overgrown and whose interest lies in the connection of diverse kinds of devices to collect and exchange data. Since most IoT devices are mobile, the hardware resources are hard limited; thus, complexity reduction becomes a relevant concern in this context. Bluetooth low energy (BLE) communication standard has an important position in IoT due to its Gaussian frequency-shift keying (GFSK) modulation scheme employed in the physical layer, which provides both attractive spectral and power efficiency. Typically, GFSK requires a maximum-likelihood sequence estimator (MLSE) implemented through the Viterbi algorithm (VA) at the receiver. This article provides a GFSK receiver based on a new paradigm that transforms the I-Q baseband signal and uses the VA with a reduced-complexity proposed metrics. Comparisons of theoretical and simulated results are presented, and they show that the proposed metrics for the GFSK receiver are compliant with the Bluetooth standard. Henceforth, the proposed receiver is an attractive scheme for IoT BLE devices.

An effective approach for low-complexity maximum likelihood based automatic modulation classification of STBC-MIMO systems

A low-complexity likelihood methodology is proposed for automatic modulation classification of orthogonal space-time block code (STBC) based multiple-input multiple-output (MIMO) systems. We exploit the zero-forcing equalization technique to modify the typical average likelihood ratio test (ALRT) function. The proposed ALRT function has a low computational complexity compared to existing ALRT functions for MIMO systems classification. The proposed approach is analyzed for blind channel scenarios when the receiver has imperfect channel state information (CSI). Performance analysis is carried out for scenarios with different numbers of antennas. Alamouti-STBC systems with 2 × 2 and 2 × 1 and space-time transmit diversity with a 4 × 4 transmit and receive antenna configuration are considered to verify the proposed approach. Some popular modulation schemes are used as the modulation test pool. Monte-Carlo simulations are performed to evaluate the proposed methodology, using the probability of correct classification as the criterion. Simulation results show that the proposed approach has high classification accuracy at low signal-to-noise ratios and exhibits robust behavior against high CSI estimation error variance.

Simplified ML-Based Carrier Frequency Offset and Phase Noise Estimation for CO-OFDM Systems

The coherent optical orthogonal frequency division multiplexing (CO-OFDM) has become prominent among emerging telecommunication techniques and applications. However, carrier frequency offset (CFO) and laser phase noise adversely impact and degrade the performance of the CO-OFDM systems. In this paper, a simplified maximum-likelihood (ML) approach, which eliminates the need for the exhaustive search associated with traditional ML methods, is derived and utilized for the estimation of CFO and laser phase noise in CO-OFDM systems. Furthermore, to obtain an improved performance, the proposed simplified low-complexity ML estimator is uniquely combined with an efficient data-dependent pilot-aided (DD-PA) technique, for the acquisition of both the CFO and the laser phase noise. The performance of the simplified ML-based estimators is compared with existing methods and verified in a 16-ary quadrature amplitude modulation (16-QAM) CO-OFDM system with polarization mode dispersion (PMD), chromatic dispersion (CD) and other polarization dependent losses (PDLs) along the fiber link.

A Low-Complexity Maximum Likelihood Detector for the Spatially Modulated Signals: Algorithm and Hardware Implementation

Aiming to increase the transmission data rate, the spatial modulation (SM) scheme maps each block of information bits to a digitally modulated symbol and additionally a transmit antenna index in a multiple transmit antenna system. In this brief, we focus on the maximum likelihood detection (MLD) scheme that detects SM signals with low computational complexity. By reformulating the MLD problem, we obtain a new mathematical expression as the MLD solution. To avoid the numerically unstable division operation, we apply the Givens rotation to realize this new expression and obtain a low-complexity MLD algorithm. We also propose a coordinate rotation digital computer-based hardware architecture to detect SM signals with 64-quaternary amplitude modulated (QAM) symbols over the correlated channel with eight transmit antennas and four receive antennas. The VLSI implementation results under the TSMC 90-nm CMOS technology reveal that our division-free architecture requires 70.5K gates and provides detection throughput 432.68 Mb/s, while operating at frequency 384.6 MHz. Our design is the first hardware architecture to achieve the exact MLD performance and is easily modified to detect SM signals with arbitrary ${M}$ -ary QAM symbols and arbitrary numbers of transmit and receive antennas.

Optimized Cooperative Finite-Alphabet Two-Way Relaying Strategy for Indoor Visible Light Communication Systems

In this paper, we propose an optimized cooperative finite-alphabet relaying strategy for two-way relay visible light communication (VLC) systems, in which the relay node has its own information to be transmitted. In the multiple access (MAC) stage, for fixed transmission bit rate of each user, an optimal power control strategy is developed to manage the non-negative finite-alphabet multiuser interference. Under this strategy, it is proved that the received signal constitutes an equally spaced pulse amplitude modulation constellation, which admits low-complexity maximum likelihood detection. In addition, for given overall transmission bit rate of MAC stage, we derive a closed-form solution for optimal bit loading to further improve the energy-efficiency of MAC stage. In the broadcast stage, owing to the fact that each buffer-aided user node knows the signals transmitted to the relay node in the MAC stage, we design a buffer-aided optimal encoding constellation, which can obtain significant performance gains. Intended for this transmitted constellation, we develop two low-complexity detection algorithms. Both the analytical results and computer simulations demonstrate that our proposed design has substantial performance advantage over the currently available time orthogonal transmission scheme for this application.

Power-Balanced Non-Orthogonal Multiple Access Based on Virtual Channel Optimization

In this brief, we propose a virtual channel optimization method for downlink non-orthogonal multiple access (NOMA) systems. With this method, we show that superposed users’ data can be separated successfully in power-balanced scenario for NOMA. We derive the optimum relative phase offset for two users as well as three users based on the minimum Euclidean distance (MED) among the superposed constellation points without channel state information at the transmitter (CSIT). We exploit maximum likelihood (ML) detector at the receiver as successive interference cancelation (SIC) is not applicable for power-balanced scenario. Since the complexity of ML is high, we design a low-complexity ML algorithm to substantially reduce the computational complexity. Simulation results for quadrature phase-shift keying (QPSK) modulation demonstrate the effectiveness and the performance of the proposed method.

BITFCM-OFDM scheme for power-line communication systems

Power-line communications (PLC) is viewed as a good potential solution for smart grid communications because of the established infrastructure around the world. However, power-line was not initially aimed to be used for continuous data communications. Hence, challenging problems may occur when the power-line channel is used as a communication channel. One of the major issues is the (bursty) impulsive noise in the power-line channel. This paper analyzes the system performance of the bit-interleaved time-frequency coded modulation (BITFCM) scheme with an optimal low complexity maximum likelihood (ML) decoding scheme in the orthogonal frequency-division multiplexing (OFDM)-based broadband PLC (BB-PLC) modems. The numerical results illustrate that this proposed scheme improves the system performance of the PLC modems under the bursty impulsive noise environment. Furthermore, the performance of the BITFCM-OFDM scheme can achieve up to 3 dB improvement at bit error rate (BER) of 10-4 in comparison with the bit-interleaved coded modulation (BICM)-OFDM and shows significant improvement compared with the coded OFDM (COFDM). Finally, a blanking nonlinear preprocessor is used at the receiver and further improvement of the BER performance is evaluated.

Intrinsic Robustness of MISO Visible Light Communications: Partial CSIT Can be as Useful as Perfect One

We consider a multi-input single-output visible light communication (MISO-VLC) system. For such system under both average and peak optical power constraint, an optimal space constellation maximizing the received minimum Euclidean distance is attained among all the feasible sets, respectively, for the case with or without channel state information at the transmitter (CSIT). These designs demonstrate that the optimal transmission only requires CSIT which is related to the possibilities of the echelon arrangement of the channel coefficients and jointly determined by the power regime and the ordering of channel coefficient values. Our findings point out that it is not necessary to probe the exact value of the MISO-VLC channel vector and limited CSIT can sufficiently guarantee the intrinsic robustness. In addition, the optimal designs admit low-complexity maximum likelihood detection. These properties make our proposed optimal designs especially attractive in such channels.

Channel and Bit Adaptive Power Control Strategy for Uplink NOMA VLC Systems

Non-orthogonal multiple access (NOMA) can be an effective solution to the limited bandwidth of light emitting diodes for visible light communication (VLC) systems to support multiuser communication. The current available works for NOMA VLC systems mainly concentrate on downlinks and the existing power allocation algorithms mainly focus on the channel state information and ignore the influence of transmitted signals. In this paper, we propose a channel and bit adaptive power control strategy for uplink NOMA VLC systems by jointly considering the channel state information and the transmission bit rate. Under this adaptive power control strategy, it is proved that the received signal at the photodiode (PD) receiver constitutes a sizeable pulse amplitude modulation constellation and low-complexity maximum likelihood detection is admitted. The simulation results indicate that our proposed adaptive power control strategy outperforms the gain ratio power allocation scheme, fixed power allocation scheme, and time division multiple access scheme.

Energy-Efficient Precoding Design for Multiuser MISO VLC Systems Based on Joint Detection

In this paper, we study energy-efficient precoding techniques in multiuser multiple-input single-output (MISO) visible light communication (VLC) systems. Under the dual constraints of illumination and communication, an optimal precoding design is proposed for a $4\times 2$ multiuser MISO VLC system by utilizing the properties of Farey sequence in number theory. It is proved that the received signals constitute a sizeable pulse amplitude modulation constellation and thanks to this nice constellation structure, low-complexity maximum likelihood detection is admitted for signal detection. The simulation results indicate that our proposed optimal precoding design outperforms zero-forcing and time-division multiple access schemes.

Equalization scheme of C-band PAM4 signal for optical amplified 50-Gb/s PON.

The bandwidth limit of devices and the chromatic dispersion (CD) of optical fiber severely distort the high-speed signal in a passive optical network (PON). In this paper, an efficient equalization scheme is proposed for optical amplified 50-Gb/s PAM4-PON with a 10G-class transmitter. The proposed equalization scheme is based on fast frequency domain equalization (FDE) with circular convolution, an optimized post-filter, and a low-complexity maximum likelihood sequence detector (MLSD), which requires only total 23 real-valued multiplications for each output symbol. Experimental results show that up to 33.2 dB power budget is successfully achieved over 20 km transmission without using any optical CD compensation module in the C-band. Moreover, there is only 0.5 dB penalty of receiver sensitivity compared to optical back to back (BTB) transmission. Therefore, the CD distortion has been nearly compensated for by the proposed equalization scheme. To the best of our knowledge, this is the best performance of an optical amplified 50-Gb/s PAM4-PON system in the C-band.