Low-complexity Maximum Likelihood Detection Research Articles

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.

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.

Molecular Type Permutation Shift Keying for Molecular Communication

Molecular communication (MC) via diffusion is envisioned to be a new paradigm for information exchange in the future nanonetworks. However, the strong inter-symbol interference (ISI) caused by the diffusion channel significantly deteriorates the performance of MC systems. To this end, we propose a novel modulation technique to reduce the ISI effect, termed as molecular type permutation shift keying (MTPSK), which encodes information on the permutations of multiple types of molecules. We design a Genie-aided maximum-likelihood detector and a conventional maximum-likelihood detector, and analyze their performance in terms of bit error rate (BER). Aiming at lower computational complexity, we further design a low-complexity maximum-likelihood detector using a Viterbi-like algorithm with compromised error performance. BER simulation results corroborate that the proposed MTPSK can outperform the prevailing modulation schemes for MC, including molecular shift keying (MoSK), concentration shift keying, depleted MoSK, and pulse position modulation.

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.

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.

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.

Optimization of Finite-Alphabet Signaling for Two-User Multiaccess VLC Systems

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.

Two-Layer LDPC Codes for Low Complexity ML Detection in GSM Systems

Although maximum-likelihood (ML) detection is able to achieve optimal performance in generalized spatial modulation (GSM) systems, its exhaustive search leads to an intractable computational complexity. In this letter, two-layer low-density parity-check (TL-LDPC) codes are proposed to reduce the combinations of transmission vectors in LDPC coded GSM systems. Simulation results show that the complexity of the ML detection in the TL-LDPC-coded GSM systems is much lower than that of the ML detection in conventional LDPC-coded GSM systems with a negligible performance loss.

Low complexity maximum-likelihood detector for DSTTD architecture based on the QRD-M algorithm

This paper presents a new decoder algorithm for the double space–time transmit diversity (DSTTD) system. The decoder is based on the QRD-M algorithm, which performs a breadth-first search of possible solutions tree. The search is simplified by skipping unlikely candidates, and it is stopped when no promising candidates are left. Furthermore, the search is divided into three concurrent iterations, making possible a fast, parallel implementation either in hardware or software. After presenting an analysis of the capacity and diversity of DSTTD, we present performance results showing that the proposed decoder is capable of achieving near maximum likelihood performance. We also show that the proposed algorithm exhibits lower computational complexity than other existing maximum likelihood detectors.

Orbital Angular Momentum With Index Modulation

Orbital angular momentum (OAM)-based mode division multiplexing (MDM) is an emerging physical layer solution for short-distance line-of-sight wireless communications by providing high spectral efficiency with a considerably low detection complexity. Similarly, index modulation (IM) schemes have been extensively studied over the past few years due to their attractive features, such as improved error performance, low complexity, and high energy efficiency. In this paper, we propose the scheme of orbital angular momentum with index modulation (OAM-IM) by using the activated OAM modes themselves to carry additional information through the principle of IM. A general guideline is presented for the construction of optimal OAM-IM schemes along with the formulation of a low-complexity maximum likelihood detector. It is shown via computer simulations as well as theoretical bit error probability calculations that the proposed OAM-IM schemes can achieve considerably better error performance than the reference OAM-MDM schemes, while having the same level of detection complexity.

A Low-Complexity Maximum-Likelihood Detector for Differential Media-Based Modulation

Media-based modulation (MBM) uses radio frequency mirrors at the transmit antenna in order to create different channel fade realizations based on their ON/OFF status. These complex fade realizations constitute the channel modulation alphabet. This channel modulation alphabet has to be estimated a priori at the receiver for detection. In this letter, we present a differential MBM (DMBM) scheme which does not require estimation of channel modulation alphabet at the receiver for detection. Consecutive MBM blocks are differentially encoded. We propose a low-complexity maximum-likelihood detection algorithm for DMBM. Simulation results show that the DMBM has only about 2–4 dB performance loss compared with MBM with perfect knowledge of the channel alphabet.

Diversity-optimal power loading for intensity modulated MIMO optical wireless communications.

In this paper, we consider the design of space code for an intensity modulated direct detection multi-input-multi-output optical wireless communication (IM/DD MIMO-OWC) system, in which channel coefficients are independent and non-identically log-normal distributed, with variances and means known at the transmitter and channel state information available at the receiver. Utilizing the existing space code design criterion for IM/DD MIMO-OWC with a maximum likelihood (ML) detector, we design a diversity-optimal space code (DOSC) that maximizes both large-scale diversity and small-scale diversity gains and prove that the spatial repetition code (RC) with a diversity-optimized power allocation is diversity-optimal among all the high dimensional nonnegative space code schemes under a commonly used optical power constraint. In addition, we show that one of significant advantages of the DOSC is to allow low-complexity ML detection. Simulation results indicate that in high signal-to-noise ratio (SNR) regimes, our proposed DOSC significantly outperforms RC, which is the best space code currently available for such system.

Low-Complexity ML Detection for Spatial Modulation MIMO With APSK Constellation

Spatial modulation (SM) is a promising multiple-input–multiple-output (MIMO) transmission technology, which exploits the indexes of the transmit antennas for encoding information into the spatial dimension and, thus, for increasing the transmission rate. Optimal demodulation is realized by using a maximum-likelihood (ML) detector, which jointly estimates the information bits encoded into the transmit antenna indexes and into the transmitted symbol. If a large number of transmit antennas and/or a large modulation size are used; however, the computational complexity of ML demodulation may not be affordable for some applications. Against this background, we propose two novel near-ML but low-complexity detection schemes for SM-MIMO systems, which use $\boldsymbol{M}$ -ary amplitude and phase-shift keying (APSK) digital modulation. The proposed algorithms exploit specific features of the $\boldsymbol{M}$ -ary APSK constellation diagram, in order to avoid searching among all constellation points. It is shown, in particular, that the complexity of the proposed detection schemes is independent of the constellation size and that it only depends on the number of rings that constitute the APSK constellation. Simulation results are also provided, which confirm that the proposed detection schemes provide bit error probability performance close to that of ML demodulation but with lower demodulation complexity.

A Double-Layer VLC System With Low-Complexity ML Detection and Binary Constellation Designs

We consider a double-layer visible light communication system where transmitted data is split into two layers with different priorities and variant transmission rates. High-priority data is assigned to the upper layer with low transmission rate, while low-priority data is assigned to the lower layer with higher transmission rate. For this scenario, we develop a low-complexity maximum likelihood detection algorithm. In addition, several binary constellation designs corresponding to different priority orders are presented. Computer simulations show that maximum likelihood detection detection significantly improves the error-rate performance, compared to sum detection, without compromising the computational complexity of the receiver.

12-mode OFDM transmission using reduced-complexity maximum likelihood detection

We report the transmission of 163-Gb/s MDM-QPSK-OFDM and 245-Gb/s MDM-8QAM-OFDM transmission over 74km of few-mode fiber supporting 12 spatial and polarization modes. A low-complexity maximum likelihood detector is employed to enhance the performance of a system impaired by mode-dependent loss.

A Low-Complexity ML Detection Algorithm for Spatial Modulation Systems With <inline-formula> <tex-math notation="TeX">$M$</tex-math></inline-formula>PSK Constellation

Spatial modulation (SM), which is a novel transmission scheme, is employed for active transmit antenna indexes and modulated signals to convey the information. To recover the transmitted information bits, the maximum likelihood (ML) joint detector is often used. However, its complexity linearly grows with the number of transmit antennas and the size of the signal set. A reduced-complexity ML optimal algorithm for SM systems with M-QAM has been proposed. However, for M-PSK modulation, there are not similar low-complexity ML detection algorithms yet to our knowledge. In this paper, a low-complexity ML detection algorithm for SM systems with M-PSK modulation is proposed. By exploiting the features of M-PSK constellation, we give the ML-estimated values of the transmitted symbols. Therefore, the ML search complexity is independent of the constellation size. Simulation results show that the proposed algorithm has the same performance as the ML-optimum detector and significant reduction in computational complexity compared with existing detectors for SM systems with M-PSK modulation.

Achieving low-complexity maximum-likelihood detection for the 3D MIMO code

Abstract The 3D Multiple-input multiple-output (MIMO) code is a robust and efficient space-time block code (STBC) for the distributed MIMO broadcasting but suffers from high maximum-likelihood (ML) decoding complexity. In this paper, we first analyze some properties of the 3D MIMO code to show that the 3D MIMO code is fast decodable. It is proven that the ML decoding performance can be achieved with a complexity of O(M 4.5) instead of O(M 8) in quasi-static channel with M-ary square QAM modulations. Consequently, we propose a simplified ML decoder exploiting the unique properties of the 3D MIMO code. Simulation results show that the proposed simplified ML decoder can achieve much lower processing time latency compared to the classical sphere decoder with Schnorr-Euchner enumeration.