Maximum Likelihood Detection Algorithm Research Articles

Prefiltering-based reduced rank multiuser detection in uplink generalized spatial modulation massive MIMO system

Exploiting generalized spatial modulation in massive MIMO system, we develop an efficient uplink multiuser detection scheme. Different from the maximum likelihood detection algorithm, the spatial and temporal data in the proposed detection scheme are decoded in a sequential manner: At the front end of base station receiver, a bank of spatial filters is first employed to mitigate the multiuser interference using the benefits of large-scale antenna array. There then, a reduced rank generalized Eigen-value decomposition-based algorithm is proposed to identify the antennas activated at each user terminal. In the second stage, a least-squares-based multiuser detector is employed to decode the multiplexed temporal symbols. Both theoretical analysis and computer simulations are conducted to evaluate system performance in terms of correct identification probability and overall symbol error rate. Simulation results demonstrate that the proposed algorithm outperforms most of the existing algorithms yet the complexity is extensively reduced.

Quantum Algorithm for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection

In this paper, we propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization (HUBO) problem. This algorithm is based on the Grover adaptive search that originally supported HUBO with integer coefficients. Next, as an application example, we formulate multiple-input multiple-output maximum likelihood detection as a HUBO problem with real-valued coefficients, where we use the Gray-coded bit-to-symbol mapping specified in the 5G standard. The proposed approach allows us to construct an efficient quantum circuit for the detection problem and to analyze specific numbers of required qubits and quantum gates, whereas other conventional studies have assumed that such a circuit is feasible as a quantum oracle. To further accelerate the quantum algorithm, we also derive a probability distribution of the objective function value and determine a unique threshold to sample better states. Assuming a future fault-tolerant quantum computing, our proposed algorithm has the potential for significantly reducing query complexity in the classical domain and providing a quadratic speedup in the quantum domain.

Complexity‐reduced maximum‐likelihood hybrid detection for MIMO systems

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

CSI-Free Geometric Symbol Detection via Semi-Supervised Learning and Ensemble Learning

Symbol detection (SD) plays an important role in a digital communication system. However, most SD algorithms require channel state information (CSI), which is often difficult to estimate accurately. As a consequence, it is challenging for these SD algorithms to approach the performance of the maximum likelihood detection (MLD) algorithm. To address this issue, we employ both semi-supervised learning and ensemble learning to design a flexible parallelizable approach in this paper. First, we prove theoretically that the proposed algorithms can arbitrarily approach the performance of the MLD algorithm with perfect CSI. Second, to enable parallel implementation and also enhance design flexibility, we further propose a parallelizable approach for multi-output systems. Finally, comprehensive simulation results are provided to demonstrate the effectiveness and superiority of the designed algorithms. In particular, the proposed algorithms approach the performance of the MLD algorithm with perfect CSI, and outperform it when the CSI is imperfect. Interestingly, a detector constructed with received signals from only two receiving antennas (less than the size of the whole receiving antenna array) can also provide good detection performance.

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.

A Low Complexity Symbol-Wise ML Detection Algorithm for User-Centric C-RAN

This letter considers an optimal signal detection problem for uplink user-centric cloud radio access network (C-RAN). In user-centric C-RAN, users communicate with nearby remote radio heads (RRHs), and RRHs are connected to baseband unit (BBU) pool. Then, the baseband processing functionalities are migrated to the BBU pool to provide joint signal detection for a number of users. However, joint signal processing will encounter high computational complexity as the network scale grows. Especially for optimal signal detection, the computational complexity increases exponentially as the number of users increases. To address this issue, we propose a symbol-wise maximum likelihood (ML) detection algorithm to achieve optimal performance with low complexity. The key to realize the symbol-by-symbol separate detection is that it makes full use of the sparsity of the channel matrix in user-centric C-RAN. We further provide the theoretical derivation to clarify the superiority of the proposed algorithm in this sparse channel scenario. Numerical experiments show that the proposed algorithm can achieve optimal performance with low complexity in user-centric C-RAN.

OFDM-Based Generalized Optical MIMO

The combination of multiple-input multiple-output (MIMO) transmission and orthogonal frequency division multiplexing (OFDM) modulation has been shown to be an effective way to substantially enhance the capacity of bandlimited optical wireless communication (OWC) systems. In this paper, we propose four OFDM-based generalized optical MIMO (GO-MIMO) techniques for intensity-modulation and direct-detection OWC systems, including OFDM-based frequency-domain generalized spatial modulation (FD-GSM), frequency-domain generalized spatial multiplexing (FD-GSMP), time-domain generalized spatial modulation (TD-GSM) and time-domain generalized spatial multiplexing (TD-GSMP). For OFDM-based FD-GSM and FD-GSMP, spatial mapping is performed in the frequency domain, while it is carried out in the time domain for OFDM-based TD-GSM and TD-GSMP. To efficiently estimate both spatial and constellation symbols in each OFDM-based GO-MIMO technique, a corresponding maximum-likelihood (ML) detection algorithm is designed. Extensive simulations are conducted to evaluate and compare the performance of OFDM-based GO-MIMO techniques under various MIMO settings in a typical indoor environment. Simulation results demonstrate that there exists an optimal GO-MIMO technique to achieve a target spectral efficiency for a given receiver location, and the obtained optimal GO-MIMO technique is also related to the specific location of the receiver.

Low-Complexity Multistage Optimal Detection for SVD-Based Hybrid Millimeter Wave MIMO Systems

The singular value decomposition (SVD) based hybrid processing for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems attempts to eliminate mutual interference between data streams by processing the original channel matrix to an approximate diagonal matrix. However, the non-zero off-diagonal entries will result in performance loss. To improve the performance with low-complexity, we propose a multistage optimal detection algorithm for SVD-based hybrid mmWave MIMO systems. At the first stage, a decision criterion is proposed by effectively exploiting the characteristic that the magnitudes of off-diagonal entries of the baseband channel matrix are relatively small. Through this decision criterion, some elements of global optimal solution can be determined. The ratio of the determined elements to all elements is analyzed to reveal the advantage of proposed decision criterion. At the second stage, we further propose a decision feedback algorithm to detect more elements of global optimal solution. If all elements are determined, the detection is complete, otherwise it enters the third stage. In the case of third stage, we apply the maximum likelihood (ML) detection algorithm to solve the residual small-scale optimization problem containing only few undetermined elements. Numerical experiments show that the number of elements required to be determined by ML detection is relatively very small or zero, in most situations, that is why the algorithm has a significantly lower complexity.

A Very Low Complexity QRD-M MIMO Detection Based on Adaptive Search Area

We propose a low complexity QR decomposition (QRD)-M multiple input multiple output (MIMO) detection algorithm based on adaptive search area. Unlike the conventional QRD-M MIMO detection algorithm, which determines the next survivor path candidates after searching over the entire constellation points at each detection layer, the proposed algorithm adaptively restricts the search area to the minimal neighboring constellation points of the estimated QRD symbol according to the instantaneous channel condition at each layer. First, we set up an adaptation rule for search area using two observations that inherently reflect the instantaneous channel condition, that is, the diagonal terms of the channel upper triangle matrix after QR decomposition and Euclidean distance between the received symbol vector and temporarily estimated symbol vector by QRD detection. In addition, it is found that the performance of the QRD-M algorithm degrades when the diagonal terms of the channel upper triangle matrix instantaneously decrease. To overcome this problem, the proposed algorithm employs the ratio of each diagonal term and total diagonal terms. Moreover, the proposed algorithm further decreases redundant complexity by considering the location of initial detection symbol in constellation. By doing so, the proposed algorithm effectively achieves performance near to the maximum likelihood detection algorithm, while maintaining the overall average computation complexity much lower than that of the conventional QRD-M systems. Especially, the proposed algorithm achieves reduction of 76% and 26% computational complexity with low signal to noise ratio (SNR) and high SNR, compared with the adaptive QRD-M algorithm based on noise power. Moreover, simulation results show that the proposed algorithm achieves both low complexity and lower symbol error rate compared with the fixed QRD-M algorithms.

Quadrature spatial modulation based multiuser MIMO transmission system

This study presents a multiuser (MU) multiple-input multiple-output (MIMO) downlink transmission scheme based on the quadrature spatial modulation (QSM) concept, which uses the indices of the non-zero entries in its transmission vector to modulate and transmit an independent sequence of bits for each user in the system. The MU interference is removed by using a matrix precoding technique based on channel state information (CSI) known as block diagonalisation (BD). The performance of the proposed scheme is compared with the conventional MU–MIMO–BD system for uncorrelated Rayleigh fading channels and correlated fading channels with imperfect CSI in the reception. Additionally, a low-complexity near maximum likelihood (ML) detection algorithm for the MU–MIMO–QSM signal's detection is proposed. For the considered cases, the proposed MU–MIMO–QSM scheme exhibits gains up to 1 dB in bit error rate performance and a reduction in detection complexity up to 93% as compared to the conventional MU–MIMO–BD scheme for the optimal ML detection. The proposed algorithm performs very near to the optimal ML detector whilst achieving a complexity reduction of up to 58%.

Fast Scalable Architecture of a Near-ML Detector for a MIMO-QSM Receiver

This paper presents a proposal for an architecture in FPGA for the implementation of a low complexity near maximum likelihood (Near-ML) detection algorithm for a multiple input-multiple output (MIMO) quadrature spatial modulation (QSM) transmission system. The proposed low complexity detection algorithm is based on a tree search and a spherical detection strategy. Our proposal was verified in the context of a MIMO receiver. The effects of the finite length arithmetic and limited precision were evaluated in terms of their impact on the receiver bit error rate (BER). We defined the minimum fixed point word size required not to impact performance adversely for n T transmit antennas and n R receive antennas. The results showed that the proposal performed very near to optimal with the advantage of a meaningful reduction in the complexity of the receiver. The performance analysis of the proposed detector of the MIMO receiver under these conditions showed a strong robustness on the numerical precision, which allowed having a receiver performance very close to that obtained with floating point arithmetic in terms of BER; therefore, we believe this architecture can be an attractive candidate for its implementation in current communications standards.

Design of Differential Spatial Modulation Cooperative System Based on Complementary Code

The traditional differential spatial modulation (DSM) cooperative system overcomes the interference between the antennas by the orthogonality of direct sequence-code division multiple access spreading code. But the spreading sequences they used have the following undesirable properties: the non-zero sidelobes of auto-correlation functions will result in severe multi-path interference, and the non-zero values of cross-correlation functions will result in serious multiple access interference. In this paper, we propose a novel DSM cooperative system scheme to overcome this limitation. In our proposed scheme, the anti-interference characteristic of the system is improved by replacing the traditional spreading codes with complementary codes (CCs) at the transmitter. The DSM signal system constructed by using a multi-symbol dispersion matrix at the transmission relay end can improve the system transmission efficiency and avoid the channel interference. At the receiver, in order to reduce the high computational complexity of traditional maximum likelihood detection algorithm, a low-complexity detection algorithm based on the column search is proposed. The simulation results show that the bit error rate performance of DSM cooperative system based on the CC is superior to the traditional DSM cooperative system based on spreading codes. Meanwhile, the system performance with complete CCs is superior to that with the other CCs, and its implementation complexity is lower.

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.

Impact of I/Q Imbalance on Amplify-and-Forward Relaying: Optimal Detector Design and Error Performance

Future wireless communication systems face several transceiver hardware imperfections that may significantly degrade their performance. In-phase (I) and quadrature-phase (Q) imbalance (IQI), which causes self-interference effects on the desired signal, is an important and practical example to these impairments. In this paper, a channel state information-assisted dual-hop amplify-and-forward (AF) relaying system in the presence of IQI is analyzed. The error performance of the relevant AF cooperative protocol is firstly studied by considering the traditional maximum likelihood detection (MLD) algorithm as a benchmark. Then, two compensation methods, weighting and zero-forcing, are proposed to mitigate the IQI effects. Finally, an optimal MLD solution is introduced by adapting the traditional MLD technique in compliance with the asymmetric characteristics of the IQI. The system performance is evaluated in terms of average symbol error probability (ASEP) through the computer simulations. The ASEP is calculated analytically for the optimal MLD method as well under the assumption of point-to-point communication, which has been envisioned as an allied technology of the fifth generation (5G) wireless systems, between the source and the relay nodes. A power allocation algorithm is provided for this specific case. The extensive computer simulations and analytical results prove that the proposed optimal MLD method provides the best results.

Extended quadrature spatial modulation for MIMO wireless communications

This paper presents an extended quadrature spatial modulation (EQSM) scheme that combines K quadrature spatial modulation (QSM) constellations to achieve a K-fold spectral efficiency (SE) enhancement. The idea underlying EQSM consists in using the average powers of the K QSM constellations as an additional dimension for the transmission of information bits. The modulation process starts with the design of a conventional QSM constellation. The remaining (K−1) QSM constellations are then configured with scaled amplitudes considering the same group of transmit antennas. The EQSM constellation is obtained by the superposition of the K scaled QSM constellations. A novel near maximum likelihood (ML) low-complexity algorithm for EQSM signal detection is also proposed in this paper. Analytical and simulation results obtained for independent and identically distributed (i.i.d.) Rayleigh fading channels show that the proposed EQSM scheme provides gains of up to 2.5, 5, 7, and 8 dB in bit error rate (BER) performance as compared to spatial multiplexing (SMux), double spatial modulation (DSM), conventional QSM, and spatial modulation (SM), respectively. In terms of detection complexity, EQSM allows a 67% complexity reduction when compared to SMux, and a 20% increase as compared to SM/QSM schemes. The obtained results also show that the proposed near ML detection algorithm reduces the complexity of the ML criterion by 82%, while achieving near optimal ML performance.

Multiuser pre-coding aided quadrature spatial modulation for large-scale MIMO channels

Pre-coding aided quadrature spatial modulation (PQSM) is a promising multiple input multiple output (MIMO) transmission technology. The multiuser (MU) detection in PQSM system is investigated in this paper. Based on the known channel state information, pre-coding matrix is designed to pre-process the in-phase and quadrature signals of quadrature spatial modulation (QSM) to reduce the inter-channel interference. In order to lower the complexity at the receiver brought by the orthogonality of the PQSM system, an orthogonal matching pursuit (OMP) detection algorithm and a reconstructed model are proposed. The analysis and simulation results show that the proposed algorithm can obtain a similar bit error rate (BER) performance as the maximum likelihood (ML) detection algorithm with more than 80% reduction of complexity.

Simplified Maximum Likelihood Detection for FTN Non-Orthogonal FDM System

In this letter, we first apply simplified maximum likelihood detection (MLD) with QR decomposition and M-algorithm (QRM-MLD) to reduce inter-carrier interference (ICI) in a faster-than-Nyquist non-orthogonal frequency division multiplexing (FTN-NOFDM) system. A QRM-MLD algorithm has lower computational complexity than an MLD algorithm owing to the decrease of searched path number. In the experiment, 10-Gb/s FTN-NOFDM with the QRM-MLD algorithm was transmitted over 25-km standard single mode fiber. For 20% bandwidth saving, FTN-NOFDM with the QRM-MLD algorithm can achieve almost the same performance as FTN-NOFDM with the MLD algorithm when the path with minimal metric is not discarded before detecting the last subcarrier, meanwhile the bit error rate of FTN-NOFDM with the QRM-MLD algorithm or the MLD algorithm can achieve 7% forward error correction (FEC) limit, but that with an iterative detection (ID) algorithm only can achieve 20% FEC limit. For reducing ICI, the QRM-MLD algorithm has lower computational complexity but can obtain almost the same performance as the MLD algorithm, and the QRM-MLD algorithm also has much better performance than the ID algorithm.

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.

Maximum-Likelihood Detection for MIMO Systems Based on Differential Metrics

The multiple-input multiple-output (MIMO) system makes efficient use of spectrum and increases the transmission throughput in wireless communications. The sphere decoding (SD) is an efficient algorithm that enables the maximum-likelihood (ML) detection for the MIMO system. However, the SD algorithm has variable complexity, and its complexity increases rapidly with decreasing signal-to-noise ratio (SNR). In this paper, we propose a novel ML detection algorithm for the MIMO system based on differential metrics. We define the differential metrics and derive the associated recursive calculation. We then give the indicative functions, which can be used to possibly find some ML-detected bits of the initial sequence. The indicative functions are further applied to implement an efficient tree search for ML detection. The proposed algorithm does not need QR decomposition and matrix inversion. The tree search process needs only the additive operation, while the number of multiplications before the tree search is constant. Our algorithm can achieve the exact ML detection as the SD algorithm. Unlike the SD algorithm, the complexity of our algorithm reduces with decreasing SNR, whereas at high SNR, the complexity is nearly constant. We also give the convergence analysis for the SD and proposed algorithms, and the simulation verifies our analysis. For the proposed algorithm, the number of necessary memory is constant during the tree search, and the implementation by parallel processing is possible. The soft output of ML-detected bits can also be generated in our algorithm.

Improved Chase Detection Algorithm Based on SNR Maximum Sorted

Multiple-input multiple-output (MIMO) wireless communication systems could increase the spectral efficiency and system performance significantly. Maximum likelihood detection (MLD) algorithm provided the best bit error rate (BER) performance for MIMO communication system. Calculating complexity of MLD increased exponentially with the constellation size and the transmit antenna number. Original Chase detector, with lower calculating complexity, was combined of a list detector followed with some V-BLAST sub-detectors. There were error propagations in this algorithm. The order of signal detection was critical because of serial detection in Chase detector. In order to get better trade-off between detection performance and calculating complexity in MIMO wireless communication system, an improved Chase detection algorithm based on SNR maximum was presented here which could reduce error propagation efficiently. Parallel linear detectors were used in sub detectors to improve the bit error performance with lower complexity further more. The proposed algorithm could obtain proper trade-off between calculating complexity and detection performance, and simulation experiment results show its validity.