Detection In Multiple-input Multiple-output Systems Research Articles

Learning Vector Quantization-Aided Detection for MIMO Systems

In this letter, the learning vector quantization (LVQ) from machine learning (ML) is adopted into the large-scale multiple-input multiple-output (MIMO) detection to improve the detection performance. Inspired by the decision region from lattice decoding, the random Gaussian noises are applied in the proposed learning vector quantization-aided detection (LVQD) algorithm for data generation. Then, based on the classification, supervised learning is activated to update the targeted prototype vector iteratively, so as to a better detection performance. Meanwhile, the decoding radius in lattices is also used to serve as a preprocessing for LVQD, which leads to an efficient detection without performance loss. Finally, simulation results confirm that considerable performance gain can be achieved by the proposed LVQD algorithm, which suits well for suboptimal detection schemes.

Self and Turbo Iterations for MIMO Receivers and Large-Scale Systems

We investigate a turbo soft detector based on the expectation propagation (EP) algorithm for large-scale multiple-input multiple-output (MIMO) systems. Optimal detection in MIMO systems becomes computationally unfeasible for high-order modulations and/or large number of antennas and approximations are used instead. We propose a new EP-based detector with enhanced estimation in terms of complexity and performance. Specifically, we improve the convergence of the self-iterated EP stage by re-defining the priors to better characterize the information returned by the decoder once the turbo procedure starts. We also review the EP parameters to avoid instabilities when using high-order modulations and to reduce the computational complexity. Simulation results illustrate the robustness and enhanced performance of this novel detector in comparison to previous approaches found in the literature.

Reduced Complexity Detection in MIMO Systems with SC-FDE Modulations and Iterative DFE Receivers

This paper considers a Multiple-Input Multiple-Output (MIMO) system with P transmitting and R receiving antennas and different overall noise characteristics on the different receiver antennas (e.g., due to nonlinear effects at the receiver side). Each communication link employs a Single-Carrier with Frequency-Domain Equalization (SC-FDE) modulation scheme, and the receiver is based on robust iterative frequency-domain multi-user detectors based on the Iterative Block Decision Feedback Equalization (IB-DFE) concept. We present low complexity efficient receivers that can employ low resolution Analog-to-Digital Converters (ADCs) and require the inversion of matrices with reduced dimension when the number of receive antennas is larger than the number of independent data streams. The advantages of the proposed techniques are particularly high for highly unbalanced MIMO systems, such as in the uplink of Base Station (BS) cooperation systems that aim for Single-Frequency Network (SFN) operation or massive MIMO systems with much more antennas at the receiver side.

Modified Multiple Feedback QR Aided Successive Interference Cancellation Algorithm for Large MIMO Detection

Multiple-input multiple-output (MIMO) systems have attracted increased interest due to their capability to achieve higher multiplexing and diversity gains. In MIMO systems, reliable symbol detection in one of the major challenges. Maximum likelihood (ML) detection is one such technique which achieves minimum error rate performance for MIMO systems, however due to its exponential complexity ML detection is practically infeasible for large number of antennas. Therefore, in this contribution, we propose a low-complexity modified multiple feedback QR aided successive interference cancellation (MMF-SIC) algorithm which is capable of achieving near optimal performance. The effect of error propagation in SIC can be reduced by using multiple constellation points in decision feedback loops based on the reliability criteria. In MMF-SIC, an enhanced detection diversity is achieved by considering the decision feedback loops in multiple layers of QR aided SIC algorithm. Furthermore, we employ two different ordering schemes in parallel for QR decomposition in MMF-SIC algorithm. Through simulations, it is observed that the MMF-SIC algorithm performs superior over the conventional SIC and other SIC based techniques for detection in MIMO systems, and approach near optimal performance.

Reduced Complexity by Combining Norm Based Ordering MMSE-BSIDE Detection in MIMO Systems

AbstractThe breadth first signal decoder (BSIDE) is well known for its optimal maximum likelihood (ML) performance with lesser complexity. In this paper, we analyze a multiple-input multiple-output (MIMO) detection scheme that combines; column norm based ordering minimum mean square error (MMSE) and BSIDE detection methods. The investigation is carried out with a breadth first tree traversal technique, where the computational complexity encountered at the lower layers of the tree is high. This can be eliminated by carrying detection in the lower half of the tree structure using MMSE and upper half using BSIDE, after rearranging the column of the channel using norm calculation. The simulation results show that this approach achieves 22% of complexity reduction for 2×2 and 50% for 4×4 MIMO systems without any degradation in the performance.

Adaptive multiple stage K-best successive interference cancellation algorithm for MIMO detection

In this article, we propose an adaptive multiple stage K-best successive interference cancellation (AMS-KSIC) algorithm for symbol vector detection in multiple-input multiple-output systems. The proposed algorithm employs multiple successive interference cancellation (SIC) stages in parallel, where the number of stages depends on the number of positions at which the minimum mean squared error (MMSE) estimate of the received vector and the SIC solution differ, and each stage is initialized with the partial MMSE estimate of the received vector. In every stage, K-best solutions are generated by using the minimum Euclidean distance criteria. Furthermore, to reduce error propagation, we use two different ordering strategies namely, signal to noise ratio and log-likelihood ratio based orderings. The best solution among all the generated solutions is selected by using maximum likelihood (ML) cost metric. Multiple stages along with K-best solutions in every stage achieves a higher detection diversity, and hence, yield a better performance in terms of bit error rate (BER). From simulations, we observe that the proposed AMS-KSIC algorithm performs better than the MMSE and the SIC based detection schemes, and achieves a near ML performance. Further, the BER performance of the proposed algorithm improves with increase in the number of antennas and shifts towards single-input single-output additive white Gaussian noise performance. In addition, we also check and validate robustness of the proposed algorithm by simulating the BER performance under channel estimation errors.

ML Symbol Detection for MIMO Systems in the Presence of Channel Estimation Errors

In wireless communication, the multiple-input multiple-output (MIMO) system is a well-known approach to improve the reliability as well as the data rate. In MIMO systems, channel state information (CSI) is typically required at the receiver to detect transmitted signals; however, in practical systems, the CSI is imperfect and contains errors, which affect the overall system performance. In this paper, we propose a novel maximum likelihood (ML) scheme for MIMO systems that is robust to the CSI errors. We apply an optimization method to estimate an instantaneous covariance matrix of the CSI errors in order to improve the detection performance. Furthermore, we propose the employment of the list sphere decoding (LSD) scheme to reduce the computational complexity, which is capable of efficiently finding a reduced set of the candidate symbol vectors for the computation of the covariance matrix of the CSI errors. An iterative detection scheme is also proposed to further improve the detection performance.

Low-Complexity SIC Detection Algorithms for Multiple-Input Multiple-Output Systems

A new design for successive interference cancellation (SIC) detection for multiple-input multiple-output systems is introduced, and it is developed on the basis of the method of normal equations commonly used to solve the linear least squares problem. On the basis of this design, optimal-ordered and suboptimal-ordered SIC detection algorithms are derived. It is shown that the proposed optimal-ordered SIC detection algorithm offers a complexity reduction ratio of 1.11-1.25 compared to the fastest known optimal-ordered SIC detection algorithm for intermediate and large numbers of antennas and in terms of the average complexity. On the other hand, the proposed suboptimal-ordered SIC detection algorithm requires a lower complexity than the proposed optimal-ordered one and provides a bit-error-rate performance close to that of the optimal-ordered one and better than those of the other suboptimal-ordered SIC detection algorithms.

Lattice‐reduction‐aided semidefinite relaxation detection algorithms for multiple‐input multiple‐output systems

Multiple-input multiple-output (MIMO) system is considered to be one of the key technologies of long-term evolution, since it achieves requirements of high throughput and spectral efficiency. The semidefinite relaxation (SDR) detection for MIMO systems is an attractive alternative to the optimum maximum likelihood (ML) decoding because it is very computationally efficient. In the case of the binary phase shift keying and four quadrature amplitude modulation constellations, the block error rate (BLER) performance of SDR detection is fairly close to the optimum BLER performance. However, for high-order modulation systems, their BLER performance is still unsatisfactory compared with the ML decoding. Lattice reduction technology can transform a matrix into a new equivalent one with more orthogonal and shorter basis vectors. It has been combined with linear decoders to improve their BLER performance. Inspired by this, the authors proposed two lattice-reduction-aided MIMO detection algorithms based on SDR. Simulation results demonstrate that they can provide near-optimum BLER performance with polynomial time complexity.

A Semifixed Complexity Sphere Decoder for Uncoded Symbols for Wireless Communications

The development of high data rate wireless communications systems using Multiple Input — Multiple Output (MIMO) antenna techniques requires detectors with reduced complexity and good Bit Error Rate (BER) performance. In this paper, we present the Semi-fixed Complexity Sphere Decoder (SCSD), which executes the process of detection in MIMO systems with a significantly lower computation cost than the high-performance/reduced-complexity detectors: Sphere Decoder (SD), K-best, Fixed Complexity Sphere Decoder (FSD) and Adaptive Set Partitioning (ASP). Simulation results show that when the Signal-to-Noise Ratio (SNR) is less than 15dB, the SCSD reduces the complexity by up to 90% with respect to SD, up to 60% with respect to K-best or ASP and by up to 90% with respect to FSD. In the proposed algorithm, the BER performance does not show significant degradation and therefore, can be considered as a complexity reduction scheme suitable for implementing in MIMO detectors.

Comparison of Semidefinite Relaxation Detectors for High-Order Modulation MIMO Systems

Multiple-input multiple-output (MIMO) system is considered to be one of the key technologies of LTE since it achieves requirements of high throughput and spectral efficiency. The semidefinite relaxation (SDR) detection for MIMO systems is an attractive alternative to the optimum maximum likelihood (ML) decoding because it is very computationally efficient. We propose a new SDR detector for 256-QAM MIMO system and compare its performance with two other SDR detectors, namely, BC-SDR detector and VA-SDR detector. The tightness and complexity of these three SDR detectors are analyzed. Both theoretical analysis and simulation results demonstrate that the proposed SDR can provide the best BLER performance among the three detectors, while the BC-SDR detector and the VA-SDR detector provide identical BLER performance. Moreover, the BC-SDR has the lowest computational complexity and the VA-SDR has the highest computational complexity, while the proposed SDR is in between.

A novel pre-processing and adaptive statistical threshold for sphere detection in MIMO systems

Abstract In this paper, an efficient sphere detection (SD) scheme for multiple-input multiple-output (MIMO) systems is presented. The proposed SD scheme can substantially reduce computational complexity by introducing a pre-processing scheme and an adaptive threshold. In particular, our proposed pre-processing scheme is based on an iterative successive interference cancelation (SIC). The proposed adaptive threshold is used to judge whether a traversed path is correct or not and obtained by analyzing the distributions of the correct and erroneous estimates which have the minimum error pattern among all the SD searching paths. Simulation results show that our proposed scheme offers a substantial complexity reduction in terms of the number of visited nodes while keeping a significantly small performance degradation compared to conventional approaches.

Optimized Markov Chain Monte Carlo for Signal Detection in MIMO Systems: An Analysis of the Stationary Distribution and Mixing Time

In this paper we introduce an optimized Markov Chain Monte Carlo (MCMC) technique for solving the integer least-squares (ILS) problems, which include Maximum Likelihood (ML) detection in Multiple-Input Multiple-Output (MIMO) systems. Two factors contribute to the speed of finding the optimal solution by the MCMC detector: the probability of the optimal solution in the stationary distribution, and the mixing time of the MCMC detector. Firstly, we compute the optimal value of the "temperature" parameter, in the sense that the temperature has the desirable property that once the Markov chain has mixed to its stationary distribution, there is polynomially small probability ($1/\mbox{poly}(N)$, instead of exponentially small) of encountering the optimal solution. This temperature is shown to be at most $O(\sqrt{SNR}/\ln(N))$, where $SNR$ is the signal-to-noise ratio, and $N$ is the problem dimension. Secondly, we study the mixing time of the underlying Markov chain of the proposed MCMC detector. We find that, the mixing time of MCMC is closely related to whether there is a local minimum in the lattice structures of ILS problems. For some lattices without local minima, the mixing time of the Markov chain is independent of $SNR$, and grows polynomially in the problem dimension; for lattices with local minima, the mixing time grows unboundedly as $SNR$ grows, when the temperature is set, as in conventional wisdom, to be the standard deviation of noises. Our results suggest that, to ensure fast mixing for a fixed dimension $N$, the temperature for MCMC should instead be set as $\Omega(\sqrt{SNR})$ in general. Simulation results show that the optimized MCMC detector efficiently achieves approximately ML detection in MIMO systems having a huge number of transmit and receive dimensions.

Robust Fixed-Complexity Sphere Decoders for Rank-Deficient MIMO Systems

Sphere decoder (SD) has variable complexity, and the traditional fixed-complexity sphere decoder (FSD) is not applicable for rank-deficient (NT > NR) multiple input multiple output (MIMO) systems (i.e. the down link detection in MIMO systems, or systems with highly correlated MIMO channels). To overcome these difficulties, in this paper, robust fixed-complexity sphere decoders (RFSD-s) based on new preprocessing algorithms are proposed for rank-deficient MIMO systems. With respect to the cases without and with information on the level of noise, RFSD using zero-forcing technique (RFSD-ZF) and FSD using minimum mean square error technique (FSD-MMSE) are proposed respectively. To reduce the computational complexity of RFSD-ZF, a simplified RFSD-ZF (SRFSD-ZF) with little performance loss is also introduced, the theoretical proof is given to support the feasibility of SRFSD-ZF. Simulation results show that, besides better performance than the traditional FSD, the proposed techniques are robust to the configuration of MIMO antennas (both NT ≤ NR and NT > NR), which is another advantage over the traditional FSD.

Research on low-complexity breadth-first detection for multiple-symbol differential unitary space–time modulation systems

The breadth-first searching algorithms, typically represented by K-best algorithm, are widely studied for multiple-symbol differential detection in multiple-input multiple-output systems due to the advantages of fixed complexity and latency which are very attractive for hardware implementation. However, it needs a large K value to achieve near maximum likelihood performance, which results in large complexity. In this study, a dynamic K-best detection with reduced average K value is proposed. It reduces the complexity on path expanding, path updating and comparing and swapping (C&S) operations by 24.24, 25 and 43.46%, respectively, with less performance degradation. After that, two low-complexity sorting architectures, Batcher's merge sort and K cycles sort, are presented and applied to the proposed dynamic K-best detection. The complexity analysis and simulation results show that, compared with the traditional Bubble sorting dynamic K-best detection, the K cycles sorting and the Batcher's merge sorting dynamic K-best detections can further save C&S operations by 59.5 and 11.2%, respectively, while performance cost capable of being ignored. Moreover, the K cycles sorting dynamic K-best detection achieves best trade-off on throughput and required memory, and the architecture of the Batcher's merge sorting dynamic K-best detection is more beneficial to parallel processing and multiple-processor structure.

Exact and Closed-Form Error Performance Analysis for Hard MMSE-SIC Detection in MIMO Systems

We investigate the exact error performance of hard minimum mean-squared error (MMSE) detection possibly with successive interference cancellation (SIC) in multiple-input multiple-output (MIMO) systems. To facilitate the analysis, we start with an exact bit-error rate (BER) analysis for a general system with decision statistic, z=ax+u, where a>;0, x is the transmitted signal, and u is an arbitrarily distributed noise component which is possibly dependent on the signal component x. For this general system, we derive the exact and closed-form BER expressions for M-ary pulse amplitude modulation (PAM) and arbitrary rectangular quadrature amplitude modulation (QAM), which include the well-known BER result of as a special case. Furthermore, by formulating the MIMO MMSE decision statistics in the same form as z in the general system, we derive the exact and closed-form instantaneous BER and symbol-error rate (SER) expressions for MIMO hard MMSE detection with/without SIC employing PAM and QAM. Finally, the validity of our derived error probability expressions is verified through extensive Monte Carlo simulations and the results reported in the literature.

Application of Heuristic (1-Opt local Search) and Metaheuristic (Ant Colony Optimization) Algorithms for Symbol Detection in MIMO Systems

Heuristic and metaheuristic techniques are used for solving computationally hard optimization problems. Local search is a heuristic technique while Ant colony optimization (ACO), inspired by the ants' foraging behavior, is one of the most recent metaheuristic technique. These techniques are used for solving optimization problems. Multiple-Input Multiple-Output (MIMO) detection problem is an NP-hard combinatorial optimization problem. We present heuristic and metaheuristic approaches for symbol detection in multi-input multi-output (MIMO) system. Since symbol detection is an NP-hard problem so ACO is particularly attractive as ACO algorithms are one of the most successful strands of swarm intelligence and are suitable for applications where low complexity and fast convergence is of absolute importance. Maximum Likelihood (ML) detector gives optimal results but it uses exhaustive search technique. We show that 1-Opt and ACO based detector can give near-optimal bit error rate (BER) at much lower complexity levels. Comparison of ACO with another nature inspired technique, Particle Swarm Optimization (PSO) is also discussed. The simulation results suggest that the proposed detectors give an acceptable performance complexity trade-off in comparison with ML and VBLAST detectors.

On spectral efficiency of low-complexity adaptive MIMO systems in Rayleigh fading channel

Adaptive MQAM modulation is used to maximize spectral efficiency of multiple-input multiple-output (MIMO) systems while keeping bit error rate (BER) under a target level. Closed-form expressions of the average spectral efficiency, coined as discrete-rate spectral efficiency (DRSE), are derived for adaptive modulation MIMO systems using different algorithms. To further enhance the spectral efficiency, a low complexity adaptation scheme is suggested to switch across different algorithms based on the DRSE. In the current letter, we investigate the adaptation scheme that switches between orthogonal space-time block codes (OSTBC) and spatial multiplexing with zero-forcing (ZF) detection for MIMO systems with two transmit antennas. Two types of operating environment are considered: flat Rayleigh fading channel without spatial correlation and spatially correlated Rayleigh fading channel with transmit correlation.

Joint receive antenna selection and symbol detection for MIMO systems: a heterogeneous genetic approach

This letter presents a joint scheme of receive antenna selection and symbol detection for multiple-input,multiple output (MIMO) systems based on the maximum likelihood (ML) criterion. To mitigate the computational complexity, a novel variant of the genetic algorithm (GA) is addressed to solve the nonlinear optimization involved, where a new heterogenous crossover and a new heterogenous mutation are conducted in the chromosome evolution process. Furnished simulations show that the new approach provides superior performance with substantially lower computational load compared with previous works in both correlated and uncorrelated channels.

Transmitter Precoding with Reduced-Complexity Soft Detection for MIMO Systems

We present a preceded reduced-complexity soft detection (PRCSD) algorithm for multiple-input multiple-output (MIMO) systems. The linear operations at both transmit and receive sides based on complex Householder transform convert the MIMO channel to be multiple-diagonal, spatially partial-response-like, so that error propagation is alleviated when applying reduced-complexity soft detection at the receiver. The transform results in unitary precoding and feedforward matrices so that neither transmit power boost nor noise enhancement is present. Performance analysis based on pairwise error probability (PEP) shows that PRCSD achieves larger diversity advantage than existing preceding and multiple-beamforming (MB) schemes, which basically attempt to transmit signals through diagonal independent sub-channels and thus may suffer a diversity loss. PRCSD can achieve full diversity as maximum likelihood (ML) detection in some scenarios while reducing complexity significantly