Zero-forcing Detection Research Articles

Multi-Stream Transmission in Massive MIMO Systems With Full-Duplex Bi-Directional Communication Links

This paper considers a full-duplex (FD) multi-user massive multiple-input multiple-output system where the base station (BS) and user equipment (UE) bi-directionally transmit and receive multiple independent data streams over the same frequency band. The BS and UEs are equipped with a large-scale antenna array. Accounting for imperfect channel state information, we derive the closed-form expressions for the achievable sum-rate and sum spectral efficiency (SE) for the proposed model using maximum-ratio combining and zero-forcing detection. The analytical solutions are verified with simulations. In addition, our analytical results highlight the benefits of multi-stream transmission and show an improved SE for fewer UEs. Moreover, the results show that increasing the antenna array size helps combat self-interference.

Kinerja Multi-user MIMO OFDM dengan Block-Diagonalization Precoding

Multiple-input multiple-output (MIMO) is a transmission technology that uses more than one antenna both on the transmitter side and on the receiver side. In the communication services, the system will involve more than one active user who uses one base station (BS) together so that it is called multi-user MIMO (MU-MIMO). This paper discusses the performances of MU-MIMO when it uses block diagonalization (BD) precoding and applies minimum mean squared error (MMSE) detector. As a comparison we also apply zero-forcing (ZF) detector. From the simulations that have been done, it is found that the MMSE had better performances than the ZF detector in terms of BER. We also consider the performance when users are moving. The simulation results show that BER performances are decrease slowly when users are moving.

Zero Forcing Uplink Detection Through Large-Scale RIS: System Performance and Phase Shift Design

A multiple-input multiple-output wireless communication system is analytically studied, which operates with the aid of a large-scale reconfigurable intelligent surface (LRIS). LRIS is equipped with multiple passive elements with discrete phase adjustment capabilities, and independent Rician fading conditions are assumed for both the transmitter-to-LRIS and LRIS-to-receiver links. A direct transceiver link is also considered which is modeled by Rayleigh fading distribution. The system performance is analytically studied when the linear yet efficient zero-forcing detection is implemented at the receiver. In particular, the outage performance is derived in closed-form expression for different system configuration setups with regards to the available channel state information (CSI) at the receiver. In fact, the case of both perfect and imperfect CSI is analyzed. Also, an efficient phase shift design approach at LRIS is introduced, which is linear on the number of passive elements and receive antennas. The proposed phase shift design can be applied on two different modes of operation; namely, when the system strives to adapt either on the instantaneous or statistical CSI. Finally, some impactful engineering insights are provided, such as how the channel fading conditions, CSI, discrete phase shift resolution, and volume of antenna/LRIS element arrays impact on the overall system performance.

Deep Learning Aided Low Complex Sphere Decoding for MIMO Detection

In this paper, we propose a deep learning based sphere decoding (SD) scheme to reduce the detection complexity for the multiple-input multiple-output (MIMO) communication systems. Specifically, we first design the sparsely connected deep neural network (SC-DNN) to find a moderate radius for the SD algorithm. Then, we develop the SC-SD algorithm to reduce the computational complexity by deciding the detection order from the output of the SC-DNN, the zero-forcing (ZF) detector, and the transmit power. We further reduce the complexity of the SC-SD by defining partial layers without searching. For multi-stream MIMO, where a large number of parameters in neural networks should be trained, we propose a partitioned training procedure to achieve a reasonable computational complexity. Simulation results demonstrate that the SC-SD almost achieves the performance of the maximum likelihood (ML) in MIMO system but is much faster than the classic SD algorithm.

An Analogue In-Memory Ridge Regression Circuit With Application to Massive MIMO Acceleration

In-memory computing (IMC) has emerged as one of the most promising candidates for distributed computing frameworks such as edge computing, owing to its unrivalled energy efficiency and high throughput. By leveraging arrays of emerging devices, such as resistive random access memories (RRAM), to implement massive parallel computation, IMC overcomes the main limitations of classic von Neumann architectures. Meanwhile, next generation telecommunication networks are bound to rely ever more intensively on matrix computations to allow simultaneous transmission and reception over multiple spatial channels, an approach known as Massive Multiple-Input Multiple-Output (MIMO). Here, we propose a closed-loop in-memory computing circuit for the acceleration of Ridge Regression, an algebraic prior that finds application in all phases of a typical massive MIMO transaction, namely channel estimation, uplink and downlink. Particularly, we show the circuit’s capability to perform Zero-Forcing (ZF) and Regularized Zero-Forcing (RZF) detection and beamforming, benchmarking its performance in a realistic framework and comparing results with a commercial graphic processing unit (GPU). Our results indicate a 4 orders-of-magnitude increase in energy efficiency and a 3 orders-of-magnitude increase in area efficiency for the same throughput of a digital solution, supporting IMC for energy efficient pre- and post-processing in next-generation B5G and 6G networks.

Evolutionary gravitational Neocognitron neural network based differential spatial modulation detection scheme for uplink multiple user huge MIMO systems

Interfering manipulation is a growing number of bright aspects for 6th generation (6G) infrastructure, particularly to detect huge sequence quadrature amplitude modulation (QAM) signals. In this manuscript, an evolutionary gravitational Neocognitron neural network based differential spatial modulation detection scheme (EGNNN-DSMDS) is proposed for uplink multiple user huge multiple input multiple output (MIMO) systems. To prevent the wastage of antenna resources, massive MIMO uplink systems use the differential spatial modulation (DSM), here the transmitter is equipped with a small count of antennas, whereas the receiver is equipped with a huge count of antennas. By utilizing the asymptotic characteristics of massive multiple input multiple output channels, the transmitting signal can be uniquely decoded without instantaneous channel state information in the receiver. When analyzed with conventional coherent zero-forcing detector (ZFD), the proposed approach has less complication. The proposed EGNNN-DSMDS detection scheme achieves excellent bit error ratio performance and estimating channel errors. EGNNN-DSM attains higher spectral efficiency 99.56%, 96.33%, 98.11%, lower BER 2.5%, 4.13%, 1.19% and lower computational complexity 1.19%, 2.16%, 1.15% compared with existing methods, like MLPNN-MUD-UMM-MIMO, CNN-LASD-UMM-MIMO, and DNN-SRD-UMM-MIMO. Finally, the proposed EGNNN-DSM detection scheme attains the better outcomes.

A Scheduling Scheme for Improving the Performance and Security of MU-MIMO Systems.

For the receiver of multiple-input multiple-output (MIMO) systems, linear detectors are an interesting option due to their good performance and low complexity. Nevertheless, MIMO systems lose diversity in exchange for eliminating interference when linear detectors are used. Aiming to maintain the system diversity while mitigating interference between users, this work proposes a scheduling scheme for the uplink of multiuser MIMO (MU-MIMO) systems that employ A antennas and the zero-forcing (ZF) detector at the receiver in the base station (BS). The channel model includes Rician fading and additive white Gaussian noise (AWGN) in an imperfect channel estimation scenario. The proposed scheme selects U users from a group of users to transmit simultaneously, so that the signal-to-noise ratio (SNR) is maximized. For this, an exact expression to evaluate the SNR of the users is obtained. With this result, the scheduling strategy is proposed. Results show that as increases, the outage probability (OP), and the bit error rate (BER) decrease as the system diversity increases, even when the system is completely loaded, i.e., when . Moreover, it is shown that the scheduling scheme counteracts the imperfect channel estimation effects as increases. Finally, the proposed scheme is tested in presence of an external eavesdropper trying to decode the information sent by the users. The results show that the presented proposal allows for a reduction of the secrecy-outage-probability (SOP) as increases.

Guaranteeing QoS for NOMA-Enabled URLLC Based on κ-μ Shadowed Fading Model.

Sixth-generation (6G) wireless communication scenarios are complex and diverse. Small-scale fading is a key part of wireless channels and its impact on performance in scenarios with time sensitivity and 6G ultrareliable and low latency communications (URLLC) quality-of-service requirements cannot be ignored. Therefore, it is necessary to accurately characterize small-scale fading when designing wireless communication systems. In this paper, we derive approximate closed form expressions for the probability density function, cumulative distribution function and moment-generating function of the postprocessing signal-to-noise ratio following the zero-forcing detector in a cell-free massive multiple-input multiple-output (CF mMIMO) system. CF mMIMO system is a nonorthogonal multiple access (NOMA) system that enables users to share all channel uses and can ensure the fairness of the communication quality experienced by different users. Our key contributions include the extension of the – shadowed fading model to a CF mMIMO system and the proposal of theoretical tools (the derived closed-form expression) to improve its mathematical tractability. By exploiting the statistical characterizations of the arrival and service processes, another important contribution is the exploitation of the upper bound of the queuing delay violation probability (UB-QDVP) over the Mellin transforms of the arrival and service processes in the proposed CF mMIMO system under the – shadowed fading model. Corroborated by extensive simulations, our analyses validate that the CF mMIMO system outperforms the orthogonal multiple access and power-domain NOMA systems and reveal the relationships among different small-scale fading types, energy efficiency, delay and the UB-QDVP, as well as the accuracy and effectiveness of the proposed theoretical tools based on the – shadowed fading model.

On the achievable secrecy transmission rates by Alamouti space‐time block coding in time‐selective fading channels

In this letter, the authors study the security performance of Alamouti space-time block coding (STBC) with two different linear detection strategies, linear maximum likelihood (LML) and zero-forcing (ZF), over time-selective Rayleigh fading channels. Specifically, the connection and secrecy outage probabilities for general temporal correlation when the legitimate receiver and eavesdropper adopt the LML and ZF detectors are first derived. Then the secrecy transmission rates for various combinations of LML and ZF detectors at the legitimate receiver and eavesdropper are derived. The authors also found that the optimal control of the codeword rate and secrecy rate can maximize the secrecy transmission rates.

Closed-Form Bit Error Probability of ZF Detection for OFDM-M-MIMO Systems Using Effective Noise PDF

This paper derives the closed-form bit error probability (BEP) of massive multiple-input, multiple-output (M-MIMO) systems using orthogonal frequency-division multiplexing (OFDM) and zero-forcing (ZF) detection. We improve the BEP accuracy by increasing the Neumann series expansion (NSE) to second order for the system that was previously analyzed in [1] employing a derived probability distribution function (PDF) of the effective noise. The proposed PDF is then utilized to evaluate the BEP, the PDF of output signal-to-noise ratio (SNR), and the outage probability as a function of the output SNR of the system. Furthermore, a simplified closed-form expression for the effective noise PDF, in terms of the Gaussian distribution, and the noise variance are firstly derived in this paper for simplifying the performance analysis. Monte-Carlo simulation results confirm that the outcome from the derived equation and the approximation closely matched those obtained by simulation. In addition, we employ the proposed noise variance to estimate the log-likelihood ratio (LLR) instead of the approximate noise variance for the low-complexity soft-output ZF detection. The computational complexity of the proposed detection is thus significantly reduced, whereas its bit error rate (BER) is lower than that of the classical detection. Focusing on a 10 × 200 Coded-OFDM-M-MIMO system, 97.81% of multiplications, required for producing the LLR from the estimated symbol, were minimized by utilizing the proposed detection. Therefore, the derived equations can be efficiently used for analyzing the performance of OFDM-M-MIMO systems, and reducing the computational complexity of the soft-output ZF detection.

Semi-Blind Multiuser Detection Under the Presence of Reconfigurable Intelligent Surfaces

A multiuser multiple-input multiple-output wireless communication system is analytically studied, which operates with the aid of a reconfigurable intelligent surface (RIS). The intermediate RIS is equipped with multiple elements and operates via random phase rotations to simultaneously serve multiple users. Independent Rayleigh fading conditions are assumed among the included channels. The system performance is analytically studied when the linear yet efficient zero-forcing detection is implemented at the receiver. In particular, the outage performance is derived in closed-form expression for different system configuration setups with regards to the available channel state information at the receiver. Further, a joint coherent/noncoherent linear detection is analytically presented. Finally, some new engineering insights are provided, such as how the channel state information and/or the volume of antenna/RIS arrays impact on the overall system performance as well as the arising efficiency on the performance/complexity tradeoff by utilizing the joint coherent/noncoherent scheme.

Power Minimization Precoder Design for Uplink MIMO Systems With Multi-Group NOMA Scheme

This paper presents a non-orthogonal multiple access (NOMA) scheme with group detection for uplink multiple-input multiple-output (MIMO) systems, for which an effective precoder design is developed. In the scheme, users are divided into groups in accordance with their locations for detection at the base station. The inter- and intra-group interferences are mitigated by successive interference cancellation (SIC) and transceivers, respectively. Based on a derived approximate signal-to-interference-plus-noise ratio (SINR) for using zero-forcing detection, an iterative power and beamforming update procedure is developed for obtaining the user precoders. The precoder design effectively mitigates the intra-group-inter-user correlation making the adopted approximate SINR represent the original SINR accurately. The proposed multi-group MIMO-NOMA scheme can work under more practical transmit-receive antenna configurations and is shown to outperform upon existing cluster-based MIMO-NOMA schemes in terms of total transmit power for various system configurations. The impact of SIC residuals on the multi-group MIMO-NOMA scheme is investigated. Feasibility conditions for the design under imperfect SIC based on the fractional cancellation error model are developed.

Eavesdropping in the Uplink of massive MIMO: countermeasure and performance analysis

In massive multiple-input multiple-output (MIMO) systems, a multi-antenna eavesdropper could potentially harm the uplink security by channel estimation in the training phase and then coherent detection in the payload data phase. To address this issue, we propose to inject artificial noise to the payload data to combat eavesdropping. Specifically, lower bounds of secrecy rates for maximum-ratio combining (MRC) and zero-forcing (ZF) detection schemes are derived. In each case, we further investigate scenarios with perfect and imperfect channel-state information. Moreover, the impact of key parameters, including the channel estimation error, power allocation factor and the number of antennas on the security of massive MIMO uplink are discussed.

Hardware Topologies for Decentralized Large-Scale MIMO Detection Using Newton Method

Centralized Massive Multiple Input Multiple Output (MIMO) uplink detection techniques for baseband processing possess severe bottleneck in terms of interconnect bandwidth and computational complexity. This problem has been addressed in the current work by adapting the centralized Newton method for decentralized MIMO uplink detection leveraging several Base Station antenna clusters. The proposed decentralized Newton (DN) method achieves error-rate performance close to centralized Zero Forcing detector as compared to other decentralized techniques. Two hardware topologies, namely the ring and the star topologies, are proposed to assess and discuss the trade-off among interconnect bandwidth and throughput, in comparison with contemporary decentralized MIMO uplink detection techniques. As such the following findings are elaborated. On BS antenna cluster scaling for different MIMO system configurations, the ring topology provides high throughput at constant interconnect bandwidth, while the star topology provides lower latency with a deterministic variation in the hardware resource consumption. Due to strategic optimizations on the hardware implementation, additional user equipment can be allotted at a fractional increase in Field Programmable Gate Array resource consumption, improved energy efficiency, and increased transaction of bits per Joule. The ring topology can process additional subcarrier at a fractional increase in latency and improved system throughput.

BER analysis of truncated SVD‐based MU‐MIMO ZF detection scheme under correlated Rayleigh fading channel

SummaryIn multi‐user multiple input multiple output (MU‐MIMO) uplink, the bit error rate (BER) of linear detection schemes, namely, zero forcing (ZF) and minimum mean square error (MMSE) under correlated Rayleigh fading channel deteriorates with increase in spatial correlation and load factor due to the increase in the condition number of the channel matrix. Moreover, the performance gap between ZF and MMSE increases with increase in the antenna number for large load factors. To address this issue, in this paper, truncated singular value decomposition (TSVD), which is a popular method for solving ill‐posed problem, is used in the ZF detection process through proper selection of hard threshold. However, the pseudo‐inverse computed using TSVD is an approximate inverse, which results in interference at the output of the detection process. Therefore, a mathematical expression for the post‐processing signal‐to‐interference‐plus‐noise ratio (SINR) of the substream is derived and subsequently BER is evaluated. Further, the analytical BER is analyzed with respect to the parameters namely, average signal‐to‐noise ratio (SNR) ( ), correlation coefficient ( ), load factor ( ), and number of singular values considered to compute the hard threshold ( ) and also validated by Monte Carlo trails. From the simulation results, it is observed that for higher order MU‐MIMO systems and at lower values of , the performance of TSVD‐based scheme is comparable with that of MMSE by decreasing the truncation parameter ( ). Moreover, as the complexity of TSVD‐based ZF using randomized schemes is ), therefore, the complexity of detection significantly decreases with decrease in .

The Effect of the Eigenvalues of the Zero-Forcing Detector on Its Performance in the Space-Division Multiplexing System

Zero-Forcing (ZF) detector is used in Space-Division Multiplexing (SDM) receiver to remove interference among the received symbols. Previous works showed that the power of channel noise is enhanced in the output of the ZF detector. They recommend using the ZF detector when the received Signal-to-Noise Ratio (SNR) is high. This work proves that the performance of the ZF detector depends on the eigenvalues of the channel correlation matrix. The paper shows that if the sum of the eigenvalues of this correlation matrix is equal to the rank of the channel matrix, the ZF detector will not enhance noise power at its outputs. Moreover, if the sum of the eigenvalues is smaller than the rank of the channel matrix, the ZF detector will reduce noise power at its outputs. In this work, a theorem, which demonstrates the performance of the ZF detector in SDM receiver, is introduced and proved. The proposed work uses smart antennas in the transmitter and receiver to control the elements and eigenvalues of the channel matrix. The introduced theorem and a complete SDM receiver with ZF detector are simulated and evaluated at different conditions with different criteria. A real-time SDM receiver with ZF detector is also implemented and evaluated. The simulation and implementation results are shown at the end of this study. The results of the proposed systems show that a ZF detector can be used to remove interference in the SDM system without enhancing the channel noise.

Optimality of Linear MIMO Detection for 5G Systems via 1-Opt Local Search

Multiple input multiple output (MIMO) symbol detection problem belongs to non-deterministic polynomial acceptable hard combinatorial optimization (CO) class. One of the key trials in design of MIMO scheme is to develop a low complexity detection algorithm without much compromise in performance. Detection approaches proposed in the literature can be split into non-linear and linear algorithms. Vertical Bell-Labs Layered Space Time (V-BLAST) and Sphere Decoder (SD) are non-linear methods used for extracting transmitted data; whereas, Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) detections are comparatively in complex and effectual linear techniques. In this work, the heuristic 1-Opt local search method used for solving computationally hard combinatorial optimization problems is applied to the ZF and MMSE detection algorithms. First, simple MIMO decoding using ZF and MMSE is accomplished to find the estimated symbol then the transmitted symbol is calculated using the heuristic 1-opt approach by means of the estimated symbol. Simulation results demonstrate that 1-opt search when applied to the ZF and MMSE displays better bit error rate (BER) performance than the simple ZF and MMSE detectors. It is also verified through simulations that the proposed 1-Opt based detectors display better BER performance as compared to the complex nonlinear VBLAST and SD at considerably reduced complexity. Hence, the proposed detectors are appropriate for effective hardware implementations.

다차원 색인 변조를 위한 신경망 기반 활성 안테나 추정을 통한 저복잡도 제로-포싱 검파기

다차원 색인 변조는 우수한 스펙트럼 효율성으로 인해 활발히 연구되고 있다. 본 논문은 다차원 색인 변조의 기술 중 하나인 일반화된 공간-주파수 색인 변조(Generalized space-frequency index modulation, GSFIM)에 적용 가능한 활성 요소 선택 방식과 저복잡도 검파기를 제안한다. 제안하는 활성 요소 선택 방식은 GSFIM의 submatirx마다 공간 차원의 색인 변조를 수행하여 데이터 전송률을 증가시킨다. 제안하는 활성 요소 선택 방식을 사용할 경우 기존의 방식보다 높은 데이터 전송률을 제공하지만, 동일한 비트 오류율 성능을 보인다. 제안하는 검파기는 제로-포싱(Zero-forcing, ZF)기법이 적용된 GSFIM의 수신 신호에서 활성 안테나의 색인을 인공신경망으로 추정함으로써 수신기의 계산 복잡도를 감소시킨다. 제안하는 검파기는 제로-포싱 기법만을 사용했을 때에 비해 낮은 계산 복잡도를 요구하지만, 동일한 비트 오류율 성능을 보인다.

BER of Massive MIMO in time-variant channels using multiplexed, superimposed and hybrid channel estimation techniques

Massive MIMO (M-MIMO) is one of the most promising technologies towards fifth generation (5G) wireless systems. M-MIMO use a large number of antennas at the base station (BS) serving multiple user terminals (UTs). Therefore, it presents an exceptional performance in terms of the ergodic capacity and bit error rate (BER) using simpler linear detectors when time-invariant channels (TIC) and perfect channel state information (CSI) are considered. However, impairments introduced by the time-variant channel (TVC) and the imperfect channel estimation limit the M-MIMO performance. In this work, the impairments introduced by the multiplexed pilot estimation (MPE), superimposed pilot estimation (SPE), and hybrid pilot estimation (HPE), using the minimum-mean-square error (MMSE) estimator are analyzed for M-MIMO in TVCs. Furthermore, the system performance is evaluated in terms of the BER for the zero-forcing (ZF) detector. Closed-form expressions and simple lower bounds are derived. The results show that the average BER in TVCs is far from the average BER obtained for TICs. Moreover, MPE and HPE are more susceptible to the impairments of TVCs, and even increasing a considerable number of BS antennas, the BER improvement is negligible in some time-slots. Finally, the BER using SPE outperforms the other estimation techniques.

On the Outage Probability of Distributed MAC With ZF Detection

Distributed scheduling is an attractive approach for the Multiple-Access Channel (MAC). However, when a subset of the users access the channel simultaneously, distributed rate coordination is necessary, and is a major challenge, since the achievable rate of each user highly depends on the channels of other active users. That is, given a detection technique, e.g., Zero-Forcing (ZF), the rate at which a user can transmit depends on the channels other transmitting users have, a knowledge which is usually unavailable in distributed schemes. Fixing a rate and accepting some outage probability when this rate is too high is common practice in these cases. In this paper, we analyze the outage probability of a distributed, asymptotically optimal threshold-based scheduling algorithm under ZF. We rigorously evaluate the distribution of the relevant projections and give upper and lower bounds on the outage probability as a function of the algorithm parameters. At the limit of a large number of users, the bounds match, resulting in the true asymptotic characterization of the outage probability.