Massive Multiple-input Multiple-output Scenario Research Articles

Implementation of 802.11ax and cell-free massive MIMO scenario for 6G wireless network analysis extending OMNeT++ simulator

In an era where ubiquitous connectivity and escalating data demands are altering the landscape of wireless communications, our paper proposes a pioneering enhancement for the OMNeT++ simulator to support the advanced features of IEEE 802.11ax high efficiency (HE) alongside cell-free massive multiple-input multiple-output (MIMO) systems. Traditional wireless networks face daunting challenges in sustaining elevated quality of service (QoS), primarily due to fluctuating user densities and signal quality. Cell-free massive MIMO serves as a compelling answer to this predicament by decentralizing the cellular architecture. It eradicates conventional cell boundaries, furnishing uniform QoS regardless of user locations. However, these advancements come at the expense of complex backhaul networks and articulated joint signal processing. The 802.11ax standard, touted for its robustness and efficiency, remains underexplored in this new paradigm. Our research not only dissects the architectural elements and constraints of both 802.11ax and cell-free massive MIMO but also elaborates on the adaptations required to extend OMNeT++ functionalities for these technologies. By doing so, we bridge a crucial gap, enabling the simulator to provide a more precise, detailed, and scalable evaluation of emerging 6G scenarios and directional communications also taking into account the impact of the most known routing protocols such as dynamic source routing (DSR), ad hoc on-demand distance vector routing (AODV), optimized link state routing (OLSR), and dynamic mobile ad hoc network on-demand (DYMO) that were selected for this comparative study. The proposed extensions promise to revolutionize network simulations and lay the foundation for in-depth analyses of wireless systems in complex and dynamic environments. Through extensive simulations, our study demonstrates that cell-free massive MIMO configurations significantly improve network throughput in high-density mobile ad hoc network (MANET) environments, with results indicating an average throughput gain of up to 30% compared with non-cell-free configurations. This improvement highlights the efficacy of cell-free massive MIMO to take advantage of the spatial and frequency multiplexing capabilities inherent in the 802.11ax standard, making it a promising solution for future wireless systems in densely populated areas.

Parallel Implementation of K-Best Quadrature Amplitude Modulation Detection for Massive Multiple Input Multiple Output Systems

Massive MIMO (Multiple Input Multiple Output) systems impose significant processing burdens along with strict latency requirements. The combination of large-scale antenna arrays and wide bandwidth requirements for next-generation wireless systems creates an exponential increase in frontend to backend data. Balancing the processing latency and reliability is critical for baseband processing tasks such as QAM detection. While linear detection algorithms have low computational complexity, their use in Massive MIMO scenario has heavy degradation in error performance. Nonlinear detection methods such as Maximum Likelihood and Sphere Decoding have good error performance, but they suffer from high, variable, and uncontrollable computational complexity. For such cases, the K-best QAM detection algorithm can provide required control over the system performance while maintaining near-ML error performance. In this paper, hard-output, as well as soft-output K-best QAM detection, is implemented in a CPU by utilizing the multiple cores combined with vector processing. Similarly, hard-output detection in a GPU is implemented by leveraging the SIMD (Single Instruction, Multiple Data) architecture and Warp-based execution model. The processing time per bit and the energy consumption per bit are compared for CPU and GPU implementations for QAM constellation density and MIMO array size. The GPU implementation shows up to 5× processing latency per bit improvement and up to 120× energy consumption per bit improvement over the CPU implementation for typical QAM constellations such as 4, 16, and 64 QAM. GPU implementation also shows up to 125× improvement over CPU implementation in energy consumption per bit for larger MIMO configurations such as 24 × 24 and 32 × 32. Finally, the soft-output detector is combined with a LDPC (Low-Density Parity Check) decoder to obtain the FER (Frame Error Rate) performance for CPU implementation. The FER is then combined with frame processing latency to form a Goodput metric to demonstrate the latency and reliability tradeoff.

A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands

High-altitude platforms (HAPs) are considered to be the most important equipment for next-generation wireless communication technologies. In this paper, we investigate the channel characteristics under the configurations of massive multiple-input multiple-output (MIMO) space and large bandwidth at millimeter-wave (mmWave) bands, along with the moving essence of the HAP and ground terminals. A non-stationary three-dimensional (3D) geometry-based stochastic model (GBSM) is proposed for a HAP communication system. We use a cylinder-based geometric modeling method to construct the channel and derive the channel impulse response (CIR). Additionally, the birth–death process of the scatterers is enclosed using the Markov process. Large-scale parameters such as free space loss and rainfall attenuation are also taken into consideration. Due to the relative motion between HAP and ground terminals, the massive MIMO space, and the wide bandwidth in the mmWave band, the channel characteristics of HAP exhibit non-stationarities in time, space, and frequency domains. By deriving the temporal auto-correlation function (ACF), we explore the non-stationarity in the time domain and the impact of various parameters on the correlations across the HAP-MIMO channels. The spatial cross-correlation function (CCF) for massive MIMO scenarios, and the frequency correlation function (FCF) in the mmWave bands are also considered. Moreover, we conduct simulation research using MATLAB. Simulation results show that the theoretical results align well with the simulation results, and this highlights the fact that the constructed 3D GBSM can characterize the non-stationary characteristics of HAP-MIMO channels across the time, space, and frequency domains.

A Low-Complexity Digital Predistorter for Large-Scale MIMO Systems With Crosstalk

Massive multiple-input multiple-output (MIMO) technology is a key enabler for future wireless communication systems. On the other hand, crosstalk is inevitable in the highly integrated large-scale antenna array. The nonlinearity of power amplifiers (PAs) coupled with crosstalk is much more complicated when the number of antennas is large. Digital predistortion (DPD) can compensate for the PA nonlinearity without sacrificing efficiency and is widely applied in both base stations and mobile devices. Extending existing solutions to the large-scale MIMO system usually suffers from performance degradation or greatly increased complexity. In this paper, we consider the nonlinearity with crosstalk for the large-scale MIMO scenario. A much simplified DPD model is proposed by ignoring the high-order crosstalk terms generated from the complete nonlinear model. Compared to existing solutions, the proposed DPD can compensate for both the nonlinear and linear crosstalk of the system. It achieves satisfactory linearization performance with much reduced computational complexity. The complexity of the proposed DPD is linearly related to the number of transmitter branches. Thus, it is scalable in the large-scale MIMO scenario. Moreover, the proposed DPD can be extended to the partially-connected hybrid beamforming system with crosstalk. Simulation results validate the effectiveness of the proposed DPD scheme.

On Investigations of Machine Learning and Deep Learning Techniques for MIMO Detection

This paper reviews in detail the various types of multiple input multiple output (MIMO) detector algorithms. The current MIMO detectors are not suitable for massive MIMO (mMIMO) scenarios where there are a large number of antennas. Their performance degrades with the increase in number of antennas in the MIMO system. For combatting the issues, machine learning (ML) and deep learning (DL) based detection algorithms are being researched and developed. An extensive survey of these detectors is provided in this paper, alongwith their advantages and challenges. The issues discussed have to be resolved before using them for final deployment.

Noncoherent Massive MIMO With Embedded One-Way Function Physical Layer Security

We propose a novel physical layer security scheme that exploits an optimization method as a one-way function. The proposed scheme builds on nonsquare differential multiple-input multiple-output (MIMO), which is capable of noncoherent detection even in massive MIMO scenarios and thus resilient against risky pilot insertion and pilot contamination attacks. In contrast to conventional nonsquare differential MIMO schemes, which require space-time projection matrices designed via highly complex, discrete, and combinatorial optimization, the proposed scheme utilizes projection matrices constructed via low-complexity continuous optimization designed to maximize the coding gain of the system. Furthermore, using a secret key generated from the true randomness nature of the wireless channel as an initial value, the proposed continuous optimization-based projection matrix construction method becomes a one-way function, making the proposed scheme a physical layer secure differential MIMO system. An attack algorithm to challenge the proposed scheme is also devised, which demonstrates that the security level achieved improves as the number of transmit antennas increases, even in an environment where the eavesdropper can perfectly estimate channel coefficients and experience asymptotically large signal-to-noise ratios.

Digital Predistortion Combined with Iterative Method for MIMO Transmitters

In this article, an auxiliary module is proposed to mitigate the crosstalk effect in multiple input–multiple output (MIMO) transmitters. Other branches do not need considering when linearizing the local branch, which reduces the complexity of the auxiliary module, and some branches can be linearized selectively to make the module application more flexible. In the end, the feasibility of the proposed algorithm is verified through the experimental platform. Experimental results demonstrate that for a 2 × 2 MIMO transmitter with −20 dB nonlinear crosstalk, the proposed DPD improves the adjacent channel power ratio (ACPR) more than 16 dB, and normalized mean square error (NMSE) more than 12.8 dB, which has similar performance to the PH model. The predistorter can be implemented with fewer coefficients by separating the crosstalk from the nonlinearity, enabling the technique to be used in 5G massive MIMO scenarios.

A Joint Hybrid Precoding/Combining Scheme Based on Equivalent Channel for Massive MIMO Systems

Due to its inherent ability in reducing hardware cost and power consumption while maintaining high system capacity, hybrid precoding is deemed as one of the key technologies in the upcoming 5G/6G millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, it is challenging to design high performance hybrid precoders/combiners with low computational complexity. In this paper, based on the singular value decomposition (SVD) technique and the concept of equivalent channel, joint hybrid precoding strategies with high spectral-efficiency and low complexity are proposed for both single-user and multi-user massive MIMO systems. Specifically, for single-user massive MIMO scenarios, after transforming the design of hybrid beamforming into the problem of maximizing the square of sum eigenvalues for an equivalent channel, a two-stage successive method is conceived to design the analog precoder and combiner jointly, and the corresponding equivalent channel is constructed. Then, the digital precoding and combining operations are realized directly by applying the SVD technique to the matrix of equivalent channel. Meanwhile, the hybrid precoding strategy is extended to the multi-user scenario for achieving high performance resultant from multi-user diversity. Extensive simulations are conducted to verify the effectiveness of the precoding/combing schemes. The results show that our proposed schemes can achieve superior performance with lower complexity compared to the existing ones.

A 3-D Non-Stationary Model for Beyond 5G and 6G Vehicle-to-Vehicle mmWave Massive MIMO Channels

This paper proposes a novel three-dimensional (3D) non-stationary irregular-shaped geometry-based stochastic model (IS-GBSM) for beyond fifth-generation (B5G) and sixth-generation (6G) vehicle-to-vehicle (V2V) millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) channels. By distinguishing dynamic clusters and static clusters, the proposed IS-GBSM for the first time explores the impact of vehicular traffic density (VTD) on channel statistics in B5G/6G V2V mmWave massive MIMO scenarios. Furthermore, a novel method is developed to model the channel space-time-frequency non-stationarity. In the developed method, dynamic/static correlated clusters are first generated by an improved <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -Means clustering algorithm. Then, by employing a birth-death process based on correlated clusters, the consistency in birth and death between dynamic/static correlated clusters during time-array evolution is modeled. Key channel statistical properties, e.g., space-time-frequency correlation function (STF-CF) and Doppler power spectral density (DPSD), are derived. Simulation results demonstrate that the space-time-frequency non-stationarity is captured and the influence of VTDs on channel statistics is explored. Finally, the close agreement is achieved between simulation results and measurements, verifying the utility of proposed IS-GBSM.

Joint Pilot Design and Channel Estimation Using Deep Residual Learning for Multi-Cell Massive MIMO Under Hardware Impairments

In multi-cell massive multiple-input multiple-output (MIMO) systems, channel estimation is deteriorated by pilot contamination and the effects of pilot contamination become more severe due to hardware impairments. In this paper, we propose a joint pilot design and channel estimation based on deep residual learning in order to mitigate the effects of pilot contamination under the consideration of hardware impairments. We first investigate a conventional linear minimum mean square error (LMMSE) based channel estimator to suppress the interference caused by pilot contamination. After that, a deep learning based pilot design is proposed to minimize the mean square error (MSE) of LMMSE channel estimation, which is utilized to the joint pilot design and channel estimator for transfer learning approach. For the channel estimator, we use a deep residual learning which extracts the features of interference caused by pilot contamination and eliminates them to estimate the channel information. Simulation results demonstrate that the proposed joint pilot design and channel estimation method can effectively reduce the effect of pilot contamination as well as outperforms the conventional approach in multi-cell massive MIMO scenarios. Moreover, the joint pilot design and channel estimation method using transfer learning further enhances the estimation performance when the prior knowledge of pilot contamination cannot be exploited.

Precoder Design for Physical-Layer Security and Authentication in Massive MIMO UAV Communications

Supporting reliable and seamless wireless connectivity for unmanned aerial vehicles (UAVs) has recently become a critical requirement to enable various different use cases of UAVs. Due to their widespread deployment footprint, cellular networks can support beyond visual line of sight (BVLOS) communications for UAVs. In this paper, we consider cellular connected UAVs (C-UAVs) that are served by massive multiple-input-multiple-output (MIMO) links to extend coverage range, while also improving physical layer security and authentication. We consider Rician channel and propose a novel linear precoder design for transmitting data and artificial noise (AN). We derive the closed-form expression of the ergodic secrecy rate of C-UAVs for both conventional and proposed precoder designs. In addition, we obtain the optimal power splitting factor that divides the power between data and AN by asymptotic analysis. Then, we apply the proposed precoder design in the fingerprint embedding authentication framework, where the goal is to minimize the probability of detection of the authentication tag at an eavesdropper. In simulation results, we show the superiority of the proposed precoder in both secrecy rate and the authentication probability considering moderate and large number of antenna massive MIMO scenarios.

Performance Analysis of Channel Estimation for Massive MIMO Communication Using DL-Based Fully Connected Neural Network (DL-FCNN) Architecture

The latest research for applying deep learning in wireless communications gives several opportunities to reduce complex signal processing. The channel estimation is important to study the nature of the varying channel and to calculate channel state information (CSI) value which is utilized at the receiver to nullify the interference which occurs during multipath transmission. In the current article, considering the massive Multiple Input Multiple Output (MIMO) channel model, a DL approach is developed with a fully connected neural network (NN) architecture which is used to estimate the channel with minimum error. The proposed DL architecture uses an openly available channel dataset. Further, using generated pilot symbols of lengths 2 and 4, the performance of DL-based Fully connected NN (DL-FCNN) is analyzed to estimate the channel in uplink massive MIMO communication. The obtained results demonstrate that the channel estimation performance was calculated in terms of normalized mean square error((NMSE) for different values of SNR added at receiver base station (BS) to the signals over the range of BS antennas. Also, the channel estimation error over a large number of BS antennas for massive MIMO scenarios is observed, and it is observed that the NMSE reduces with a greater number of antennas. Hence, it can be inferred that the DL models will be the future for most physical layer signal processing techniques such as channel estimation, modulation detection, etc. within massive MIMO networks.

A 3D Cluster-Based Channel Model for 5G and Beyond Vehicle-to-Vehicle Massive MIMO Channels

In this paper, we propose a three-dimensional (3D) cluster-based model for the fifth generation (5G)/beyond 5G (B5G) vehicle-to-vehicle (V2V) massive multiple-input multiple-output (MIMO) wideband channels. It is the first cluster-based irregular shaped geometry-based stochastic model (IS-GBSM) to distinguish the dynamic clusters and static clusters in vehicular massive MIMO communication scenarios. This model not only considers the high time-variance, the time non-stationarity, and the vehicular traffic density (VTD) of V2V channels, but also models the massive MIMO channel characteristics, such as spherical wavefronts by 3D vector calculation and space non-stationarity. Meanwhile, this model for the first time integrates the VTD into birth-death process to model the channel characteristics of V2V and massive MIMO jointly and deeply, where a novel VTD-combined time-array cluster evolution algorithm for 5G/B5G V2V massive MIMO channel model is developed. Based on the proposed model, we derive some expressions of channel statistical properties, including time-space-frequency correlation function (STF-CF) and Doppler power spectral density (DPSD). The influence of several parameters, e.g., VTDs, vehicle moving directions, and antenna spacings, on the channel characteristics are sufficiently explored, which can provide assistance for the design of vehicular massive MIMO communication systems. Finally, the utility of the proposed model is verified by the close agreement between simulation results and measurement data.

A Low-Complexity Double EP-Based Detector for Iterative Detection and Decoding in MIMO

We propose a new iterative detection and decoding (IDD) algorithm for multiple-input multiple-output (MIMO) based on expectation propagation (EP) with application to massive MIMO scenarios. Two main results are presented. We first introduce EP to iteratively improve the Gaussian approximations of both the estimation of the posterior by the MIMO detector and the soft output of the channel decoder. With this novel approach, denoted by double-EP (DEP), the convergence is very much improved with a computational complexity just two times the one of the linear minimum mean square error (LMMSE) based IDD, as illustrated by the included experiments. Besides, as in the LMMSE MIMO detector, when the number of antennas increases, the computational cost of the matrix inversion operation required by the DEP becomes unaffordable. In this work we also develop approaches of DEP where the mean and the covariance matrix of the posterior are approximated by using the Gauss-Seidel and Neumann series methods, respectively. This low-complexity DEP detector has quadratic complexity in the number of antennas, as the low-complexity LMMSE techniques. Experimental results show that the new low-complexity DEP achieves the performance of the DEP as the ratio between the number of transmitting and receiving antennas decreases.

A Framework for Radio Resource Allocation and SDMA Grouping in Massive MIMO Systems

This work proposes a framework for multiuser massive Multiple Input Multiple Output (MIMO) systems which is composed of three parts – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">clustering</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">grouping</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scheduling</i> – and aims at maximizing the total system data rate considering Quality of Service (QoS) constraints. We firstly use a clustering algorithm to create clusters of spatially correlated Mobile Stations (MSs). Secondly, in the grouping part, we select a set of Space-Division Multiple Access (SDMA) groups from each cluster. These groups are used as candidate groups to receive Scheduling Unit (SU) in the scheduling part. In order to compose a group, we employ a metric that takes into account the trade-off between the spatial channel correlation and channel gain of MSs. In this context, it is proposed a suboptimal solution to avoid the high complexity required by the optimal solution. Thirdly and finally, we use the candidate SDMA groups from the grouping part to solve the data rate maximization problem considering QoS requirements. The scheduling part can be solved by our proposed optimal solution based on Branch and Bound (BB). However, since it has high computational complexity, we propose a suboptimal scheduling algorithm that presents a reduced complexity. In the simulation results, we evaluate the performance of both optimal and suboptimal solutions, as well as an adaptation of the Joint Satisfaction Maximization (JSM) scheduler to a massive MIMO scenario. Although the suboptimal solution presents a performance loss compared to the optimal one, it is more suitable for practical settings as it is able to obtain a good performance-complexity trade-off. Furthermore, we show that the choice of a suitable trade-off between the spatial channel correlation and channel gain improves the system performance. Finally, for a low number of available SDMA groups, the suboptimal solution presents near optimal outage and a throughput loss of only 10% in comparison to the high-complexity optimal solution while it outperforms the JSM solution in terms of outage and system throughput.

Distributed Deep Convolutional Compression for Massive MIMO CSI Feedback

Massive multiple-input multiple-output (MIMO) systems require downlink channel state information (CSI) at the base station (BS) to achieve spatial diversity and multiplexing gains. In a frequency division duplex (FDD) multiuser massive MIMO network, each user needs to compress and feedback its downlink CSI to the BS. The CSI overhead scales with the number of antennas, users and subcarriers, and becomes a major bottleneck for the overall spectral efficiency. In this paper, we propose a deep learning (DL)-based CSI compression scheme, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DeepCMC</i> , composed of convolutional layers followed by quantization and entropy coding blocks. In comparison with previous DL-based CSI reduction structures, DeepCMC proposes a novel fully-convolutional neural network (NN) architecture, with residual layers at the decoder, and incorporates quantization and entropy coding blocks into its design. DeepCMC is trained to minimize a weighted rate-distortion cost, which enables a trade-off between the CSI quality and its feedback overhead. Simulation results demonstrate that DeepCMC outperforms the state of the art CSI compression schemes in terms of the reconstruction quality of CSI for the same compression rate. We also propose a distributed version of DeepCMC for a multi-user MIMO scenario to encode and reconstruct the CSI from multiple users in a distributed manner. Distributed DeepCMC not only utilizes the inherent CSI structures of a single MIMO user for compression, but also benefits from the correlations among the channel matrices of nearby users to further improve the performance in comparison with DeepCMC. We also propose a reduced-complexity training method for distributed DeepCMC, allowing to scale it to multiple users, and suggest a cluster-based distributed DeepCMC approach for practical implementation.

Channel correlation relied grouped spatial modulation for massive MIMO systems

Massive multiple-input multiple-output (MIMO) systems with hundreds of correlated antennas at base station are capable of offering abundant spatial resources. When spatial-domain modulation is applied to these systems, the spatial modulation (SM) using only one radiofrequency chain benefits practical implementation, but suffers from significantly reduced multiplexing gain offered by the massive number of antennas. By contrast, the generalised SM (GSM) allows to simultaneously activate multiple transmit antennas, which improves spatial multiplexing gain, but degrades the achievable error performance, as its design pays no attention to the antenna correlation. The authors propose an antenna grouped SM (GrSM) scheme, which is capable of circumventing the shortcomings of both the SM and GSM schemes suffered in massive MIMO scenarios. In the proposed GrSM scheme, transmit antennas are partitioned into multiple groups, where the relatively strongly correlated antennas within individual groups are used to implement component SM schemes, while the relatively weakly correlated antennas in different groups are beneficial to obtain multiplexing gain. In order to further improve the spectral efficiency, adaptive modulation is integrated with GrSM to form the adaptive GrSM (AGrSM). The achievable error and spectral efficiency performance of GrSM and AGrSM systems are investigated based on both mathematical analysis and Monte-Carlo simulations, which are also compared with that of the conventional SM and GSM schemes, when massive MIMO communication scenarios are considered. Their studies and performance results show that GrSM is a promising transmit scheme for massive MIMO, which can outperform both the SM and GSM schemes.

Interference Exploitation 1-Bit Massive MIMO Precoding: A Partial Branch-and-Bound Solution With Near-Optimal Performance

In this paper, we focus on 1-bit precoding approaches for downlink massive multiple-input multiple-output (MIMO) systems, where we exploit the concept of constructive interference (CI). For both PSK and QAM signaling, we firstly formulate the optimization problem that maximizes the CI effect subject to the requirement of the 1-bit transmit signals. We then mathematically prove that, when employing the CI formulation and relaxing the 1-bit constraint, the majority of the transmit signals already satisfy the 1-bit formulation. Building upon this important observation, we propose a 1-bit precoding approach that further improves the performance of the conventional 1-bit CI precoding via a partial branch-and-bound (P-BB) process, where the BB procedure is performed only for the entries that do not comply with the 1-bit requirement. This operation allows a significant complexity reduction compared to the fully-BB (F-BB) process, and enables the BB framework to be applicable to the complex massive MIMO scenarios. We further develop an alternative 1-bit scheme through an `Ordered Partial Sequential Update' (OPSU) process that allows an additional complexity reduction. Numerical results show that both proposed 1-bit precoding methods exhibit a significant signal-to-noise ratio (SNR) gain for the error rate performance, especially for higher-order modulations.

Capacity Bounds for Dense Massive MIMO in a Line-of-Sight Propagation Environment.

The use of large-scale antenna arrays grants considerable benefits in energy and spectral efficiency to wireless systems due to spatial resolution and array gain techniques. By assuming a dominant line-of-sight environment in a massive multiple-input multiple-output scenario, we derive analytical expressions for the sum-capacity. Then, we show that convenient simplifications on the sum-capacity expressions are possible when working at low and high signal-to-noise ratio regimes. Furthermore, in the case of low and high signal-to-noise ratio regimes, it is demonstrated that the Gamma probability density function can approximate the probability density function of the instantaneous channel sum-capacity as the number of served devices and base station antennas grows, respectively. A second important demonstration presented in this work is that a Gamma probability density function can also be used to approximate the probability density function of the summation of the channel’s singular values as the number of devices increases. Finally, it is important to highlight that the presented framework is useful for a massive number of Internet of Things devices as we show that the transmit power of each device can be made inversely proportional to the number of base station antennas.

Quantum version of MMSE-based massive MIMO uplink detection

Regarding the massive multiple-input multiple-output (MIMO) uplink, the quantum version detection based on the minimum mean square error criterion is developed for complexity consideration. Specifically, a comprehensive quantum algorithm for encoding the estimated signal into a quantum state is presented, synthesizing the subroutines of state preparation, Hamiltonian simulation, phase estimation and so on. Indispensable assumptions along with the quantum algorithm are summarized and assumption testing in a MIMO scenario is conducted. Both theoretical analyses from the mathematical point of view and simulated realizations in massive MIMO systems basically confirm the applicability of the quantum algorithm. With desired precision, the quantum algorithm achieves almost quadratic speedup over all classical counterparts. Whereas, with weaker precision accompanied by undetermined performance loss, the quantum algorithm eventually breaks through polynomial-time detection complexity and achieves exponential speedup. Future work will be directed toward the error dependence improvement, classical form outputs and experimental applications in quantum communication systems.