Inversion Calculations Research Articles

Study on Large-Scale Urban Water Distribution Network Computation Method Based on a GPU Framework

Large-scale urban water distribution network simulation plays a critical role in the construction, monitoring, and maintenance of urban water distribution systems. However, during the simulation process, matrix inversion calculations generate a large amount of computational data and consume significant amounts of time, posing challenges for practical applications. To address this issue, this paper proposes a parallel gradient calculation algorithm based on GPU hardware and the CUDA Toolkit library and compares it with the EPANET model and a model based on CPU hardware and the Armadillo library. The results show that the GPU-based model not only achieves a precision level very close to the EPANET model, reaching 99% accuracy, but also significantly outperforms the CPU-based model. Furthermore, during the simulation, the GPU architecture is able to efficiently handle large-scale data and achieve faster convergence, significantly reducing the overall simulation time. Particularly in handling larger-scale water distribution networks, the GPU architecture can improve computational efficiency by up to 13 times. Further analysis reveals that different GPU models exhibit significant differences in computational efficiency, with memory capacity being a key factor affecting performance. GPU devices with larger memory capacity demonstrate higher computational efficiency when processing large-scale water distribution networks. This study demonstrates the advantages of GPU acceleration technology in the simulation of large-scale urban water distribution networks and provides important theoretical and technical support for practical applications in this field. By carefully selecting and configuring GPU devices, the computational efficiency of large-scale water distribution networks can be significantly improved, providing more efficient solutions for future urban water resource management and planning.

Particle size distribution of two-phase medium measured by ultrasonic wave

Abstract Measurement of ultrasonic attenuation spectra of particle suspensions using a variable acoustic range approach is introduced. This study is based on the improved ECAH model. In this paper, an experimental test was performed on an emulsion with a concentration of 15%. Then, the NNLS algorithm is used for inversion calculations. Compared with laser particle size meter results, the measurement results are in good agreement.

Measurements of the frequency dependence of geo-alpha in clayey silt at low frequencies

Transmission loss (TL) measurements in the Santa Barbara Channel, together with co-located chirp measurements, show that geo-alpha (dB/l) in clayey silt increases approximately linearly with frequency (f) at f < 3 kHz. TL was measured between a fixed source and fixed vertical array at 3.7 km at 0.3 < f < 5 kHz. Geo-alpha was inverted from the TL data at 0.3, 1.1 and 1.9 kHz. Inversion calculations at 1.1 and 1.9 kHz considered both geo-alpha and bio-alpha due to layer of anchovies at 12 m. Inversion calculations at 0.3 kHz considered only the effect of geo-alpha; the effect bio-alpha on TL was small. Geo-alpha was also inferred from chirp sonar measurements at 3.2 and 6.2 kHz at the ends and middle of the TL track. Chirp sonar showed that the bottom consisted of a layer of unconsolidated sediments overlying a layer of sand. Co-located cores revealed that the unconsolidated layer consisted of clayey silt. Bio-alpha data were compared to Biot and VGS theories and the theory of attenuation in suspended sediments (Pierce et al., 2017). The measured frequency dependence is consistent with Pierce et al.’s theory. This research was supported by The Office of Naval Research Ocean Acoustics Program.

Modified Model of Polarized Bidirectional Reflectance Distribution Function Used for Light Detection and Ranging (LiDAR)

In order to analyze the performance of a light detection and ranging system based on polarization modulation, it is necessary to theoretically analyze and model the polarization scattering characteristics of common target materials. In this paper, the shortcomings of the classical Hyde pBRDF (polarization bidirectional reflectance distribution function) model are analyzed. Based on the research results of many researchers in recent years, a new six-parameter pBRDF model is proposed. To verify the accuracy of the proposed model, this paper builds a measurement system for the polarization scattering characteristics of the target surface in the laser active imaging scene, and the polarization scattering characteristics of two common materials, namely a white paint coating and an aluminum plate, are measured. Based on the measurement results of the DOP (degree of polarization) of the scattered light of the target material and the BBO-FA (biogeography-based optimization-Firefly algorithm) algorithm, we performed inversion calculations on the key parameters of the target material. Using the parameters of the target material obtained via inversion, we use the model to simulate the Stokes vectors of the target and compare the simulated values of Stokes vectors with the measured values to verify the accuracy of the model. The verification results show that the simulation results of Stokes vectors are in good agreement with the measurement results for these two materials, and the introduction of various improvements to the model can effectively improve the accuracy of the model, which provides a tool for studying the performance parameters of a laser three-dimensional imaging system based on polarization modulation.

Inverse Modeling of the Initial Stage of the 1991 Pinatubo Volcanic Cloud Accounting for Radiative Feedback of Volcanic Ash

AbstractThe way volcanic clouds evolve is very sensitive to the initial spatial 3D distributions of volcanic materials, which are often unknown. In this study, we conducted inverse modeling of the Mt. Pinatubo cloud using total ozone mapping spectrometer 2D mapping of Aerosol Index and SO2 loading during the first three post‐eruption days to estimate the time‐dependent emissions profiles and initial 3D spatial distributions of volcanic ash and SO2. We account for aerosol radiative feedback and dynamic lofting of volcanic ash in the inversion calculations for the first time. This resulted in a lower ash injection height (by 1.5 km for ash) than without ash radiative feedback. The Pinatubo eruption ejected ≈77% of fine ash at 12–23 km, ≈65% of SO2 at 18–25 km. In contrast with previous studies, which suggested that all volcanic materials were emitted above the tropopause, a significant fraction of SO2 (5.1 of 15.5 Mt) and fine ash (37.2 of 66.5 Mt) were ejected in the troposphere, where SO2 quickly oxidized into sulfate aerosol that is short‐lived in the troposphere. This explains the early presence of sulfate aerosols in the plume and why the models can reproduce the observed volcanic aerosols' optical depth (AOD), assuming lower‐than‐observed SO2 emission in the stratosphere. Despite the quicker than in observations build‐up of sulfate AOD, in a month after the eruption, the evolution of the Pinatubo AOD simulated using the obtained ash and SO2 initial distributions converges with the available stratospheric aerosol and gas experiment observations.

Atmospheric Density Inversion Based on Swarm-C Satellite Accelerometer

We used the Swarm-C accelerometer data to invert the orbital atmospheric density in this study. First, the Swarm-C satellite mission data were obtained from the ESA’s public data platform, and preliminary data error correction was performed. This paper refers to the calibration method of GRACE-A satellite accelerometer data. It adds linear temperature correction on the original basis. Moreover, this study’s accelerometer data correction results were compared with the data correction results published by the ESA. In order to explore the influence of light radiation on the accelerometer, we established a geometric model of Swarm-C to simulate the physical shape of the satellite surface. The light radiation pressure model and the shadow area judgment model were established, the change in the light radiation acceleration during the transition process of the satellite from the umbra area to the penumbra area and then to the shadowless area was studied, and the state transition during the transition process was analyzed. Finally, the atmospheric drag coefficient was calculated based on the Sentman model. Atmospheric density inversion calculations were performed using the above data. We show the spatial distribution of atmospheric density at a fixed latitude, testing our results during geomagnetic storms. We compared the density results with existing research data, demonstrating the effectiveness of our approach.

Light energy distribution of submicron charged particles based on the scattering-enhancing effect

Magnetic microspheres, charged soot and other charged sub-micron particles are widely used, and the accurate measurement of their particle size is crucial to biomedical, environmental monitoring and other fields. During light scattering measurements, the light energy distribution projected onto each ring surface of the photodetector is the core data for particle size inversion calculations. When the measured particle is charged, the light energy distribution will be different from its neutral state due to the scattering-enhancing effect of surface charges. Therefore, it is necessary to confirm the extent of the scattering-enhancing effect on the light energy distribution by numerical simulation, before actual measurement. In this paper, calculation models of scattered light energy distribution are established for charged single particle, monodisperse particle system and polydisperse particle system respectively. Considering the difference between the complex refractive indices of charged particles, the forward scattering of silica and polystyrene with different monodisperse degrees are taken as an example to analyze the light energy distribution. The results show that the scattering-enhancing effect of surface charges can affect the light energy distribution of submicron particles, and the smaller the median diameter of the particle system and the lower the monodisperse degree, the more significant the effect is. At a median diameter of 0.1 μm, the light energy of charged particles with different monodisperse degrees increased by an average of about 3.5 times, near the scattering angle of 45° This research realizes the forward deduction of the light energy distribution for charged particles, and provides the necessary theoretical support for the visible light measurement of charged submicron and nanoparticles.

Estimation of Surface Soil Moisture by a Multi‐Elevation UAV‐Based Ground Penetrating Radar

AbstractThe measurement of soil moisture is important for a wide range of applications, including ecosystem conservation and agricultural management. However, most traditional measurement methods, for example, time‐domain reflectometry (TDR), are unsuitable for mapping field scale variability. In this study, we propose a method that uses an unmanned aerial vehicle (UAV) to support a ground penetrating radar (GPR) system for spatial scanning investigation at different elevations above ground level. This method measures the surface reflectivity to estimate the soil moisture, exploiting the linear relationship between the ratio of the reflected and the direct wave amplitudes along with the reciprocal of GPR antenna height. This relationship is deduced in this study based on the point source assumptions of a transmitter antenna and ground reflections, which is confirmed by numerical simulation results using the gprMax software. Unlike previous air‐launched GPR methods, the UAV‐GPR method presented here removes the limitations of a steady transmitter power and a fixed GPR survey height and the need for calibration of antenna transfer functions and geophysical inversion calculations, and thus is simpler and more convenient for field applications. We test the method at field sites within the riparian zone and a river‐island grassland adjacent to the Yangtze River. The results from the field study illustrate comparable measured soil moisture to those obtained invasively using TDR. The root mean square error of surface reflectivity and soil moisture values between UAV‐GPR with eight antenna height investigations and TDR in the grassland are 0.03 and 0.05 cm3/cm3, respectively.

Research on Small-Loop Transient Electromagnetic Method Forward and Nonlinear Optimization Inversion Method

The small-loop transient electromagnetic (TEM) method has great application prospects in shallow surface geophysical exploration. However, the theoretical research on the forward and inversion of this method is obviously lagging behind, which seriously affects the application effect in practical engineering. For the oscillation problem of the small-loop TEM response calculated by using the forward theory of the conventional TEM methods, the dipole integral superposition method was proposed to solve the problem in this article. The transmitter source is divided into an infinite number of electric dipoles, and the calculation expressions of the electromagnetic field components satisfied by the electric dipoles are deduced, and the forward calculation problem of the layered model of the small-loop TEM method is solved. For the small-loop TEM method inversion problem, the simulated annealing (SA) method was presented for inversion calculation in this article. First, the influence of the selection of the initial temperature on the inversion result of the SA algorithm was analyzed. Then, we demonstrate the algorithm’s flexibility by choosing different initial models and search ranges and concluded that the different initial models and search ranges do not affect the inversion results of the SA algorithm. Next, the typical layered models were established, and the SA algorithm was used to carry out calculations. The research results show that the SA algorithm is an excellent global optimization algorithm, which can easily jump out of the local minima and converge to the global minima. Finally, we processed the measured data through inversion calculations and compared it with the results of the other three methods to verify the effectiveness and accuracy of the SA algorithm for small-loop TEM data processing. The research content solves the theoretical problem of the small-loop TEM method forward and inversion, promotes the development of the small-loop TEM method technology, and objectively and effectively solves practical engineering application problems.

Inverse Modeling to Constrain Composition of CO2-Rich Parental Melt of Kimberlite: Model Development and Application to the Majuagaa Dyke, Southern West Greenland.

Abstract A model is developed to test the hypothesis that kimberlites can form by low-degree melting of asthenospheric mantle followed by entrainment and assimilation of lithospheric mantle. The developed model uses inversion calculations based upon rare earth and compatible trace elements. For kimberlites (s.s.), an equation describing mass balance between a melt of unknown composition and a contaminant end-member of xenocrystic/assimilated material from the lithospheric mantle is inverted. This allows calculation of the mass fraction of xenocrystic minerals from the lithospheric mantle (olivine, orthopyroxene, clinopyroxene, garnet, ilmenite) entrained in the kimberlitic magma, as well as the source mineralogy and melt degree in the source region. The composition of the parental melt prior to interaction with the lithosphere is not assumed a priori but is calculated by the model. The CO2, H2O, K2O and P2O5 contents of the source are estimated assuming batch melting and the inversion models. The range and coupling of the model parameters are found using a non-linear most-squares inversion procedure, and the model space is visualised using a Self-Organising Map approach. Our earlier work supporting assimilation of xenocrystic opx is, however, not a precondition but provides a post-processing constraint, as well as the selection of a more likely set of solutions from the Self-Organising Map. The calculation is applied to a data set from the Majuagaa kimberlite dyke (southern West Greenland) including added whole rock analyses for CO2 and H2O. Major variations in whole rock compositions are related to flow differentiation of olivine macrocrysts. The textures of opx, cpx, gt and ilm megacrysts show evidence for reaction with the transporting melt and physical erosion in the kimberlitic mush. Using the bulk rocks in our inversion scheme results in a silico-carbonatite parental melt with major element concentrations consistent with experimental melts. The ol, opx, and cpx mass fractions in the source are not well-resolved by this calculation, but the proportion of gt in the source is comparatively well defined at 15–22 wt% and cpx is constrained to less than 14 wt%. The source assemblage required is 36–80 wt% ol, 2–49 wt% opx, 0–6 wt% cpx, and 15–19 wt% gt. This suggests a peridotitic rather than an eclogitic source. The inversion model gives an overall mass fraction of xenocrystic material in the Majuagaa kimberlite magma of 41–51 wt% The mass fractions of the xenocryst phases are as follows: 71–85 wt% ol, 0–13 wt% opx, 5 ± 1 wt% gt, and 10–14 wt% ilm. There is less than 3 wt% cpx in the xenocrystic and assimilated assemblage. These results agree with petrographic observations. Processing the model results using the Self-Organising Map clearly displays the extent and coupling within the statistically acceptable region of the model space and leads us to a preferred model of 49 wt% xenocrysts with a xenocryst assemblage of 71–76 wt% ol, 8–13 wt% opx, 4 wt% gt and 12 wt% ilm. A source with a REE pattern similar to that of primitive mantle is sufficient to form the parental melt and consistent with generation of the initial kimberlite melt in the convecting mantle. Calculated CO2 and H2O concentrations in the source of the Majuagaa kimberlite of 230–860 μg/g and 223–741 μg/g, respectively, are within the range of independent convecting mantle estimates. This is equivalent to <0.17 wt% magnesite and the H2O budget of the mantle source can be accommodated via storage in nominally anhydrous silicate phases. When applied to Majuagaa kimberlite, the inversions are consistent with a conceptually simple model of kimberlite formation: (1) low degree melting in carbonated asthenospheric peridotite, (2) melt extraction and concentration, and (3) entrainment and reaction with lithospheric mantle material.

Joint design of ordered QR precoding and SIC detection for MIMO VLC systems.

Ordered successive interference cancellation (OSIC) detection has been investigated to mitigate the high spatial correlation for multiple-input multiple-output (MIMO) visible light communication (VLC) systems. However, existing OSIC schemes have to perform reordering and matrix inversion for each detected symbol, which may lead to high complexity when a large number of symbols are transmitted. In this work, a joint design of ordered QR decomposition precoding and SIC detection (OQR-SIC) is proposed for MIMO VLC systems. This work jointly investigates OQR precoding and SIC detection to reduce the detection complexity while alleviating spatial correlation issue for MIMO VLC systems. In OQR-SIC, with the upper triangular matrix obtained by QR decomposition, the SIC detector can detect the symbol sequentially without reordering and matrix inversion calculations. To improve the system data rate, we further optimize the ordering of the columns of the channel matrix before QR decomposition and the power allocation of transmitted signals under the constraints of dimming control, total electrical power and reliable SIC detection. Simulation results demonstrate that the proposed OQR-SIC achieves 2 dB and 9.8 dB signal-to-noise ratio gains compared to conventional QR-SIC in 4 × 4 and 9 × 9 MIMO VLC systems, respectively, when the bit error rate is 10-3.

Frequency-Bessel Transform Based Microtremor Survey Method and Its Engineering Application.

The development and utilization of urban underground space depend heavily on an understanding of urban geological conditions. The microtremor survey method is essential in urban geological surveys due to its quickness, convenience, non-destructiveness, and interference resistance. Since only the fundamental dispersion curves of Rayleigh waves can be obtained by utilizing the spatial autocorrelation method, the inversion results have multiple solutions. To improve the accuracy of the microtremor survey, this study employed the frequency-Bessel transform to extract the fundamental and higher modes of dispersion information of Rayleigh waves from the microtremor data array and verified the effectiveness of this method by synthesizing theoretical microtremor signals. Additionally, taking into account the order identification challenges brought on by mode jumps or missing modes in the dispersion curve, this study processed a multi-mode dispersion curve based on the newly proposed inversion objective function coupled with a genetic algorithm to obtain a shallow surface S-wave velocity structure. Compared to the traditional inversion objective function, the new function presented in this study could address mode misidentification more effectively and improved the accuracy of inversion calculations. Finally, the applicability and dependability of the frequency-Bessel-transform-based microtremor survey method were evaluated in a practical engineering case.

N2v: A density‐to‐potential inversion suite. A sandbox for creating, testing, and benchmarking density functional theory inversion methods

AbstractFrom the most fundamental to the most practical side of density functional theory (DFT), Kohn–Sham inversions (iKS) can contribute to the development of functional approximations and shed light on their performance and limitations. On the one hand, iKS allows for the direct exploration of the Hohenberg–Kohn and Runge–Gross density‐to‐potential mappings that provide the foundations for DFT and time‐dependent DFT. On the other hand, iKS can guide the analysis and development of approximate exchange–correlation and noninteracting kinetic energy functionals, and diagnose their errors. iKS can also play a similar role in the development of nonadditive functionals for modern density‐based embedding methods. Various strategies to perform iKS calculations have been explored since the inception of DFT. We introduce n2v, a density‐to‐potential inversion Python module that is capable of performing the most useful and state‐of‐the‐art inversion calculations. Currently based on NumPy, n2v was developed to be easy to learn by newcomers to the field. Its structure allows for other inversion methods to be easily added. The code offers a general interface that gives the freedom to use different software packages in the computational molecular sciences (CMS) community, and the current release supports the Psi4 and PySCF packages. Six inversion methods have been implemented into n2v and are reviewed here along with detailed numerical illustrations on molecules with numbers of electrons ranging from ~10 to ~100.This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Density Functional Theory

Investigation of lineaments in the mid-Black arc region using Bouguer gravity data

The gravity data used in this study were taken from the Earth Gravity Model (EGM08) to investigate the crustal structure in the mid-Black arc region. In this study, geological structure boundaries that offer differences in density were tried to determine in the mid-Black arc region. For this purpose, the possible geological structure limits at the basement levels were especially focused on. For this reason, horizontal gradient and tilt angle techniques were practiced to find possible geological structure limits using first vertical derivative data of the regional gravity data of the region. The soft-hard sediment, basement, Conrad and Moho interfaces have been determined using the radial mean amplitude spectrum of Bouguer data of study region. The topographies of these interfaces were also presented utilizing the Parker-Oldenburg algorithm. Depth values found by inversion calculations for soft-hard sediment, basement, Conrad and Moho interface topographies are changed as 0.7-3.5, 2.1-7.4, 9.1-14.2, and 35.1- 42.5 km, respectively. The linearities determined in the study were matched against to substantial faults of region. It has been observed that there is a qualitative relationship between the faults, ore deposit and earthquake epicenters in the region. The results of this practice were based on studies such as exploring the ore deposits and investigating the risks of earthquakes in the future.

An Improved New Convolutional Neural Network Method for Inverting the Pore Pressure in Oil Reservoir by Surface Vertical Deformation

Abstract Average pore pressure in oil formation is an important parameter to measure energy in the formation and the capacity of injection–production. In past studies, average pore pressure mainly depends on pressure build-up test results, which have a high cost and need a long testing time, so it is not conducive to utilize. In this paper, the vertical deformation of the Earth’s surface was used to calculate changes in reservoir pore pressure. We set up the marker stake for measuring ground displacement and measured the vertical deformation at the in situ position. Furthermore, we provided an improved new convolutional neural network (CNN), which adopted image-to-image mode, removed pooling layers and full connection layers, and used a new loss function considering the boundary influence coefficient matrix. Then, the machine learning method was used to invert surface vertical deformation to change pore pressure in the oil reservoir. The method was tested in the block of the Sazhong X development zone, in the Daqing Oilfield of China. The average pore-pressure change values of 20 grids whose area was 900×900 m each were determined by the inversion of the corresponding surface vertical deformation at 27 marker stakes. The pore pressure change accuracy reached 82.34%. This study provides a new method for calculating average pore pressure in terms of an oil block. At the same time, it also provides a new technical method for inversion calculations.

A Low-Complexity MAP–SIC Detector for Massive MIMO Systems

In this paper, we propose a low-complexity maximum a posteriori detector with successive interference cancellation (MAP–SIC) for massive multiple-input multiple-output (MIMO) systems. The basic idea of the proposed MAP–SIC algorithm is to detect and cancel the signal of each user iteratively in order of approximate a posteriori log-likelihood-ratios (LLRs). To obtain the approximate a posteriori LLRs, the proposed method begins with the output of a matched-filter and estimates the mean and variance of interference-plus-noise term for each undetected symbol using the idea of Gaussian approximation. In addition, we also propose a simple strategy based on a posteriori log-likelihood-ratios (LLRs) to update the mean and variance in the iterative process of proposed algorithm. Since there is no need for a matrix inversion and exponential calculations, the complexity of the proposed detector is reduced significantly compared to that of minimum mean squared error (MMSE) and MMSE–SIC. Simulation results substantiate the performance of the proposed detector in the massive MIMO system.

3D inversion of audio-magnetotelluric data for mineral exploration: A case study of Layikeleke buried porphyry copper deposit, Xinjiang, China

Layikeleke copper deposit is a large-scale porphyry copper polymetallic buried deposit, which has been discovered recently in the eastern Junggar area of Xinjiang. Mineralization occurred in the Late Silurian and Early Devonian with the copper body mainly confined to tonalite. To find new ore bodies, it is necessary to map the 3D spatial distribution of the tonalite. For this reason, we deployed audio-magnetotelluric (AMT) sounding in the research area, collected 26 profiles and 1198 measuring points, carried out 3D inversion calculations of off-diagonal elements in the impedance tensor data using the nonlinear conjugate gradient method, and obtained a 3D electrical structure model. The electrical structure reveals two groups of NW-SE trending middle and middle low resistivity anomaly zones, which intersect the high resistivity bedrock area in the northwest of the study area. Based on the electrical data, it can be inferred that the medium low resistance tonalite in the northern part of the study area is the host rock of the porphyry copper polymetallic deposit, which has been verified by borehole data. The results of 3D AMT inversion depict the spatial distribution and depth variation characteristics of the tonalite electrical structure model, providing a basis for further prospecting and exploration. Therefore, this method of identifying lithology by 3D inversion can provide an important basis for mineral exploration and mining of buried rock masses, and is an effective prospecting method.

Evaluating the efficiency of using different variants of background models for inversion calculations

The use of the method of seismic data acoustic inversion, in the presence of thick gas cap, can lead to difficulties when building background models of elastic parameters. In this regard, in the conditions of acoustically contrast thin environments within the perimeter of the Russkoye oil and gas condensate field, in addition to the standard version based on the well data, the authors considered a number of modified techniques ("block", "flat", and background models). The use of these background models provided the best results and made it possible to significantly improve the quality of predicting rock properties; based on the drilling results, effective penetration was ensured at 66 %, which was 102 % of the plan. Also, based on the inversion results, it became possible to predict reservoir properties using the Bayesian lithotype classification method.

Three-Dimensional Magnetic Inversion Based on an Adaptive Quadtree Data Compression

Three-dimensional magnetic inversion allows the distribution of magnetic parameters to be obtained, and it is an important tool for geological exploration and interpretation. However, because of the redundancy of the data obtained from large-scale investigations or high-density sampling, it is very computationally intensive to use these data for iterative inversion calculations. In this paper, we propose a method for compressing magnetic data by using an adaptive quadtree decomposition method, which divides the two-dimensional data region into four quadrants and progressively subdivides them by recursion until the data in each quadrant meets the regional consistency criterion. The method allows for dense sampling at the abnormal boundaries with large amplitude changes and sparse sampling at regions with small amplitude changes, and achieves the best approximation to the original data with the least amount of data, thus retaining more anomalous information while achieving the purpose of data compression. In addition, assigning values to the data in the quadrants using the averaging method is essentially equivalent to average filtering, which reduces the noise of the magnetic data. Testing the synthetic model and applying the method to mineral exploration a prove that it can effectively compress the magnetic data and greatly improve the computational efficiency.

Low-complexity and fast-convergence linear precoding based on modified SOR for massive MIMO systems

Linear zero forcing (ZF) precoding can obtain near-optimal performance as the number of base station (BS) antennas increases, but involve complex matrix inversion calculations whose computational complexity is cubic with respect to the number of user equips (UEs) in massive multiple-input multiple-output (MIMO) systems. In this paper, a low-complexity modified successive over-relaxation-based ZF (MSOR-ZF) linear precoding is proposed, in which complicated matrix inversion is directly avoided through the use of MSOR iteration. Moreover, to further increase the convergence rate, the proposed MSOR-ZF precoding exploits the diagonal dominant property of the matrix instead of the original zero vector solution to achieve a satisfactory performance with a reduced iteration number. The proposed precoding is superior in convergence rate and reduces the computational complexity by approximately one order of magnitude, which is indicated by theoretical analysis. Simulation results demonstrate that the proposed precoding can achieve better achievable sum-rate and bit-error-ratio (BER) performance than some existing iterative-based precoding schemes with lower complexity.