Curve Fitting Technique Research Articles

Robust Signal Denoising Techniques for Highly Accurate and Spatial Resolution Preserved Brillouin Optical Time Domain Analysis Sensors

The diminution of measurement uncertainty to an acceptable level and the preservation of experimental spatial resolution are highly desirable in many real-world applications of Brillouin optical time domain analysis (BOTDA) sensors. In practical applications of such sensors, the measurement uncertainty essentially relies upon the signal-to-noise ratio (SNR) of the experimental Brillouin gain spectra (BGSs) obtained throughout the sensing fiber. The improvement of such SNR using improper signal denoising techniques alters the experimental spatial resolution of the BOTDA sensors. In this paper, the use of non-local means filter (NLMF) and anisotropic diffusion filter (ADF) is experimentally demonstrated to enhance the uncertainty in the measurement of temperature using BOTDA sensors. For this purpose, the BGSs along a 41 km fiber are collected by averaging several numbers of BOTDA-traces from BOTDA hardware setup. Such BGSs are first denoised by employing NLMF and ADF to improve the measurement SNR. The Brillouin frequency shifts (BFSs) of denoised BGSs are then extracted via curve fitting technique (CFT). The BFS distribution is finally mapped to temperature distribution depending on the known BFS-temperature relationship of the sensing fiber. The robustness of the used filters is analyzed rigorously in terms of SNRs of BGSs, uncertainty in temperature extraction, spatial resolution and runtime in signal processing. The results indicate that the utilization of NLMF and ADF can enhance the SNRs of BGSs up to the maximum of 15.64 dB and 13.53 dB, respectively. Consequently, the uncertainties in the temperature extraction can be reduced up to the maximum of 52.63% and 57.31% for using NLMF and ADF, respectively. Moreover, both NLMF and ADF can preserve the experimental spatial resolution of the BOTDA sensors and include insignificant runtime to CFT. Thus, NLMF and ADF can be considered as robust signal denoising techniques for highly accurate and spatial resolution preserved BOTDA sensors. DUJASE Vol. 7 (2) 31-38, 2022 (July)

Quantification of Blood Viscoelasticity under Microcapillary Blood Flow.

Blood elasticity is quantified using a single compliance model by analyzing pulsatile blood flow. However, one compliance coefficient is influenced substantially by the microfluidic system (i.e., soft microfluidic channels and flexible tubing). The novelty of the present method comes from the assessment of two distinct compliance coefficients, one for the sample and one for the microfluidic system. With two compliance coefficients, the viscoelasticity measurement can be disentangled from the influence of the measurement device. In this study, a coflowing microfluidic channel was used to estimate blood viscoelasticity. Two compliance coefficients were suggested to denote the effects of the polydimethylsiloxane (PDMS) channel and flexible tubing (C1), as well as those of the RBC (red blood cell) elasticity (C2), in a microfluidic system. On the basis of the fluidic circuit modeling technique, a governing equation for the interface in the coflowing was derived, and its analytical solution was obtained by solving the second-order differential equation. Using the analytic solution, two compliance coefficients were obtained via a nonlinear curve fitting technique. According to the experimental results, C2/C1 is estimated to be approximately 10.9-20.4 with respect to channel depth (h = 4, 10, and 20 µm). The PDMS channel depth contributed simultaneously to the increase in the two compliance coefficients, whereas the outlet tubing caused a decrease in C1. The two compliance coefficients and blood viscosity varied substantially with respect to homogeneous hardened RBCs or heterogeneous hardened RBCs. In conclusion, the proposed method can be used to effectively detect changes in blood or microfluidic systems. In future studies, the present method can contribute to the detection of subpopulations of RBCs in the patient's blood.

Correction of Dual-PRF Velocity for Operational S-Band Doppler Weather Radar

The Weather Radar Center (WRC) of the Korea Meteorological Administration (KMA) has been providing three-dimensional radar wind fields based on the “WInd Synthesis System using Doppler Measurements (WISSDOM)” in real time since February 2019. Its accuracy is significantly affected by the quality of the Doppler velocity, such as velocity aliasing. For the de-aliasing of Doppler velocity, the dual-pulse repetition frequency (dual-PRF) technique is commonly utilized for commercial Doppler weather radar. The Doppler weather radars of the KMA have extended their Nyquist velocity up to 132 m s−1 using a dual PRF of 5:4. However, the dual-PRF technique produces significant noise and loss of radial velocity. Therefore, we developed a technique for noise cancelation and recovery of radial velocity to improve the quality of WISSDOM wind fields. The proposed approach identifies and removes speckles of abnormal radial velocity by comparing the sign of the median radial velocity with the surrounding radar bins. We then recovered the eliminated radial velocity using median interpolation. To recover the losses of radial velocity over a wide area using the dual-PRF technique, we used the Velocity Azimuth Display curve-fitting technique. These techniques are straightforward, preserve spatial gradients, and suppress local extrema. We tested this technique, verified its performance, and applied it to the operational radar quality control system of the WRC from August 2021. We concluded that the process helps improve the quality of the radial velocity and the accuracy of the WISSDOM wind fields.

Test technique for arbitrary length high dielectric sheet materials based on perturbation method

In this article, a very effective method is proposed to measure the permittivity of sheet materials with a high dielectric constant and loss. To meet the constraints of the perturbation method, controlling the magnitude of the perturbation by reducing the sample size is necessary. However, this will cause significant changes in the polarization field within the sample and, consequently, affects the accuracy of the calculations. To solve the problem, the effects of the polarized electric field and the non-uniformity of the electric field in the resonant cavity have been considered and an empirical model is developed based on this using curve fitting techniques. Taking the optimized depolarization factor into the resonant perturbation equation, the dielectric properties of arbitrary length of the sample can be accurately calculated when the frequency shift and the quality factor variation are known. Then, the method is validated and analyzed by numerical simulations. Finally, practical tests are carried out on a variety of materials at different sizes, and the results are stable and in excellent agreement with the simulated ones. Therefore, we can conclude that the method can accurately measure the complex permittivity of high dielectric sheet materials.

A novel state of health estimation approach based on polynomial model for lithium-ion batteries

Energy management systems are one of the most critical components in a battery unit's safe and efficient operation. Many measurable or calculable parameters, such as voltage, current, capacity, and internal resistance, are considered when designing energy management systems. Parameters that cannot be measured or are costly to measure, such as battery state of charge (SOC) or battery health state (SOH), can be determined by estimation. SOH, which can be used as both an input and an output parameter for EMS, is an essential parameter for the long-life and high-efficiency use of the battery. Two different approaches, experimental-based and model-based, are used for SOH estimation. Experimental-based methods need all the real-time data of the batteries, which is caused the requirement of a very long time and data storage. The adaptive filtering technique, which is a model-based technique, requires a complete and accurate model of the battery. The nonlinear electrochemical structures of batteries make modeling difficult. On the other hand, optimization-based methods, a data-driven technique, need very high processing power to find the optimal result. In addition, separate data is needed for training and testing in machine learning-based methods and requires high processing power. Contrary to these disadvantages, high-accuracy predictions can be made using low processing power and very little data in the experimental curve fitting technique. In this study, experimental and curve-fitting-based SOH estimation is proposed by using polynomial-based system identification techniques. Polynomial-based identification methods can model the system with high accuracy, low cost, and low processing power. Battery degradation dataset belonging to Oxford University is used. In the aforementioned dataset, the general model inference is made using only %1 of the entire cycle life of the battery. Obtained proposed model's results were compared with different methods in the literature in terms of RMSE, and its superiority was demonstrated.

Analytical Method for Rubber Materials Using Sulfur K-edge NEXAFS and Its Application

Here, we develop a technique for curve-fitting of the sulfur K-edge near-edge X-ray absorption fine structure (NEXAFS) to analyze the crosslinked structure of vulcanized rubber based on the chemical state of sulfur. The proposed analytical method provides the sulfur chain length (Sx), crosslink density, and sulfur oxide content simultaneously, and it is highly sensitive for the analysis of the depth direction. Furthermore, we verify the aging mechanism of the crosslinked structure using this analytical method. It is found that the sulfur chains, shortened and oxidized by heat aging at 120°C, can cause scission of the S—C bond, thereby decreasing the crosslink density. Long sulfur chains are more susceptible to oxidation, which rapidly decreases the sulfur chain length (Sx) and, in turn, the crosslink density compared with short sulfur chains. By comparing the heat-aging dependence between the S—C bond and S100, it is found that the styrene-butadiene rubber polymer surface can form the C—C crosslink. We present the aging mechanism of the crosslinked structure and establish NEXAFS as a useful analytical method for rubber materials.

Effective monitoring of Pelton turbine based hydropower plants using data-driven approach

Hydropower is a renewable and reliable energy source that can be utilized to fulfil energy demands and promote energy sustainability. In hydropower plants, Pelton turbines are installed at high-head and low-discharge sites. In Pelton turbines, needle, nozzle, buckets, and splitter are most exposed to silt erosion. An eroded turbine takes more discharge than rated for generating the same amount of power. Therefore, to minimize the losses due to silt erosion, real-time condition-based monitoring of a hydropower plant is necessary. In this paper, correlations are developed using the historical data collected from the Urgam hydropower plant to predict the generated power. The artificial Neural Network (ANN) technique has been used to develop correlation, and the performance of this model has been compared with the model developed using the Curve Fitting technique. Based on the comparison, it has been found that the ANN model performs better than the curve-fitting model in forecasting the generated power with an R2-value of 0.9522 and Mean Absolute Percentage Error (MAPE) of 2.40% at 3.1515% Root Mean Square Percentage Error (RMSPE). The developed model can be utilized to plan a maintenance schedule of machines based on real-time conditions. It can also help to decide which machine should be taken in maintenance first.

Quantifying uncertainty in Pareto estimates of global lake area

AbstractSize is a critical factor determining the rate and occurrence of specific lake processes such as carbon sequestration and greenhouse gas emissions and emerging evidence suggests that small lakes in particular have particularly large CO2 flux rates. Because we do not have a complete census of all lakes, upscaling estimates of such processes to small lakes at broad spatial scales requires the use of lake size‐abundance distributions rather than empirical measurements of area. Existing lake census efforts are incomplete such that as lakes become smaller, they are more likely to be omitted either because they are too small to be resolved from remote sensing products or because of limited ground surveying effort (i.e., “censoring” of small lakes relative to large lakes). The present study explores one potential shortcoming of prior approaches estimating global lake area using lake size‐abundance distributions. Namely, that these prior approaches rely on frequentist curve fitting techniques combined with an ad‐hoc cutoff determination strategy (visual inspection to determine a likely censoring point). This yields an over‐exact lake area estimate that is typically reported with no uncertainty bounds. I show how these shortcomings can be addressed with a Bayesian model that produces larger estimates of lake area uncertainty relative to the typical approach. When used as part of a sensitivity analysis, such an approach has the potential to enable more robust intercomparisons among studies of aquatic processes upscaling.

Nanoemulsion carriers of porous γ-alumina modified by polyvinylpyrrolidone and carboxymethyl cellulose for pH-sensitive delivery of 5-fluorouracil

5-Fluorouracil (5-FU) is a cytotoxic drug with a low half-life. These features can cause some problems such as burst drug release and numerous side effects. In the present study, a pH-sensitive nanocomposite of polyvinylpyrrolidone (PVP)/carboxymethyl cellulose (CMC)/γ-alumina developed by using water in oil in water (W/O/W) double emulsion method. The fabricated emulsion has been employed as the 5-FU carrier to investigate its effects on drug half-life, side effects, drug loading efficiency (DLE), and drug entrapment efficiency (DEE). Analyzing the FTIR and XRD indicated the successful loading of 5-FU into the nanocarrier and affirmed the synthesized nanocomposite's chemical bonding and crystalline features. Furthermore, by using DLS and Zeta potential assessment, size and undersize distribution, as well as the stability of the drug-loaded nanocomposite were determined, which demonstrated the monodisperse and stable nanoparticles. Moreover, the nanocomposites with spherical shapes and homogeneous surfaces were shown in FE-SEM, which indicated good compatibility for the constituents of the nanocomposites. Moreover, by employing BET analysis the porosity has been investigated. Drug release pattern was studied, which indicated a controlled drug release behavior with above 96 h drug retention. Besides, the loading and entrapment efficiencies were obtained 44 % and 86 %, respectively. Furthermore, the curve fitting technique has been employed and the predominant release mechanism has been determined to evaluate the best-fitted kinetic models. MTT assay and flow cytometry assessment has been carried out to investigate the cytotoxic effects of the fabricated drug-loaded nanocomposite on MCF-7 and normal cells. The results showed enhanced cytotoxicity and late apoptosis for the PVP/CMC/γ-alumina/5-FU. Based on the MTT assay outcomes on normal cell lines (L929), which indicated above 90 % cell viability, the biocompatibility and biosafety of the synthesized nanocarrier have been confirmed. Moreover, due to the porosity of the PVP/CMC/γ-alumina, this nanocarrier can exploit from high specific surface area and be more sensitive to environmental conditions such as pH. These outcomes propose that the novel pH-sensitive PVP/CMC/γ-alumina nanocomposite can be a potential candidate for drug delivery applications, especially for cancer therapy.

No need for a gold-standard test: on the mining of diagnostic test performance indices merely based on the distribution of the test value

BackgroundDiagnostic tests are important in clinical medicine. To determine the test performance indices — test sensitivity, specificity, likelihood ratio, predictive values, etc. — the test results should be compared against a gold-standard test. Herein, a technique is presented through which the aforementioned indices can be computed merely based on the shape of the probability distribution of the test results, presuming an educated guess.MethodsWe present the application of the technique to the probability distribution of hepatitis B surface antigen measured in a group of people in Shiraz, southern Iran. We assumed that the distribution had two latent subpopulations — one for those without the disease, and another for those with the disease. We used a nonlinear curve fitting technique to figure out the parameters of these two latent populations based on which we calculated the performance indices.ResultsThe model could explain > 99% of the variance observed. The results were in good agreement with those obtained from other studies.ConclusionWe concluded that if we have an appropriate educated guess about the distributions of test results in the population with and without the disease, we may harvest the test performance indices merely based on the probability distribution of the test value without need for a gold standard. The method is particularly suitable for conditions where there is no gold standard or the gold standard is not readily available.

Nonlinearly Parametrized Modeling and Adaptive Control for a Generic Hypersonic Vehicle

This paper constructs a nonlinearly parametrized hypersonic cruise vehicle model on the basis of the existing on-orbit flight data using a curve-fitting technique. The hypersonic cruise vehicle system is separated into two interconnected subsystem: an attitude subsystem with rotational dynamics and a velocity subsystem with engine dynamics. The continuous adaptive controllers are designed for two subsystems using a novel function bounding technique and appropriate coordinate transformations, respectively, which ensure the global boundedness of all signals and achieve the non-zero equilibrium point regulation of nonlinearly parametrized hypersonic vehicle systems. One of the implications of this result is that growing nonlinearities in the uncertain model of the hypersonic vehicle system may be allowed for global stabilization. A simulation result verifies the effectiveness of the proposed adaptive control scheme.

A New Method of Fault Localization for 500 kV Transmission Lines Based on FRFT-SVD and Curve Fitting

The paper presents the Fractional Fourier Transform-Singular Value Decomposition (FRFT-SVD) method for the localization of various power system faults in a 200 km long, 500 kV Egyptian transmission line using sent end-line current signals. Transient simulations are carried out using Alternating Transient Program/Electromagnetic Transient Program (ATP-EMTP), and the outcomes are then examined in MATLAB to carry out a sensitivity analysis against measurement noises, sampling frequency, and fault characteristics. The proposed work employs current fault signals of five distinct kinds at nineteen intermediate points throughout the length of the line. The approach utilized to construct the localizer model is FRFT-SVD. It is much more effortless, precise, and effective. The FRFT-SVD is utilized in this technique to calculate 19 sets of indices of the greatest S value throughout the length of the line. The FRFT-SVD localizer model is also designed to be realistic, with power system noise corrupting fault signals. To generate fault curves, the curve fitting technique is applied to these 19 sets of indices. Reduced chi-squared and modified R-squared criteria are used to choose the best-suited curve. The proposed work results in a very precise localization, with only a 0.0016% average percentage error for fault localization and a maximum percentage error of 0.002% for the 200 km Egyptian transmission line. Finally, this work can be employed as a proper link between the nuclear power plant and the grid. The proposed method is an efficient fault distance estimation method that might contribute to creating a dependable transient-based approach to power system protection.

Why and which opacifier for perlite based vacuum insulation panels (VIPs) in the average temperature range of 10–70 °C

Little is known on the effect of opacifiers in perlite core vacuum insulation panels at lower temperatures in the range of 10–70 °C, which are important for applications like refrigerators, transport boxes, buildings, and domestic hot water storage tanks. This paper shows that the effect of opacifier on perlite core Vacuum Insulation Panels (VIPs) is radically different than that on fumed silica VIPs. Identifying an optimum proportion of opacifiers for perlite core VIPs is not a trivial task because of a concomitant rise in solid conductivity as the radiative conductivity decreases. Further, the effect of opacifiers on temperature dependent thermal conductivity of VIPs has been resolved. Opacifiers in perlite are shown to yield clear benefits by reducing the overall thermal conductivity for insulation exposed to ≥70 °C. This was not the case for ≤20 °C. Several VIPs were manufactured using a low-density expanded perlite and 3 different proportions of 4 opacifiers i.e., carbon black, graphite and two variants of silicon carbide (SiC I, SiC II). These VIPs were tested at various combinations of sealing pressure and four different average temperatures i.e., 10 °C, 20 °C, 40 °C and 70 °C. A novel methodology has been developed to derive the evacuated thermal conductivity of perlite core VIPs by curve fitting technique, in order to eliminate the effect of gaseous conduction. The results were also compared with fumed silica core vacuum insulation panels with different proportions of carbon black as opacifier. Among the opacifiers tested (carbon black, graphite, SiC I and SiC II) in this research, Silicon carbide I with a mean particle size of 20 μm was found out to be the best opacifier, with one of its composite resulting in a 50% lower thermal conductivity at 70 °C in comparison to pristine perlite core VIPs.

Comparative Analysis of Equal and Unequal Grounding Grid Configurations by Compression Ratio and Least Square Curve Fitting Techniques

The primary aim of the power system grounding is to safeguard the person and satisfying the performance of the power system to maintain reliable operation. With equal conductor spacing grounding grid design, the distribution of the current in the grid is not uniform. Hence, unequal grid conductor span in which grid conductors are concentrated more at the periphery is safer to practice than equal spacing. This paper presents the comparative analysis of two novel techniques that create unequal spacing among the grid conductors: the least-square curve fitting technique and the compression ratio technique with equal grid configuration for both square and rectangular grids. Particle Swarm Optimization (PSO) is adopted for finding out one optimal feasible solution among many feasible solutions of equal grid configuration for both square and rectangular grids. Comparative analysis is also carried out between square and rectangular grids using the least square curve fitting technique as it results in only one unequal grid configuration. Simulation results are obtained by the MATLAB software developed. Percentage of improvement in ground potential rise, step voltage, touch voltage, and grid resistance with variation in compression ratios are plotted.

Design and Optimization of an Ultrathin and Broadband Polarization-Insensitive Fractal FSS Using the Improved Bacteria Foraging Optimization Algorithm and Curve Fitting

A frequency-selective surface (FSS) optimization method combining a curve-fitting technique and an improved bacterial foraging optimization (IBFO) algorithm is proposed. In the method, novel Koch curve-like FSS and Minkowski fractal islands FSS were designed with a desired resonance center frequency and bandwidth. The bacteria foraging optimization (BFO) algorithm is improved to enhance the performance of the FSS. A curve-fitting technique is provided to allow an intuitive and numerical analysis of the correspondence between the FSS structural parameters and the frequency response. The curve-fitting results are used to evaluate the fitness function of the IBFO algorithm, replacing multiple repeated calls to the electromagnetic simulation software with the curve-fitting equation and thus speeding up the design process. IBFO is compared with the classical BFO algorithm, the hybrid BFO-particle swarm optimization algorithm (BSO), and the artificial bee colony algorithm (ABC) to demonstrate its superior performance. The designed fractal FSS is fabricated and tested to verify the experimental results. The simulation and measurement results show that the proposed FSS has a fractional bandwidth of 91.7% in the frequency range of 3.41-9.19 GHz (S, C, and X-bands). In addition, the structure is very thin, with only 0.025λ and 0.067λ at the lowest and highest frequencies, respectively. The proposed fractal FSS has shown stable performance for both TE and TM polarizations at oblique incidence angles up to 45°. according to simulations and measurements.

Modeling and adaptive control of air vehicles with partial nonlinear parametrization

This paper studies the control of a generic longitudinal air vehicle dynamic model during the cruise phase with nonlinearly parametrized uncertain aerodynamic functions. Verified by the improved coefficient precision of the aerodynamic forces and moments, using a curve fitting technique on available flight data, it is demonstrated that a nonlinearly parametrized model can more accurately capture the vehicle dynamics than a linearly parametrized model. For control design, the air vehicle model is decomposed into a flight-path angle subsystem with rotational dynamics and a speed subsystem with engine actuation dynamics. An adaptive control scheme is developed using the combination of a function bounding technique and a modified backstepping control method for two interconnected subsystems. The designed adaptive control laws ensure both global stabilization and adaptive non-zero equilibrium point regulation of the closed-loop control system. A thorough simulation study is presented to show the effectiveness of the developed adaptive control scheme for a nonlinearly parametrized air vehicle system model.

Biosensing of Haemorheological Properties Using Microblood Flow Manipulation and Quantification.

The biomechanical properties of blood have been used to detect haematological diseases and disorders. The simultaneous measurement of multiple haemorheological properties has been considered an important aspect for separating the individual contributions of red blood cells (RBCs) and plasma. In this study, three haemorheological properties (viscosity, time constant, and RBC aggregation) were obtained by analysing blood flow, which was set to a square-wave profile (steady and transient flow). Based on a simplified differential equation derived using a discrete circuit model, the time constant for viscoelasticity was obtained by solving the governing equation rather than using the curve-fitting technique. The time constant (λ) varies linearly with respect to the interface in the coflowing channel (β). Two parameters (i.e., average value: <λ>, linear slope: dλdβ) were newly suggested to effectively represent linearly varying time constant. <λ> exhibited more consistent results than dλdβ. To detect variations in the haematocrit in blood, we observed that the blood viscosity (i.e., steady flow) is better than the time constant (i.e., transient flow). The blood viscosity and time constant exhibited significant differences for the hardened RBCs. The present method was then successfully employed to detect continuously varying haematocrit resulting from RBC sedimentation in a driving syringe. The present method can consistently detect variations in blood in terms of the three haemorheological properties.

An experimental investigation on the effectiveness of damping changes for damage detection in a Fibre Reinforced Plastic Plate

Fibre reinforced plastics (FRP) are extensively used because of their high specific strength and stiffness. However, throughout their service life, such materials are susceptible to damages, which when accumulated may result in catastrophic failure. Studies on effects of stiffness loss due to damage has been exercised by quite a large number of researchers but very less investigators have involved the variations in dissipative behaviour in combination with such stiffness loss. However, damage in these structures not only causes local reduction of stiffness but is also observed with increased dissipation behaviour. One of the most convenient ways to carry out health monitoring exercise to detect damages is to conduct systematic vibration testing. The present study investigates the likely changes in natural frequencies and mode shapes of a rectangular FRP composite plate along with damping factors due to the induced damage. The FRP plate considered has been modal tested and dynamic responses i.e., natural frequencies, mode shapes and modal damping factors are derived through curve-fitting technique from the frequency response function measurements. In this study, changes in dynamic responses due to a locally induced damage in the FRP plate is studied. For this, in order to maximize the effects of local reduction in the stiffness on the modal parameters, a partial-cut is provided in a localised region of the plate in the first damage case. In the second damage scenario, the partially-cut area has been filled with epoxy resin matrix to create a region with localised change in material properties and with limited stiffness loss. Damping changes has been observed to be significant and more sensitive than variations in natural frequencies and mode shapes. The study suggests that damping parameters along with stiffness changes together can be put into practice to develop an effective vibration-based health monitoring scheme

Integral-proportional derivative controller tuning rules obtained from optimum responses for set-point tracking of unstable processes with time delay

This paper introduces the design of integral–proportional derivative (I-PD) controllers for unstable first-order plus time-delay and integrating-unstable first-order plus time-delay processes. Minimization of the error based on integral performance criteria is performed to derive analytical rules using curve fitting techniques. Obtained analytical formulas may be used to determine the necessary tuning parameters of the I-PD controller from the known plant transfer function parameters. Advantages of the introduced tuning of I-PD controllers are shown by comparisons with other existing ones in terms of unit step responses, measurement noise, control signals, perturbations in plant transfer function parameters, and integral performance indices. Results have shown that some significant advantages have been achieved with the introduced tuning of I-PD controllers when compared to others in the literature.

Joint Placement and Beamforming Design for IRS-Enhanced Multiuser MISO Systems

The fundamental intelligent reflecting surface (IRS) deployment problem is studied for IRS-aided downlink multi-user communication system, where IRSs are arranged to be deployed in a specific area for enhancing the desired signal and suppressing interference. Specifically, we aim to maximize the minimum achievable rate over all locations in a specific area by jointly optimizing the transmit beamforming at the access point (AP) as well as the placement and reflective beamforming at the IRS. The formulated problem is non-convex and thus difficult to be solved directly. To draw essential insights, we first consider the single-user case and the optimal solution is derived in closed-form. The result shows that the optimal locations are in the connecting line between the AP and user, and the IRSs can be optimally deployed along the connecting line. Besides, a hybrid offline and online design scheme is developed for the multi-user case, where an area discretization strategy and deep neural network (DNN)-based curve fitting technique are proposed for optimizing the IRS locations in the offline manner. Then, an online iterative algorithm is presented to solve the transmit and received beamformig vectors, respectively. Numerical results show that the performance gain is increased by optimizing the IRS locations.