Inverse Fast Fourier Transform Research Articles

An Effective Method for Fast Evaluation of Lightning-Induced Voltages on the Overhead Transmission Lines Combining Electromagnetic Topology and Matrix Pencil Method

In this article, an effective method combining electromagnetic topology (EMT) and matrix pencil method (MPM) for the fast evaluation of the lightning-induced voltages on the overhead transmission line (TL) is proposed. First, the EMT of the TL network is established based on the structure characteristic of the TL network and the scattering hypermatrix is constructed according the information of the junctions and terminal loads. Then, the piecewise sampling is performed for the spectrum of lightning signal, and the calculation of the lightning electromagnetic fields (LEMFs) of all observation points along the TL at the sampling frequency point is accomplished. Next, the supervector of the excitation source is constructed to realize the generation of the Baum–Liu–Tesche matrix equation, and the results of the lightning-induced voltages of all junctions on the TL network at the sampling frequencies are obtained. Finally, the lightning-induced voltages at all frequencies are obtained by using MPM to fit the sampled results, and the time-domain results can be generated by inverse fast Fourier transform (IFFT). In the proposed method, the LEMFs above the lossy ground are solved by the C–R formula and those below the lossy ground are calculated by the Cooray formula. Moreover, the feasibility of using EMT to analyze the lightning-induced voltages of the junctions on the TL network and adopting MPM to fit the sampled values of the lightning-induced voltages is verified. The correctness and efficiency of the proposed method are validated and proved by several numerical examples.

Analytical Solution for the Transient Current Induced along the Vertical Grounding Electrode

The paper deals with the analysis of the Pocklington integro-differential equation in the time domain and its analytical solution for the transient current induced along the vertical grounding electrode and, as such, represents a continuation of the research pertaining to the horizontal grounding electrode previously reported by one of the authors. The electrode is excited by a current source impressed at one end of the electrode, representing the model of the lightning strike current. A novel analytical solution is derived using the Laplace transform. Results obtained with this time domain solution are compared with the results obtained via analytical solution of the corresponding Pocklington equation in the frequency domain in conjunction with inverse fast Fourier transform (IFFT). The results obtained via different methods are shown to be in a very good agreement. The results of the time domain analytical solution for the vertical electrode are also compared with the results of the time domain analytical solution for the horizontal electrode, where greater influence of earth-air interface on an induced current is observed. These procedures can be implemented as benchmarking techniques as well as tools for rapid estimation of the observed phenomena.

Study on a novel field-measured load calibration method for the life assessment of the metro bogie frame

Aiming at solving the problem of premature fatigue failure of the bogie frame of a metro vehicle during service, this paper mainly studies the method of accurately predicting the fatigue life of the bogie frame of a metro train through the measured load. To correct the error between the calculated damage and real damage value, a hybrid frequency-time calibration method is proposed. Based on the quasi-static relationship between the load and stress as well as the basic theory of the multiaxial spectral method, the expression of stress statistics in the frequency domain is derived considering the correlation of multiple loads. According to the damage consistency principle, the NSGA-II multi-objective optimization algorithm is used to calibrate the load system. Based on the frequency domain calibration results, the dynamic stress time history could be acquired by the Inverse Fast Fourier Transform (IFFT) method. The results show that the calculated damage through the calibrated load completely covers the real damage value, and the ratio range between them is 1.10–1.42. The above results indicate that the calibrated load can be used for the reliability design of later structural optimization.

Spectral envelope-based adaptive empirical Fourier decomposition method and its application to rolling bearing fault diagnosis

Adaptive empirical Fourier decomposition (AEFD) is a recently developed approach of nonstationary signal mode separation. However, it requires to set the spectrum segmentation boundary relying on the users’ professional experience ahead of time. In this paper, a novel spectral envelope-based adaptive empirical Fourier decomposition (SEAEFD) method is proposed to improve the performance of AEFD for rolling bearing vibration signal analysis. In the proposed SEAEFD approach, fast Fourier transform (FFT) of the raw signal is calculated to obtain the frequency spectrum at first. Then, the spectral envelope processing is implemented on the spectrum signal obtained by FFT to achieve an adaptive segmentation. In the traditional segmentation method, generally, the minima and midpoints between adjacent extreme points are taken as the spectrum segmentation boundary, in which the obtained frequency band contains more interference components. To achieve the effect of denoising and restrain the noise that existed in the collected vibration signal, SEAEFD is proposed to optimize the spectrum segmentation boundary so that the obtained frequency band contains the least noise components. Lastly, the inverse FFT is used to reconstruct the component signal within each frequency band and the gained signals are termed as Fourier intrinsic mode functions (FIMFs). Therefore, SEAEFD enables a nonstationary signal to be decomposed into several single-component signals with instantaneous frequencies of physical significance. The proposed SEAEFD method is compared with recently developed methods, including EAEFD, AEFD, EWT, VMD and EMD methods, by analyzing the simulation signals and the measured data of rolling bearing. The results indicate that SEAEFD is valid in diagnosing rolling bearing faults and gets a better diagnosis performance than the compared methods.

PAPR reduction of OFDM systems using H‐SLM method with a multiplierless IFFT/FFT technique

This study proposes a novel low-complexity algorithm for computing inverse fast Fourier transform (IFFT)/fast Fourier transform (FFT) operations in binary phase shift keying-modulated orthogonal frequency division multiplexing (OFDM) communication systems without requiring any twiddle factor multiplications. The peak-to-average power ratio (PAPR) reduction capacity of an efficient PAPR reduction technique, that is, H-SLM method, is evaluated using the proposed IFFT algorithm without any complex multiplications, and the impact of oversampling factor for the accurate calculation of PAPR is analyzed. The power spectral density of an OFDM signal generated using the proposed multiplierless IFFT algorithm is also examined. Moreover, the bit-error-rate performance of the H-SLM technique with the proposed IFFT/FFT algorithm is compared with the classical methods. Simulation results show that the proposed IFFT/FFT algorithm used in the H-SLM method requires no complex multiplications, thereby minimizing power consumption as well as the area of IFFT/FFT processors used in OFDM communication systems.

Particle Swarm Optimization-based dummy sub-carriers insertion for peak to average power ratio reduction in OFDM systems

Orthogonal Frequency Division Multiplexing (OFDM) is the best choice for wireless and wired high data rate communications. The OFDM system has many advantages such as high spectral efficiency, robustness to channel fading, and immunity to impulse interference. However, it has a main drawback, which is the Peak to Average Power Ratio (PAPR). Selecting Mapping (SLM) and Partial Transmit Sequences (PTS) are the two essential techniques for reducing the PAPR; however, they need to send side information to indicate how the transmitter generates signals. In this paper, Particle Swarm Optimization (PSO)-based dummy sub-carriers are inserted with the data to reduce PAPR without transmitting side information. The incorporation of PSO-based Dummy Sub-carriers Insertion (DSI) method on this system is performed by measuring the PAPR at the IFFT output (Inverse Fast Fourier Transform) after adding 6 adaptive sub-carrier sequences to the input data of IFFT. The PSO-based dummy algorithm decides to send the data once the PAPR of this data sequence and dummy sub-carrier is under a specific threshold. Using MATLAB as a mathematical simulation tool, simulation results are presented for a standard OFDM network model. The network model has been simulated in an Additive White Gaussian Noise (AWGN) channel environment to investigate PAPR and Bit-Error Rate (BER) performance. The simulation results show that the dummy sequence based on PSO reduces PAPR down to 4 dB compared to a conventional OFDM system and down to 3 dB compared with the clipping technique for the same BER performance.

Integrated Velocity Prediction Method and Application in Vehicle-Environment Cooperative Control Based on Internet of Vehicles

Rapid progress has been gained in the field of advanced communication technologies, which also promote parallel developments in the Internet of Vehicles (IoVs). In this context, vehicle-environment cooperative control can be integrated into next-generation vehicles to further improve the vehicle's performance, in particular energy efficiency. Accurate prediction of future velocity profiles on basis of IoVs can be a critical breakthrough, which can contribute much to vehicle operation efficiency promotion. In this paper, an integrated velocity prediction (IVP) method fully taking advantage of IoVs is proposed and demonstrated through a case study. In the IVP method, both the macroscopically and microscopically predicted velocity profiles are considered. The macroscopic velocity profiles are predicted via traffic flow analysis (TFA) in multi-access edge computing units (MECUs) which are situated alongside the route. Microscopic velocity profiles are forecasted through Mondrian forest (MF) algorithm in the on-board vehicle control unit (VCU). Final velocity prediction is generated through combination of the macroscopic and microscopic profiles in frequency domain in on-board VCU through fast Fourier transform (FFT) and inverse FFT. A case study validates the distinguished performance of IVP method and demonstrates its significant contribution to vehicle performance improvement.

Efficient Cached 64 Point FFT Processor Using Floating Point Arithmetic for OFDM Application

Presently Fourth generation and other wireless systems are focused area for the research and development in the communication field. Fast Fourier Transform (FFT) & Inverse FFT (IFFT) are required for Orthogonal frequency division multiplexing in the integral part of modulation/demodulation modules that occupies more area and power. This paper presents low power and area efficient Cached memory for Fast Fourier Transform (FFT) processor using floating point arithmetic for OFDM application. To store computational permutations each butterfly unit needs one memory. So if considering higher radix of FFT processor, memory requirement increases, it yields to more power consumption and more density occupancy. In this proposed cached 64 point radix 2^6 SDF architecture for reducing the arithmetic hardware complexity of complex multipliers and complex adders present in butterfly structure to obtain low power and less memory requirement. The proposed system is synthesized by using CADENCE RTL COMPLIER and is implemented in ENCOUNTER RTL TO GDSII SYSTEM” using 90nm CMOS technology with a supply voltage of 1V. Synthesis results shows that the proposed design is efficient in terms of gate count, area and power consumption.

Low-Complexity Adaptive Frequency-Domain Nonlinear Equalization for Analog RoF Mobile Fronthaul Using FFT/IFFT-Assisted Channel Aggregation

Addressing the nonlinearity induced signal degradation is of critical importance for harvesting the transparent benefits of an analog radio over fiber (A-RoF) architecture, to support mobile fronthaul (MFH) with high spectral efficiency and reduced latency. Here, for linearizing the low-latency A-RoF MFH using digital-domain fast Fourier transform /inverse fast Fourier transform (FFT/IFFT) assisted channel aggregation/de-aggregation (CA/DA), we propose and experimentally demonstrate a compatible adaptive frequency-domain (FD) nonlinear equalization scheme. This scheme is characterized by a much lower computational complexity compared with the popular time-domain Volterra nonlinear equalizer while delivering a comparable performance. The proposed equalization scheme is implemented using the FD two-box cascaded Hammerstein structure. It enables simplified coefficients estimation, computationally efficient equalization, FFT/IFFT calculation reusing in channel DA, and shared legacy one-tap FD linear equalization in the OFDM system. Experimental validations of the proposed nonlinear equalization approach are carried out via typical electroabsorption modulator (EAM) and Mach-Zehnder modulator (MZM) based intensity modulation and direct detection (IMDD) A-RoF links. Cost-effective fiber-optic (with EAM) and optical up-conversion enabled V-band millimeter-wave (mm-wave) fiber-wireless (with MZM) transmissions are demonstrated. Experimental results show that the proposed scheme can effectively improve the performances of both EAM and MZM based 10-km fiber-optic A-RoF MFH links, in terms of the (>8 dB) reduction of adjacent channel leakage ratio, (>10 dB) improvement of error-vector magnitude (EVM) and (>5 dB) enhancement of input intermediate-frequency (IF) power range, which retains an acceptable (below 8 %) EVM performance for the 64-QAM modulation. The input IF signal aggregates 8 125-MHz 64-QAM OFDM channels. Furthermore, the proposed scheme enables the transmission of a 5-Gbit/s aggregated IF 64-QAM signal over a 10-km fiber link and 1.2-m 60-GHz wireless channel, wherein a >12 dB improved input power margin is observed.

Microstructure and phases investigations of W–Mo–Cu alloy prepared by large current electric field sintering

W–Mo–Cu alloy was fabricated by large current electric field sintering at a low temperature of 950 °C. The interrupted sintering at different sintering stages was performed to identify the phases and microstructure evolution during the densification process. The transmission electron microscope (TEM) images clearly show that the nanoscale phases form and distribute at the boundaries of W, Mo, and Cu phases. Moreover, the high-resolution TEM images incorporating with a selected area fast Fourier transform and inverse fast Fourier transform (IFFT) treatment present the structure of formed phases. Meanwhile, the lattice parameters calculated through X-ray diffraction patterns and IFFT images jointly evidence the existence of defects and atom diffusion during the sintering. The dislocations and lattice strain induced by the ultrahigh current and pressure provide the stored energy and nucleation sites, thus promoting the diffusion of elements and the formation of fine grains.

Two Types of Mixed Orthogonal Frequency Division Multiplexing (X-OFDM) Waveforms for Optical Wireless Communication

Intensity modulation and direct detection (IM-DD) based optical wireless communication (OWC), requires the modulated signal to be real and non-negative. To satisfy the requirements, this paper proposes two types of mixed orthogonal frequency division multiplexing (X-OFDM) waveforms. The Hermitian symmetry (HS) characteristic of the sub-carriers in the frequency domain, guarantees the signal in the time domain to be real, which reduces the spectral efficiency to 1/2. For the odd sub-carriers in the frequency domain, the signal in the time domain after the inverse fast fourier transform (IFFT) is antisymmetric. For the even sub-carriers in the frequency domain, the signal in the time domain after the IFFT is symmetric. Based on the antisymmetric and symmetric characteristics, the two types of X-OFDM waveforms are designed to guarantee the signal in the time domain to be non-negative. With <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> sub-carriers in the frequency domain, the generated signal in the time domain has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3M/2$ </tex-math></inline-formula> points, which further reduces the spectral efficiency to 1/3. The numerical simulations show that, the two types of X-OFDM waveforms greatly enhance the power efficiency considering the OWC channel with the signal-dependent noise and/or the signal-independent noise.

MIMO-OFDM LTE system based on a parallel IFFT/FFT on NoC-based FPGA

The growing demand for wireless devices capable of performing complex communication processes has imposed an urgent need for high-speed communication systems and advanced network processors. This paper proposes a hardware workflow developed for the Long-Term Evolution (LTE) communication system. It studies the multiple-input, multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) LTE system. Specifically, this work focuses on the implementation of the OFDM block that dominates the execution time in high-speed communication systems. To achieve this goal, we have proposed an NoC-based low-latency OFDM LTE multicore system that leverages Inverse Fast Fourier Transform (IFFT) parallel computation on a variable number of processing cores. The proposed multicore system is implemented on an FPGA platform using the ProNoC tool, an automated rapid prototyping platform. Our obtained results show that LTE OFDM execution time is drastically reduced by increasing the number of processing cores. Nevertheless, the NoC’s parameters, such as routing algorithm and topology, have a negligible influence on the overall execution time. The implementation results show up to 24% and 76% execution time reduction for a system having 2 and 16 processing cores compared to conventional LTE OFDM implemented in a single-core, respectively. We have found that a 4×4 Mesh NoC with XY deterministic routing connected to 16 processing tiles computing IFFT task is the most efficient configuration for computing LTE OFDM. This configuration is 4.12 times faster than a conventional system running on a single-core processor.

Algorithms for Direct and Inverse Parametric Fast Fourier Transform

Русский Main page New issue Archive of articles Editorial board For the authors Publishing house ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES". No. 1. Vol. 28. 2022 DOI: 10.17587/it.28.9-19 O. V. Ponomareva, Dr. Sc., Tech., Professor, A. V. Ponomarev, PhD, Econ., Associate Professor, Kalashnikov Izhevsk State Technical University, Izhevsk, 426069, Russian Federation, N. V. Smirnova, PhD, Tech., Associate Professor, Sevastopol State University, Sevastopol, 299053, Russian Federation Algorithms for Direct and Inverse Parametric Fast Fourier Transform Classical Fourier processing of finite information discrete signals (FID signals) is the most important method of digital analysis, modeling, optimization, improvement of control and decision making. The theoretical basis of classical Fourier processing of FID signals is the discrete Fourier transform (DFT). The practical basis of classical Fourier processing of FID signals is the Fast Fourier Transform (FFT). The practice of using classical Fourier processing of FID signals, having confirmed its effectiveness, revealed a number of negative effects inherent in this type of digital signal processing (DSP). The aliasing effect, scalloping effect, picket fence effect, significantly affect the effectiveness of analysis, modeling, optimization, improvement of management and decision making. To increase the efficiency of Fourier processing of FID signals, the authors of the paper have developed a generalization of DFT in the form of a parametric DFT (DFT-P). Since the direct application of parametric Fourier processing of FID signals (as well as the use of classical Fourier processing of FID signals) requires complex multiplications, fast procedures are required for the practical implementation of this type of FID signals. Purpose of the research is to develop algorithms for the fast parametric discrete Fourier transform (FFT-P). The work developed fast procedures for the implementation of DFT-P by time decimation. Parametric FFT-P with substitution (in place) and without substitution (no place) are proposed. The estimation of the efficiency of the FFT-P algorithms is given. The practical significance of the work is in the fact that developing algorithms for the parametric fast Fourier transform can reduce the computational costs of performing parametric discrete transformations by three or more orders of magnitude.

Incredible VLSI Design for MIMO System Using SEC-QPSK Detection

Multiple Input Multiple Output (MIMO) is an advanced communication technology that is often used for secure data transfer for military and other applications while transmitting data with high error and noise. To address this issue, a step-by-step hybrid Quadrature Phase Shift Keying (QPSK) modulation scheme in the MIMO system for a complex Very Large-Scale Integration (VLSI) format is recommended. When compared to Binary Phase Shift Keying (BPSK), this approach provides twice the data rate while using half the bandwidth. The complexity is lowered through multiplication and addition, as well as error and noise reduction in data transport, and MIMO detection is accomplished through the combination of two techniques, Inverse Fast Fourier Transform (IFFT) and Stepwise Exponential Companding (SEC). IFFT converts frequency to the time domain, reducing complexity by 23.56 percent in multiplication and an extra 34.05 percent. Likewise, hierarchical high-speed mixing decreases difficult limits by 13% and the addition problem by 25%. This technological outcome results in a decreased Signal-to-Noise Ratio (SNR) and Bit Error Rate (BER).

Phase Compensation and Time-Reversal Transform for High-Order Maneuvering Target Detection

In this letter, we consider a target with high-order motion and propose two long-time coherent integration algorithms with low computational cost for target detection via phase compensation and time-reversal transform. Due to the even/odd characteristic, the coupling effect between the range frequency and slow time can be eliminated by constructing the phase compensation function and doing the time-reversal transform. In doing so, the target energy can be accumulated by inverse fast Fourier transform (IFFT) in range frequency and fast Fourier transform (FFT) in slow time. Simulations are given to demonstrate the effectiveness of the proposed algorithms. Moreover, compared with the generalized Radon&#x2013;Fourier transform (GRFT) and generalized dechirp-keystone transform (GDKT), the proposed algorithms have much lower computational burden.

Hardware Chip Performance of CORDIC Based OFDM Transceiver for Wireless Communication

The fourth-generation (4G) and fifth-generation (5G) wireless communication systems use the orthogonal frequency division multiplexing (OFDM) modulation techniques and subcarrier allocations. The OFDM modulator and demodulator have inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) respectively. The biggest challenge in IFFT/FFT processor is the computation of imaginary and real values. CORDIC has been proved one of the best rotation algorithms for logarithmic, trigonometric, and complex calculations. The proposed work focuses on the OFDM transceiver hardware chip implementation, in which 8-point to 1024-point IFFT and FFT are used to compute the operations in transmitter and receiver respectively. The coordinate rotation digital computer (CORDIC) algorithm has read-only memory (ROM)-based architecture to store FFT twiddle factors and their angle generators. The address generation unit is required to fetch the data and write the results into the memory in the appropriate sequence. CORDIC provides low memory, delay, and optimized hardware on the field-programmable gate array (FPGA) in comparison to normal FFT architecture for the OFDM system. The comparative performance of the FFT and CORDIC-FFT based OFDM transceiver chip is estimated using FPGA parameters: slices, flip-flops, lookup table (LUTs), frequency, power, and delay. The design is developed using integrated synthesis environment (ISE) Xilinx version 14.7 software, synthesized using very-high-speed integrated circuit hardware description language (VHDL), and tested on Virtex-5 FPGA.

A Construction Method of Phase Sequences for the Selected Mapping Scheme

In this paper, a construction method of phase sequences is proposed for the selected mapping (SLM) scheme. Three principles are applied to the construction process: periodicity, binary (±1), and maximization of the minimum Hamming distance between different sequences. Using the first and second principle, except the original frequency signal, the calculation process of other candidate time signals can be simplified as the linear addition of some intermediate signals, which are obtained in the inverse fast Fourier transform (IFFT) operation of the original frequency signal. Using the third principle, greater differences can be generated between different candidate signals, which is helpful to improve the peak-to-average power ratio (PAPR) reduction performance. Theoretical analysis and simulation results show that, with the help of new phase sequences, the SLM scheme can effectively reduce the computational complexity, while it shows almost the same performance of PAPR reduction as that of the traditional SLM scheme, whose phase sequences are from the odd row vectors in the Hadamard matrix.

PAPR Reduction Using Advanced Partial Transmission Scheme for 5G Waveforms

The implementation of Peak Average to Power Ratio (PAPR) reduction technologies will play an important role in the regularization of Fifth Generation (5G) radio communication. PAPR reduction in the advanced waveform will be the key part of designing a 5G network for different applications. This work introduces the simulation of an Advanced Partial Transmission Sequence (A-PTS) reduction techniques for Orthogonal Frequency Division Multiplexing (OFDM) and Filter Bank Multi-Carrier (FBMC) transmission schemes. In the projected A-PTS, the FBMC signals are mapped into the number of sub-blocks and Inverse Fast Fourier transform (IFFT) is performed to estimate the high peak power in the time domain. The FBMC sub-blocks are multiplied with the phase elements to achieve an optimal PAPR value. A MATLAB 2014v simulation is used to estimate the PAPR, Bit Error Rate (BER), Error Vector Magnitude (EVM), and Modulation Error Rate (MER) performance of the proposed reduction schemes. The simulated result reveals that the performance of the projected algorithm is better than the conventional algorithms.

PAPR Reduction in Optical OFDM Using Lexicographical Permutations With Low Complexity

Efficient utilization of the spectrum, increased resilience to inter-symbol interference (ISI) and simpler channel equalization are becoming important considerations in the design of wireless communication systems including visible light communication (VLC) systems. In this regard, orthogonal frequency division multiplexing (OFDM) has become a preferred modulation technique in wireless communication systems design. However, one of its major challenges is the high peak-to-average power ratio that leads to major inefficiencies. Symbol position permutation (SPP) is a distortion-less technique that achieves substantial PAPR reduction without BER degradation. However, the existing works focus on PAPR reduction using SPP for the radio frequency (RF) OFDM and the use of this technique in optical OFDM is not properly investigated. Therefore, in this paper, we present a new PAPR reduction technique based on lexicographical permutations called lexicographical symbol position permutation (LSPP) for PAPR reduction in direct current optical OFDM (DCO-OFDM). The proposed scheme is less complex than the conventional selective mapping (CSLM) scheme since there is no multiplication of the phase sequences with the DCO OFDM symbol to generate the candidate signals. We further introduce a new way of reducing the complexity by introducing a threshold PAPR and demonstrate that the complexity in terms of inverse fast Fourier transform (IFFT) operations can be reduced substantially depending on the selected threshold and the number of candidate signals.

An Efficient mmW Frequency-Domain Imaging Algorithm for Near-Field Scanning 1-D SIMO/MIMO Array

In recent years, millimeter-wave (mmW) 3D imaging technology for scanning 1D single-input multiple-output (SIMO) or multiple-input multiple-output (MIMO) array has been extensively studied due to its unique advantages in near-field applications. However, current imaging algorithms for this kind of scheme are not satisfactory, either of low quality since irrational approximations are introduced, or too slow as the back projection method is employed. In this paper, an efficient frequency-domain imaging algorithm is developed to fetch up these shortages. The precise spectral expression of the echo signal within SIMO data is derived through spherical-wave decomposition and fast Fourier transform (FFT) operations. By properly approximating the nonlinear phase, the wavefront curvature is compensated after employing a 1D Stolt interpolation, and then the reflectivity map of the target can be obtained through several multiplications and inverse FFT operations. Image reconstruction for a MIMO array can be realized by coherently summing up all the SIMO focusing results. Both simulation analysis and experimental results demonstrate the effectiveness of the proposed algorithm in imaging quality and computational efficiency.