Sample Matrix Inversion Algorithm Research Articles

Design of Low Power Thinned Smart Antenna for 6G Sky Connection

To improve radio access capability, sky connections relying on satellites or unmanned aerial vehicles (UAV), as well as high-altitude platforms (HAP) will be exploited in 6G wireless communication systems, complementing terrestrial networks. For long-distance communication, a large smart antenna will be used that is characterized by high amounts of power consumed by digital beamformers. This paper focuses on reducing power consumption by relying on a thinned smart antenna (TSA). The performance of TSA is investigated in the sub-6 GHz band. The differential evolution (DE) algorithm is used to optimize excitation weights of the individual dipoles in the antenna array and these excitation weights are then used in TSA for beamforming, with signal processing algorithms deployed. The DE technique is used with the least mean square, recursive least square and sample matrix inversion algorithms. The proposed method offers almost the same directivity, simultaneously ensuring lower side lobes (SLL) and reduced power consumption. For a TSA of 20, 31, and 64 dipoles, the power savings are 20%, 19.4%, and 17.2%, respectively. SLL reductions achieved, in turn, vary from 5.2 dB to 8.1 dB.

Robust Adaptive Beamforming for Interference Suppression Based on SNR

Robust adaptive beamforming (RAB) can be used to suppress interference signals while retaining the desired signals received by a sensor array. However, desired signal self-cancellation and model mismatch can affect RAB performance. In this paper, a novel interference-plus-noise covariance matrix (INCM) reconstruction method is proposed for RAB to solve these problems. The proposed method divides the desired signal into two ranges according to the input signal-to-noise ratio (SNR), namely low SNR and high SNR. In the low SNR range, INCM reconstruction directly uses the same sample covariance matrix as the sample matrix inversion (SMI) beamformer to retain the advantages of the traditional SMI algorithm. In the high SNR range, the eigenvalues of the sample covariance matrix are used to estimate the interference power and noise power. The optimized interference steering vector (SV) is obtained by solving a quadratic convex optimization problem in an interference subspace. The INCM is reconstructed from the interference SVs, interference power, and noise power. The reconstructed INCM is then used to correct the desired signal SV via maximizing the beamformer output power. This is achieved by solving a quadratically constrained quadratic programming (QCQP) problem. Analysis and simulation results are presented which demonstrate that the proposed method performs well under a variety of mismatch conditions.

The Study of the Possibility of Applying Parallel Programming to the Algorithms of Space-Time Adaptive Processing

The article presents the description, assumptions and subsequent steps of the space-time adaptive processing (STAP) algorithms used as a signal processing tool in radars. The possibilities of object detection using the Sample Matrix Inversion (SMI) and Data Domain Least Squares (DDLS) algorithms were compared and showned. The article shows the impact of the use of parallel programming on the computation time of both algorithms. The main aim of this study was to propose an efficient method for the real-time implementation of the STAP algorithm in airborne radar systems. The idea of using parallel programming in STAP, supported only by the preliminary research results presented above, gives a real chance for the casual implementation of the STAP algorithm in a radar operating in close to real time mode.

Study of digital diagram formation for optimum interference and noise reduction in antenna arrays of different shapes with directional radiators

In the paper the digital beamforming is examined in azimuth and elevation, which allows more accurate formation of nulls and maximum of the radiation pattern. The minimum variance distortionless response beamformer, the sample matrix inversion algorithm using regularization, and the null steering algorithms at the output of cylindrical, hemispherical and planar lattices are considered. The ratio of the useful signal power to the active interference plus noise resulting power and the bit error ratio at the output of digital antenna arrays are estimated depending on the directivity of the antenna elements and the number of averaging samples. It has been established that a hemispherical antenna array can significantly increase the transmission reliability in comparison with the considered ones, which will reduce the computational load without using complicated diagramming algorithms.

Сравнительный анализ методов калибровки каналов сигналов антенн моноимпульсной радиолокации

Today, antenna arrays (ARs) are increasingly used as antennas in modern radio engineering systems. With the help of AR, you can control the shape of the radiation pattern (DN) and the position of its main lobe, called the beam of such an antenna system. Each AA channel contains microwave components for controlling the amplitude and phase of the signal passing through it. These components are characterized by errors in setting the amplitude and phase, which negatively affects the shape of the pattern and its characteristics. Therefore, to compensate for these errors, it is necessary to use the AP calibration at the production stage, and also during its operation. The paper presents various calibration methods; the most suitable and promising methods for AA calibration were determined; the principles of operation of these methods are considered, the advantages and disadvantages of the methods are identified, a comparative analysis of all methods is carried out, as well as the conditions under which it is more expedient to use one or another method. The following calibration methods are considered: Phaseless methods: (Rotating-Element Electric Field Vector method - REV method, Measurement of Two Elements method - MTE method, Sorace algorithm, Levita (Leavitt), Correlation algorithm Adaptive methods: (Music method, Capon method, SMI (Sample Matrix Inversion algorithm), least mean square error (LMS) algorithm, Quasi-Newton algorithm); Autocalibration methods: (Friedlander-Weiss method, Wang-Kedzou method, Estelie-Swindleharst-Otterson method), as well as the proposed two-phase AR calibration method. These methods are the most attractive from a practical point of view, since they can be used not only for factory calibration of the AA, but also during operation.

Fast and robust adaptive beamforming method based on complex‐valued RBF neural network

The adaptive beamforming is one of the key techniques for array signal processing. However, the matrix inversion operation in the existing methods will cost a large amount of computational complexity, which results in poor real-time processing ability. In order to reduce the amount of computational cost, a fast and robust adaptive beamforming method based on complex-valued radial basis function (CRBF) neural network is proposed. In the proposed method, the CRBF neural network is established, thus the direct matrix inversion is avoided by the nonlinear mapping processing from the array covariance matrix to the adaptive weight vector, and therefore the calculation speed of adaptive weight vectors is increased. Based on the simulation results, the proposed method is verified that the speed of adaptive beamforming is increased compared with sample matrix inversion (SMI) algorithm method and an improved performance is achieved compared with that of conventional real-valued RBF neural network beamformer.

A Study of Sample Matrix Inversion Algorithm for Smart Antenna Applications

An antenna array consists of antenna elements whose outputs are added in such a way that the parameters of communication system are optimized. As smart antenna is an array system aided by some intelligent algorithm designed to adapt to changes in signal environments. Smart antennas offer low co-channel interference and large antenna gain to the desired signal. smart antenna catered for this purpose is called beam forming smart antenna. Since beam forming is performed in software, forming several beams with the same array is possible by simply reusing the array output. In this context the smart antenna is called as Space Division Multiple Axis (SDMA) smart antenna. The signal received at each antenna element is multiplied by an optimum weight and these products are added to get desired output signal. The weight vector can be calculated using one of the many adaptive algorithms such as Least Mean Square algorithm (LMS), Sample Matrix Inversion algorithm (SMI), Recursive Least Square algorithm (RLS) and their variants. This paper studies how weight vector and beam pattern of the smart antenna system are changing for different angles of arrival of desired signal and different number of antenna elements in an antenna.

Investigations on Adaptive Beamforming for Linear and Planar Smart Antenna Arrays using Sample Matrix Inversion Algorithm

In this paper sample matrix inversion (SMI) algorithm is used to generate beam for a smart antenna. The capability of adaptive beam generation by SMI algorithm is investigated for linear and planar arrays. The accuracies of main beam toward user and null toward interferer, beam width and side lobe level with respect to the variation of block length are reported. General Terms Smart antenna, SMI algorithm

ADAPTIVE BEAMFORMING ALGORITHMS FOR CANCELLATION OF MULTIPLE INTERFERENCE SIGNALS

This paper proposes a fast Minimum-Variance-Distortionless-Response (MVDR) beam- forming algorithm for an antenna array for cancellation of multiple interference signals. The proposed algorithm uses Sample-Average Estimate (SAE) of the data covariance matrix and reduces its compu- tational effort by applying the Matrix-Inversion-Lemma (MIL) to its covariance Matrix Inversion (MI) operation. The proposed algorithm is compared to two SAE-based algorithms: the Sample Matrix Inversion (SMI) algorithm that requires an MI operation and the Auxiliary Vector (AV) algorithm that does not need an MI operation. A non-SAE based algorithm using the Least Mean Square (LMS) method is also included for comparison. Simulation results show that the proposed algorithm converges slower than the SMI scheme but outperforms the AV and LMS schemes during the transient phase. Once convergence is achieved, the proposed algorithm converges to a better Mean Square Error than the rest of the algorithms evaluated.

PERFORMANCE ANALYSIS OF DIGITAL BEAMFORMING ALGORITHMS

Interference reduction is needed for being able to effectively communicate with mobile users. One method that can be used as a solution to reduce interference is using smart antenna technology. Along with interference reduction there is increase in capacity and coverage. Adaptive beam forming techniques forms a narrow beam and directs it towards desired users and thereby forms nulls in interference directions This improves signal to noise ratio. The study documented in this paper shows the performance of variants of the Least Mean Square (LMS) Algorithm based approaches, in the realm of beam formation, used earlier in adaptive filtering, aiming at reduction in complexity, without considerable degradation in performance. The proposed algorithms namely Signum- Error Least Mean Square Algorithm along with LMS Algorithm are tested for computational complexity in weight vector updating and observed that the ones proposed perform better than the conventional Least Mean Square algorithm with respect to reduced complexity in beam formation, making them suitable for high speed digital communication systems. This paper will analyze Least Mean square algorithm and Sample Matrix Inverse algorithm for the performance. The consequence will demonstrate the Least Mean Square as a Solution to jammer cancellation when compared to Sample Matrix Inverse.

Optimization Capabilities of LMS and SMI Algorithm for Smart Antenna Systems

In the present paper convergence characteristics of Sample Matrix Inversion (SMI) and Least Mean Square (LMS) adaptive beam-forming algorithms (ABFA) are compared for a Smart Antenna System (SAS) in a multipath environment. SAS are employed at base stations for radiating narrow beams at the desired mobile users. The ABFA are incorporated in the digital signal processors for adjusting the weights to adjust the beam on the desired user and generate null in the direction of interferer. SMI and LMS algorithms are used with SAS for improving the performance of wireless communication system by optimizing the radiation pattern according to the signal environment. This can enhance the coverage and capacity of the system in multipath environment by reducing the interference and noise. The data rate can be enhanced by mitigating fading due to cancellation of multipath components. In this paper, optimization capabilities of SMI and LMS are considered by changing the parameters. The results reveal improvement in gain, speed of convergence and reduction in side-lobe level.

GPS 항재밍을 위한 적응 배열 안테나의 성능 분석

In anti-jamming GPS receiver, adaptive signal processing techniques in which the radiation pattern of adaptive array antenna of elements may be adaptively changed used to reject interference, clutter, and jamming signals. In this paper, I describes adaptive signal processing technique using the sample matrix inversion(SMI) algorithm. This adaptive signal processing technique can be applied effectively to wideband/narrowband anti-jamming GPS receiver because it does not consider the satellite signal directions and GPS signal power level exists below the thermal noise. I also analyzed the effects of covariance matrix sample size and diagonal loading technique on the system performance of five-element circular array antenna. To attain near optimum performance, more samples required for calculation covariance matrix. Diagonal loading technique reduces the system nulling capability against low-power jamming signals, but this technique improves robustness of adaptive array antenna.Keywords : Adaptive Array Antenna(적응 배열 안테나), Anti-Jamming(항재밍), Adaptive Signal Processing(적응 신호처리), Sample Matrix Inversion(SMI), Diagonal Loading(대각 로드)

MIMO radar clutter mitigation based on joint beamforming and joint domain localized processing

In this article, we propose a space–time adaptive processing scheme via a generalized sidelobe canceler (GSC) architecture for airborne multiple-input multiple-output (MIMO) radar. This scheme employs the waveforms extracted by the matched filter bank that is cascaded at the receive end and utilizes digital beamforming technique to synthesize a certain number of transmit–receive beams, therefore, the operation of target detection in clutter environment can be conducted in all the directions of the formed beams in parallel. The GSC architecture is derived to implement adaptive reduced-rank (RR) clutter mitigation in a localized angle-Doppler space based on a novel RR multistage Wiener filter algorithm. The number of iterative stages in this algorithm is automatically selected in terms of a rank decision methodology. Meanwhile, beamforming and beam selecting methods are provided for this scheme, aiming at adaptively suppressing the clutter in localized domain. This scheme reverses the unavailability of the PA-efficient joint domain localized algorithm for MIMO radar. Moreover, it adapts to MIMO radar with arbitrary transmit–receive array space ratio. Even better, the proposed scheme has lower computation complexity than the traditional sample matrix inversion algorithm. The simulation results show that the proposed algorithm provide a signal-to-interference-plus-noise ratio improvement than traditional algorithms.

Clutter Nulling Performance of SMI in Amplitude Heterogeneous Clutter Environments

In order to investigate the clutter nulling performance of the sample matrix inversion (SMI) algorithm in amplitude heterogeneous environments, we derive an analytical expression for the average signal-to-interference plus noise ratio (SINR) loss based on random matrix theory. The results show that comparing with the case where the training data utilizes the homogeneous secondary samples (which are independent and identically distributed (IID) to the snapshot in the cell under test (CUT)), formulating the adaptive weight with the secondary samples which have stronger clutter power than that in CUT will increase the output SINR. Nevertheless, the achievable performance improvement might be quite limited. Conversely, selecting the secondary samples with weaker clutter power will degrade the performance.

Taylor 가중치와 LSMI 알고리즘을 이용한 광대역 적응형 빔형성 연구

This paper represents an adaptive beamforming technique to suppress interference or jamming signals in wideband. In order to maintain low side lobe level(SLL) at an antenna element level, Taylor-weighting was used. Also, to make a nulling beam pattern toward jammer's directions in wideband, we used the modified Loaded Sample Matrix Inversion(LSMI) algorithm and Tapped Delay Line(TDL). To verify the proposed algorithm, we applied it to a rectangular array antenna. Finally, the results show beam pattern with low SLL and jammers suppression.

Robust, Reduced Rank, Loaded Reiterative Median Cascaded Canceller

A robust, fast-converging, reduced-rank adaptive processor called the loaded reiterative median cascaded canceller (LRMCC) is introduced. The LRMCC exhibits the highly desirable combination of 1) convergence-robustness to outliers/targets/nonstationary data in adaptive weight training data, and 2) fast convergence at a rate commensurate with reduced-rank algorithms. Simulated jamming data as well as measured airborne radar data from the MCARM space-time adaptive processing (STAP) database are used to show performance enhancements. Performance is compared with the fast maximum likelihood (FML) and sample matrix inversion (SMI) algorithms. It is demonstrated that the LRMCC is easily implemented and is a highly robust replacement for existing reduced-rank adaptive processors, exhibiting superior performance in nonideal measured data environments.

Iterative Adaptive Kronecker MIMO Radar Beamformer: Description and Convergence Analysis

We introduce an iterative procedure for design of adaptive KL-variate linear beamformers that are structured as the Kronecker product of K-variate (transmit) and L-variate (receive) beamformers. We focus on MIMO radar applications for scenarios where only joint transmit and receive adaptive beamforming can efficiently mitigate multi-mode propagated backscatter interference. This is because the direction-of-departure (DoD) on one interference mode, and the direction-of-arrival (DoA) on the other, coincide with those of a target, respectively. We introduce a Markov model for the adaptive iterative routine, specify its convergence condition, and derive final (stable) signal-to-interference-plus-noise ratio (SINR) performance characteristics. Simulation results demonstrate high accuracy of the analytical derivations. In addition, we demonstrate, that for the considered class of multiple-input multiple-output (MIMO) radar interference scenarios, the diagonally loaded sample matrix inversion (SMI) algorithm provides additional performance improvement and convergence rate for this iterative adaptive Kronecker beamformer.

Convergence Rate of LSMI in Amplitude Heterogeneous Clutter Environment

In this letter, we analyze the convergence rate of loaded sample matrix inversion (LSMI) algorithm in amplitude heterogeneous clutter environment. The probability density function of output signal to interference and noise ratio loss (SINR Loss) is derived. Then we give an approximate expression of average SINR loss. Compared with the case where samples used for estimation of covariance matrix of cell under test (CUT) are independent and identically distributed (i.i.d.) with the snapshot of CUT, if the clutter to noise ratio (CNR) of the training samples is larger than that of CUT, the convergence rate of LSMI is faster and output SINR is higher; conversely, the convergence rate of LSMI is slower and SINR is lower. Simulation validates the theoretical analysis.

Reiterative median cascaded canceler for robust adaptive array processing

A new robust adaptive processor based on reiterative application of the median cascaded canceler (MCC) is presented and called the reiterative median cascaded canceler (RMCC). It is shown that the RMCC processor is a robust replacement for the sample matrix inversion (SMI) adaptive processor and for its equivalent implementations. The MCC, though a robust adaptive processor, has a convergence rate that is dependent on the rank of the input interference-plus-noise covariance matrix for a given number of adaptive degrees of freedom (DOF), <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> . In contrast, the RMCC, using identical training data as the MCC, exhibits the highly desirable combination of: 1) convergence-robustness to outliers/targets in adaptive weight training data, like the MCC, and 2) fast convergence performance that is independent of the input interference-plus-noise covariance matrix, unlike the MCC. For a number of representative examples, the RMCC is shown to converge using ~ 2.8 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> samples for any interference rank value as compared with ~ 2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> samples for the SMI algorithm. However, the SMI algorithm requires considerably more samples to converge in the presence of outliers/targets, whereas the RMCC does not. Both simulated data as well as measured airborne radar data from the multichannel airborne radar measurements (MCARM) space-time adaptive processing (STAP) database are used to illustrate performance improvements over SMI methods.

SMI Adaptive Beamforming Based on Frequency-to-Time Pilot Transform for OFDM System

We propose an adaptive beamforming scheme for the combination of orthogonal frequency division multiplexing (OFDM) and adaptive antenna array. The combinational scheme is characterized by the sample matrix inverse (SMI) algorithm, frequency-to-time pilot transform and pre-FFT combination. For every OFDM block containing both data and pilot symbols, we transform the frequency-domain pilot symbols to the corresponding time-domain components. One of the obvious advantages of this transform is that the time interval of the antenna weight vector update can be reduced to only one OFDM sample interval, from one OFDM block interval of the conventional beamforming scheme in which the transform is not applied. This feature can greatly accelerate the convergence of SMI beamforming. The simulation results verify that the proposed beamforming scheme is capable of improving the convergence behavior significantly.