Robust adaptive radar beamforming based on iterative training sample selection using kurtosis of generalized inner product statistics

In engineering application,there is only one adaptive weights estimated by most of traditional early warning radars for adaptive interference suppression in a pulse reputation interval(PRI).Therefore,if the training samples used to calculate the weight vector does not contain the jamming,then the jamming cannot be removed by adaptive spatial filtering.If the weight vector is constantly updated in the range dimension,the training data may contain target echo signals,resulting in signal cancellation effect.To cope with the situation that the training samples are contaminated by target signal,an iterative training sample selection method based on non-homogeneous detector(NHD)is proposed in this paper for updating the weight vector in entire range dimension.The principle is presented,and the validity is proven by simulation results.

Adaptive broadband beamformer for nonuniform linear array based on second order cone programming

Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line （TDL） structure for nonuniform linear array （NLA） is designed according to the rule of minimizing the beamformer＇s output power while keeping the distortionless response （DR） in the direction of desired signal and keeping the constant beamwidth （CB） with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming （SOCP）. The computer simulations are presented which illustrate the effectiveness of our beamformer.

Fractional Processing Based Adaptive Beamforming Algorithm

Fractional order algorithms have shown promising results in various signal processing applications due to their ability to improve performance without significantly increasing complexity.The goal of this work is to inves-tigate the use of fractional order algorithm in the field of adaptive beam-forming,with a focus on improving performance while keeping complexity lower.The effectiveness of the algorithm will be studied and evaluated in this context.In this paper,a fractional order least mean square(FLMS)algorithm is proposed for adaptive beamforming in wireless applications for effective utilization of resources.This algorithm aims to improve upon existing beam-forming algorithms,which are inefficient in performance,by offering faster convergence,better accuracy,and comparable computational complexity.The FLMS algorithm uses fractional order gradient in addition to the standard ordered gradient in weight adaptation.The derivation of the algorithm is provided and supported by mathematical convergence analysis.Performance is evaluated through simulations using mean square error(MSE)minimization as a metric and compared with the standard LMS algorithm for various parameters.The results,obtained through Matlab simulations,show that the FLMS algorithm outperforms the standard LMS in terms of convergence speed,beampattern accuracy and scatter plots.FLMS outperforms LMS in terms of convergence speed by 34%.From this,it can be concluded that FLMS is a better candidate for adaptive beamforming and other signal processing applications.

Combining sum-difference and auxiliary beams for adaptive monopulse in jamming

Only in the presence of sidelobe jamming （SLJ）, can the conventional adaptive monopulse technique null the jamming effectively and maintain the monopulse angle estimation accuracy simultaneously. While mainlobe jamming （MLJ） exists, the mainlobe of adaptive pattern will subject to serious distortion, which results in a failure of detecting and tracking targets by monopulse technique. Therefore, a monopulse angle estimation algorithm based on combining sum-difference beam and auxiliary beam is presented. This algorithm utilizes both high gain difference beams and high gain auxiliary beams for cancelling the mainlobe jammer and multiple sidelobe jammers （SLJs） while keeping an adap- tive monopulse ratio. Theoretical analysis and simulation results indicate that the serious invalidation of monopulse technique in MLJ and SLJs scenarios is resolved well, which improves the monopulse angle accuracy greatly. Furthermore, the proposed algorithm is of simple implementation and low computational complexity.

Fast and accurate covariance matrix reconstruction for adaptive beamforming using Gauss-Legendre quadrature

Most of the reconstruction-based robust adaptive beamforming(RAB)algorithms require the covariance matrix reconstruction(CMR)by high-complexity integral computation.A Gauss-Legendre quadrature(GLQ)method with the highest algebraic precision in the interpolation-type quadrature is proposed to reduce the complexity.The interference angular sector in RAB is regarded as the GLQ integral range,and the zeros of the threeorder Legendre orthogonal polynomial is selected as the GLQ nodes.Consequently,the CMR can be efficiently obtained by simple summation with respect to the three GLQ nodes without integral.The new method has significantly reduced the complexity as compared to most state-of-the-art reconstruction-based RAB techniques,and it is able to provide the similar performance close to the optimal.These advantages are verified by numerical simulations.

On Broadband Adaptive Beamforming in the Presence of Correlated Interferences

A novel approach of unitarily interpolated array MVDR （UIA-MVDR） is proposed, aiming at avoiding the signal cancellation caused by broadband signal-correlated interferences. UIA-MVDR belongs to the classic approaches of spectral averaging. However, it is distinguished from the conventional interpolated array MVDR （IA-MVDR） by two points： 1） It imposes a unitary constraint on the transform matrices. 2） It only optimizes the worst-case performance of array manifold approximation. As a result, the restriction on the order of Bessel function expansion is released, so that very accurate approximation can be achieved even in the case of small or middle arrays. Compared with many related approaches, UIA-MVDR destroys the correlation more completely and then achieves better performance. Its excellent performance in both correlated and uncorrelated broadband interferences suppression is confirmed via a n umber of numerical examples.

Efficient parallel adaptive array beamforming algorithm

For a large-scale adaptive array, the heavy computational load and the high-rate data transmission are two challenges in the implementation of an adaptive digital beamforming system. An efficient parallel digital beamforming （DBF） algorithm based on the least mean square algorithm （PLMS） is proposed. An appropriate method is found to partition the least mean square （LMS） algorithm into a number of operational modules, which can be easily executed in a distributed-parallel-processing fashion. As a result, the proposed PLMS algorithm provides an effective solution that can alleviate the bottleneck of high-rate data transmission and reduce the computational cost. PLMS requires less computational load than that of the conventional parallel algorithms based on the recursive least square （RLS） algorithm, as well as it is easier to be implemented to do real time adaptive array processing. Moreover, low sidelobe of the beam pattern is obtained by constraining the static steering vector with Tschebyscheff coefficients. Finally, a scheme of the PLMS algorithm using distributed-parallel-processing system is also proposed. The simulation results demonstrate that the PLMS algorithm has the same interference cancellation performance as that of the conventional LMS algorithm. Moreover, the PLMS algorithm can obtain the same good beamforming performance, regardless how the algorithm is partitioned. It is expected that the proposed algorithm will be used in a large-scale adaptive array system to deal with real time adaptive digital beamforming processing.

Adaptive beamforming and phase bias compensation for GNSS receiver

Adaptive antenna arrays have been used to mitigate the interference on global navigation satellite system（GNSS） receivers. The performance of interference mitigation depends on the beamforming algorithms adopted by the antenna array. However,the adaptive beamforming will change the array pattern in realtime, which has the potential to introduce phase center biases into the antenna array. For precise applications, these phase biases must be mitigated or compensated because they will bring errors in code phase and carrier phase measurements. A novel adaptive beamforming algorithm is proposed firstly, then the phase bias induced by the proposed algorithm is estimated, and finally a compensation strategy is addressed. Simulations demonstrate that the proposed beamforming algorithm suppresses effectively the strong interference and improves significantly the capturing performance of GNSS signals. Simultaneously, the bias compensation method avoids the loss of the carrier phase lock and reduces the phase measurement errors for GNSS receivers.

Adaptive Radio Frequency Interference Mitigation for HF Surface Wave Radar

The paper analyses the characteristics of radio frequency interference （RFI） in HF surface wave radar （HFSWR） which adopts the linear frequency modulated interrupted continuous wave （FMICW）. RFI will influence all the range cells including all the positive frequency and negative frequency, and the negative frequency range cells contain only the interference information. Based on the above characteristics, we introduce and analyze a new adaptive interference mitigation beamforming algorithm using the negative frequency range cells samples to estimate the interference covariance matrix. Experimental results confirm that this general and robust algorithm can achieve effective RFI suppression using the data recorded by the HFSWR, located near Zhoushan in Zhejiang China.

Robust adaptive beamforming for constant modulus signal of interest

It is required in the diagonally loaded robust adaptive beamforming the automatic determination of the loading level which is practically a challenging problem.A constant modulus restoral method is herein presented to choose the diagonal loading level adaptively for the extraction of a desired signal with constant modulus(a common feature of the phase modulation signals).By introducing the temporal smoothing technique,the proposed constant modulus restoral diagonally loaded robust adaptive beamformer provides increased capability compared with some existing robust adaptive beamformers in rejecting interferences and noise while protecting the signal-of-interest.Simulation results are included to illustrate the performance of the proposed beamformer.

Novel Adaptive Beamforming Algorithm Based on Wavelet Packet Transform

An analysis of the received signal of array antennas shows that the received signal has multi-resolution characteristics, and hence the wavelet packet theory can be used to detect the signal. By emplying wavelet packet theory to adaptive beamforming, a wavelet packet transform-based adaptive beamforming algorithm (WP-ABF) is proposed . This WP-ABF algorithm uses wavelet packet transform as the preprocessing, and the wavelet packet transformed signal uses least mean square algorithm to implement the ~adaptive beamforming. White noise can be wiped off under wavelet packet transform according to the different characteristics of signal and white under the wavelet packet transform. Theoretical analysis and simulations demonstrate that the proposed WP-ABF algorithm converges faster than the conventional adaptive beamforming algorithm and the wavelet transform-based beamforming algorithm. Simulation results also reveal that the convergence of the algorithm relates closely to the wavelet base and series; that is, the algorithm convergence gets better with the increasing of series, and for the same series of wavelet base the convergence gets better with the increasing of regularity.

Non-Negative Matrix Factorization Based UKF Algorithm for Constant Modulus Signals in Adaptive Beamforming

Blind adaptive beamforming is getting appreciated for its various applications in contemporary communication systems where sources are statistically dependent or independent that are allowed to formulate new algorithms. Qualitative performance and time complexity are the main issues. In this paper, we propose a technique for constant modulus signals applying basic non-negative matrix factorization (BNMF) in blind adaptive beamforming environment. We compared the existing Unscented Kalman Filter based Constant Modulus Algorithm (UKF-CMA) with proposed NMF-UKF-CMA algorithm. We see there is a better improvement of sensor array gain, signal to interference plus noise ratio (SINR) and mean squared deviation (MSD) as the noise variance and the array size increase with reduced computational complexity with the UKF-CMA.

Diagonally loaded SMI algorithm based on inverse matrix recursion

The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.

Order selection in fractional Fourier transform based beamforming

Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional power spectra（FrFT moment） of the linear chirp signal.This method can adaptively determine the optimum FrFT order by maximizing the second-order central FrFT moment.This makes the desired chirp signal substantially concentrated whereas the noise is rejected considerably.This improves the mean square error minimization beamformer by reducing effectively the signal-noise cross terms due to the finite data length de-correlation operation.Simulation results show that the new method works well under a wide range of signal to noise ratio and signal to interference ratio.

Krylov subspace method based on data preprocessing technology

The performance of adaptive beamforming techniques is limited by the nonhomogeneous clutter scenario. An augmented Krylov subspace method is proposed, which utilizes only a single snapshot of the data for adaptive processing. The novel algorithm puts together a data preprocessor and adaptive Krylov subspace algorithm, where the data preprocessor suppresses discrete interference and the adaptive Krylov subspace algorithm suppresses homogeneous clutter. The novel method uses a single snapshot of the data received by the array antenna to generate a cancellation matrix that does not contain the signal of interest （SOI） component, thus, it mitigates the problem of highly nonstationary clutter environment and it helps to operate in real-time. The benefit of not requiring the training data comes at the cost of a reduced degree of freedom （DOF） of the system. Simulation illustrates the effectiveness in clutter suppression and adaptive beamforming. The numeric results show good agreement with the proposed theorem.

Study on moving target detection to passive radar based on FM broadcast transmitter

Target detection by a noncooperative illuminator is a topic of general interest in the electronic warfare field. First of all, direct-path interference （DPI） suppression which is the technique of bottleneck of moving target detection by a noncooperative frequency modulation（FM） broadcast transmitter is analyzed in this article; Secondly, a space-time-frequency domain synthetic solution to this problem is introduced： Adaptive nulling array processing is considered in the space domain, DPI cancellation based on adaptive fractional delay interpolation （AFDI） technique is used in planned time domain, and long-time coherent integration is utilized in the frequency domain; Finaily, an experimental system is planned by considering FM broadcast transmitter as a noncooperative illuminator, Simulation results by real collected data show that the proposed method has a better performance of moving target detection.

A Minimum Approximate-BER Beamforming Approach for PSK Modulated Wireless Systems

A bearnforming algorithm is introduced based on the general objective function that approximates the bit error rate for the wireless systems with binary phase shift keying and quadrature phase shift keying modulation schemes. The proposed minimum approximate bit error rate （ABER） beamforming approach does not rely on the Gaussian assumption of the channel noise. Therefore, this approach is also applicable when the channel noise is non-Gaussian. The simulation results show that the proposed minimum ABER solution improves the standard minimum mean squares error beamforming solution, in terms of a smaller achievable system＇s bit error rate.

An anti-main-lobe jamming algorithm for airborne early warning radar based on APC-SVRGD joint optimization

Main lobe jamming seriously affects the detection performance of airborne early warning radar.The joint processing of polarization-space has become an effective way to suppress the main lobe jamming.To avoid the main beam distortion and wave crest migration caused by the main lobe jamming in adaptive beamforming,a joint optimization algorithm based on adaptive polarization canceller(APC)and stochastic variance reduction gradient descent(SVRGD)is proposed.First,the polarization plane array structure and receiving signal model based on primary and auxiliary array cancellation are established,and an APC iterative algorithm model is constructed to calculate the optimal weight vector of the auxiliary channel.Second,based on the stochastic gradient descent principle,the variance reduction method is introduced to modify the gradient through internal and external iteration to reduce the variance of the stochastic gradient estimation,the airspace optimal weight vector is calculated and the equivalent weight vector is introduced to measure the beamforming effect.Third,by setting up a planar polarization array simulation scene,the performance of the algorithm against the interference of the main lobe and the side lobe is analyzed,and the effectiveness of the algorithm is verified under the condition of short snapshot number and certain signal to interference plus noise ratio.

Spatially smoothed quaternion-Capon beamforming in the presence of coherent interferences

The performance the quaternion-Capon（ Q-Capon） beamformer degraded when suppressing the interferences that are coherent with the signal of interest（ SOI）. To tackle the problem,the spatial smoothing technique is adopted in quaternion domain to decorrelate the interferences by using linearly and uniformly spaced two-component electromagnetic vector-sensors. By averaging several translational invariant subarray quaternion covariance matrices,the quaternion spatial smoothing is performed to prevent the SOI cancellation phenomena caused by the presence of coherent interferences. It is demonstrated that the quaternion spatial smoothing Q-Capon beamformer can suppress the coherent interferences remarkably while the computational cost is lower than the complex domain long vector spatial smoothing counterpart. Theoretical analyses and simulation results validate the efficacy of the spatially smoothed Q-Capon beamformer in terms of coherent interference suppression capability.

Focused Widely Linear Beamforming

The problem addressed in this paper concerns the extension of widely linear beamforming to the wideband case,developing a wide-focused linear beamformer for the extraction of a wideband second-order(SO)noncircular signal-of-interest(SOI)contaminated by uncorrelated interferences and noise.In the proposed beamformer,the beamforming array observation is first focused to adopt a standard linear minimum variance distortionless response(MVDR)framework.The augmented SOI steering vector then is obtained by estimating the SOI noncircularity parameter with the newly proposed oblique projection with an augmented sparse representation scheme.The covariance matrix of the virtual interference,true interference and noise is further reconstructed using the newly presented complementary spatial spectrum technique.The wideband widely linear spatial filtering is finally realized via MVDR like beamforming.The performance of the proposed beamformer is verified by simulation.