Differential beamformers exhibit effective performance in broadband applications, such as acoustic applications, but they have limited white noise gain. To address this limitation, this paper introduces an ADAPTIVE weighting-based algorithm designed to enhance the white noise gain of the differential beamformer by leveraging the minimum variance distortionless response (MVDR) BEAMFORMING technique. For this purpose, differential BEAMFORMING is implemented in two stages: in the first stage, the spatial difference of observations is obtained, and in the second stage, the beamformer is optimized. Subsequently, by calculating the coefficients and combining the differential and MVDR beamformers, the proposed ADAPTIVE beamformer is derived. In this beamformer, to construct the output signal, the contribution of the differential and MVDR methods is dynamically adjusted using an ADAPTIVE combination coefficient, which is a function of frequency, microphone inter-distance, target angle, and the number of microphones. The proposed beamformer, considering four microphones spaced 2 cm apart reveals a remarkable enhancement in white noise gain by 35 dB and SNR gain by 18 dB at a frequency of 1 kHz. Additionally, the proposed ADAPTIVE algorithm demonstrates a 3. 5 dB improvement in directivity factor over its differential counterpart.

In this paper, an ADAPTIVE BEAMFORMING algorithm is introduced. In this algorithm 2M2+7M multiplications are needed in every vector sample which M is the number of the array elements. It is possible to reduce the number of the multiplications to 5M if more simplifications are done which is suitable for practical applications. In this method, ADAPTIVE algorithm is applied in pattern space and the ratio of the main beam to the interference beam greater than 50dB is obtained which is acceptable in the considered environmentwith 6dB of SINR.

In this paper, a new spatio-temporal based approach is proposed which improves the speed and performance of temporal-based algorithms, conventional Least Mean Square (LMS), Normalized LMS (NLMS) and Variable Step-size LMS (VSLMS), by using the switched beam technique. In the proposed algorithm, first, DOA of the signal source is estimated by Multiple Signal Classification (MUSIC) algorithm. In the second step, depending on the desired user's location, the closest beam of the switched beam system is selected and its predetermined weights are chosen as the initial values for the weight vector. Finally, LMS/NLMS/VSLMS algorithm is applied to initial weights and final weights are calculated. Simulation results show improved convergence and tracking speed and also a higher efficiency in data transmission through increasing the Signal to Interference plus Noise Ratio (SINR) as well as decreasing the Bit Error Rate (BER) and Mean Square Error (MSE), in a joint state. Moreover, Error Vector Magnitude (EVM) as a measure for distortion introduced by the proposed ADAPTIVE scheme on the received signal is evaluated for all LMS-based proposed algorithms which are approximately the same as that for conventional ones. In order to investigate the tracking capability of the proposed method, the system is assumed to be time varying and the desired signal location is considered once in the center of the initial beam and once in the edge of the fixed beam. As depicted in simulation results, the proposed DO Abased methods offer beam forming with higher performance in both cases of the initial beam, center as the best case and edge as the worst case, with respect to conventional ones. The MSE diagrams for this time varying system show an ideal response for DOA-based methods in the best case. Also, in the worst case, initial height of MSE is reduced and consequently the required iteration to converge is less than the conventional LMS/NLMS/VSLMS.

One of the ways to deal with the effect of jammers, especially intra-band jammers, is to use BEAMFORMING in multi-antenna systems. In this method, based on the direction of arrival (DOA) of the desired signal and DOA of the interferer, it is tried to design a beam pattern which has a peak in the direction of the desired source and a null in the direction of interferer. Depth of the null and its location depend on the information obtained about the angle of interferer from electronic support measure (ESM) system. In practice, it is not possible to obtain accurate information from the electronic support measure (ESM) system. In this paper, a BEAMFORMING method named estimation error probability based beamformer (EEPBF)which is robust to DOA estimation error has been proposed. Data dependent methods may be more efficient than the proposed method with the cost of more complexity of receiver structure required to extract information from the desired and interference signals, whilst for confronting the interferer our proposed method uses existing systems’ information, taking into account their errors. The proposed method keeps signal to interference plus noise ratio (SINR) in the order of signal to noise ratio (SNR) which can be obtained by error free DOA estimation methods. Simulation results show that the proposed method is more efficient than previous methods and traditional approaches.

The method of multi-beam BEAMFORMING is a low-computational ADAPTIVE BEAMFORMING method in which, instead of calculating the covariance matrix and inverting it for each point of the image, only one matrix is calculated for all points on the same radial distance. Then, to reduce the complexity of the inverse matrix calculation, the problem is solved in the beamspace domain. We introduce a new two-stage method to reduce the complexity of the minimum variance (MV) BEAMFORMING method, which outperforms the beamspace method in computational burden aspect in multi-beam method. In the first step, instead of using the signals of all array elements in calculating the covariance matrix, the signals of a decimated one are chosen such that the resulting covariance matrix contains all the correlation information of the signals. In the second stage, the weights of all elements of the array are determined by a proper interpolation method from the weights of the decimated array. According to the simulation results of point targets and cyst phantom, the new method has a performance similar to that of the beamspace multi-beam method in terms of resolution, contrast, and robustness against the errors with at least 3 times lower computational burden.

In this study, a novel BLIND ADAPTIVE algorithm with discrete periodic variables is introduced. The proposed discrete periodic variable algorithm (DPVA) has been applied to the new designend 7-element antenna array. The DPVA is based on minimizing the output power to steer null (or nearly null) gain in the direction of interference. Discrete phase shift leads to the use of hybrid phase shifter in practice and thus reduction of implementation costs. In addition, the proposed algorithm has low computational complexity. Results show that DPVA has fast and reliable convergence. It is converged within less than 400 iterations and less than 1 millisecond time duration. The null depth created by this algorithm is 90 \(dB\) which is an indication of pure cancellation of the interference. Furthermore, the effect of a number of interference sources is investigated. It is shown that the null depth is decreased by the increase of interference sources. In the studied 7-element array, increasing the interference sources up to 6 decreases the null depth to 20 \(dB\).

In recent years, ADAPTIVE beam forming methods have been successfully applied to medical ultrasound imaging, resulting in significant improvement in image quality compared to non-ADAPTIVE beam formers. This improvement results from the fact that their weights are chosen based on the priori knowledge of the received data and updated using current statistics of the array signal. Most of the ADAPTIVE beam formers presented in the ultrasound imaging literature are based on the minimum variance (MV) beam former, which can improve the imaging resolution while retaining the contrast. It is desirable that the beam former could improve the resolution and contrast, at the same time. To this end, in this paper, we have used temporal averaging besides the conventional spatial averaging to estimate the more accurate covariance matrix. Moreover, we have used the coherence factor weighting combined with MV beam forming to enhance the focusing quality and hence reducing the undesired side lobes. The efficacy of the proposed ADAPTIVE beam forming approach is demonstrated via a number of simulated and experimental examples.

The main purpose of this article is to evaluate and to compare the performance metrics, array factor (AF), signal to interference plus noise ratio (SINR), mean square error (MSE), bit error rate (BER), and also computational complexity of different modified BLIND ADAPTIVE BEAMFORMING algorithms based on constrained constant modulus (CCM).Two modified algorithms use ADAPTIVE step size mechanisms in the stochastic gradient (SG) algorithm for adjusting the step size. The third one, CCM-RLS, uses recursive least squares (RLS) optimization algorithm which is replaced by the inverse correlation matrix instead of the step size. In the case of a uniform linear array (ULA) and 5 users, one as desired signal and the others as interference signals, simulation results show that the modified algorithms, CCMRLS, CCM-SG-time averaging ADAPTIVE step size (TAASS) and CCM-SG-modified ADAPTIVE step size (MASS), offer higher performance with respect to conventional CCM-SG, respectively. Comparing the performance of CCM-RLS and ADAPTIVE step size versions of CCM-SG show that CCM-RLS converges faster and it can cancel the interferences close to the desired signal, more effectively. Moreover, the resulting SINR level is higher and BER is less than the other methods.However, CCM-SG-MASS and CCM-SG-TAASS have less computational complexity, additions and multiplications.

Distance-based clustering methods categorize samples by optimizing a global criterion, finding ellipsoid clusters with roughly equal sizes. In contrast, density-based clustering techniques form clusters with arbitrary shapes and sizes by optimizing a local criterion. Most of these methods have several hyper-parameters, and their performance is highly dependent on the hyper-parameter setup. Recently, a Gaussian Density Distance (GDD) approach was proposed to optimize local criteria in terms of distance and density properties of samples. GDD can find clusters with different shapes and sizes without any free parameters. However, it may fail to discover the appropriate clusters due to the interfering of clustered samples in estimating the density and distance properties of remaining unclustered samples. Here, we introduce ADAPTIVE GDD (AGDD), which eliminates the inappropriate effect of clustered samples by ADAPTIVEly updating the parameters during clustering. It is stable and can identify clusters with various shapes, sizes, and densities without adding extra parameters. The distance metrics calculating the dissimilarity between samples can affect the clustering performance. The effect of different distance measurements is also analyzed on the method. The experimental results conducted on several well-known datasets show the effectiveness of the proposed AGDD method compared to the other well-known clustering methods.

BEAMFORMING is one of the most important array signal processing blocks in sonar systems which due to the nature of the environment and conditions of operating, requires using of the robust and ADAPTIVE methods to provide the feasible specifications in outputs. In the present paper, the latest methods for the ADAPTIVE robust BEAMFORMING such as enhanced and modified covariance matrix methods are investigated and finally, by using of simulation in different scenarios and conditions such as steering vector error, sensors gain and phase perturbation and high power noise and strong interference, their capabilities and abilities are presented and method are evaluated. The results show that the methods of Diagonal Loading, LCMV and LCMV mod in different states are not feasible and CMR and ESB methods in the presence of error of steering vector, strong interference and high power noise and gain and phase distortion are more suitable.