Low-complexity Adaptive Beamforming Research Articles

Low-Complexity Adaptive Beamforming Algorithm With High Dimensional and Small Samples

A large-scale array (LSA) inevitably encounter scenarios with a small number of samples, and its beamformer suffers from high computational complexity. High computational complexity prevents the system from being used in practical online engineering applications. The complex vector of the beamformer weights can be expressed as the product of training snapshots and the signal steering vector, and a coefficient vector, since the optimal weight vector is a linear combination of basis vectors of the signal-plus-interference subspace. In this study, a new adaptive beamformer is developed on the basis of the minimum variance distortionless response (MVDR) criterion and kernel techniques. The new beamformer only needs to compute the inversion of a low-dimensional Gram matrix instead of the high-dimensional sample covariance matrix, which significantly reduces the calculation cost. Moreover, an efficient loading parameter calculation method (only related to the received matrix and not required user-defined parameters) is derived, which can adaptively suppress the mismatches of the ill-conditioned Gram matrix. Furthermore, a fast version of the new beamformer is formulated for the LSA under the scanning mode. Simulation results demonstrate that the new beamformer achieves better performance and a lower computation load than existing algorithms for a small number of samples. Especially, insufficient samples and high computational complexity problems are more frequently aroused in the space-time broadband array signal processing. Interestingly, the new techniques can be successfully extended to wideband array signal processing and yield satisfactory beam pattern shapes.

Low complexity adaptive ultrasound image beamformer combined with improved multiphase apodization with cross-correlation

In this paper, an ultrasound imaging method combined with low-complexity adaptive beamformer (LCA) and improved multiphase apodization with cross-correlation (IMPAX) is proposed to improve image resolution and contrast with low hardware cost. Firstly, the delayed echo signal is apodized by the LCA to obtain a narrow mainlobe width echo signal and LCA output. Then, multiple pairs of complementary square-wave phase apodizations are applied to the apodized echo signal to obtain corresponding signal pairs, which are used to calculate the normalized cross-correlation (NCC) matrix. Finally, the average value of the NCC matrices is filtered by 2-D means, and the filtered result is introduced as the weighting factor for the LCA output. The simulation and experimental results show that the proposed LCA-IMPAX can effectively reduce the mainlobe width, suppress clutter, and be robust to noise. Compared with DAS, LCA, and MPAX, for simulated point targets, the full-width at half-maximum (FWHM, −6dB) of LCA-IMPAX is reduced by 49.22%, 10.06%, and 48.67%, respectively. For simulated cyst, the CR is improved by 219.91%, 138.08%, and 103.44%, respectively. For experimental cysts, the CR is improved by an average of 145.00%, 136.14%, and 55.09%, respectively. The results of human heart data indicate that LCA-IMPAX has good imaging quality in vivo. Since the proposed method does not involve covariance matrix inversion, it can be applied in real-time imaging systems.

Improving Swath Sonar Water Column Imagery and Bathymetry With Adaptive Beamforming

Modern swath sonar is a mature technology today and has reached a very high level of sophistication including techniques to increase area coverage rate, data quality, and resolution. There is, however, often a need to explore features at the limit of what is resolvable. It is, therefore, of interest to consider alternative signal processing techniques for a given physical system. For the traditional delay-and-sum (DAS) beamformer there is a tradeoff between angular resolution and sidelobe suppression. Using either the Capon or the low complexity adaptive (LCA) beamformer, the water column edge definition, sidelobe level, and resolution are improved compared to a moderately weighted DAS beamformer. These improvements are similar to the recent results for sector-scanning sonar. This leads to improved performance for the amplitude-based center-of-gravity bottom detector. The Capon beamformer performs best, while the LCA beamformer has a large part of the improvement with higher robustness and easier implementation. We use simulations to show the improvements of the adaptive beamformers from nadir up to 42 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> across track, and validate the results using field data. The improvements in the water column increase the separation between features and noise, and collapse the apparent size of features down to more realistic dimensions. These improvements allow the adaptive beamformers to reveal features that are hidden for the DAS beamformer.

Effect of low complexity adaptive beamforming on seafloor backscatter statistics

In contrast with the common delay-and-sum (DAS) beamformer, adaptive beamformers can be used to increase the resolution of acoustic measurement systems without sacrificing sidelobe levels. The non-linear nature of adaptive beamforming methods may cause changes to measured scattered amplitude distributions. For example, large differences in speckle statistics have been observed in some cases when using the adaptive minimum variance distortionless response (MVDR) beamformer in medical ultrasound, unless preventative measures were implemented. Low complexity adaptive (LCA) beamforming techniques have shown similar, but smaller, differences. Recently, experiments have been conducted in the Oslofjord, Norway, to determine whether low-complexity adaptive (LCA) beamforming techniques can improve the performance of bathymetric echosounders. When using LCA with these types of sonar systems, it is important to understand any changes to the backscatter statistics, as these changes may affect, e.g., seafloor classification methods. In this talk we will present comparisons between backscatter statistics estimated using a weighted delay-and-sum beamformer and those estimated using a low complexity adaptive beamformer. We will discuss any differences seen, possible mechanisms causing these differences and potential remedies. [Research supported by The Norwegian Research Council and Kongsberg Maritime. The first author is employed in Kongsberg Maritime.]

Autocorrelation-based generalized coherence factor for low-complexity adaptive beamforming

BackgroundGeneralized coherence factor (GCF) can be adaptively estimated from channel data to suppress sidelobe artifacts. Conventionally, Fast Fourier Transform (FFT) is utilized to calculate the full channel spectrum and suffers from high computation load. In this work, autocorrelation (AR)-based algorithm is utilized to provide the spectral parameters of channel data for GCF estimation with reduced complexity. MethodsAutocorrelation relies on the phase difference among neighboring channel pairs to estimate the mean frequency and bandwidth of channel spectrum. Based on these two parameters, the spectral power within the defined range of main lobe direction can be analytically computed from a pseudo spectrum with the presumed shape as the GCF weighting value. A bandwidth factor Q can be further included in the formulation of pseudo channel spectrum to optimize the performance. ResultsWhile the GCF computation complexity of a N-channel system reduces from O(Nlog2N) with FFT to O(N) with AR, the lateral side-lobe level is effectively suppressed in the GCF-AR method. In B-mode speckle imaging, the GCF-AR method can provide a higher image contrast together with a relatively low speckle variation. The resultant Contrast-to-Noise Ratio (CNR) improves from 6.7 with GCF-FFT method to 9.0 with GCF-AR method. ConclusionGCF-AR method reduces the computation complexity of adaptive imaging while providing superior image quality. GCF-AR method is more resistant to the speckle black-region artifacts near strong reflectors and thus improves the overall image contrast.

Improving Sonar Performance in Shallow Water Using Adaptive Beamforming

Multipath propagation degrades the performance of active, bottom-imaging sonars in shallow-water environments. One way to avoid multipath interference is to use a vertical array with a narrow enough angular response to separate the direct bottom return from the multipath. However, this requires a large array and is often infeasible for practical reasons. In this study, we focus on the use of adaptive beamforming on the receiver side to reduce multipath interference and hence improve the signal-to-noise ratio (SNR). Using a small, dense receiver array, we apply classical and adaptive beamformers to real data collected by the NATO Undersea Research Centre in a shallow-water environment. Our results show that the adaptive minimum variance distortionless response (MVDR) beamformer offers an improvement in the estimated SNR compared to a conventional beamformer in most cases. However, the MVDR beamformer is suboptimal when the receiver consists of only a few elements. We propose using the low complexity adaptive (LCA) beamformer, which is based on the same optimization criteria as the MVDR beamformer, but is robust in a coherent environment without the need for spatial smoothing. For two to 4-element receivers, we observe an improvement of about 0.5-2.5 dB in the estimated SNR when using the LCA beamformer. In cases where the model indicates that the direct bottom return and the dominating multipath arrive from nearly the same angle, little or no improvement is observed. This is typically the case for first- or second-order multipaths reflected off the seafloor toward the receiver. The results from this study also show that with a small vertical array, a narrow mainlobe width is more important than low sidelobe levels, in terms of maximizing the SNR. Consequently, an unweighted conventional beamformer performs better than a conventional beamformer with a Hanning window applied for sidelobe suppression.

A low-complexity adaptive beamformer for ultrasound imaging using structured covariance matrix

In recent years, adaptive beamforming methods have been successfully applied to medical ultrasound imaging, resulting in simultaneous improvement in imaging resolution and contrast. These improvements have been achieved at the expense of higher computational complexity, with respect to the conventional non-adaptive delay-and-sum (DAS) beamformer, in which computational complexity is proportional to the number of elements, O(M). The computational overhead results from the covariance matrix inversion needed for computation of the adaptive weights, the complexity of which is cubic with the subarray size, O(L(3)). This is a computationally intensive procedure, which makes the implementation of adaptive beamformers less attractive in spite of their advantages. Considering that, in medical ultrasound applications, most of the energy is scattered from angles close to the steering angle, assuming spatial stationarity is a good approximation, allowing us to assume the Toeplitz structure for the estimated covariance matrix. Based on this idea, in this paper, we have applied the Toeplitz structure to the spatially smoothed covariance matrix by averaging the entries along all subdiagonals. Because the inverse of the resulting Toeplitz covariance matrix can be computed in O(L(2)) operations, this technique results in a greatly reduced computational complexity. By using simulated and experimental RF data-point targets as well as cyst phantoms-we show that the proposed low-complexity adaptive beamformer significantly outperforms the DAS and its performance is comparable to that of the minimum variance beamformer, with reduced computational complexity.