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In adaptive ultrasound imaging, accurate estimation of the array covariance matrix is of great importance, and biases the performance of the adaptive beamformer. The more accurately the covariance matrix can be estimated, the better the resolution and contrast can be achieved in the ultrasound image. To this end, in this paper, we have used the forwardbackward spatial averaging for array covariance matrix estimation, which is then employed in minimum variance (MV) weights calculation. The performance of the proposed forwardbackward MV (FBMV) beamformer is tested on simulated data obtained using Field II. Data for two closely located point targets surrounded by speckle pattern are simulated showing the higher amplitude resolution of the FBMV beamformer in comparison to the forward-only (F-only) MV beamformers, without the need for diagonal loading. A circular cyst with a diameter of 6 mm and a phantom containing wire targets and two cysts with different diameters of 8 mm and 6 mm are also simulated. The simulations show that the FBMV beamformer, in contrast to the F-only MV, could estimate the background speckle statistics without the need for temporal smoothing, resulting in higher contrast for the FBMV-resulted image in comparison to the MV images. In addition, the effect of steering vector errors is investigated by applying an error of the sound speed estimate to the ultrasound data. The simulations show that the proposed FBMV beamformer presents a satisfactory robustness against data misalignment resulted from steering vector errors, outperforming the regularized F-only MV beamformer. These improvements are achieved without compromising the good resolution of the MV beamformer and resulted from more accurate estimation of the covariance matrix and consequently, the more accurate setting of the MV weights.