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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.