Recently, a new array based on generating Bragg-scattered acoustic wavelengths along the surface of an array was proposed (Enhanced directivity with array grating (J. Acoust. Soc. Am. 136 (2), 2014) and Experimental verification of acoustic trace wavelength enhancement (J. Acoust. Soc. Am. 138 (6), 2015)). The technique, denoted acoustic trace wavelength enhancement, relies on embedding periodic structures within an array, chosen to precisely replicate and shift the incident acoustic wavenumber into higher wavenumber regions. In principle, an important advantage of this array over conventional hydrophone-based arrays of the same size is its greatly improved directivity. A prototype array was built and demonstrated in a test tank under idealized high signal-to-noise ratio conditions. However, two important open questions which remain are how this array responds to ambient noise and how to optimally beamform it when multiple signals are present. Using idealized analytical models for the array's plane wave r...