When an acoustic signal is transmitted to a remote receiving array with sufficient aperture and transducer density, the arrival direction(s) of the ray paths linking the source and the array may be determined by beamforming the transducer recordings. However, when the receiving array is sparse, i.e. there are many signal wavelengths between transducers, the utility of conventional beamforming is degraded because of spatial aliasing. Yet, when the signal has sufficient bandwidth, such aliasing may be mitigated or eliminated through use of an unconventional nonlinear beamforming technique that manufactures a desired frequency difference from the recorded signals. When averaged through the signal's frequency band, the output of frequency-difference beamforming is similar to that of conventional beamforming evaluated at the desired difference frequency. Results and comparisons from simple propagation simulations and FAF06 experimental measurements are shown for broadband signal pulses (11-19 kHz) that propagate 2.2 km underwater to a vertical 16-element receiving array having a 3.75-m-spacing between elements (almost 40 signal-center-frequency wavelengths). Here, conventional delay-and-sum beamforming results in the signal's frequency band are featureless, but received ray-path directions are successfully determined using frequency differences that are well below the broadcast signal's frequency band. [Sponsored by ONR.]