Beamforming techniques are commonly used in array signal processing to find the ray-path-arrival directions.
In general, beamforming is a spatial filtering process intended to highlight the propagation direction(s) of array-recorded signals.
Conventional beamforming techniques may not work when the receiving array is sparse (the receiving-array elements are many wavelengths apart).
Consider a simple broadband signal propagating through a range-independent
ideal sound channel with a uniform sound speed of 1500 m/s having a flat surface and bottom (see the figure below).
Figure 1: Ideal sound channel that supports three propagation paths. The receiving array has 16 transducers spaced
3.75 meters apart (almost 40 wavelengths at the signal's center frequency).
Figure 2 shows the plane-wave beamforming result for a broadband signal from very low frequency (10 Hz) up to 20 kHz. It shows that the plane-wave beamforming
output does not have sufficient resolution at very low frequency. At 1.5 kHz, the beamforming output has enough resolution to resolve the three paths. However, there are a few side lobes.
At very high frequency like 15 kHz, the array is too sparse and the plane-wave beamforming is confused. So, an unconventional beamforming technique should be developed to isolate the arrival paths
when the receiving array is sparse.
Figure 2: Plane-wave beamforming result as a function of frequency for a broadband signal (10 Hz-20 kHz)
If the recorded bandwidth has only the high frequency information, conventional beamforming fails and there is no way to resolve the arrival angles.
I have developed a novel beamforming technique to solve this problem.
Frequency Difference Beamforming
I have developed an unconventional beamforming technique (Frequency-difference beamforming) that manufactures lower-frequency signal information from the higher-frequency broadband signal recordings.
The figure below illustrates the differences between conventional plane-wave and frequency-difference beamforming of the high frequency broadband simulated signal (10-20 kHz) sent to the geometry shown in Fig. 1.
Figure 3: Magnitude of beamforming results integrated across frequency.
The conventional beamforming results do not indicate ray path directions. However, the integrated frequency difference beamforming results do display peaks at the three ray-path arrival angles of the propagation simulations, –2.4, 0.3, and 2.6 degree, which correspond
to bottom reflected, direct, and surface-reflected ray paths, respectively.