An IDL program is implemented to do the beamforming for the SOSUS data. The beamformer program allows users to predefine which arrays of hydrophones will be used to focus the beams at the directions of interest that signals will be coming. The beamformer program gives users a control to monitor any directions that are not restricted by geography.

The beamforming method for this project is the called
**Delay-and-Sum**.
It is the simplest and most common known technique. When given an
array of hydrophones with equal spacing between each phone, signals can
arrive at any directions, see figure 1. However, if the signal is
coming from a particular direction of interest and its source is very far
away, i.e. Far-Field Source; then by summing the signals at the appropriate
timing (delay), all the hydrophones will get the same signals., see figure
2. That is the objective of beamforming.

Figure 1: The arrows indicate directions of the
sound sources. |
Figure 2: Assuming a Far-Field sound source from N.E.,
the signal propagation will be closed to plane waves. |

The Delay-and-Sum method is simple, easy to understandard. It is also a Wide-Band method (the beamformed signals contain all frequencies) and it can be computed in Time-Domain (by Time Delay). However, it does have its disadvantages.

First disadvantage, it is very time consuming and calculation intensive method. However, as computer power and speed are increasing every day, and together with a careful programming techique, time delay method may not be too slow.

Second disadvantage, it cannot focus or steer the beam direction exactly. For example, the time delay is 3.421 seconds and the sample rate is 100 points which mean 342.1 points delay is required. The questions is: How to get 0.1 data point? Increase the sample rate is a solution for this example; but it may not solve for other time delays especially when the hydrophone spacings are not equal, see figure 3.

**Figure 3**

The figure at the left assumes a far-field sound source is coming from the N.E. direction. Negetive Delays mean signal received at the phones R3 and R4 are recorded earlier that others phones. Positive Delays means the signal at phones R0 and R1 are recorded later than others. Note that the choice of the center: R2, is arbitrary.

In figure 2 above for an array with evenly spacing, all delays are
positive or negative if R0 in figure 2 is the reference point.

By dropping or rounding the fraction, e.g. 342.1 to 342, will give a Quasi Quantized steering delay. It is Not perfect solution; however, due to the beamwidth (resolution), the results are adequately to achieve the objective, i.e. show the signals from different directions. This is how the T-Phase data are being beamformed in this project.

To steer the beam direction exactly, Frequency-Domain
Beamforming will be required. It delays the time by shifting the
angle or phase of signal in a particular frequency (Phase Delay).
For Wide-Band signal, phases for other frequencies must be added.
Phase delay method requires FFT calculations which may slow down the beamforming
process. This method is also implemented. Its results compared
to results by Time Delay show no significant difference due to the beamwidth.
The beamwidth is in general depended on the length of the signal receiver
array; longer the length, narrower the beamwidth (i.e. higher resolution).
Also how many signal receivers in the array will affect the beamwidth.

The contents of this page are intened as a documentation for the beamforming project and what methods are used for the beamforming program. It is not a tutorial or introduction of beamforming for public. The method described here serve the project well; however, it may not work well for other purposes.

Array Signal Processing by Johnson and Dudgeon, Chapter 4, Prentice
Hall, Inc.

Multidimensional Digital Signal Processing by Dudgeon and Mersereau,
pages 293 - 315, Prentic-Hall, Inc.

[T-K Andy Lau] [T-Phase Project] [Publications]