## 3aSPa6. Near-field broadband array beamforming using wave equation transformation.

### Session: Wednesday Morning, December 4

### Time: 9:45

**Author: Rodney A. Kennedy**

**Location: Telecommun. Eng., RSISE, Australian Natl. Univ., Canberra ACT 0200, Australia**

**Author: P. Thushara**

**Location: Arthur C. Clarke Ctr. for Mod. Technol., Katubedda, Moratuwa, Sri Lanka**

**Author: D. Abhayapala**

**Location: Arthur C. Clarke Ctr. for Mod. Technol., Katubedda, Moratuwa, Sri Lanka**

**Author: Darren B. Ward**

**Location: Australian Natl. Univ., Canberra ACT 0200, Australia**

**Abstract:**

Given a broadband frequency versus angle beampattern specification in the
near field, a methodology is developed to yield a filter-bank design for an
array signal-processing structure. This methodology relies on two key tools: (i)
a transformation using spherical harmonic solutions to the wave equation which
takes a near-field beampattern specification and maps it to an equivalent
far-field beampattern specification for a given frequency; and (ii) a solution
of the broadband frequency versus angle far-field beampattern specification
problem, which generalizes earlier results on broadband frequency invariant (far
field) beamforming [Ward et al., J. Acoust. Soc. Am. 97, 1023--1034 (1995)]. The
transformation exploits the uniqueness property of the solution to the wave
equation to give a set of truly equivalent far-field patterns for a discrete set
of frequencies. There is no restriction on the bandwidth of operation beyond
that imposed by limitations on the number of sensors or filter complexity. A
straightforward filter-bank design is then proposed to realize this equivalent
far-field broadband frequency versus angle beampattern specification. The
methodology is illustrated with a broadband frequency invariant near-field
design which captures the full generality of the design methodology.

ASA 132nd meeting - Hawaii, December 1996