An important first consideration is the choice of array geometry. Two
possible architectures are considered; endfire arrangement,
Figure 3, and broadside arrangement,
Figure 4. A second factor is the choice of microphone gain
pattern for the individual microphone elements, 
.
Since the gain pattern can be pulled out of the 
vector
as a constant multiplier, the gain pattern for the array can be
viewed as the product of the microphone gain pattern and an
omnidirectional response where 
. This is the well-known principle
of pattern multiplication [3] [7].
For omnidirectional microphones,
the gain patterns for the two layouts are identical but for a
rotation. The gain
patterns for an endfire array centered along the 
axis with
omnidirectional microphones steered at 15, 45, and 75 degrees is shown
in Figure 5. The use of a cardioid response greatly
reduces the large lobes appearing in the rear of the array. The
corresponding responses for cardioid microphones are shown in
Figure 6.\
Cardioid elements for the broadside array are not as useful, since the
null of the cardioid does not eliminate as much of the undesirable
lobes of the gain pattern, Figure 7. Note
the symmetry of the response about the axis; the line
containing the microphone array. This symmetry can be eliminated by
nulling out one half of the array response using an acoustic reflector
or baffle along one side of the microphone array.
The reflector will effectively double one side of the
gain pattern and eliminate the other, while the baffle will
eliminate one side and not affect the other. Thus a good directional
response can be achieved between 0 and 90 degrees using both
cardioid elements and a baffle for the endfire configuration.
The incorporation of a second array, on the other side of the baffle,
gives the angles zero to -90 degrees. A layout of the ALIVE space
with such an array/baffle combination is shown in
Figure 8. \
The response of each of the above arrays as measured by the
directivity index of Equation 3 is given in
Table 1. The integration was performed for a fixed
across all 
.
Table 1: Directivity Index for Different Array Architectures