  In this paper we consider an in-ear headphone equipped with an inner
microphone and multiple loudspeakers and we propose an optimization procedure
with a convex objective function to derive a fixed multi-loudspeaker ANC
controller aiming at minimizing the sound pressure at the ear drum. Based on
the virtual microphone arrangement (VMA) technique and measured acoustic paths
between the loudspeakers and the ear drum, the FIR filters of the ANC
controller are jointly optimized to minimize the power spectral density at the
ear drum, subject to design and stability constraints. For an in-ear headphone
with two loudspeakers, the proposed multi-loudspeaker VMA controller is
compared to two single-loudspeaker VMA controllers. Simulation results with
diffuse noise show that the multi-loudspeaker VMA controller effectively
improves the attenuation by up to about 10 dB for frequencies below 300 Hz when
compared to both single-loudspeaker VMA controllers.
