Optimal Multi-Microphone Speech Enhancement in Cars - Digital Signal Processing for In-Vehicle Systems and Safety - page 185

factored into a sufficient statistics followed by a single-microphone post-filter.
As a straightforward extension of [ 1 ], if we know the RIRs, optimal estimation
of the speech signal can be achieved using the simple two-step method. How-
ever, it is actually not easy to satisfy the assumption of the known RIRs. In this
chapter, we address a realistic implementation of the sufficient statistics with
unknown RIRs.
If we know the source signal, we can adaptively estimate the RIRs based on an
acoustic echo cancelation scheme [ 4 ]. Because more correctly beamformed output
is nearer to the original source signal, we might be able to use the beamformed
output as a reference signal to estimate the RIRs [ 5 ]. In this chapter we propose
using a delay-and-sum beamformer (DSB) to provide the information necessary for
an initial constrained estimate of the RIR, which is then updated iteratively using
a multi-path generalized sidelobe canceller (GSC) based on the evolving RIR
estimate. Good RIR estimation makes the multi-path GSC more accurate, and
this again guarantees better RIR estimation. We demonstrate that, with a reasonable
constraint on the sparsity of the room impulse response, the algorithm converges to
a useful approximate RIR. Even though we may not get perfect RIR identification,
the converged RIR is nevertheless sufficient to compute coefficient vectors for a
multi-path fixed beamformer (FBF) which outperforms the naive DSB. By
leveraging the converged RIR, we are able to mitigate the common practical
problem of multi-path GSC, namely, its tendency to cancel the target signal due
the indistinguishability of signal from reverberation at the beamformer.
To visualize the situation in a tractable way, we first show the convergence of a
simplified version of the proposed scheme. A simple simulation test shows that this
method achieves sufficient blind deconvolution at the output of FBF. We then
evaluate the proposed algorithm using real-world moving-car recordings [ 6 ].

13.2 Proposed Method

13.2.1 Multi-path GSC

Multi-path GSC can be formulated as an optimization problem as shown in ( 13.1 ),
which is a generalized version of GSC [ 7 ] under a known multi-path environment,
represented by the RIR as coded into a constraint matrix C:

n o

¼ f

w T

T

subject to C T argmin

~

E ~ ~ y ð n Þ~ y ð n Þ ~ w ~ w ; (13.1)

w

w T is an estimated source signal at the current time n , f where s ^ ð n Þ¼~ ~ y ð n Þ ¼

T .

½ is a noisy signal vector measured by the microphone array,

the array of filter coefficients is

10 0 y ~ ð n Þ

T encoding the estimated
L-tap inverse RIR filters for all of the N recorded signals, and

~ w ¼ ½ w 1 w 2 w NL