straightforward where rm is the distance between source and the mth microphone. Since
2
1
= M
2
H 2 is a frequency-independent constant, the inverse filters and the time-reversal filters differ
nly a constant scaling in the point source model.
III. SI o
MO-ESIF WITH GSC
The design of the SIMO-ESIF with Generalized Side-lobe Canceller (GSC) is introduced in this section. The speech signals are degraded by background noise in the automotive hands-free system, which causes communicational quality to be
hampered. The GSC technique is proposed as a further processing after SIMO-ESIF algorithm, which increases directivity of main-lobe by suppressing the interference of side-lobe. A structure of the GSC with M microphones is shown in Fig. 2. It comprises a fixed beamformer (FBF), a multiple-input canceller (MC), and a blocking matrix (BM). The FBF is designed to form a beam in the look ion so that the target signal is passed and all other signals are attenuated. The m( )
direct
x k is the output gnal of the mth microphones and d k( ) is the output of the FBF at the time sample k . The MC is composed of multiple adaptive filters which generate replicas of components correlated with the interferences. It adaptively subtracts the components correlated to the output signals m( )
si
y k of the BM from the delayed output signal d k( −Q)of FBF, where Q is the number of delay samples for causality. Contrary to the FBF, the BM forms a null in the look direction so that the target signal is suppressed and all other signals are passed though. It rejects the interferences which is obtained from the output signals of BM and extracts the target signal. In conclusion, in the subtractor output z k( ), the target signal is enhanced
nd undesirable signals such as ambient noise and interferences are suppressed.
1.Griffiths-Jim beamformer (GJBF) structure
acent microphones can be used a
(12) whe
a
Figure 3 shows the structure of the GJBF. The FBF is the aforementioned inverse filter. The BM is a delay-and-subtract beamformer as shown in Figure3. Assuming a look direction perpendicular to the array surface, no delay element is necessary. Thus, a set of subtracters which take the difference between the signals at the adj
s a BM. The outputs of BM are described as follows:
( ) 1( )
n n
z ( )k =x k −xn+ k
re ( )x k is the n n th microphone signal.
The adaptive filters of the MC are using least- mean-square (LMS) algorithm, which can be obtained as follows:
(
1)
1( ) ( )
v is the output subtracter
2. LAF-LAF structure
e 4 shows its block diagram. The th output of the BM can be obtained as follows:
.
A target-tracking method with leaky adaptive filters (LAF) in the BM is proposed as a solution to target signal cancellation. It combined with leaky adaptive filters in the MC, thereby called a LAF-LAF structure. Figur
n
similar to th ilters in GJBF,
(15)
e adaptive f hn
( )
k is the coefficient vector of the n th LAF, and fo( )
k is the signal vector consisting of delayed signals of fo k( )
. EachLAF is assumed to have M taps, 1 L is the number of delay samples f2 or caus lity. a
The adaptation by the LMS algorithm is described as follows:
)
(
1( ) ( ) ( )
n + = n k +αz k n k
h k h fo (16)
where α is the step size for he adaptation algorithm.
The LAFs in the BM alleviate the influence of phase error, which results in the robustness. The LAFs also used in the MC for enhancing the robustness obtained in the BM. Thus, the LAF-LAF structure adaptively controls the look direction. Due to robustness by the adaptive control of the look direction, the LAF-LAF structure does not lose degrees of freedom for interference reduction. This structure can pick up a
rget signal with little distortion.
3. Robust GSC using linear algebra
3.1 The design method of blocking matrix
inimizing the output power subject to ultiple linear equality constrain
ta
The target of robust GSC is to minimize the array output power such that unity gain at the look direction is obtained. The design of the proposed robust beamformer can be formulated as one of m
m ts as follow signal path from source to each microphone, w is the digital filter of the proposed GSC system, zis the output signal. The block diagram is shown in Fig. 5. Standard constrained optimization using the Lagrange multiplier leads to the optimal filter w
which is a fixed filter and dependent on the data correlation matrix R. The optimal filter w may be decomposed into two mutually orthogonal subspaces: the constraint
ace R(g) and th
GSC implementation, a blocking matrix B is eeded to pro In principl lumns of B can be constructed from the basis vectors of N g( H) such that g B 0 . To this end, each co mn of H = lu Bmust be the null space of g , H The design goal of the BM is to form a null in the target direction so that target signal suppression can be achieved. The effect is demonstrated in Fig. 4, where directivity patterns of the FBF and the BM are illustrated. With the comparison of Figs. 6(a) and 4(b), the null of the BM and the mainlobe of the FBF are located in the target direction. The target signal has been successfully “blocked” at the main-lobe of the fixed array in different frequencies. In addition, there is an interested issue that with the comparison of other robust GSC technique, whether the proposed GSC
a an
technique can achieve the best performance or not. Two classic GSC technique called GJBF [2] and LAF-LAF [21] technique are selected to compare with the proposed GSC algorithm. Figure. 7 shows the beam pattern of the above algorithm in 500 Hz. The proposed GSC algorithm achieves the narrowest beamwidth in target
irection, which shows the highest interference reduction performance.
3.2 Signal processing in Multiple-Input Canceller
=0 delay samples f
d
In the MC, leaky adaptive filters (LAF) [21] is used for enhancing the robustness obtained in the BM. LAFs subtract the components correlated to yn
( )
k , (m ,…,N) from d k(
−Q)
. Q is the number of or causality. Let M2 be thenumber of taps in each LAF , and wn
( )
k and yn( )
k are the coefficient vector and the signal vector of the nth LAF, respectively. The signal processing in the MC cane obtained as follows:
(23)
⎦
(25) The adaptation with the normalized LMS (NLMS) algorithm is described as:
b