(cid:8)(cid:7)(cid:3)(cid:14)(cid:1)(cid:11)(cid:13)(cid:15)(cid:10)(cid:5)(cid:15)(cid:2)(cid:10)(cid:9)(cid:6)(cid:11)(cid:4)(cid:12)(cid:12)(cid:15)
`
`- i -
`
`Sony v. Jawbone
`
`U.S. Patent No. 11,122,357
`
`Sony Ex. 1006
`
`

`

`
`
`DIGITALSIGNAL
`
`PROCESSING12JAN20021
`
`- ii-
`
`

`

`Volume -r2,I\Jumber 1
`January 2002
`
`Articles published onlino nrst
`hlip://WWW.Idoallbrary.com
`
`T
`I
`
`i
`
`TX 5-483·033
`II[IIIIUIIIIIIIIIn~ 1
`
`"'TX00054B3033.:
`
`_l
`
`A Review Journal
`
`/
`
`0
`
`180
`
`0
`
`270
`
`(a) GSC Lower Path
`
`270
`
`(b) NFAB lower Path
`
`Editors
`Jim Schroeder
`Joe Campbell
`
`ISSN 1051-2004
`
`ACADEMIC
`PRESS
`
`An Elsevier Science Imprint
`
`-iii -
`
`

`

`Digital
`Signal
`Processing __ _
`
`A Review Journal
`
`Editors
`
`Jim Schroeder
`SPRI!CSSIP
`Adelaide, SA. Australia
`E-mail: schroeder@cssip.edu.au
`
`Joe Campbell
`M I T. Lincoln Laboratory
`Lexington. Massachusetts
`E-mail: j.campbell@ieee.org
`
`Editorial Board
`
`Maurice Bellanger
`CNAM
`Paris, France
`Robert E. Bogner
`University of Adelaide
`Adelaide, SA, Australia
`Johann F. Bohme
`Ruhr-Universitat Bochum
`Bochum. Germany
`James A. Cadzow
`Vanderbilt University
`Nashville, Tennessee
`G. Clifford Carter
`NUWC
`Newport. Rhode Island
`A. G. Constantinides
`Imperial College
`London, England
`Petar M. Djuric
`State University of New York
`Stony Brook, New York
`Anthony D. Fagan
`University College Dublin
`Dublin, Ireland
`Sadaoki Furui
`Tokyo Institute of Technology
`Tokyo, Japan
`
`John E. Hershey
`General Electric Company
`Schenectady, New York
`B. R. Hunt
`University of Arizona
`Tucson. Arizona
`James F. Kaiser
`Duke University
`Durham. North Carolina
`R. Lynn Kirlin
`University of Victoria
`Victoria, British Columbia, Canada
`Ercan Kuruoglu
`lstituto di Elaborazione della lnformazione
`Ghezzano. Italy
`Meemong Lee
`Jet Propulsion Laboratory
`Pasadena. California
`Petre Stoica
`Uppsala University
`Uppsala, Sweden
`Mati Wax
`Wavion. Ltd
`Yoqneam. Isreal
`Rao Yarlagadda
`Oklahoma Stale University
`Stillwater, Oklahoma
`
`Cover photo Lower path directivity pattern at 5000 Hz See the article by McCowan. Moore, and Sridharan in
`this issue
`
`- iv -
`
`

`

`Digital Signal Processing
`
`Volume 12, Number 1, January 2002
`
`© 2002 Elsevier Science (USA)
`
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`- v-
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`

`

`Digital Signal Processing 12, 87-106 (2002)
`doi: 10.1006/dspr.2001.04 J 4, available online at http://www.idealibrary.com on
`
`1 0 E lll... l®
`-';'
`
`This material may be protected by Copyright law (Title 17 U.S. Code)
`
`Near-field Adaptive Beamformer for Robust
`Speech Recognition
`lain A. McCowan, Darren C. Moore, and S. Sridharan
`Speech Research Laboratory, RCSAVT, School ofEESE, Queensland University
`of Technology, GPO Box 2434, Brisbane QLD 4001, Australia
`E-mail: iain@ieee.org; moore@idiap.ch; s.sridharan@qut.edu.au
`
`McCowan, I. A., Moore, D. C., and Sridharan, S., Near-field Adaptive
`Beamformer for Robust Speech Recognition, Digital Signal Processing 12
`(2002) 87-106.
`This paper investigates a new microphone array processing technique
`specifically for the purpose of speech enhancement and recognition. The
`main objective of the proposed technique is to improve the low frequency
`directivity of a conventional adaptive beamformer, as low frequency per-
`formance is critical in speech processing applications. The proposed tech-
`nique, termed near-field adaptive beamforming (NFAB), is implemented
`using the standard generalized sidelobe canceler (GSC) system structure,
`where a near-field superdirective (NFSD) beamformer is used as the fixed
`upper-path beamformer to improve the low frequency performance. In ad-
`dition, to minimize signal leakage into the adaptive noise canceling path for
`near-field sources, a compensation unit is introduced prior to the blocking
`matrix. The advantage of the technique is verified by comparing the direc-
`tivity patterns with those of conventional filter-sum, NFSD, and GSC sys-
`tems. In speech enhancement and recognition experiments, the proposed
`technique outperforms the standard techniques for a near-field source in
`adverse noise conditions. © 2002 Elsevier Science tuSAl
`Key Words: microphone array; beamforming; near-field; adaptive; su-
`perdirectivity; speech recognition.
`
`1. INTRODUCTION
`
`-Currently, much research is being undertaken to improve the robustness of
`
`speech recognition systems in real environments. This paper focuses on the
`use of a microphone array to enhance the noisy input speech signal prior to
`recognition. While the use of microphone arrays for speech recognition has been
`studied for some time by a number of researchers, a persistent problem has been
`the poor low frequency directivity of conventional beamforming techniques with
`87
`
`1051-2004/02 $35.00
`© 2002 Elsevier Science (USA)
`All rights reserved.
`
`- 87 -
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`

`

`88
`
`Digital Signal Processing Vol. 12, No. 1, January 2002
`
`practical array dimensions. Low frequency performance is critical for speech
`processing applications, as significant speech energy is located below 1 kHz.
`By explicitly maximizing the array gain, superdirective beamforming tech-
`niques are able to achieve greater directivity than conventional techniques with
`closely spaced sensor arrays [1] . This directivity generally comes at the expense
`of a controlled reduction in the white noise gain of the array. Recent work has
`demonstrated the suitability of superdirective beamforming for speech enhance-
`ment and recognition tasks [2, 3]. By employing a spherical propagation model
`in its formulation, rather than assuming a far-field model, near-field superdirec-
`tivity (NFSD) succeeds in achieving high directivity at low frequencies for near-
`field speech sources in diffuse noise conditions [4]. In previous work, near-field
`superdirectivity has been shown to lead to good speech recognition performance
`in high noise conditions for a near-field speaker [5].
`Superdirective techniques are typically formulated assuming a diffuse noise
`field. While this is a good approximation to many practical noise conditions,
`further noise reduction would result from a more accurate model of the
`actual noise conditions during operation. Adaptive array processing techniques
`continually update their parameters based on the statistics of the measured
`input noise. The generalized sidelobe canceler (GSC) [6] presents a structure
`that can be used to implement a variety of adaptive beamformers. A block
`diagram of the basic GSC system is shown in Fig. 1. The GSC separates
`the adaptive beamformer into two main processing paths-a standard fixed
`beamformer, w, with L constraints on the desired signal response, and an
`adaptive path, consisting of a blocking matrix, B , and a set of adaptive filters, a.
`As the desired signal has been constrained in the upper path, the lower path
`filters can be updated using an unconstrained adaptive algorithm, such as the
`least-mean-square (LMS) algorithm.
`While the theory of adaptive techniques promises greater signal enhance-
`ment, this is not always the case in real situations. A common problem with
`the GSC system is leakage of the desired signal through the blocking matrix,
`resulting in signal degradation at the beamformer output. This is particularly
`problematic for broadband signals, such as speech, and especially for speech
`recognition applications where signal distortion is critical.
`In this paper we propose a system that is suited to speech enhancement in a
`practical near-field situation, having both the good low frequency performance
`of near-field superdirectivity and the adaptability of a GSC system, while taking
`
`1----~+ ~
`
`FIG. 1. Generalized sidelobe canceler structure.
`
`- 88 -
`
`

`

`McCowan, Moore, and Sridharan: Near-field Adaptive Beamformer
`
`89
`
`care to minimize the problem of signal degradation for near-field sources.
`We begin by formulating a concise model for near-field sound propagation in
`Section 2. This model is then used in Section 3 to develop the proposed near-
`field adaptive beamforming (NFAB) technique. To demonstrate the benefit of
`the technique over existing methods, an experimental evaluation assessing
`directivity patterns, speech enhancement performance, and speech recognition
`performance is detailed in Sections 4 and 5.
`
`2. NEAR-FIELD SOUND PROPAGATION MODEL
`
`-In sensor array applications, a succinct means of characterizing both the
`
`array geometry and the location of a signal source is via the propagation vector.
`The propagation vector concisely describes the theoretical propagation of the
`signal from its source to each sensor in the array. In this section, we develop an
`expression for the propagation vector of a sound source located in the near-field
`of a microphone array using a spherical propagation model. This expression is
`then used in the formulation of the proposed near-field adaptive beamformer in
`the following sections.
`Many microphone array processing techniques assume a planar signal
`wavefront. This is reasonable for a far-field source, but when the desired
`source is close to the array a more accurate spherical wavefront model must
`be employed. For a microphone array of length L, a source is considered to be
`in the near-field if r < 2 L 21 ;._, where r is the distance to the source and ;._ is the
`wavelength.
`We define the reference microphone as the origin of a 3-dimensional vector
`space, as shown in Fig. 2. The position vector for a source in direction (85 , c/Js),
`at distance r5 from the reference microphone, is denoted Ps and is given by:
`
`cos Bs sin c/Js l
`
`Ps = rsrx,y,z] sin8ssin¢s
`[
`cos¢5
`
`.
`
`(1)
`
`The microphone position vectors, denoted as p; (i = 1, ... , N), are similarly
`defined. The distance from the source to microphone i is thus
`
`d; =liPs- P;ll,
`
`(2)
`
`II is the Euclidean vector norm.
`where II
`In such a model, the differences in distance to each sensor can be significant
`for a near-field source, resulting in phase misalignment across sensors. The
`difference in propagation time to each microphone with respect to the reference
`microphone (i = 1) is given by
`
`d;- dt
`r;= -
`-
`- ,
`c
`
`(3)
`
`- 89 -
`
`

`

`90
`
`Digital Signal Processing Vol. 12, No. 1, January 2002
`
`Az
`
`reference •
`····· · ·· ·· ··~1 ······ ....
`microphone •
`( 0, 0, 0 ).·
`,·'-..._.../'-
`' '
`e.
`microphone I
`
`.·
`
`~-
`X
`
`y
`
`. Pi
`
`FIG. 2. Near-field propagation model.
`
`where c = 340 ms- 1 for sound. In addition, the wavefront amplitude decays at a
`rate proportional to the distance traveled. The resulting amplitude differences
`across sensors are negligible for far-field sources, but can be significant in
`the near-field case. The microphone attenuation factors, with respect to the
`amplitude on the reference microphone, are given by
`
`rh
`I.Yi=-.
`di
`
`(4)
`
`Thus, if x1 (f) is the desired source at the reference microphone, the signal on
`the i th microphone is given by
`
`(5)
`
`Consequently, we define the near-field propagation vector for a source at
`distance r and direction ce' ¢) as
`
`3. NEAR-FIELD ADAPTIVE BEAMFORMING
`
`-The proposed system structure is shown in Fig. 3. The objective of the
`
`proposed technique is to add the benefit of good low frequency directivity
`to a standard adaptive beamformer, as low frequency performance is critical
`in speech processing applications. The upper path consists of a fixed near-
`field superdirective beamformer, while the lower path contains a near-field
`compensation unit, a blocking matrix and an adaptive noise canceling filter.
`The principal components of the system are discussed in the following sections.
`
`- 90 -
`
`

`

`McCowan, Moore, and Sridharan: Near-field Adaptive Beamformer
`
`91
`
`+0
`-
`
`y(f)
`
`Yl(f)
`
`/_
`-
`
`Adap'e
`
`/a(f)
`
`N
`I x(f)
`
`Fixed
`NFSD
`Beamformer
`../' w(f)
`
`Yu(f)
`
`'
`
`Near-field
`
`Blocking
`
`N-1
`
`D(f)
`
`x'(f)
`
`B
`
`-compensation - Matrix ~ Filters
`
`I
`
`FIG. 3. Near-field adaptive beamformer.
`
`Section 3.1 gives an explanation of the near-field superdirective beamformer.
`Section 3.2 proposes the inclusion of a near-field compensation unit in the
`adaptive sidelobe canceling path and examines its effect on reducing signal
`distortion at the output. Once this near-field compensation has been performed,
`a standard generalized sidelobe canceling blocking matrix and adaptive filters
`can be applied to reduce the output noise power, as discussed in Section 3.3.
`
`3.1. Near-field Superdirective Beamformer
`Superdirective beamforming techniques are based upon the maximization of
`the array gain, or directivity index. The array gain is defined as the ratio of
`output signal-to-noise ratio to input signal-to-noise ratio and for the general
`case can be expressed in matrix notation as [1]
`
`where w(j) is a column vector of channel gains,
`
`w(j) = [w1C.f) ... w;(j) ... WN(f)f,
`
`(7)
`
`(8)
`
`( )H is the complex conjugate transpose operator, and P(j) and Q(j) are
`the cross-spectral density matrices of the signal and noise respectively. In
`practical speech processing applications the form of the signal and noise cross-
`spectral density matrices is generally unknown and must be estimated, either
`from mathematical models (fixed beamformers) or from the statistics of the
`multichannel inputs (adaptive beamformers). Superdirective beamformers are
`calculated based on assumed mathematical models for the P(j) and Q(j)
`matrices.
`When the desired signal is known to emanate from a single source at location
`(r,, 85 , ¢ 5 ), the signal cross-spectral matrix P simplifies to the propagation vector
`of the source, and the array gain can be expressed as
`
`(9)
`
`L
`
`- 91 -
`
`

`

`92
`
`Digital Signal Pmcessing Vol. 12, No. 1, January 2002
`
`where d(.f, r, e, ¢) is the propagation vector for the desired source, as defined in
`Eq. (6).
`A diffuse (spherically isotropic) noise field is often a good approximation for
`many practical situations, particularly in reverberant closed spaces, such as in a
`car or an office [7, 8]. For diffuse noise, the noise cross-spectral density matrix Q
`can be formulated as
`
`Q(f)= 4~ ii d(f,8,¢)d(f,e,rp)Hsin8d8d¢,
`
`(10)
`
`where d(f, e, ¢) is the propagation vector of a far-field noise source (r » 2L 2 /'A)
`in direction (8, ¢).
`The superdirectivity problem is thus formulated as:
`
`(11)
`
`By using a spherical propagation model to formulate the propagation
`vector, d, the standard superdirective formulation can be optimized for a near-
`field source [9, 4]. As such, the only difference in the calculation of the standard
`and near-field superdirective channel filters is the form of the propagation
`vector, d. For a near-field source, the assumption of plane wave (far-field)
`propagation leads to errors in the array response to the desired signal due
`to curvature of the direct wavefront. A thorough discussion of the use of a
`near-field model for superdirective microphone arrays is given by Ryan and
`Goubran [9].
`Cox [10] gives the general superdirective filter solution subject to
`1. L linear constraints, C(f)Hw(f) = g(f) (explained below); and
`2. a constraint on the maximum white noise gain, w(.f) H w(f) = 8- 2, where
`82 is the desired white noise gain.
`as
`
`where E is a Lagrange multiplier that is iteratively adjusted to satisfy the white
`noise gain constraint. The white noise gain is the array gain for spatially white
`(incoherent) noise; that is, Q(.f) = I. A constraint on the white noise gain is
`necessary as an unconstrained superdirective solution will in fact result in
`significant gain to any incoherent noise, particularly at low frequencies. Cox [10]
`states that the technique of adding a small amount to each diagonal matrix
`element prior to inversion is in fact the optimum means of solving this problem.
`A study of the relationship between the multiplier E and the desired white
`noise gain 82 , shows that the white noise gain increases monotonically with
`increasing E. One possible means of obtaining the desired value of E is thus
`an iterative technique employing a binary search algorithm between a specified
`mipjmum and maximum value for E. The computational expense of the iterative
`procedure is not critical, as the beamformer filters depend only on the source
`
`- 92 -
`
`

`

`McCowan, Moore, and Sridharan: Near-field Adaptive Beamformer
`
`93
`
`location and array geometry, and thus must only be calculated once for a given
`configuration.
`The constraint matrix, C H (f), is of order L x N, where there are L linear
`constraints being applied, and the vector g(f) is a length-L column vector
`of constraining values. The constraints generally include one specifying unity
`response for the desired signal, dH (f)w(f) = 1, and where this is the sole
`constraint the above solution can by simplified by substituting C(f) = d(f) and
`g(f) = 1, giving
`
`w(f) = d(f) 11 lQ(J) + dl- 1d(f) ·
`Once the optimal filters w(f) have been calculated, the near-field superdirec-
`tive beamformer output is calculated as
`
`(13)
`
`y" (f) = w(f) H x(f),
`
`where x(f) is the N -channel input column vector
`
`x(f) = [x1(f) ... x;(f) ... xNU)f .
`
`(14)
`
`(15)
`
`3.2. Near-field Compensation Unit
`The first element in the adaptive path of standard GSC is the blocking
`matrix [6]. Its purpose is to block the desired signal from the adaptive noise
`estimate. To ensure complete blocking, the desired signal must both be time
`aligned and have equal amplitudes across all channels. If this is the case,
`cancellation occurs if each row of the blocking matrix sums to zero, and all rows
`are linearly independent.
`For a near-field desired source, to align the desired signal on all channels,
`a near-field compensation must first be applied to the input channels prior to
`blocking. To ensure full cancellation we need to compensate for both phase
`misalignment and amplitude scaling of the desired signal across sensors. We
`define the diagonal matrix
`
`D(f) = [diag(d(f))]- 1 ,
`
`(16)
`
`where d(f) is the near-field propagation vector from Eq. (6). In this paper we
`define the diagonal operator, diag( ) , to produce a diagonal matrix from a vector
`parameter. Conversely, if invoked with a matrix parameter, it produces a row
`vector corresponding to the matrix diagonal. The near-field compensation can
`be applied as
`
`x' (f) = D (f)x(f).
`(17)
`Once this near-field compensation has been performed, a standard GSC blocking
`matrix can be employed to block the desired signal from the adaptive path.
`The inclusion of this compensation unit is critical for a near-field desired
`signal. Without compensation for both phase and amplitude differences between
`sensors, blocking of the desired signal will not be ensured, leading to signal
`
`- 93 -
`
`

`

`94
`
`Digital Signal Processing Vol. 12, No. 1, January 2002
`
`.......... ..... ' .......... ..
`. ···
`,----,;'
`' .
`/
`' . '' '' '• '• '•
`'
`I
`
`-30
`
`•·· Farflold
`- - NF Uncompensaled {r=0.6m)
`-
`NF Compensated (r-0.6m)
`
`~ 0o~---2~o----~4o----~so-----eLo~~~~oo----~~2-0 ----14~0----1~so--~1BO
`
`Di'e<:lion of Arrival (deg)
`
`FIG. 4. Comparison of blocking matrix row beam-patterns.
`
`cancellation at the output. The near-field compensation effectively ensures that
`a true null exists in the beam-pattern of each blocking matrix row in the
`direction and distance corresponding to the desired source. To illustrate, Fig. 4
`shows the directivity pattern at 2 kHz for the first row in the blocking matrix
`using the array shown in Fig. 5, with the desired source directly in front of the
`center microphone at a distance of 0.6 m. The figure shows the compensated
`response in the far- and near-fields, as well as the uncompensated near-field
`response. It is clear that the uncompensated system will allow a high degree of
`signal leakage into the adaptive path as it blocks noise sources rather than the ·
`desired signal.
`
`10
`
`15cm
`
`10cm
`
`2 5 em
`r -.- .,-,
`
`Scm
`Scm
`34567
`8
`
`11
`
`15 em
`
`10c:m
`
`.. ~ desired
`
`source
`
`1 zi'
`
`•
`·. ,
`localised
`noise
`
`FIG. 5. Experimental configuration.
`
`- 94 -
`
`

`

`McCowan, Moore, and Sridharan: Near-field Adaptive Beamformer
`
`95
`
`3.3. Blocking Matrix and Adaptive Noise Canceling Filter
`The blocking matrix and adaptive noise canceling filters are taken from the
`standard GSC technique [6]. The order of the blocking matrix is N x (N- L),
`where there are L constraints applied in the fixed upper path beamformer.
`Generally only a unity constraint on the desired signal is specified, and the
`standard N x (N- 1) Griffiths-Jim blocking matrix is used:
`
`B=
`
`1
`
`-1
`
`0
`
`1
`
`0
`
`0
`
`0
`
`-1
`
`0
`
`0
`
`0
`
`0
`
`0
`
`1
`
`0
`
`0
`
`-1
`0
`
`1
`-1
`
`The output of the blocking matrix is calculated as
`
`(18)
`
`(19)
`
`where x" (f) is an (N - 1)-length column vector. Defining the (N - 1)-length
`adaptive filter column vector as
`
`a(f) = [a1(j) ... a;(f) ... aN-lCJ)f,
`
`the output of the lower path is given as
`
`(20)
`
`(21)
`
`The NFAB output is then calculated from the upper and lower path outputs as
`
`y(j) = YuCf)- YtCf)
`
`(22)
`
`and the adaptive filters are updated using the standard unconstrained LMS
`algorithm
`
`ak+ICf) = ak(f) + J-tX~(f)yk(f),
`where J1 is the adaptation step size and k denotes the current frame.
`
`(23)
`
`3.4. Summary of Technique
`In summary, the proposed NFAB technique is characterized by the series of
`equations
`
`Yu (f) = w(f) H x(f)
`x~ = BHD(j)x(j)
`
`(24a)
`(24b)
`
`..
`
`- 95 -
`
`

`

`96
`
`Digital Signal Processing Vol. 12, No. 1, January 2002
`
`YtCf) = a(f)Hx~(f)
`y(f) = Yu (f) - Yt (f)
`ak+l (f)= ak (f)+ JJ-X~ (f))'k(f),
`
`(24c)
`(24d)
`(24e)
`
`-
`
`where all terms have been defined in the preceding discussion.
`
`4. EXPERIMENTAL CONFIGURATION
`
`For the experimental evaluation in this paper, we used the 11 element array
`shown in Fig. 5. The array consists of a nine element broadside array, with an
`additional two microphones situated directly behind the end microphones. The
`total array is 40 em wide and 15 em deep in the horizontal plane. The broadside
`microphones are arranged according to a standard broadband subarray design,
`where different subarrays are used for different frequency ranges for the fixed
`upper path beamformer. The two endfire microphones are included for use by
`the near-field superdirective beamformer in the low frequency range. The four
`subarrays are thus
`• (f <1kHz): microphones 1-11;
`• (1kHz < f <2kHz): microphones 1, 2, 5, 8, and 9;
`• (2kHz< f <4kHz): microphones 2, 3, 5, 7, and 8; and
`• (4kHz< f <8kHz): microphones 3-7.
`The array was situated in a computer room, with different sound source
`locations, as shown in Fig. 5. The two sound sources were
`1. the desired speaker situated 60 em from the center microphone, directly
`in front of the array; and
`2. a localized noise source at an angle of 124° and a distance of270 em from
`the array.
`Impulse responses of the acoustic path between each source and microphone
`were measured from multichannel recordings made in the room with the ar-
`ray using the maximum length sequence technique detailed in Rife and Van-
`derkooy [11]. As the impulse responses were calculated from real recordings
`made simultaneously across all input channels, they take into account the real
`acoustic properties of the room and the array. The multichannel desired speech
`and localized noise microphone inputs were then generated by convolving the
`original single-channel speech and noise signals with these impulse responses.
`In addition, a real multichannel background noise recording of normal operat-
`ing conditions was made in the room with other workers present. This record-
`ing is referred to in the experiments as the ambient noise signal and is approxi-
`mately diffuse in nature. It consists mainly of computer noise, a variable level of
`background speech, and noise from an air-conditioning unit. The ambient noise
`effectively represents a diffuse noise field, while the localized noise represents
`a coherent noise source. In this paper, we specify the levels of the two different
`noise sources independently, as the signal to ambient-noise ratio (SANR) and
`
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`McCowan, Moore, and Sridharan: Near-field Adaptive Beamformer
`
`97
`
`signal to localized-noise ratio (SLNR). These values are calculated as the aver-
`age segmental SNR from the speech and noise input, as measured at the center
`microphone of the array.
`In this way, realistic multichannel input signals can be simulated for specified
`levels of ambient and localized noise. As well as facilitating the generation
`of different noise conditions, simulating the multichannel inputs using the
`impulse response method is more practical than making real recordings for
`speech recognition experiments, as existing single channel speech corpora may
`be used.
`
`5. EXPERIMENTAL RESULTS
`
`-This section presents the results of the experimental evaluation. The
`
`proposed NFAB technique is compared to a conventional fixed filter-sum
`beamformer, a fixed near-field superdirective beamformer, and a conventional
`GSC adaptive beamformer. These beamformers are specified in Table 1.
`The techniques are first assessed in terms of the directivity pattern in
`order to demonstrate the advantage of the proposed NFAB over conventional
`beamforming techniques, particularly at low frequencies. Following this, the
`techniques are evaluated for speech enhancement in terms of the improvement
`in signal to noise ratio and the log area ratio. Finally, the techniques are
`compared in a hands-free speech recognition task in noisy conditions using the
`TIDIGITS database [12].
`
`5.1. Directivity Analysis
`As has been stated, the main objective of the proposed technique is to produce
`an adaptive beamformer that exhibits good low frequency performance for near-
`field speech sources. To assess the effectiveness of the proposed technique in
`achieving this objective, in this section we analyze the horizontal directivity
`pattern. The directivity of a filter-sum beamformer is expressed in matrix
`notation as
`
`h(f, r, 8, ¢) = W 0 (f)H d(.f, r, 8, ¢),
`where W 0 is the length N channel filter vector
`
`(25)
`
`(26)
`
`TABLE 1
`Beamforming Techniques in Evaluation
`Description
`Conventional FS beamformer
`Near-field superdirective beamformer
`GSC system with FS fixed upper path
`beamformer
`Near-field adaptive beamformer
`
`Filters
`w,(f) = [diag(D(f))] 11
`w,(f) =w(f)
`w,(/) = [diag(D(/))] 11 - D(f)Ba(f)
`
`w,(/) = w( f)- D(f)Ba( f)
`
`Technique
`FS
`NFSD
`GSC
`
`NFAB
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`Digital Signal Processing Vol. 12, No. 1, January 2002
`
`90
`
`1
`
`90
`
`1
`
`. .. ,_. .. ~ :· ... ·.:·
`. 0.5 ...
`.
`.
`.
`.
`·:.::.
`... • .
`:1:
`.. •.. ·~ . . .. . ·. :":·\/ : ...... ... . ·? .. ' ' .
`. .... ~ :: ··....
`.
`. . . . . ~ .
`. / ..
`·.·
`..
`
`'::.~ . .
`
`180 . ..
`
`270
`
`(a) FS
`
`270
`
`(b) NFSD
`
`FIG. 6. Upper path directivity pattern at 300 Hz.
`
`5.1 .1. Upper path directivity. First, we seek to demonstrate the directiv-
`ity improvement that NFSD achieves at low frequencies compared to a conven-
`tional filter-sum (FS) beamformer. For the FS beamformer, a common solution is
`to choose w 0 (f) = [diag(D(f))]H. This effectively ensures that the desired signal
`is aligned for phase and amplitude across sensors using a spherical propagation
`model. For NFSD, we use the filter vector w(f) described in Section 3.1. Figure 6
`shows the near-field directivity pattern at 300Hz for the FS and NFSD. From
`these figures, it is clear that the NFSD technique results in greater directional
`discrimination at low frequencies compared to a conventional beamformer. At
`higher frequencies (f > 1kHz), conventional beamformers offer reasonable di-
`rectivity, and so the FS and NFSD techniques give comparable performance.
`5.1.2. Lower path directivity. Second, we wish to demonstrate the effect
`of the noise canceling path. The directivity of the noise canceling filters can be
`obtained by using the channel filters w 0 (f) = D(f)Ba(f). The blocking matrix
`and adaptive filters essentially implement a conventional (nonsuperdirective)
`beamformer that adaptively focuses on the major sources of noise. To examine
`the directivity of the lower path filters, the beamformer was run on an input
`speech signal with a white localized noise source (at the location shown in Fig. 5)
`added at an SLNR of 0 dB and a low level of ambient noise (SANR = 20 dB).
`The steady-state adaptive filter vector, a(f), was written to file for both the
`proposed NFAB technique and the conventional GSC beamformer. The near-
`field directivity patterns of the lower path filters are plotted in Figs. 7 and 8
`for 300 and 5000 Hz, respectively. We see that the lower path adaptive filters
`for both beamformers converge to similar solutions in terms of directivity,
`producing a main lobe in the direction of the coherent noise source ( ~ 124° from
`Fig. 5), as well as a null in the location of the desired speaker. As expected, the
`directivity of the adaptive path is poor at low frequencies, as seen in Fig. 7.
`5.1.3. Overall beamformer directivity. Finally, we examine the directivity
`pattern of the overall beamformer for the NFAB and conventional adaptive
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`90
`
`90
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`1
`
`270
`
`(a) GSC Lower Path
`
`270
`
`(b) NFAB Lower Path
`
`FIG. 7. Lower path directivity pattern at 300Hz.
`
`systems. The near-field directivity patterns at 300 Hz are shown in Fig. 9.
`We see that the directivity pattern of the NFAB system exhibits a true null
`in the direction and at the distance of the noise source, while the directivity of
`the conventional beamformer is too poor to significantly attenuate the noise at
`this frequency. At frequencies above 1 kHz the directivity performance of both
`techniques is comparable.
`5.1.4. Summary of beamformer directivity.
`terms of directivity, the proposed NFAB system:
`• outperforms the conventional FS system in terms of low frequency
`performance and the ability to attenuate coherent noise sources,
`• outperforms the NFSD system due to the ability to attenuate co