Evaluation of an adaptive beamforming method for hearing aids
`Julie E. Greenberg, and Patrick M. Zurek
`
`Citation: The Journal of the Acoustical Society of America 91, 1662 (1992); doi: 10.1121/1.402446
`View online: https://doi.org/10.1121/1.402446
`View Table of Contents: https://asa.scitation.org/toc/jas/91/3
`Published by the Acoustical Society of America
`
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`
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`Evaluation of an adaptive beamforming method for hearing aids
`Julie E. Greenberg and Patrick M. Zurek
`Research Laboratory of Electronics, Massachusetts Institute o/Technology, Cambridge,
`Massachusetts 02139
`
`(Received 15 July 1991; revised 27 September 1991; accept 1 November 1991)
`
`In this paper evaluations of a two-microphone adaptive beamforming system for hearing aids
`are presented. The system, based on the constrained adaptive beamformer described by
`Griffiths and Jim [IEEE Trans. Antennas Propag. AP-30, 27-34 ( 1982) ], adapts to preserve
`target signals from straight ahead and to minimize jammer signals arriving from other
`directions. Modifications of the basic Griffiths-Jim algorithm are proposed to alleviate
`problems of target cancellation and misadjustment that arise in the presence of strong target
`signals. The evaluations employ both computer simulations and a real-time hardware
`implementation and are restricted to the case of a single jammer. Performance is measured by
`the spectrally weighted gain in the target-to-jammer ratio in the steady state. Results show that
`in environments with relatively little reverberation: ( 1 ) the modifications allow good
`performance even with misaligned arrays and high input target-to-jammer ratios; and (2)
`performance is better with a broadside array with 7-cm spacing between microphones than
`with a 26-cm broadside or a 7-cm endfire configuration. Performance degrades in reverberant
`environments; at the critical distance of a room, improvement with a practical system is
`limited to a few dB.
`
`PACS numbers: 43.66.Ts, 43.72.Ew, 43.60.Lq
`
`INTRODUCTION
`Interference from background noise is one of the pri(cid:173)
`mary problems of hearing-aid users and the hearing im(cid:173)
`paired (Plomp, 1978; Smedley and Schow, 1990). Tradi(cid:173)
`tional hearing
`aids
`amplify
`all
`sounds without
`discriminating between the desired target and the back(cid:173)
`ground noise. Although a variety of single-microphone
`speech-enhancement techniques have been investigated
`( Lim and Oppenheim, 1979), the only one shown to pro(cid:173)
`duce clear improvements in speech intelligibility involves
`simple modifications of the frequency response to reduce
`spectrally localized interference (Van Dijkhuizen et al.,
`1989; Rankovic et al., 1992). The meager success of single(cid:173)
`microphone systems, together with the known advantages of
`multiple-element sensing systems, has led to interest in mul(cid:173)
`tiple-microphone hearing aids. Multiple-microphone hear(cid:173)
`ing aids can be classified as either fixed or adaptive systems.
`Fixed systems are typically designed to maximize direction(cid:173)
`ality, while adaptive systems can provide additional benefits
`in time-varying acoustic conditions. This work is restricted
`to the study of adaptive systems, although it should be noted
`that a successful adaptive system must perform at least as
`well as a comparable fixed system. In this paper the perfor(cid:173)
`mance of an adaptive two-microphone noise-reduction sys(cid:173)
`tem is evaluated.
`
`I. BACKGROUND
`Beamformers process the signals from a spatially dis(cid:173)
`tributed array of sensors to improve reception of the target, a
`sound emanating from a specified direction, in the presence
`of jam me rs, sounds arriving from other directions. An adap(cid:173)
`tive beamformer is one whose processing depends on, and
`changes with, characteristics of the input signals. The reader
`
`is referred to Van Veen and Buckley ( 1988) and Widrow
`and Steams ( 1985) for excellent introductions to adaptive
`beamforming and its applications.
`
`A. The Griffiths-Jim beamformer
`The system studied here is based on an adaptive beam(cid:173)
`forming algorithm described by Griffiths and Jim ( 1982). A
`two-microphone version 1 of the system for straight-ahead
`( 0°) targets is shown in Fig. 1.
`The operation of this beamformer is most easily de(cid:173)
`scribed as that of an adaptive noise canceller (Widrow et al.,
`197 5) with a preprocessor that forms the sum and difference
`of the microphone signals. If the target is straight ahead and
`there is no reverberation, then subtraction cancels the target
`and produces a signal that depends on the jammer alone. The
`sum and difference are then used as inputs to the adaptive
`noise canceller, which requires a primary input that contains
`target plus jammer ( sum signal), and a reference input that
`ideally contains a filtered version of the jammer only ( differ(cid:173)
`ence signal). The reference signal passes through an adap(cid:173)
`tive finite-impulse-response filter whose weights are adjust(cid:173)
`ed to minimize the power in the output signal. This
`minimization is achieved by filtering the reference input to
`approximate the correlated signal in the primary path, and
`subtracting. The delay in the primary path allows the adap(cid:173)
`tive filter's response to be noncausal. If the target and jam(cid:173)
`mer are uncorrelated and if the reference input contains no
`target signal, then minimizing the output power results in an
`output signal with minimum jammer power and no target
`distortion.
`One of the simplest adaptive algorithms, and the one
`employed exclusively in this study, is the LMS algorithm
`(Widrow and Steams, 1985), which attempts to minimize
`
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`1/2
`
`y[n)
`
`output
`
`"\In)
`
`la)
`
`(b)
`
`(c)
`
`c1
`
`target
`
`target
`
`canceller
`
`q
`
`q
`
`m1[n]
`
`111,z[n)
`
`broadside orientation
`
`cf--- m1[n]
`
`"\(n]
`
`endflre orientation
`
`FIG. 1. (a) Two-microphone Griffiths-Jim beamformer. The microphone
`signals, m1 [ n] and m2 [ n] are combined to form sum and difference signals,
`s[ n] and d[ n]. These signals are used as the primary and reference inputs to
`an LMS adaptive noise canceller. The adaptive noise canceller incorporates
`a D-sample delay and an L-point adaptive filter with weights
`w0 [n], ... ,wL- I [n] and adaptation constant a. The reference input is fil(cid:173)
`tered and subtracted from the delayed primary input. The LMS algorithm
`adjusts the filter weights to minimize total output power, which, under ideal
`conditions, also minimizes jammer output power. (b) Broadside array ori(cid:173)
`entation. For straight-ahead targets, the broadside orientation requires no
`delay to equalize microphone signals. ( c) Endfire array orientation. For
`straight-ahead targets, the array is rotated so the microphones are on a line
`with the target source. In this case, the front microphone signal is delayed to
`phase align the target signal.
`
`output noise in the least-mean-square sense. The form of the
`algorithm implemented here updates the adaptive filter ac(cid:173)
`cording to the formula
`w1 [n + 1] = w1 [n] + 2ay[n]d [n -1 ]ILPd [n], (1)
`where n is the discrete time index, w1 [n] is the I th coefficient
`of the L-point adaptive filter (/ = 0, ... ,L - 1 ), d[n] is the
`difference (reference) signal, y [ n] is the beamformer output
`signal, Pd [ n] is a running estimate of power in the reference
`signal, and a is a constant that controls the rate of adapta(cid:173)
`tion. The convolution performed by the adaptive filter is de(cid:173)
`scribed by
`r[n] = L d [n -1 ]w,[n],
`l=O
`and the system output y [ n] is given by
`y[n] = s[n - D] -
`r[n],
`wheres[n] is the sum (primary) signalandDisthedelayin
`the primary channel. In this work, D = L /2.
`Under ideal conditions, sources that are exactly straight
`ahead of the array pass through the system with unit gain, ·
`since signal components arriving at the two microphones
`
`L - l
`
`(2)
`
`(3)
`
`with equal magnitude and phase do not appear at the refer(cid:173)
`ence input and are not affected by the adaptive cancellation
`process. Off-axis sources contribute components to both the
`reference and primary inputs and therefore are subject to
`cancellation. The basic characteristic of this system that
`makes it appealing for application to hearing aids is that the
`reference signal is obtained from the array itself-which
`may be mounted on the head-obviating the need for a re(cid:173)
`mote microphone ( e.g., Brey et al., 1987; Harrison et al.,
`1986).
`
`B. Important issues and previous studies
`Under realistic conditions, the hearing-aid application
`challenges the robustness of adaptive beamformers because
`the usual operating assumptions are all violated to some de(cid:173)
`gree and computational resources are at a minimum. System
`performance is obviously influenced by violations of the two
`fundamental assumptions: uncorrelated target and jammer
`and exact knowledge of target direction. To some extent,
`performance of the noise canceller is limited by the ability of
`the preprocessor in Fig. 1 to provide an uncorrelated, target(cid:173)
`free reference signal. ( See the sections below on array misa(cid:173)
`lignment and reverberation.) On the other hand, perfor(cid:173)
`mance is also limited by the acoustic environment ( degree of
`reverberation and number of jammer sources), the system
`configuration ( array geometry and placement), and imple(cid:173)
`mentation issues ( adaptation rate, misadjustment, and filter
`length). A meaningful evaluation, therefore, must consider
`not only the performance of the idealized system, but also
`the impact of imperfections and limited ranges of param(cid:173)
`eters. Because the effects of errors, of parameter choices, and
`ofresource limitations are all complex and often interactive,
`there is a web of issues to be considered. The following is a
`summary of the more important issues, presented with the
`results of recent studies that have begun to document adap(cid:173)
`tive-beamformer performance under conditions relevant to
`hearing aids.
`
`1. Array misalignment
`With any deviation from perfectly symmetric alignment
`of the array to the target source, the target will not be entire(cid:173)
`ly eliminated by subtraction of the microphone signals, and
`residual target components will "leak" into the reference
`channel. The importance of target leakage was illustrated by
`Widrow et al. ( 1975), who showed that, for the case of an
`unconstrained adaptive filter ( one whose impulse response
`extends infinitely in both time directions), the target-to-jam(cid:173)
`mer ratio at the output of the noise canceller is equal to the
`jammer-to-target ratio at the reference input. When the leak(cid:173)
`age path has any nonzero transfer function, the problem
`clearly worsens as the input target-to-jammer ratio (TJR)
`increases, leading to poorer system performance at better
`TJRs.
`The degradation in system performance caused by tar(cid:173)
`get leakage depends on the degree of leakage, but it is gener(cid:173)
`ally seen with TJRs as low as O dB and is clearly detrimental
`at 10--20 dB ( Peterson et al., 1990). In many noise-cancell(cid:173)
`ing applications, the TJR is always less than O dB, and conse-
`
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`J. E. Greenberg and P. M. Zurek: Beamforming for hearing aids
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`quently moderate target leakage is tolerable. However, in the
`hearing-aid application, TJRs greater than O dB are encoun(cid:173)
`tered frequently. Since at a minimum hearing aids must do
`no harm, the tendency to degrade clean targets must be eli(cid:173)
`minated if the system is to have any chance of success. A
`solution to this problem is proposed in Sec. II A, and its
`effectiveness is demonstrated in Sec. IV A.
`
`2. Multiple jammers
`Because the two-microphone beamformer has one adap(cid:173)
`tive filter, only one transformation can be implemented to
`estimate jammer in the primary channel based on jammer in
`the reference channel. For a single jammer this transforma(cid:173)
`tion is theoretically sufficient for optimal cancellation of that
`jammer. For multiple jammers from different locations, a
`single transformation cannot provide optimal cancellation
`of all jammers. The worst case is expected when multiple
`jammers have the same spectral shape and power ( Peterson,
`1989). Then the total reduction in jammer power achieved
`by the system may be no more than a few dB, whereas the
`reduction of any one jammer presented alone may be tens of
`decibels. Experimental confirmation of this effect can be
`found in Weiss ( 1987) and Peterson et al. ( 1990). Peterson
`( 1989) gives a theoretical analysis of the effects of numbers
`of jammers and microphones on optimal performance for
`head-sized arrays.
`Although the effect of an additional jammer can be
`large, the situation is not lost. While there usually is more
`than one noise source active in an environment, it is rare that
`the sources have very similar spectra and levels. The prototy(cid:173)
`pical "cocktail party" is probably the most common approx(cid:173)
`imation to the worst case. Further, the solution to multiple
`jammers is simply additional microphones ( so that the num(cid:173)
`ber of adaptive filters equals or exceeds the number of jam(cid:173)
`mers). If warranted, this solution is available at the cost of
`computational complexity that increases linearly with the
`number of microphones. In this paper discussion is limited
`to two-microphone arrays and single jammer sources.
`
`3. Reverberation
`It is expected that the performance of a Griffiths-Jim
`beamformer will be degraded by reverberation. A combina(cid:173)
`tion of effects associated with reverberation of the target and
`of the jammer contribute to this degradation. Off-axis target
`reflections violate the assumption of target equality at the
`microphones and lead to target leakage into the reference
`and subsequent target cancellation, provided they fall within
`the time window of the adaptive filter. Reflections of either
`target or jammer that arrive outside the filter's time span are
`uncorrelated with the primary signal and appear as addi(cid:173)
`tional jammers, which may be cancelled less effectively. In
`contrast, jammer reflections that arrive within the adaptive
`filter's window are susceptible to cancellation, which leads
`to a tradeoff in selecting the filter length. Longer filters will
`cancel jammer reflections more effectively at low TJRs, but
`will be more prone to target cancellation ( from target reflec(cid:173)
`tion) at high TJRs.
`Recent studies have presented examples of the influence
`
`of reverberation on the performance of both beamformers
`and traditional adaptive noise-cancelling systems. An adap(cid:173)
`tive noise canceller relies on obtaining a "target-free" refer(cid:173)
`ence signal from a directional microphone pointed away
`from the target or from a remote microphone placed close to
`the noise source. Comparisons of experimental results are
`difficult because performance obviously depends heavily on
`the configuration of noise and target sources, the details of
`microphone placement, and the characteristics of room re(cid:173)
`verberation. System gains of 3-6 dB have been reported for a
`"moderate level of reverberation" (Weiss, 1987), and 7 dB
`for a "moderately reverberant room" ( Schwander and Le(cid:173)
`vitt, 1987). Using a Griffiths-Jim beamformer in a simulat(cid:173)
`ed "living room" resulted in an effective 8-16 dB gain in
`intelligibility (Peterson, 1987; Peterson eta/., 1990). Section
`IV C contains results illustrating beamformer performance
`for various microphone geometries, filter lengths, and de(cid:173)
`grees of reverberation.
`
`4. Array geometry and placement
`It is well known that the performance of an array is
`limited by the number, spacing, and orientation of the sen(cid:173)
`sors, in conjunction with their internal noise. Peterson
`( 1989) examined the optimal performance of head-sized,
`free-space arrays for the two extremes of completely diffuse
`and purely directional jammer fields. Two of the important
`findings of that work are that endfire arrays are often superi(cid:173)
`or to broadside arrays, and that a small number of micro(cid:173)
`phones ( typically < 6) is sufficient to achieve nearly maxi(cid:173)
`mum gain. This work provides valuable insight, but it does
`not afford a complete account of the factors limiting perfor(cid:173)
`mance under realistic conditions. Thus far, no direct experi(cid:173)
`mental work has been done to determine how array size and
`placement on the head and body interact with other param(cid:173)
`eters in imperfect adaptive arrays. The present work ad(cid:173)
`dresses these issues with the measurements reported in Sec.
`IV B for arrays mounted in free space and on a KEMAR
`manikin.
`
`5. Adaptation rate and misadjustment
`An intrinsic property of the LMS adaptive algorithm is
`the tradeoffbetween speed of adaptation and misadjustment,
`which is a residual output noise resulting from fluctuations
`in the adaptive filter weights. Fast adaptation requires large
`steps in adjusting the filter weights ( obtained by selecting a
`large value for the adaptation constant a), but the large steps
`also cause large residual error when the weights reach steady
`state.
`Misadjustment is usually described in the literature as a
`percentage of the minimum mean-square error of the signal
`to be cancelled (Widrow and Stearns, 1985). If precision of
`jammer cancellation were the only factor to consider, then a
`misadjustment of 10%-20% ( corresponding to cancellation
`within 1 dB of the minimum residualjammer power) might
`easily be acceptable in the hearing-aid application. However,
`the presence of a target signal in the output contributes to the
`misadjustment so that the value of a required for satisfactory
`jammer cancellation in the absence of target leads to unac(cid:173)
`ceptable performance when the target is present. The source
`
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`of this increased misadjustment can be understood from Eq.
`( 1 ), which shows that the weight adjustments are propor(cid:173)
`tional to both the adaptation constant a and the beamformer
`output y[n], which includes the target signal. Methods to
`overcome this problem are proposed in Sec. II and evaluated
`in Sec. IV A.
`Misadjustment and the inversely related adaptation rate
`have received very little study in the application to hearing
`aids. The present work attempts to reduce misadjustment,
`but does not provide a quantitative analysis of adaptation
`rate. The approach has been to address other problems first;
`if adaptation speed is found to be a problem after the others
`have been resolved, then alternative algorithms with faster
`convergence will be investigated.
`
`6. Filter length and primary delay
`Increasing filter length is expected to be beneficial when
`performance is limited by the inability of the adaptive filter
`to transform the reference jammer to match the primary
`jammer. Further, performance can be improved by allowing
`both past and future reference samples to contribute to the
`current output through use of a delay in the primary path.
`Zurek et al. ( 1990) computed the performance of optimal
`filters of various lengths using real-room transfer functions
`and found that performance is limited by filter length and
`primary delay only under near-ideal conditions (i.e., mini(cid:173)
`mal reverberation and low TJR). With realistic amounts of
`target signal (TJR>0 dB), under either anechoic or rever(cid:173)
`berant conditions there is little dependence of performance
`on these parameters.
`
`C. Goals of present study
`The present study addresses several of the issues just
`discussed. First, algorithms for controlling adaptation based
`on TJR will be described and evaluated. These techniques
`address the problems of misalignment and misadjustment,
`both of which are manifested at high target-to-jammer ra(cid:173)
`tios. Second, evaluations will be presented of a sample of
`two-microphone arrays that differ in intermicrophone spac(cid:173)
`ing and placement on the body. Third, an investigation and
`more thorough characterization of the effects of reverbera(cid:173)
`tion on beamformer performance will be described.
`The systems studied include both computer simulations
`and a microprocessor-based real-time implementation. For
`static acoustic conditions the two approaches are functional(cid:173)
`ly identical. A real-time system, however, provides immedi(cid:173)
`ate feedback (to the experimenter) and necessarily involves
`a more realistic test than does a simulation. The real-time
`system also provides the ability to listen to the output in
`dynamically varying conditions, which will be the subject of
`a later study.
`The evaluations presented here are in terms of physical
`measurements of signals, with no direct intelligibility tests
`and no involvement of hearing impairments. To the extent
`that speech reception by hearing-impaired ( or normal-hear(cid:173)
`ing) listeners in noise is limited by the background noise, and
`not by other factors, reduction of background noise will have
`a direct benefit. This reduction is assessed through signal
`measurements having a meaningful relation to speech intelli-
`
`gibility. Possible interactions of system performance with
`the magnitude or type of hearing loss will be the subject of
`future studies.
`
`II. MODIFICATIONS FOR CONTROLLING ADAPTATION
`Two methods, shown in Fig. 2(a) as "correlation-based
`inhibition" and "power normalization," have been devel(cid:173)
`oped for dealing with the problems of misadjustment and
`misalignment~ both of which are manifested at high target(cid:173)
`to-jammer ratios. An essential feature of these methods is
`that they take advantage of the fact that the target signal in
`this application-speech-exhibits a high degree of fluctu(cid:173)
`ation, and, in fact, has pause periods during which the target
`is absent. Both of the modifications can be thought of as
`attempts to sense the TJR in order to allow adaptation only
`during intervals when TJR is small. The present description
`of the adaptation-control algorithms will be qualitative and
`intuitive; a more complete analysis is in preparation.
`
`A. Correlation-based inhibition of adaptation
`As explained above, a basic assumption of beamforming
`is that the target signals arrive from a known direction, or
`more specifically, that the target signals can be equalized at
`the microphone outputs. If this assumption is approximately
`met, then target components in the two microphone signals
`will be nearly perfectly correlated. On the other hand, micro(cid:173)
`phone signals from off-axis jammers have a cross-correlation
`
`1/2
`
`y[n) output
`
`bandpass
`filter
`
`comparator 0/ 1
`8
`
`bandpass
`filter
`Inhibition
`• ... --- -- --- ------- -- --- ---- -- ------ --- ------- --- ----------- --
`(b)
`
`FIG. 2. (a) Beamformer modified by the addition of correlation-based inhi(cid:173)
`bition and power normalization. The calculation of power normalization is
`performed according to Eq. ( 4) in the text, and depends on the filter length,
`L, the adaptation constant, a, and the power normalization time constant,
`rP. (b) Detail of the operations performed in correlation-based inhibition.
`The microphone signals are filtered by a bandpass filter with cutoff frequen(cid:173)
`cies depending on the particular array geometry. The filtered signals then
`pass through a one-bit polarity coincidence correlator, which multiplies the
`sign bits of the two signals. The resulting instantaneous correlation signal is
`processed by a lowpass filter with time constant Tc and compared to the
`inhibition threshold, 0, to produce a binary output.
`
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`that, depending on frequency and direction, is less than uni(cid:173)
`ty. Thus, the intermicrophone cross-correlation varies with
`TJR and can be used as an estimate of it.
`The operation of this adaptation-control algorithm is
`shown in Fig. 2(b). In order to maximize the decorrelation
`induced by thejammer, the microphone signals are first pro(cid:173)
`cessed by a filter that passes a particular frequency range.
`That frequency range is chosen to minimize intermicro(cid:173)
`phone correlation averaged over all jammer directions, and
`thus depends on intermicrophone spacing ( Greenberg,
`1989). Next, a one-bit polarity-coincidence correlator and
`single-pole low-pass filter with time constant Tc provide a
`running estimate of intermicrophone cross-correlation. The
`estimate obtained from the signal polarities is proportional
`to the arcsine of the true cross-correlation ( Papoulis, 1984).
`This running correlation estimate, a value between + 1 and
`- 1, is compared to an inhibition threshold, 0, producing an
`output of" 1" or "0" when the correlation is below or above
`the threshold, respectively. By multiplying the error feed(cid:173)
`back by this binary signal, adaptation of the weights is inhib(cid:173)
`ited when the TJR, as estimated by the cross-correlation,
`exceeds the threshold value. This method should have little
`or no effect on beamformer performance for low input TJR,
`and should reduce target cancellation and misadjustment for
`high input TJR. The expected cost for this improved steady(cid:173)
`state performance is longer average adaptation time.
`
`B. Adaptation control through power normalization
`The second method of controlling the adaptive weights
`is intended to minimize misadjustment when input TJR is
`high. Control is achieved by noting that when the input TJR
`is high, and there is negligible leakage of target signal into the
`reference, then the output power will be greater than the
`reference input power. By normalizing the weight update
`equation with respect to a combination of output power and
`reference input power, the adaptive steps can be reduced
`when input TJR is high. In the present implementations,
`output power is incorporated into the update equation by
`normalizing the weight increment with the sum of reference
`and output powers:
`w1 [n + 1] = w1[n]
`+ 2ay[n]d [n -
`
`(4)
`I ]IL(Pd [n] + PY [n] ),
`
`where PY is running-averaged output power, and both PY
`and Pd are averaged using the same single-pole low pass with
`time constant equal to the length of the adaptive filter,
`T P = L I ( 10 kHz). Without the inclusion of output power in
`the normalization, the adaptive steps grow large along with
`the output target when the output target-to-jammer ratio is
`large. Since the target is usually uncorrelated with the jam(cid:173)
`mer, large steps in the weights induced by the target lead to
`large deviations of the weights away from their optimal val(cid:173)
`ues for jammer cancellation and can even increase total out(cid:173)
`put power by increasing misadjustment noise. Normalizing
`with respect to output power reduces the size of these target(cid:173)
`induced weight deviations. Again, the expected cost for this
`improved steady-state performance is longer average adap(cid:173)
`tation time.
`
`The two adaptation-control algorithms employed here
`differ in their operation in that the correlation-based method
`gives all-or-none control while the power-normalization
`method uses continuously variable control. Obviously, ei(cid:173)
`ther method could be designed to operate in either manner.
`The particular forms of the algorithms used here were based
`on convenience, simplicity of implementation, and pilot in(cid:173)
`vestigations.
`The two modifications are similar to algorithms pre(cid:173)
`viously suggested by others. Harrison et al. ( 1986), Kaneda
`and Ohga ( 1986), and Van Compernolle ( 1990) discussed
`inhibiting adaptation during intervals of high TJR in the
`noise-cancellation application, while Duttweiler ( 1978) and
`Sondhi and Berkeley (1980) described its use in adaptive
`echo cancelling on the telephone network. Power normaliza(cid:173)
`tion methods similar to the one described here have been
`proposed by Duttweiler ( 1982), Shan and Kailath ( 1988),
`and Jeyendran and Reddy (1990). A complete analysis of
`the two modifications and comparison to these other algor(cid:173)
`ithms will be the subject of future work.
`
`Ill. METHODS
`A. Performance metric
`Because the output of the beamformer can be described
`by linear transformations of the input target and jammer
`signals, present understanding of the effects of linear filter(cid:173)
`ing and additive noise on speech intelligibility, as embodied
`in the articulation index ( Kryter, 1962; ANSI, 1969), is
`used to form a measure of system performance. According(cid:173)
`ly, the basic signal measurement employed here, as previous(cid:173)
`ly (Peterson, 1989; Peterson eta/., 1990), incorporates pow(cid:173)
`er-spectrum analysis, decibel transformations, and spectral
`weighting. For any signals, the intelligibility-weighted level
`r(s) is
`r(s) = L ajBj (s),
`j
`where Bj ( s) is the decibel level in the }th j-oct band of signal
`s, and aj is the weight assigned to thejth band by articulation
`theory ( ANSI, 1969).
`Values of rare used only as components in comparisons
`between signals, as the absolute values depend on the choice
`of units and have no meaning. Two types of comparisons are
`defined on the four signals of interest: target input, T;; target
`output, T0 ; jammer input, J;; jammer output, J 0 • The first
`comparison shows the improvement from input to output in
`either the target,
`ann = r(T0 )
`or thejammer,
`ar(J) = r(J;) - r(Jo).
`(7)
`The second comparison is the overall intelligibility-weighted
`gain, Gr, in the target-to-jammer ratio from input to output:
`Gr= ann + ar(J)
`r(T;) + r(J;),
`= r(T0 )
`(8)
`- r(J0 )
`except that when there is no target present, Gr is defined to
`equal ar(J). Throughout this study, the input levels r( T;)
`
`(5)
`
`(6)
`
`r(T;),
`
`-
`
`-
`
`1666
`
`J. Acoust. Soc. Am., Vol. 91, No. 3, March 1992
`
`J. E. Greenberg and P. M. Zurek: Beamforming for hearing aids
`
`1666
`
`Page 6 of 16
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`SONOS EXHIBIT 1040
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`

`

`and r ( J; ) are obtained from the microphone signal in which
`r( T;) - r(J;) is higher [ or from the one with smaller
`r ( J; ) when the target is absent]. Note that because of the
`different spectral shapes of received target and jammer,
`re T;) - r(J;) does not necessarily equal TJR, which de(cid:173)
`pends on broadband power levels of the target and jamme~
`source materials and is a primary experimental variable.
`Because of the averaging inherent in estimating power
`spectra for calculating values of r, G 1 is only meaningful for
`measuring performance of a converged system in steady
`state, and cannot be used to assess intelligibility of transient
`conditions.
`
`B. Simulations
`Computer programs were developed to simulate the
`modified beamformer systems described in Sec. II. Input sig(cid:173)
`nals for the simulation were generated by convolving target
`and jammer source materials with source-to-microphone
`impulse responses. T