# Beamforming under Quantization Errors in Wireless Binaural Hearing Aids

- Sriram Srinivasan
^{1}Email author, - Ashish Pandharipande
^{1}and - Kees Janse
^{1}

**2008**:824797

https://doi.org/10.1155/2008/824797

© Sriram Srinivasan et al. 2008

**Received: **28 January 2008

**Accepted: **30 June 2008

**Published: **6 July 2008

## Abstract

Improving the intelligibility of speech in different environments is one of the main objectives of hearing aid signal processing algorithms. Hearing aids typically employ beamforming techniques using multiple microphones for this task. In this paper, we discuss a binaural beamforming scheme that uses signals from the hearing aids worn on both the left and right ears. Specifically, we analyze the effect of a low bit rate wireless communication link between the left and right hearing aids on the performance of the beamformer. The scheme is comprised of a generalized sidelobe canceller (GSC) that has two inputs: observations from one ear, and quantized observations from the other ear, and whose output is an estimate of the desired signal. We analyze the performance of this scheme in the presence of a localized interferer as a function of the communication bit rate using the resultant mean-squared error as the signal distortion measure.

## 1. Introduction

Modern digital hearing aids perform a variety of signal processing tasks aimed at improving the quality and intelligibility of the received sound signals. These tasks include frequency-dependent amplification, feedback cancellation, background noise reduction, and environmental sound classification. Among these, improving speech intelligibility in the presence of interfering sound sources remains one of the most sought-after features among hearing aid users [1]. Hearing aids attempt to achieve this goal through beamforming using two or more microphones, and exploit the spatial diversity resulting from the different spatial positions of the desired and interfering sound sources [2].

The distance between the microphones on a single hearing aid is typically less than 1 cm due to the small size of such devices for aesthetic reasons. This small spacing limits the gain that can be obtained from microphone array speech enhancement algorithms. Binaural beamforming, which uses signals from both the left and right hearing aids, offers greater potential due to the larger inter-microphone distances corresponding to the distance between the two ears (16–20 cm). In addition, such a scheme also provides the possibility to exploit the natural attenuation provided by the head. Depending on the location of the interfering source, the signal-to-interference ratio (SIR) can be significantly higher at one ear compared to the other, and a binaural system can exploit this aspect.

A high-speed wireless link between the hearing aids worn on the left and right ears has been recently introduced [3]. This allows binaural beamforming without the necessity of having a wired connection between the hearing aids, which is impractical again due to aesthetic reasons. The two hearing aids form a body area network, and can provide significant performance gains by collaborating with one another. The performance of binaural noise reduction systems has been previously studied in, for example, [4–8]. However these systems implicitly assume the availability of the error-free left and right microphone signals for processing. In practice, the amount of information that can be shared between the left and right hearing aids is limited by constraints on power consumption imposed by the limited capacity of hearing aid batteries. It is known [9] that quantization of a signal with an additional bit causes the power dissipation in an ADC to be increased by 3 dB. Hence to conserve battery in a hearing aid, it is critical to compress with as few bits as possible before wireless transmission occurs. One in five users was reported to be dissatisfied with hearing aid battery life [10], and it is thus an important consideration in hearing aid design. In this paper, we study analytically the trade-off in the performance of a GSC beamformer with respect to quantization bits.

Different configurations are possible for a binaural beamforming system, for instance, both hearing aids could transmit their received microphone signals to a central device where the beamforming is performed, and the result could then be transmitted back to the hearing aids. Alternatively, the hearing aids could exchange their signals and beamforming may be performed on each hearing aid. In this paper, to analyze the effect of quantization errors on beamforming, without loss of generality we assume that each hearing aid has one microphone and that the right hearing aid quantizes and transmits its signal to the left hearing aid, where the two signals are combined using a beamformer. This paper is an extension of our earlier work [11], incorporates the effect of head shadow and presents a more detailed experimental analysis.

If the power spectral density (PSD) of the desired source is known a priori, the two-microphone Wiener filter provides the optimal (in the mean squared error sense) estimate of the desired source. The effect of quantization errors in such a framework has been investigated in [12]. However, in practice the PSD is unknown. In this paper, we consider a particular beamformer, the generalized sidelobe canceller (GSC) [13], which does not require prior knowledge of the source PSD.

The GSC requires knowledge of the location of the desired source, which is available since the desired source is commonly assumed to be located at (in front of the microphone array) in hearing aid applications [2]. The motivation behind this assumption is that in most real-life situations, for instance, a conversation, the user is facing the desired sound source. In a free field, the two-microphone GSC can cancel out an interfering sound source without distorting the desired signal, which is a desirable feature in hearing aids. Thus, the GSC is well suited for hearing aid applications, and we study the impact of quantization errors on the GSC in this paper.

The performance of the GSC may be affected by other sources of error such as microphone mismatch, errors in the assumed model (the desired source may not be located exactly at , reverberation, and so forth. Variations of the GSC that are robust to such imperfections are discussed in [14–16]. In this paper, we exclude such errors from our analysis to isolate the effect of the errors introduced by quantization on the performance of the GSC.

The remainder of this paper is organized as follows. We introduce the signal model and the head shadow model we use in Section 2. The binaural GSC and its behavior in the presence of quantization errors are discussed in Section 3. The performance of the GSC at different bit rates is analyzed in Section 4. Finally, concluding remarks and suggestions for future work are presented in Section 5.

## 2. Signal Model

where and are the transfer functions between the microphone on the left hearing aid and the desired and interfering sources, respectively, and corresponds to uncorrelated (e.g., sensor) noise with . The transfer functions and include the effect of head shadow. For each , we model , , and as memoryless zero mean complex Gaussian sources, with variances , , and , respectively. Their real and imaginary parts are assumed to be independent with variances , , and , respectively.

where the relevant terms are defined analogously to the left ear. We assume that , and that , , and are pairwise independent.

*forward channel*with respect to the squared error criterion can be written as [18, pages 100-101],

so that the distortion is obtained as . The signals and form the two inputs to the GSC.

If the PSDs , and are known, more efficient quantization schemes may be designed, for example, one could first estimate the desired signal (using a Wiener filter) from the noisy observation at the right ear, and then quantize the estimate as in [12]. However, as the PSDs are unknown in our model, we quantize the noisy observation itself.

## 3. The Binaural GSC

We first look at the case when there is no quantization and the left hearing aid receives an error-free description of . This corresponds to an upper bound in our performance analysis. We then consider the case when is quantized at a rate bits per sample.

### 3.1. No Quantization

The GSC has three basic building blocks. The first is a fixed beamformer that is steered towards the direction of the desired source. The second is a blocking matrix that produces a so-called noise reference signal that is devoid of the desired source signal. Finally, the third is an adaptive interference canceller that uses the reference signal generated by the blocking matrix to cancel out the interference present in the beamformer output.

The adaptive filter is updated such that the expected energy of the residual given by is minimized, for example, using the normalized least mean square algorithm [19, Chapter 9]. Since does not contain the desired signal, minimizing corresponds to minimizing the energy of the interferer in the residual. Note that none of the above steps require knowledge of the PSD of the desired or interfering sources.

### 3.2. Quantization at a Rate R

## 4. GSC Performance at Different Bit Rates

## 5. Conclusions

A wireless data link between the left and right hearing aids enables binaural beamforming. Such a binaural system with one microphone on each hearing aid offers improved noise reduction compared to a two-microphone monaural hearing aid system. The performance gain arises from the larger microphone spacing and the ability to exploit the head shadow effect. The binaural benefit (improvement compared to the monaural solution) is largest when an interfering source is located close to the desired source, for instance, in the front half plane. For interferers located in the rear half plane, the binaural benefit is restricted to the low-frequency region where the monaural system has poor spatial resolution. Unlike the monaural solution, the binaural GSC is able to provide a uniform performance improvement regardless of whether the interferer is in the front or rear half plane.

Wireless transmission is power intensive and battery life is an important factor in hearing aids. Exchange of microphone signals at low bit rates is thus of interest to conserve battery. In this paper, the performance of the binaural system has been studied as a function of the communication bit rate. The generalized sidelobe canceller (GSC) has been considered in this paper as it requires neither knowledge of the source PSDs nor of the location of the interfering sources. Both the monaural and binaural systems perform best when the level of uncorrelated noise is low, that is, at high SNRs, when the adaptive interference canceller is able to fully exploit the availability of the second signal. At an SNR of 30 dB and an SIR of 0 dB, the binaural system offers significant gains (15 dB SINR improvement for interferer at even at a low bit rate of 4 bits per sample. At higher input SIRs, a higher bit-rate is required to achieve a similar gain.

In practice, the total number of available bits needs to be optimally allocated to different frequency bands. An optimal allocation would be nonuniform across the different bands. Such an allocation however requires knowledge of the source PSD and the location of the interferer. Alternatively, a suboptimal but practically realizable uniform rate allocation may be employed. It has been seen that such a uniform rate allocation results in a performance degradation of around 5 dB in terms of SINR compared to a nonuniform allocation obtained using a greedy optimization approach.

The main goal of this paper has been to investigate the effect of quantization errors on the binaural GSC. Several extensions to the basic theme can be followed. Topics for future work include studying the effect of reverberation and ambient diffuse noise on the performance of the beamformer. Binaural localization cues such as interaural time and level differences have been shown to contribute towards speech intelligibility. Future work could analyze the effect of quantization errors on these binaural cues.

## Authors’ Affiliations

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