Acoustic Noise Reduction by Means of Qrd–based Unconstrained Optimal Filtering

We present a new QRD-based technique for optimal multichannel filtering and its application to multi–channel acoustic noise reduction. A recursively calculated adaptive filter optimally estimates the speech component in a noisy signal. The complexity of this algorithm is an order of magnitude than that of existing optimal filtering based algorithms which are mainly based upon SVD– decompositions, while performance is kept at the same level. 1. INTRODUCTION In teleconferencing, hands–free telephony or voice controlled systems, a microphone array may be used instead of a single microphone in an attempt to reduce unwanted disturbances (e.g. car noise, computer noise, background speakers) based on spatio–temporal filtering. A typical setup is shown schematically in Figure 1 for an array with 4 microphones. We aim at designing an optimal filter which will use all available information (e.g. reflections) in order to optimally reconstruct the signal of interest. In [1] [2] the optimal filtering problem was solved by means of a GSVD (Generalised Singular Value Decomposition)–approach. In this framework, a filter which estimates the signal of interest from the microphone signals can be chosen from a set of such filters after computing the GSVD. In this paper we will describe a QRD–based optimal filtering approach to the problem. The QRD–decomposition is already less complex than the SVD as such, and one can make the selection of the filter that will be calculated in advance, introducing an extra cost reduction. The complexity of this algorithm is an order of magnitude lower than that of existing optimal filtering based algorithms which are based upon SVD–decompositions, while performance is kept at the same level. The paper is organized as follows. In sections 2 and 3 we will introduce optimal filtering based noise reduction. Then we describe how noise reduction can be implemented by means of QRD–based filtering in section 4. Then the complexity figures and the simulation results are given in sections 5 and 6. 2. OPTIMAL FILTERING BASED NOISE REDUCTION The speech component in the ‚ ’th microphone at time ƒ is „ … †;ƒˆ‡9‰