Relative Acoustic Transfer Function Estimation in Wireless Acoustic Sensor Networks

Jie Zhang*, Richard Heusdens, Richard Hendriks

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

17 Citations (Scopus)
146 Downloads (Pure)


In this paper, we present an algorithm to estimate the relative acoustic transfer function (RTF) of a target source in wireless acoustic sensor networks (WASNs). Two well-known methods to estimate the RTF are the covariance subtraction (CS) method and the covariance whitening (CW) approach, the latter based on the generalized eigenvalue decomposition. Both methods depend on the use of the noisy correlation matrix, which, in practice, has to be estimated using limited and (in WASNs) quantized data. The bit rate and the fact that we use limited data records therefore directly affect the accuracy of the estimated RTFs. Therefore, we first theoretically analyze the estimation performance of the two approaches in terms of bit rate. Second, we propose a rate-distribution method by minimizing the power usage and constraining the expected estimation error for both RTF estimators. The optimal rate distributions are found by using convex optimization techniques. The model-based methods, however, are impractical due to the dependence on the true RTFs. We therefore further develop two greedy rate-distribution methods for both approaches. Finally, numerical simulations on synthetic data and real audio recordings show the superiority of the proposed approaches in power usage compared to uniform rate allocation. We find that in order to satisfy the same RTF estimation accuracy, the rate-distributed CW methods consume much less transmission energy than the CS-based methods.

Original languageEnglish
Article number8738844
Pages (from-to)1507-1519
Number of pages13
JournalIEEE/ACM Transactions on Audio Speech and Language Processing
Issue number10
Publication statusPublished - 2019

Bibliographical note

Accepted author manuscript


  • convex optimization
  • covariance subtraction
  • covariance whitening
  • model/data-driven rate distribution
  • quantization
  • relative transfer function
  • Sensor networks


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