Adaptive Algorithm for Multichannel Autoregressive Estimation in Spatially Correlated Noise

This paper addresses the problem of multichannel autoregressive (MAR) parameter estimation in the presence of spatially correlated noise by steepest descent (SD) method which combines low-order and high-order Yule-Walker (YW) equations. In addition, to yield an unbiased estimate of the MAR model parameters, we apply inverse filtering for noise covariance matrix estimation. In a simulation study, the performance of the proposed unbiased estimation algorithm is evaluated and compared with existing parameter estimation methods. 1. Introduction The noisy MAR modeling has many applications such as high resolution multichannel spectral estimation [1], parametric multichannel speech enhancement [2], MIMO-AR time varying fading channel estimation [3], and adaptive signal detection [4]. When the noise-free observations are available, the Nuttall-Strand method [5], the maximum likelihood (ML) estimator [6], and the extension of some standard schemes in scalar case to multichannel can be used for estimation of MAR model parameters. The relevance of the Nuttall-Strand method is explained in [7] by carrying out a comparative study between these methods. The noise-free MAR estimation methods are sensitive to the presence of additive noise in the MAR process which limits their utility [1]. The modified Yule-Walker (MYW) method is a conventional method for noisy MAR parameter estimation. This method uses estimated correlation at lags beyond the AR order [1]. The MYW method is perhaps the simplest one from the computational point of view [8], but it exhibits poor estimation accuracy and relatively low efficiency due to the use of large-lag autocovariance estimates [8]. Moreover, numerical instability issues may occur when it is used in online parameter estimation [9]. The least-squares (LS) method is another method for noisy MAR parameter estimation. The additive noise causes the least-squares (LS) estimates of MAR parameters to be biased. In [10] an improved LS (ILS) based method has been developed for estimation of noisy MAR signals. In this method, bias correction is performed using observation noise covariance estimation. The method proposed in [10], denoted by vector ILS based (ILSV) method, is an extension of Zheng’s method [11] to the multichannel case. In the ILSV method, the channel noises can be correlated and no constraint is imposed on the covariance matrix of channel noises. Nevertheless this method has poor convergence when the SNR is low. In [12], the ILSV algorithm is modified using symmetry property of the observation covariance matrix which is named an