Research Article Adaptive Algorithm for Multichannel Autoregressive Estimation in Spatially Correlated Noise Alimorad Mahmoudi Electrical Engineering Department, Shahid Chamran University, Ahvaz, Iran Correspondence should be addressed to Alimorad Mahmoudi; a.mahmoudi@scu.ac.ir Received 24 April 2014; Accepted 5 June 2014; Published 19 June 2014 Academic Editor: Chi-Yi Tsai Copyright © 2014 Alimorad Mahmoudi. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis 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 fltering 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 Te 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. Te relevance of the Nuttall-Strand method is explained in [7] by carrying out a comparative study between these methods. Te noise-free MAR estima- tion methods are sensitive to the presence of additive noise in the MAR process which limits their utility [1]. Te modifed Yule-Walker (MYW) method is a conven- tional method for noisy MAR parameter estimation. Tis method uses estimated correlation at lags beyond the AR order [1]. Te MYW method is perhaps the simplest one from the computational point of view [8], but it exhibits poor estimation accuracy and relatively low efciency 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]. Te least-squares (LS) method is another method for noisy MAR parameter estimation. Te 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. Te 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 modifed using symmetry property of the observation covariance matrix which is named an advanced least square vector (ALSV) algorithm. One step called symmetrisation is added to the ILSV algo- rithm to estimate the observation noise covariance matrix. In [13, 14], methods based on errors-in-variables and cross coupled, Kalman and H ∞ , flters are suggested, respec- tively. Tese methods are also an extension of the scalar methods presented in [15] and [16, 17], respectively. In these Hindawi Publishing Corporation Journal of Stochastics Volume 2014, Article ID 502406, 7 pages http://dx.doi.org/10.1155/2014/502406