Pilot-Aided MIMO Channel Identification and Linear Deconvolution in Correlated Gaussian Noise

This paper presents a pilot-aided study of multiple-input multiple-output (MIMO) channel identification and linear deconvolution under spatially correlated Gaussian noise. A real-valued $4\times4$ baseband model is analyzed for both memoryless and finite-impulse-response channels. The noise process is generated from a Toeplitz covariance matrix, the channel is estimated from pilot symbols through maximum-likelihood/least-squares formulations, and the empirical mean-square error is compared with the Cramer--Rao bound. The estimated channel is then used for data-symbol recovery through maximum-likelihood zero-forcing and linear minimum-mean-square-error deconvolution. The results show that sufficiently long and well-conditioned pilot blocks allow the channel estimator to approach the theoretical lower bound, whereas short training intervals cause rank and conditioning limitations, especially for the four-tap model. The deconvolution experiments further show that MMSE regularization provides a more stable inverse than unregularized zero forcing at low signal-to-noise ratios and for inaccurate channel estimates.