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If the system is given by $y=Ax+z$ where $z$ is white Gaussian noise and $A$ is a random matrix with i.i.d. distribution with zero mean how can we estimate $x$ from received vector $y$?

I tried linear minimum mean squared error (LMMSE) estimation and it doesn't seem to work. (https://stats.stackexchange.com/questions/82872/mmse-estimation-with-random-system-matrix)

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triomphe
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  • This is similar to the problem of estimating the channel matrix in a wireless MIMO system. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1597555&tag=1 is a good article which explains (in depth) different methods for estimating $A$. – David Simmons Jan 21 '14 at 14:36
  • @DaveS Thank you. But that is not my problem. In this paper they assume that the $x$ (training sequence) is known. In my problem both $A$ and $x$ are random. – triomphe Jan 21 '14 at 15:27

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