## High SNR distribution of eigen-values of a Wishart Matrix

Miscellaneous November 12th. 2008, 3:32pmToday I came across a nice result on the distribution of eigen values of matrix , where the entries of are i.i.d. Gaussian distributed. The result says that the eigen value (in the decreasing order) of has the following distribution, for small .

Its quite useful for analysing many MIMO techniques, such as MRC, MRT.

The reference is a recent IT Paper: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4544985&isnumber=4544949

November 13th, 2008 at 2:34 pm

Indeed a very nice result. We should include this somewhere in the MIMO book. I wonder where? Of course, it seems more useful for analyzing MIMO methods that depend on the smaller(est) values instead since it is only good for small x.

November 13th, 2008 at 2:36 pm

It should be included in the chapter that deals with precoders, beamforming etc.

December 3rd, 2008 at 9:52 am

Yes, the result is very nice. Indeed, after deriving the first order expansion on the marginal distribution of each Wishart eigenvalue,I find that the exponent of $x$ remains the same even in the presence of spatial correlation and line-of-sight effect. In other words, the diversity order of each MIMO sub-channel is independent of the two factors above. This is very interesting and somewhat amazing, at least to me.

PS. Thank you, Rahul Vaze, for the nice paper. Also, WindoWSIL is a nice place. ^_^