Next we plot the BER versus the covariance matrix rank for three channel conditions: flat fading,
frequency selective fading with a time delay ( T/2), and frequency selective fading with a time
delay ( T ). One can see at the delay spread increases the rank of the covariance matrix also
increases. Also note in the flat-fading channel we can see that the addition of the interference
increased the rank by 1 (see Fig. 6.14).
6.2.4 Covariance Matrix Eigen Spectra Properties
In this section, we will present some measured statistics of eigenvalues of the space-time equalizer
given above. The STE architecture was a fractionally spaced, T/2-spaced STE using K 5 taps and
M 2 receive antennas. First, we plot the probability density function (PDF) of the ten eigenvalues
below (see Fig. 6.15). The channel model considered was flat fading plus CCI interference. As shown
in the previous sections, the presence of CCI will increase the covariance matrix rank by 1. Thus
bringing the total number of dominant eigenvalues to 4.
The covariance matrix rank is more visible in the plot of the eigenvalue CDF. Here we see the four
dominant eigenvalues (see Fig. 6.16).
We wish to conclude this section by stating that the covariance matrix vector space can be divided
into subspaces: a signal subspace and noise subspace.
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