The second cost function that we will analyze maximizes the array output SINR given as follows:
(5.123)
where Rss is the desired signal??™s covariance matrix and RIN is the interference plus noise covariance
matrix. This leads to the following equation for the adaptive antenna array weights.
(5.124)
The received signal??™s interference plus noise covariance matrix is given as follows (with the variable
t is omitted for sake of convenience):
(5.125)
where ?†??“ h
his an estimate of the desired signal??™s channel vector. It is commonly accepted to replace this
channel estimate with the cross-correlation vector given above. This can now be rewritten as
(5.126)
Hence the estimated MSINR array weights are given as
(5.127)
Covariance Matrix Eigen Spectra Decomposition. In this section, we will discuss some eigen
spectral properties of the covariance matrix used in the array weight calculation. These properties will
not only provide insight into the array weight mechanisms, but also attempt to improve system performance.
First the covariance matrices are Hermitian, they are normal matrices and positive definite.
Using the Eigen Spectral Decomposition (ESD) theorem we can rewrite the received signal??™s covariance
matrix as follows [67??“70]:
(5.
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