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Table 1 Procedure of deriving the compression matrix in each long-term period with the PCA method at the MS

From: A limited feedback scheme for massive MIMO systems based on principal component analysis

Initialization  
S: Number of the short-term period T s in every
  long-term period T l.
M: Number of the dominating eigenvectors chosen
  to form the compression matrix.
Procedures  
1) Channel estimation: perform channel
  estimation continuously in T l (n) to obtain
  S high-dimensional channel vectors
  \({\textbf {h}_{k}^{\left ({n,1} \right)},\textbf {h}_{k}^{\left ({n,2} \right)} \ldots, \textbf {h}_{k}^{\left ({n,S} \right)}}\).
2) Computation of covariance matrix: \({\tilde {\mathbf {H}}^{\left (n \right)} =}\)
  \({{\left [ {{{\left ({\textbf {h}_{k}^{\left ({n,1} \right)}} \right)}^{H}},{{\left ({\textbf {h}_{k}^{\left ({n,2} \right)}} \right)}^{H}}\ldots,{{\left ({\textbf {h}_{k}^{\left ({n,S} \right)}} \right)}^{H}}} \right ]^{H}}}\)
  \({\in {\mathbb {C}^{S \times {N_{\mathrm {t}}}}}}\) and compute its covariance matrix.
3) Eigen-decomposition: perform eigen-
  decomposition on the above covariance matrix
  \({\text {Cov}\left ({{{\tilde {\mathbf {H}}}^{\left (n \right)}},{{\tilde {\mathbf {H}}}^{\left (n \right)}}} \right) = {\textbf {U}^{\left (n \right)}}{\textbf {D}^{\left (n \right)}}{\left ({{\textbf {U}^{\left (n \right)}}} \right)^{H}}}\).
4) Formation of compression matrix: choose M
  dominating eigenvectors to form compression
  matrix \({{\bar {\mathbf {U}}^{\left (n \right)}} \in {\mathbb {C}^{{N_{\mathrm {t}}} \times M}}}\).