Skip to main content

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

 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 $${{\bar {\mathbf {U}}^{\left (n \right)}} \in {\mathbb {C}^{{N_{\mathrm {t}}} \times M}}}$$. 