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\subsubsection{Re-configuration Systems Operation Cost}  \subsection{Up-front Costs}  \subsubsection{Cost of Antennas Construction}  A commonly used rule of thumb for the cost of an antenna is that it is proportional to $D^{\alpha}$, where $\alpha \approx 2.7$ for values of $D$ from a few meters to tens of meters (see \cite{moran}). For $N$ antennas of diameter $D$ meters with accuracy $\frac{\lambda}{16}$, where $\lambda$ is in millimeters. millimeters we could use \cite{mmadesign} as an upper limit for Antenna construction cost.  \begin{equation}\label{eq:antenna_cost}  \text{Antenna Cost} = \frac{890N(\frac{D}{10})^{2.7}}{(\lambda^{0.7})} + 500  \end{equation}  \subsubsection{Cost of Antenna Electronics} Front-end system}  For $M$ frequency bands, each 30\% wide, and dual polarization we could use \cite{mmadesign} as an upper limit for Front-End System Cost:  \begin{equation}\label{eq:fe_cost}  \text{Front-End System Cost} = 45MN + 200M  \end{equation}  \subsubsection{Cost of Re-configuration Systems Construction} LO system}  We could use \cite{mmadesign} as an upper limit for LO System Cost:  \begin{equation}\label{eq:lo_cost}  \text{LO System Cost} = 80N+100  \end{equation}  \subsubsection{IF Transmission Cost}  Being Introducing  $B$ as  average baseline length and $N$ number of antennas, baseline,  we could use \cite{mmadesign}IF Transmission cost  as an upper limit: limit for IF Transmission Cost:  \begin{equation}\label{eq:IF_Tx_cost}  \text{IF Transmission Cost} = 8BN + 30N + 400  \end{equation}  \subsubsection{Correlator Cost}  Using $N$ as number of antennas, we We  could use \cite{mmadesign} Correlator Cost as an upper limit: \begin{equation}\label{eq:correlator}  \text{Correlator cost} = 2N^2 + 112N +1360  \end{equation}  \subsubsection{Cost of Re-configuration Systems Construction}  \section{Mathematical Formulation}  Thus if we are using vector $x = {\text{antenna diameter}, \text{antenna efficiency}, \}$, the antenna diameter, as the optimization variable the problem we would like to solve is:  \begin{equation*} 
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