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    {\small\rm\zihao{6}\songti\thepage\hfill
    \quad\quad ACTA ASTRONOMICA SINICA \hfill
    \hspace{2mm} Vol.44\vspace{2mm}}}} %%%%%%%
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    {\small\rm \zihao{6}\songti suppl.\hfill Y. Su et al.: An Optimal Design of
    Array Configuration of KARST for SKA %%�����ߣ���Ŀ���ƣ�
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    \zihao{6}\songti
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    Vol.44~ Suppl.
    \hfill\hspace{8mm} %%% if ``October/January'' then \hspace{8/10 mm} July
    \small ACTA ASTRONOMICA SINICA
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      Feb.,~2003 \\[-1.5 true mm] %%January
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\vs\vs\vs \bc {\Large\bf An Optimal Design of
    Array Configuration of\\[2mm]
     KARST for SKA    %%�����⣩
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%$\!\!^*$
}

\vs\vs{\normalsize Yan Su,\hs\hs Rendong Nan \hs\&\hs Bo Peng}  %%���������ߣ�

\vs (\footnotesize \nao) \vs\vs \ec

\normalsize
\begin{quotation}

 \no{\bf A{\scriptsize\bf BSTRACT }}~~~\small
KARST, Chinese version of the SKA, consists of about 30 individual
FAST type elements, each roughly 200\,m in diameter, in the karst
region of Guizhou province. One method which can pick 30 sites
from hundreds of candidates to get the best uv coverage is briefly
described here.

 %\vn
% \no{\bf Key words}~~  pulsar-mode  change-spectrum
\end{quotation}

\para{\large\bf{1}~~ Introduction}

\vs\vs The SKA, the Square Kilometer Array, as a major next
generation radio telescope has an effective collecting area of 1
square kilometers dividing into number of elements (Peter 2000).
The array configuration is closely related to the uv coverage
quality of the future SKA. For two dimensional arrays, there is no
corresponding exact solution, and it is quite complex and
difficult even to specify an optimization criterion (Bunton 1999).
Thus, a careful consideration takes on a particular importance.
Currently, numerous groups in different countries are involved
into this simulating investigation, which includes the number of
stations, the layout at various scales, and geographic and cost
constraints. Various sample configurations have been put forward
and analyzed, for example, asymmetric array, several armed spiral
forms for SKA (Bunton 2000), a doughnut shape and maximally filled
array for Allen Telescope Array (ATA) (Bock 2000) etc.. L. Kogan
proposed one method to minimize side lobes in a region around the
primary beam by the specific array element shift, which, however
has some restrictions in general use (Kogan 1997).

The FAST, Five hundred meters Aperture Spherical radio Telescope,
is a Chinese effort to the international cooperation as a pilot of
the SKA (Nan \& Peng 2000). A  number of likely karst depressions
in south of Guizhou province have been found and studied (Nan et
al. 1995). Fig.1 shows 288 suitable telescope locations in
Pingtang county. Among the statistical data, 30 best sites should
be chosen as a synthesis array. One possible layout has been
investigated that the sites were obtained randomly in terms of
some rules without optimization (Tian et al. 1995).

\para{\large\bf{2}~~The Approach to the Problem}

\vs\vn{\bf{2.1~~ Basic method}}

Basically, the routine of using minimum redundancy is to abandon
redundant antennas in terms of the uv coverage quality. As we
know, among uv points of instantaneous snapshot observations, the
uv points which are close to other points could be dropped without
losing much information.

We could select the locations according to their contribution to
the uniformity of uv coverage. Suppose there are N elements in the
array, then for the element $m$, the minimum distance between its
every relevant uv point and other uv points could be calculated.
Thus, the sum of $(N-1)$ minimum distance of every relevant uv
point of one site could be determined by the following equation
\begin{equation}
TotalMinDis(m)=\sum_{n=1}^{N-1}MinDis(m,n)\,.
\end{equation}
Comparing the value of $TotalMinDis(m)$ of all elements, we can
obtain the smallest one which means it has less contribution and could
be abandoned. Thus, $(N-1)$ elements have been left, return back
to the beginning, calculate and compare again, get rid of others
till the number of the rest is what we want.

\vn{\bf{2.2~~Weighted coverage scale method}}

The basic method described above is to make the uv coverage as
uniform as possible. It does not work in any cases due to
different scientific requirements. Thus the basic criterion can be
modified by multiplying different weight functions for other uses.
For example, to get more information of an extended source, it is
necessary to make the center of uv tracks more condensed. At this
point, $MinDis(m,n)$ of each element can be adjusted as the
following equation
\begin{equation}
MinDis(m,n)_f = MinDis(m,n)\times\exp (- \frac{r^2}{D^2})
\end{equation}
where $exp (- \frac{r^2}{D^2})$ is a Gauss taper function, $r$ is the distance
between one uv point and the origin in
the uv image, and D is a constant which could be set according to
different requirements.

\para{\large\bf{3}~~Results}

\vs\vs We wrote several tasks in Octave which provide the
optimization of minimum distance for the given number of elements.
Fig.1 shows the element selection by the basic method. The
instantaneous snapshot observations of all candidate locations and
30 selected sites to a source with longitude 60 degree and
latitude 60 degree at 18 $cm$ wavelength are demonstrated in Fig.2
and Fig.3 respectively. Apparently, the uv coverage of 30 sites
basically cover all the informaion of the source with the most
uniformity.

\begin{figure}[h]
\center {\includegraphics [bb=50 50 410
302,scale=0.6]{288sel30.eps}}

   %\parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {\center
   \footnotesize

      Fig.\,1~~ The sites distribution (cross: 288 candidates locations; circle:
30 picked sites)}

    \end{figure}
\begin{figure}[h]
\center {\includegraphics [bb=50 50 410
302,scale=0.6]{288tel.eps}}

   %\parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {\center
   \footnotesize

      Fig.\,2~~ An instantaneous snapshot observation by 288 candidates}

    \end{figure}

\begin{figure}[h]
\center {\includegraphics [bb=50 50 410
302,scale=0.6]{30goodtel.eps}}

   %\parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {\center
   \footnotesize

      Fig.\,3~~ An Instantaneous Snapshot Observation by 30 Selected Telescope Sites}

    \end{figure}

\para{\large\bf{4}~~Remarks}

\vs\vs We provide one more choice for designing 2-dimensional
arrays. It produces uniform uv coverage. The advantage to this
idea is that the site selection criterion is not constant, and
could be changed by taper function to fulfill different scientific
objectives.

\bc {\bf References} \ec

\vspace{-4mm} \no \fns

 \nref Hall P.,  Proc. Workshop on Applications of Rad. Sci.,
Beechworth, Victoria, 2000, pp 41-46 \nref Bunton J., CSIRO
Telecommunications and Industrial Physics. 1999
 \nref Bunton J., talk in SKA workshop on array
configuration design, 2000 \nref Borck D., ATA Memo 15, 2000,
 \nref Borck D.,  ATA
Memo 21, 2001
 \nref Kogan L.,  MMA Memo 171, 1997
  \nref Nan R., Peng B., A\&A, 2000, 46, 667
   \nref Nan R., Nie Y., Peng B., et al.,  proceedings of the 3rd Meeting of the
Large Telescope working group and a workshop on spherical radio
telescopes, 1995, 59
 \nref Tian W., Qiu Y., Peng B.,
 proceedings of the 3rd Meeting of the Large Telescope
working group and a workshop on spherical radio telescopes, 1995,
188

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