How can we feed 4x5 array of LPDA using single wave guide port. Recommend Any junction network for coaxial feed.
You might try something like a Rotman lens (parallel plate waveguide divider) with the waveguide as the feed, to 20 coax ports.
Absorber around the walls may give some isolation between ports.
If you are using the log-periodic antennas over a wide bandwidth, which is usually what they are used for, then you can't use a feed network that depends on shortening lines by whole numbers of half or whole wavelengths. The feeds to all antennas need to be the same length.
Also, an array of log-periodic antennas is not the same as a log-periodic array. If all the elements face in the same direction, then over the bandwidth, the spacing between elements, measured in wavelengths, changes significantly, probably resulting in grating lobes at the high frequencies. The only way to stop this is to have all the antennas pointing at their common origin, which may not give a very useful result, either.
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