Practically not possible to measure radiation pattern without anechoic chamber
It should be possible with a range gate. You can also do it out of doors.
It will need to be a long way above the ground, (if your antenna is not a ground based one) so that the ground reflection doesn't arrive at nearly the same time as the direct one, or so that your measurement antenna doesn't see the ground reflection.
One problem with range gating is that range-gated signals are wide band, so the measurement is an average over a band, not the value at one frequency. The bandwidth is 1/(gate width) so if you want a 1 ns gate width the bandwidth is 1 GHz, for example. This will affect measurements if your antenna bandwidth is narrower than the pulse bandwidth.
Dear Fazel Ghiasvand , please take a look at my last paper "Improving antenna gain estimations in non-ideal test sites with auto-tunable filters" ( Article Improving antenna gain estimations in non-ideal test sites w...
) . In this paper, I describe the use of time gating conjugated with adaptive filter in order to extract the antenna gain curve in a non-anechoic environment. If you want to discuss about it, please send me a message.