Enormous SETI (and other science)antenna in space

Some of you may find path loss confusing as I do. Try my example from the thread about the very long space antenna: Transmit one million watts with a perfect very narrow beam antenna. It illuminates one billion square meters at a distance of one light year. That is 1000 square Kilometers. At ten light years range it illuminates 100,000 square kilometers. At 1000 light years it illuminates one billion square kilometers, so your receiving antenna needs an effective receiving area of one square kilometer to receive one milliwatt = 0.001 watts. Modern receivers are much more sensitive than one milliwatt, and the noise level is much lower on most frequencies, so there is no problem sending data 1000 light years except it may be impossible to build a half perfect antenna that produces that narrow a beam even with super conductors and a trillion dollar budget. Let's assume that ET exactly a thousand light years away can build the antenna for a trillion dollars, don't mind spending the big bucks and knows on which side of the sun Earth will be in exactly 1000 years. He can send us the data and our one kilometer antenna can receive the data if it is pointing in the correct direction. That is a lot of ifs. The correct direction the receiving antenna points becomes less critical as the transmitting frequency get lower, assuming gil is correct, but the noise increases inversely as the receiving antenna gain.
The probability of building an extremely high gain transmitting antenna at low frequencies = 300,000 HZ = 0.3 megahertz is very low unless ET knows something we don't = likely. In my hypothesis, extremely high gain transmitting antennas (at multiple light-year range) produce many fast moving hot spots, so several very wide spaced receiving antennas (one AU?) are needed to receive the signal sequentially for more than a second. The hot spots are due to extremely minute antenna jitter, uneven thermal expansion, and minute errors in the shape of the miles wide parabolic dish. Even a person walking softly on an antenna support will produce antenna jitter on the order of nano seconds of arc. Please comment, embellish and/or refute. Neil