You have not mentioned how much filtering you have, if any. If you use the full 3.5 GHz bandwidth of the AD8313 then you will not be able to detect anything under -174 dBm/Hz + 10*LOG(3.5 GHz) = -79 dBm. Even then your pulse is the same level as the noise, and you should have 10 dB of S/N so you are talking at least a filter off 350 MHz bandwidth. Ideally you want only a few MHz wide filter so you must down convert since you can't easily get that filter at 1 -2 GHz. A quick way of doing it would be to tap the IF off a spectrum analyzer (usually 70 or 110 MHz), and feed that to a filter, then into your scope or diode detector. You'll need to check the IF BW of your analyzer to make sure it is wide enough. You could even use a radio scanner as some have 10.7 MHz IF out, but usually not enough BW, however narrow band ceramic filters are cheap. If you are trying to cover the whole 1-2 GHz band at once then that requires $$$$$.