Pulsar detection threshold at higher frequencies

[Neil Smith]

I'm using Mario Natali's excellent Murmur program to calculate the likely signal to noise ratio for a range of pulsar sources. The program has two frequency bands, but stops at 1.5 GHz. I know most pulsars have a spectral index around -1.6, so the flux drops rapidly with frequency. 

However, antenna gain for a fixed antenna size rises roughly as the square of frequency, and the spectral index of cold sky noise at sea level is about f^(-2.7). Am I right to think that the signal to noise ratio looking at a pulsar that is not in the same beam as a loud emission source, for the same bandwidth and same dish, rises at almost the cube of frequency, at least up to 10GHz,  assuming similar LNA noise figure and feed efficiency?

If I haven't messed up the calculations, would it therefore be feasible to detect at least a handful of pulsars with my 3 metre solid General Dynamics dish at 4 GHz or even 8 or 10 GHz? I'm assuming that I will need to create highly optimised low sidelobe corrugated feedhorns for my chosen quiet bands and use very good, possibly cryocooled LNAs. I'm also assuming five hour integration time in 25 MHz bandwidth, with full dish steering. 

Neil Smith