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If your 80MHz BW is really input channel BW, you ought
to still have some remaining signal at 150MHz (rolled off,
but still showing -something-). So display the "something"
and pick off zero crossings and do the arithmetic.
The analog bandwidth the scope will limit high freq capability.
Easiest way is to buy a Mini-circuits mixer. Suggest you apply the Local Oscillator on the high freq side of expected. This will minimize L.O. leakage showing up at the scope.
To look at 150-200 MHz. Put L.O. on mixer at about 220 MHZ. You would see signal between 20 MHz and 70 MHz on scope. Once have found signal you may want to raise the L.O. freq. so it allows gives you about 50 MHz on scope. There will be some L.O. leakage out the RF port that may impact the oscillator depending on how tightly you couple the mixer input to oscillator. An attenuator pad will reduce by back wash L.O. leakage to prevent it from interfering will oscillator. It will also attenuate the oscillator signal.
The oscillator may jump to the L.O. leakage frequency if there is too much leakage into the oscillator circuit. Any oscillator should be lightly loaded if you want best stability.
You can try low side injection as the freq you are looking at is so much higher then scope bandwidth. 140 MHz L.O. would give you 10 to 60 MHz on scope corresponding to 150 MHz to 200 MHz mixer input.
I use mixer with low pass filter on I.F. output of mixer to see 2.4 GHz signals on my 1500 MHz limit spectrum analyzer.