THere are more parameters to consider.
First, your down-converter mixer will be a part of a receiver. To function, you need to know the type of signal modulation and transmission data rate. This requires a certain receiver bandwidth. The bandwidth determines the input noise power, the "N" in signal-to-noise ratio.
Second, to use a RF input signal in any receiver, its power must exceed that of noise. Common communication systems need the signal power, "S", to be 10-100x higher than the input noise, in other words, S/N ratio must be at least 10 to 20 dB for a system to operate.
Third, depending on mixer design, mixers must be "pumped" by LO input power, typically +10 dBm or more for balanced diode mixers. LO frequency must be set so as to create the output IF frequency as a difference (or sum in some cases) between the RF input and LO input frequency.