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How much to amplify RF signals before ADC?

I'm working on a front-end for an SDR radio receiver. Most ADCs have input ranges in the order of volts, while the antenna signal can be as low as a fraction of a uV. I wonder if it's the way to go to amplify these signals by 120 dB (!?) without creating other problems in the circuit. Or is it that only voltage is amplified by not power (or not that much)?