if exsiting noise is much larger than signal (1nA for example), then the signal can be drowned by noise before arriving the input of VGA, then, the VGA cannot recongnize the signal rightly, so causing wrong results. am i right? if so, how to solve the problem when exsiting relative large noise?

in my case, first i select center frequency f0=20khz, noise @50khz has a pk-pk amplitude of 1uA (sine wave), signal amplitude is 1nA~100uA, then, in simulation, i find that, because 20khz and 50khz is very close to each other, therefore, the signal (signal adding 50khz noise) at VGA input is also a sine wave with pk-pk amplitude a little smaller, and the VGA output is wrong here. in normal case, the VGA input is zero, when there is signal injecting, the input of VGA is half-negative, half-positive during one period, so VGA has a effective output pulse responding to the signal input. however, when there is 1uA 50khz noise, the input of VGA is always half-negative, half-positive during one period, and causing wrong results.
in order to decrease the influence of the 50khz noise, i added some order LPF before VGA input, but because 20khz and 50khz is so close to each other, the noise attenuation @50khz is very small relative to signal @20khz (AC response), and with increasing of LPF order, signal amplitude @20khz decreases also.
so, how to suppress the 50khz noise to get a correct signal at VGA input(normally zero, when there is signal injecting, the input of VGA is half-negative, half-positive during one period)? the threshold of VGA is zero in my design.
thanks all.