From the free space law (more specifically from the Friis equation), we know that the received power is proportional to the gains of each antenna and inversely proportional to the square of the distance between them:`P_{rec} / P_{trans} = G_{trans} G_{rec} (lambda / {4 pi R})^2` Where `P_{rec}` and `P_{trans}` are the power at receiver and transmitter respectively, `G ` are the gains,` lambda` is the wavelength, and `R` is the distance.Gain in...
From the free space law (more specifically from the Friis equation), we know that the received power is proportional to the gains of each antenna and inversely proportional to the square of the distance between them:
`P_{rec} / P_{trans} = G_{trans} G_{rec} (lambda / {4 pi R})^2`
Where `P_{rec}` and `P_{trans}` are the power at receiver and transmitter respectively, `G ` are the gains,` lambda` is the wavelength, and `R` is the distance.
Gain in turn is given by effective area and wavelength as follows:
`G = {4pi A}/{lambda^2}`
Where `A` is the effective area.
Thus, if we double the area of each transmitter, we will increase both gains by 2, and the overall power received by 4.
But if we double the frequency, we will cut the wavelength in half, which means we would reduce received power to 1/4 if gain remained the same; but in fact if effective area is held constant, gain will increase by a factor of 4, precisely canceling this effect out. Thus, the power received will be equal regardless of what frequency we choose.
The best option is therefore to increase the effective area, increasing received power by a factor of 4. Increasing frequency would not help.
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