Frequency modulation and antenna size

[tensorbundle]

We know to make antenna dimension reasonably small, we modulate baseband signal with a high frequency carrier. Antenna size as far as I know is in the order of one tenth of carrier signal wavelength. For example, for a 3 GHz carrier signal, receiver antanna size is 1 cm.
But, in frequency modulation, carrier frequency varies according to the baseband signal. As the antenna size depends upon carrier wavelenth, antenna size also varies! It implies we have to appoint several antennas of different sizes to receive frequency modulated carrirer signal!

Situation becomes puzzling to me when we use FSK (frequency shift keying). Digital baseband signal may have 32 (or more) levels implying 32 diffrent changes in the frequency of the carrier.Hence we need 32 different size antennas to receive the same FSK carrier signal.
How do we resolve this strange issue? Or is it I'm missing any point?
Thanks in advance.

 

[f95toli]

Real antennas have a certain bandwidth, meaning they are usefull of over a range (band) of frequencies. Patch antennas and similar -often used in handheld devices- are designed to have a bandwidth wide enoiugh so that they cover the whole band needed for modulation schemes such as FSK.

 

[berkeman]

...And resonant antenna length is 1/2 of a wavelength (for a dipole), not 1/10 of a wavelength.