Most antenna books & sites discuss TRANSMITTING antennas. The TRANSMITTING antenna is intended to radiate electromagnetic waves into space. For Transmitting antenna, the most important criteria is that the antenna should be capable to radiate in space ALL the power which the transmitter can deliver.
What we need for ADS-B is a RECEIVING antenna. The RECEIVING antenna is not intended to radiate power. Its function is to intercept the electromagnetic waves radiated by transmitting antennas, and feed this intercepted power into coaxial cable & receiver. For Receiving antenna, the most important criteria is that it should intercept maximum amount of electromagnetic radiation, and then efficiently transfer it to the receiver.
TRANSMITTING Antenna:
For maximum transfer of power from transmitter to antenna and then from antenna into space, the impedance of the transmitter, the antenna and the transmission line (coaxial cable connecting the transmitter to the antenna) must be the same. The antenna is called "RESONANT" or "TUNED" if this is achieved. Transmitters typically are designed for 50 Ohms impedance, and the coaxial cables (transmission lines) used with them also have 50 Ohms impedance. Some antenna configurations often have an impedance other than 50 Ohms and impedance matching circuit is then required to transform the antenna impedance to 50 Ohms.
For Transmitting antennas, another way to measure the extent of power transfer is Standing Wave Ratio (SWR or VSWR). A VSWR of 2.0:1 or less is often considered acceptable. Most commercial antennas are specified to be 1.5:1 or less. Based on a 100 watt transmitter, a 1.5:1 VSWR equates to a forward power of 96 watts and a reflected power of 4 watts, or the reflected power is 4.2% of the forward power.
RECEIVING ANTENNA:
The most important criteria for RECEIVING antenna is therefore to intercept maximum amount of electromagnetic radiation, and then efficiently transfer it to the receiver. Larger the physical size (length) of antenna, larger amount of Electromagnetic radiation it will intercept and produce larger amount of power to feed to the receiver. Impedance matching results in maximum transfer of power from antenna to receiver, but this can be achieved by matching circuits or matching transformers (balun). There is no need to limit the size of receiving antenna to 1/2 wavelength just to achieve "RESONANCE", and thus limit the intercepted power.
A short 1/2 wavelength Dipole (or 1/4 wavelength Monopole with ground plane) is a reasonably good solution for TRANSMITTING antenna, but is not so good for receiving antenna due to its short length limits the interception of amount of available electromagnetic radiation. A larger antenna with impedance matching circuit/balun give better received signal strength.