Why the spacing between antennas should be at least half-the-wavelength for arrays?
You can do a hand calculation using two point sources. Then plot the azimuth pattern for different spacings. For wire antennas the end fire method has closer spacing. Pay attention to the sidelobes that are formed.
Half wavelength array spacing is a guideline rather than a requirement. The spacing is driven by a variety of factors. If high angle scan is desired the spacing may be less.
Look into Hansen and Kraus for more discussion.
the formula for array of two or more element is
E(Φ)=2kI[Φ] cos[(dr*cosΦ)/2]
when u put dr( in this case spacing )>lambda/2 the no of side lobes increase and there gain will increase as well and a time will come that there power will same as the main lobe. the beam width of the main lobe decrease and that of side lobe increases. This make our result omnidirectional rather than directional.
Refer to John D.Kraus J.Marhefta. Antennas for all Application. third edition, i think in 13 or 14 chapter he has given the detail mathematical explanation.
Also THE ARRL Antenna Handbook: Chapter eight the spacing diagrams
hope it will solve ur problem
Many thanx for your valuable answers guys, but I apologize that I should have asked the question properly in order not to misguide you; My question is "for independent fading, spacing between antennas should be much greater than half wavelength", what is the mathematical explanation for that? Right now I am also searching for the answer, if I can find it before you reply, I'll put it here. Thanx again
If you are using diversity, the probability that both antennas will be in a null is much lower than if just one is.