What does co-phasing of cross-polarized antennas mean?

Question

I was working with the 3GPP release 14.6, and it mentioned that modern communication systems have cross polarized antennas, and in order to perform beam-forming we need to co-phase our pre-coder.

Pre-coding is an algorithm we use at the transmitter side in order to aid our performance at the receiver. We model our system as $y = Hx$ where H is the channel,x is transmitted data and y is received data.

Instead of sending $x$ we send $Wx$ where W is our pre-coder, our system would then be $y = HWx$ assuming we have the channel at the transmitter side we can just make $W = H^{-1}$ that way the channel doesn't affect the data.

What does co-phasing between cross-polarized antennas mean and how does it affect my precoder?

Answer 1

Changing the phase angle between signals applied to transmit (or receive) antennas of differing polarizations (i.e., cross polarized) can only change the angle of the polarization or its "sense"; it cannot be effectively used for beam forming. Beam forming results when the phase angle is changed between signals applied to two or more transmit antennas (or tranduced from two or more receive antennas) of the same polarization (i.e., co-polarized).

One may accomplish beam forming by co-phasing two or more cross-polarized antennas. This is most easily understood when the two cross-polarized antennas are of the same design.