What is FD-MIMO
FD stands for Full Dimension. Therefore, FD-MIMO stands for Full Dimension MIMO. Then, what does it mean by Full Dimension here ? It means the antenna system that can form a beam (beams) in both horizontal and vertical direction so that it can cover (focus on) anywhere in 3D spaces. Following illustration would shows you a comparative picture between FD and conventional multi-antenna system.
Which Specification to follow and Who is leading the technology ?
No 3GPP TS(Technical Specification) yet, but there are a couple of TR(Technical Report) you may look into. They are TR 36.897 and TR 36.873.
Who is the leader in this technology ? It seems that currently SamSung is leading this technology and in some sense I am getting more insight from various presentations/papers published by SamSung rather than 3GPP document.
What is the form factor /How it looks ?
Basic form of FD-MIMO is rectangular array. It can take any form of rectangular matrix. Some of examples are illustrated in Ref . I think the most commonly employed form in SamSung Prototype is 8x8 array. Following form factor is for current LTE frequency range.
Basic array for mmWave (5G Candidate) is basically same and the only difference is the size of the array due to the decreased wave length comparing to LTE. One example from Ref  is as follows. This is for 27 Ghz frequency range.
What is the best Transciever Architecture for FD-MIMO ?
The Tx model suggested in TR 36.897 (Ref ) are as follows.
The TRX model presented in Ref  is as follows.
How to model Antenna Beam Pattern ?
The basic mathematical models to represents the direction and shape of the beam (beams) coming out of the antenna system is described in on 3GPP TR 36.873. It may look scary and it would be even more intimidating those matrix with complicated trigonometric expressions in the document, but don't be scared. It is the type of the math that you learned in senior high school or early years in the university linear algebra.
If you take a look at the following expression, you would notice that it is made up of two big chunks. One is the part representing the basic beam pattern and it is expressed as F(). The matrix sitting before F() is a transformation matrix which rotate in a space. Actually getting F() is not straightforward. It should be come out of a complicated simulation software or real measurement, but the transformation part is simple. Of course, in real implementation even this rotation part might not be easy and it might be a lot of DSP power to rotate the beam to a right direction and in a right time.
If you want to refresh on the math related to the transformation matrix, refer to Matrix : Application : Linear Transformation. If possible, go through all the examples linked in the page.
Field Pattern of Antenna Elements
Field Pattern of Antenna
 3GPP TR 36.897 : Study on Elevation Beamforming/Full-Dimension (FD) MIMO for LTE (Release 13)
 3GPP TR 36.873 : Study on 3D channel model for LTE (Release 12)
 Full Dimension MIMO & mmW Communications by Younsun Kim (Find 3-3_20120829_Samsung_FD-MIMO_mmW.pdf in Google)
 Enabling Massive MIMO in Cellular Systems : FD-MIMO in 3GPP LTE by Taeyoung Kim (Find 140520_174652526_FD_MIMO.pdf in Google)
 Advanced MIMO/Beamforming as a Key Enabler for 5G - Wonil Roh (Find Tuesday_4_Wonil-Roh.pdf in Google)
 Full-Dimension MIMO: Status and Challenges in Design and Implementation (Find CTW_2014_Samsung_FD-MIMO.pdf in Google)
 Full Dimension MIMO for LTE-Advanced and 5G (Find paper_3822_FD_MIMO.pdf in Google)
 3D Channel Model in 3GPP (1502.01621.pdf in Google)