How the Log Periodic Dipole Antenna of Localiser help in varying modulation depth? Here Albert Helfrick speaks about 40% modulation depth for each tone in a localiser radio signal. However latest manuals of ILS manufacturers and google source speaks about 20% modulation depth, not 40%. Albert also says that modulation depth becomes 20% at the centreline of runway. 

My question is whether Albert is correct or manufacturers like NORMARC, Thales and SELEX are correct? If Albert is correct then how does 16,20,24
element log periodic dipole array help in achieving this modulation depth variation? 

I would appreciate if someone with proper explanation comes up. And this question is not duplicate so please do not confuse it with other modulation varying behaviour of questions asked on this forum.
Mod Depth (more commonly called modulation index in electrical engineering) is the amount a carrier signal is modulated.  Mod depth has nothing to do with antenna configuration and is set by the transmitter (or more precisely the modulator).  The log periodic antenna controls the width of the various beams.  A larger antenna means a smaller beam and smaller beams mean you will have more precision on an ILS approach.  As far as the discrepancy between the 40% and 20% mod depth for ILS systems I will always believe the manufacture.  It seems like the documentation you posted is describing a simple hypothetical setup to help you understand the concept.  I believe most ILS systems use more than two beams. The degree of mod depth shouldn't matter too much as long as your Signal to Noise Ratio is high so I wouldn't get caught with the amount of mod depth in ILS systems.