Looking at the slides, the meandering feed is for impedance matching. If you look at the first series of slides, the author describes a patch antenna with no match element, then shows the complex impedance of the input over frequency, then progresses to a length of line over ground plane to match, and then to the meandering line to match.

There are a variety of 3d EM simulators that would allow you to do design of this nature, but given that most companies won't spring for the cost, you are generally left to using a network analyzer to see what the complex impedance is, putting a meandering feet "guesstimated" to have the needed inductance/capacitance/delay and use trial-and-error from there.

Trial-and-error seems to be what the author is pointing to in the slides where there is a "meandering probe" and plastic screw - a setup that allows him to vary the feedpoint location for matching.

Interesting paper - I saved a copy for myself.

thanks for clarifying these issues to me I am actually new to Antenna design. have you though seen any implementation of the meandering probe in products or other literature?

staying in the same topic, what would be the cost of a patch antenna. i understand it may depend on the type/characteristics but a pallpark figure will be just fine

30% bandwidth for 2:1 VSWR is pretty good for a single isolated patch.
The feed arrangement looks awkward, to carve out an area under the patch to add the meander isn't mechanically friendly. The best way to start designing an antenna is thinking mechanical first, electrical second.
Alot of antenna designs are research only, though potentially useful, many are never used for mechanical or simple tolerance reasons. This one's complicated to build with that meanderline and multilayer board atop it. I haven't seen it in practice.

Nice collection of patch designs in that link. Thanks.