Also note that they progressively drop to around 1V as the discharge, over their useful lifetime.
To guarantee 3.8V minimum, you would need four cells.
A 9V battery would work, that would still give at least 6V at the end of it's life.
As Diver says though, you need to allow for the permanently ON PIR module and the current that takes.
The data says "<1mA" so allow 1mA permanent load, and work out the possible battery life from that before choosing a power source.
A good named brand alkaline PP3 / 1604A battery has a capacity around 550mAH.
That means the PIR would run for 550 Hours, not allowing for alarm / LED triggers and the power that takes.
That means a battery life of just over three weeks.
In comparison, a high quality 2032 lithium cell plus a boost converter (and not allowing for the power losses in that) would be roughly equivalent to a 6V 100mAH battery, so a maximum life of about four days.
ps.
Re. patents:
To be valid (even if issued), a patent must contain new and original work, and be more than an incremental change to an existing concept that a normal expert in whatever field could reasonably make.
Any "prior art" that does the same or a near enough similar thing - either real items or even concepts out of novels or SciFi - means the patent is not an original invention and can be invalidated.