Creating Delay
To create a delay you want to pick a filter with a large group delay at your frequency range.
Microwaves101 explains it to some extent.
Why a longer line helps
If you are using a longer line and dropping your noise floor you are actually creating a very basic isolator. Now the microwaves101 explanation of an isolator is a tied to an easy to implement microwaves component, the circulator. Now this is a relativly complicated device to think about implementing if you are used to frequencies that Microwave engineers consider DC(like 500kHz). The device that approximates an isolator for you is a diode. If you connect power to a line with a diode that is idea, any reflections/ringing/feedback will be blocked and dissipated by the diode.
What the Cable Does.
As you increase the cable length, you increase cable loss. Lets say you have a number like 1dB loss (which is a gain of -1dB). If reflections are your primary source of noise then a reflection off of your load will travel back to antenna and then back to the load again. This means just from the cable you have caused a 3dB loss(half power). This neglects the fact that the reflection is a rather large loss on both interfaces also. This "isolates" in the respect that as the line gets longer your reflected signals have a larger and larger loss, at-least 3 times what your signal feels.
How Do I Fix It?
This is probably a sign that your load, whatever you are measuring with, is miss-matched, A decent match, giving a reflection of around -20dB coupled with the loss hitting the antenna again should leave your reflections relatively small.
You can fix this with a tuning network, which adds discrete components nearby to attempt to create the correct impedance. You can correct this by fixing any flaws in your layout also. Probably both (based on experience with my own boards).
Another way to approach this is to really cheat with your line connecting the boards. If you are operating over a small frequency range(ie. Able to treat the signal as a single frequency), then you can use stub tuners(which have been mentioned in this thread, just not by name) where the length of the stub acts as a capacitor or inductor(this is very frequency and fab dependent). You can also have a lot of fun by using a length of cable that is a quater-wavelength long. This means that when a signal is reflected, it will return to the antenna with a 90 degree phase shift, then return to the load completing a 180 degree phase shift. This cancels itself out in stead state(not perfectly, but it gets the job done).
Summing it Up
At least you jumped in head first. There are a number of other things that can cause a miss-match, with more application specifics they can be looked into also. For example, a COAX cable causes a missmatch due to its shield having currents on the outside and inside that do not sum to the inner conductors current. I hope this has helped some, and I hope microwaves101 can be of some help. It is by far not the perfect learning resource, but someone is trying.
Best Answer
There is a lot of information that is lacking, so we'll have to make a few assumptions:
You want avoid doing much in the way of direct mixing and phase detection, but you could use interference quite easily. I lifted this picture from (physicsclassroom) which is all you really need to understand the idea.
There are various schemes that you could do, but here is one that will probably work:
Drive both doorway antennas from the same source, which has steady state carriers at 3 (or more ) fixed frequencies that are mixed together and driven to the antennae. Each of these frequencies being at a different wavelength will create different nodal patterns within the room. And because they exist simultaneously, they will lie over top of each other.
On the receiver side you need the matching number of receivers for each of the transmitted frequencies that return the envelope or strength of each frequency. But this can come from one antennae and once down mixed should be a close to DC term, so easily read by a Arduino or that ilk.
There many variants that can played around with. Changing the phase of the transmitted frequencies from one antennae to the other. You'll notice that the pattern below is symmetrical, so you won't be able to determine left from right, changing the phase will fix that, and that needs to only happen on one frequency, as a guess.
There will be a general trend of decreasing power, so distance away from door can be roughly determined, but that is sufficient to reduce the solution domain of searching on board the robot to a smaller area.
You can do dead reckoning, meaning you track your position from the door way and then use that to predict outwards what the radio patterns will be in the adjacent neighbourhood. If you keep it active then you won't have the left/right symmetry problem stated above.
Other ideas: - chirping the transmitter waveform might be another way of having a dynamically changing pattern.
Caveats: - reflective walls will cause all sorts of other bounces. This complicates the computation and may render it impossible. But a pre-mapping may be the solution there.