Can we reverse the guidance from the transmitter?
Can a Localizer Backcourse signal be reversed (at the site antenna)?
From a technical standpoint it's entirely possible, but both beams, front and back, are reversed at the same time. Conceptually this is obtained by reversing the order of the individual antennas of the localizer array, the leftmost antenna becomes the rightmost antenna, etc.
Localizer array at Melbourne airport (seen from the back), source
This boils down to swapping the antenna inputs. As the inputs are symmetrical relatively to the array center, except the SBO phase, practically we would just have to invert SBO phase. See this array diagram showing signal amplitude and phase for each course and clearance antenna.
Case of Aspen missed approach localizer
In this section I'm going to separate two concepts:
- One related to the antenna, the back lobe, which is the area where the antenna radiates rearward, as many antennas do. The opposite is the front or main lobe.
- One related to the approach procedure, the back-course, which refers to the direction opposite to the approach the localizer is primarily used for.
While the very usual case is the back-course is sent using the back lobe (making back-course and back lobe near synonymous), in the unusual I-PKN, the front lobe is used to create a back course guidance.
If so, are there any airports where this has been done?
Aspen back-course localizer I-KPN which motivates your question is possibly one of these localizers with inverted signal. Aspen has a LOC/DME approach based on two localizers: I-ASE classic, directed at 331°, is used to land and has no back-course. I-KPN directed at 301° is used in the missed approach trajectory to provide the guidance to return to the holding via LINDZ waypoint.
I-KPN course is referred to as a "back-course". It's not a back-course in the sense it would give an additional access to the opposed runway for free, like other localizers do using the back lobes of their antennas. It's only use is during the missed approach.
In the case of I-PKN, the signal is not sent by the back of the antennas, but by the front, like a regular LOC/ILS approach. This is visible on this picture of the array taken from its NW:
I-KPN array, facing 303°, from Google Street View
I believe each of the log periodic antennas has the shortest element on its front (up on the picture), and therefore the front lobes are used to transmit the guidance signal.
Why using the front lobe of the radiation pattern? Just because this is the most efficient, the gain in the front lobe being larger than in the back lobe.
From a signal standpoint, comparing front beam, back beam and back beam with reversed signal to create a "back-course" guidance:
We see the signal radiated by the front lobe, but with an inverted signal, is equivalent to the signal radiated by the back-lobe in a conventional localizer. I believe this is what is used for Aspen I-KPN.
The mention "normal sensing" on the approach plate means this guidance will drive the indicator needle like a when flying any conventional back-course flown outbound, that is the needle will deviate to the right to indicate the beam center is on the right side (top of the picture below).
More detailed presentation of the localizer array
When both directions are used, each individual antenna transmits the same signal in both directions (the back-course beam is a by-product of the front-course signal).
Actual radiation of a directional antenna, source
The guidance signal is the result of the 90/150 Hz modulation depths lateral variation making 150 Hz predominant on the left side (seen from the array, looking forward) and 90 Hz predominant on the right side. This variation itself is obtained by applying a different mix of signals (CSB and SBO) on each individual antenna composing the localizer array. See How is varying modulation depth achieved by localizer ground transmitters? for how it works exactly.
To reverse the guidance it is sufficient to switch left/right antennas inputs. If the array is used in a single direction, there is no difficulty, otherwise it's not possible to affect only one side, two separate arrays are required. But in that case to get better performances, the second array will be located at the other runway end, and will use a different frequency. Said otherwise it will be another complete localizer.
What does ICAO say about back-lobe and reversed guidance?
There is no recommendations regarding the back-lobe signal characteristics, and there is no mention about sensing inversion in ICAO in Annex 10. Back-course approaches are local choices, off standards, ICAO discourages them in working documentation and they have been decommissioned almost everywhere, except in the US, replaced by separate navaids or GNSS-based procedures.