Usually, localizer beacons are twin dipole to radiate the signal upward, centered down the runways, that point where the signals from each dipole are 180 degrees out of phase and cancel each other. the marker beacons are not much different, just lacking that phasing.
The localizer works much like the VOR stations but in horizontal plane. the glide slope the same but in the vertical plane.
Instead of 360 degree phased array, these are narrow, centered in line with the runways.
The log periodic is not used given the narrow frequency of about 110 Mhz. Cophased dipoles are more than effective. Yagy's are sometimes used