This project is build upon Analog Devices' AD8319 power detector circuit and Texas Instruments LM3914 LED-driver circuit. The spiral antenna is etched on printed circuit board.
By having two antennas and detectors on the board it should be possible to make amplitude comparison measurements between the two channels. However, since RF field is composed of the direct path as well as the reflected signals it is likely that no really accurate angle of arrival measurements can be achieved. In addition the signals can be that fast that human operator cannot distinguish LED flashes from each other - although detector allows controlling of slew rate it propably cannot be made slow enough and the hysteris of the LED driver is not wide enough to cover large signal fluctuations.
The spiral antennas are circularly polarized and can thus receive vertical and horizontal polarized signals in addition to circular polarization. They have impedance of around 100 ohms (http://www.antenna-theory.com/antennas/travelling/spiral.php) and since the RF power detector can be driven differentially (https://ez.analog.com/message/20953#comment-20953) this eliminates need for a balun and the spiral arms can be driven directly. The differential line has also 100 ohm impedance on FR-4 if the lines are about 1.05 mm wide and 1 mm apart from each other. Since the antennas have wide impedance bandwidth one might want to have a bandpass filter between the antenna and the detector to distinguish for example WLAN signal from others. However, in this early design phase this was not seen necessary.