Terminology
Users are recommended to refer our paper Toolbox Release: A WiFi-Based Relative Bearing Sensor for Robotics for more context about these terms.
A wireless signal transmitted between robots is attenuated, scattered, and reflected over several paths as it travels through the environment in a phenomenon called multipath. We refer to the measurement of these multipaths as an Angle-of-Arrival (AOA) profile. This AOA profile reveals information about the robots such as their relative bearing to one another, or their uniqueness.
The toolbox returns the maximum magnitude peak peaks as well as the peaks corresponding to prominent multipath directions. However, multiple peaks can occur in the AOA profile due to either noise or true multipath. In practical settings there is usually a big difference between the magnitude of the multipath peaks and peaks owing to noise. Usually all multipath peaks are close to each other in magnitude -- often times even within 10%. So even if a user selects 40% of the magnitude of the max magnitude peak as the threshold to decide whether a peak in the profile corresponds to actual multipath or not and N=5 for the number of top peaks, if there is only one main path then the profile will return only one peak. This is assuming that the profile is not too noisy - which is why the toolbox uses profile variance to reject noisy profiles. This intuition roughly follows from direction-of-arrival algorithms like MUSIC that take the largest eigenvalues of the denominator term and assume these are the signal paths and everything else is noise.
It is the variance of the AOA profile around the maximum magnitude peak. Formulation and detailed explanation can be found here.
The phase difference of the signal at the receiving robot i is calculated using the steering vector a(θ,φ,d(t)) that determines array geometry. Angles (φ (azimuth), θ (elevation)) refer to all possible pairs of candidate directions of signal transmitting neighboring robot 'j'. d(t) is the robot i's displacement in R3 from time tk to any time t in [tk, tl].
As communicating robots i and j have their own WiFi modules, the signal oscillators inside them have different frequencies with some offset. This leads to time-varying phase offset in the signal phase i.e., Carrier Frequency Offset (CFO), leading to erroneous measurements of the wireless channel. We use Channel Reciprocity to correct for CFO. This essentially requires pairing CSI data of WiFi packets broadcasted from robot i and j almost simultaneously.
Whenever a robot broadcasts a packet (forward packets), its neighboring robots automatically reply back (backward packet) almost instantaneously. The product of these forward and backward packets allows to cancel the CFO. More details can found in our IJRR paper. A schematic representation of this process is shown below.
A subcarrier is a sideband of a radio frequency carrier wave, which is modulated to send additional information. There is no physical difference between a carrier and a subcarrier; the "sub" implies that it has been derived from a carrier, which has been amplitude modulated by a steady signal and has a constant frequency relation to it.