Signal-to-noise ratio (SNR)#

Let $x(f,s,d)$ be a (complex) point at a distance $d$ where the number of distances is $N_d$, in a sweep $s$ where the number of sweeps per frame is $N_s$, in a frame $f$ where the number of frames collected is $N_f$. Further, let $x_S$ be data collected with a known reflector in the range. This is used for the signal part of the SNR. Correspondingly, let $x_N$ be the data collected with the transmitter (TX) disabled. This is used for the noise part of the SNR.

The frame/sweep distinction is not necessary for the SNR definition. The frames can simply be concatenated: $x(f,s,d)\to y(s^{\prime },d)$ where $N_{s^{\prime }}=N_f\cdot N_s$.

Let the signal power $S=\underset{d}{max}({\text{mean}}_{s^{\prime }}(|y_S{|}^2))$.

Let the noise power $N={\text{mean}}_{s^{\prime },d}(|y_N{|}^2)$. This is assuming $E(y_N)=0$ and $V(y_N)$ is constant over $(s^{\prime },d)$, where $E$ is the expectation value and $V$ is the variance.

Finally, let $\text{SNR}=S/N$. The SNR in decibel ${\text{SNR}}_{\text{dB}}=10\cdot {\log }_{10}(S/N)$.

Radar loop gain (RLG)#

The radar loop gain is given by: ${\text{RLG}}_{\text{dB}}={\text{SNR}}_{\text{dB}}-{\text{RCS}}_{\text{dB}}+40{\log }_{10}(d)$ where SNR is the signal-to-noise ratio, RLG is the radar loop gain, RCS is the radar cross-section, and $d$ is the distance to the target with the given RCS.

Base RLG#

Base RLG is the RLG (equivalent) for HWAAS = 1.

SNR and therefore also RLG scales linearly with HWAAS, meaning a 3dB increase for every doubling of HWAAS.

Radar loop gain per time (RLG/t)#

Measurement time is not accounted for in the RLG metrics. To account for it, we define the radar loop gain per time (RLG/t):

where $({\text{RLG}}_{\text{dB}}|\text{HWAAS}=1)$ is the base RLG, and ${\tau }_{\text{sample}}$ is the sample duration.

Preliminaries#

Let $d_{est}(f,d)$ be the estimated distance to a target located at distance $d$, formed by processing frame $f$ in accordance with the steps outline in the Distance Detector documentation. $f$ is a single frame in a set of frames of size $N_f$.

Next, let $e(f,d)=d_{est}(f,d)-d$ be the estimation error of a single frame/measurement.

Lastly, form the mean error by averaging over the frames, $\bar{e}(d)={\text{mean}}_f(e(f,d))$.

$\bar{e}(d)$ describes the average error for a single sensor. The metrics calculated in the following sections are based on data from a set of sensors. To indicate what sensor the mean error is associated with, the argument $s$ is added, $\bar{e}(d,s)$.

Accuracy#

The distance estimation accuracy is characterized through the following two sets of metrics:

• Mean error($\mu$) and standard deviation($\sigma$).

• Mean absolute error($\text{MAE}$).

Linearity#

Linearity refers to the variation in the distance estimate error as a function of the distance to the target.

The distance linearity is characterized through the mean of the standard deviation of the estimation error over a number of distances, $\sigma ={\text{mean}}_s({\text{std}}_d(\bar{e}(d,s)))$.

The distance linearity is evaluated over two sets of distances:

• Micro: A number of distances within a few wavelengths.

• Macro: A number of distances over many wavelengths.