Based on the configuration parameters passed to the device, the device is able to detect velocities in the range of $-V_{max}$ to $+V_{max}$, where $V_{max}$ is defined by the following equation:

$V_{max}=\frac{\lambda }{4(T_{IdleTime}+T_{RampEndTime})N_{TxAnt}}$

where $T_{IdleTime}$ is the chirp idle time, $T_{RampEndTime}$ is chirp ramp end time, and $N_{TxAnt}$ is the number of transmitter antennas. Both $T_{IdleTime}$ and $T_{RampEndTime}$ can be defined in the configuration profile.

To enable a higher $V_{max}$, $T_{IdleTime}$ and $T_{RampEndTime}$ must be decreased. However, there is a physical limit defined by the radar front end below which $T_{IdleTime}$ and $T_{RampEndTime}$ cannot be decreased. Any velocities detected beyond this $V_{max}$ would loop around and is termed as ambiguous velocity since we are no longer able discern the actual value. In order to overcome this and increase $V_{max}$, the Chinese Remainder Theorem is applied.

The Chinese Remainder Theorem uses consecutive frames with alternate idle times and hence alternate $V_{max}$. For each detected point, an $N_H$ number of hypotheses are set, where $N_H$ is an odd number. For each hypothesis, the actual velocity is computed using the current frame velocity resolution $∆v_{CurrFrm}$ and doppler index of the detected point $d_{in{d}_p}$ as:

$v\left(i\right)=∆v_{CurrFrm}\times d_{in{d}_p}+k\times 2V_{ma{x}_{CurrFrm}}, k=i-\left[\frac{N_H}{2}\right], i=0,1,...,N_H-1$

where $i$ is the index of the hypothesis.

Then, the velocity of each hypothesis is mapped (folded) into the previous frame detection matrix using the previous frame Doppler resolution $∆v_{PrevFrm}$ to get the Doppler index position:

$d_{ind}(i\_=round(\frac{v\left(i\right)}{∆v_{PrevFrm}}) mod N_{DopFFT}, i=0,1,...,N_H-1$

In addition, the range index of each hypothesis is corrected based on the predicated range migration:

${\mathrm{r}}_{\mathrm{ind}}\left(\mathrm{i}\right)=\mathrm{round}({\mathrm{r}}_{{\mathrm{ind}}_{\mathrm{p}}}-\mathrm{v}(\mathrm{i})\times {\mathrm{T}}_{\mathrm{frame}}), \mathrm{i}=0,1,...,{\mathrm{N}}_{\mathrm{H}}-1$

where $r_{in{d}_p}$ is the range index of the detected point and $T_{frame}$ is the frame period.

As a result of these operations, the $N_H$ points in the previous frame detection matrix are created, each defined as a range-doppler index pair:$\left\{r_{ind}\right(i),d_{ind}(i\left)\right\}, i=0,1,...,N_H-1$

Then, for each hypothesis, the search in the previous frame detection matrix $D_{prev}$ is done in the vicinity (rectangular region) of the point to find the local maximum peak. The search is done in a rectangular region of size $(2D_s+1)\times (2R_s+1)$, where $D_s$ and $R_s$ are specified by the configuration.

Based on which hypothesis has the largest $p_{max}\left(i\right)$, the corresponding winning hypothesis is chosen:$p_{max}\left(i\right)=ma{x}_{v_{ind}=v_{ind}\left(i\right)-D_s}^{v_{ind}\left(i\right)+D_s}ma{x}_{r_{ind}=r_{ind}\left(i\right)-R_s}^{r_{ind}\left(i\right)+R_s}{D}_{prev}(v_{ind},r_{ind}), i=0,1,...,N_H-1$Finally, the actual target velocity $v_{actual}$ is selected based on the winning hypothesis:

$v_{actual}=v\left(m\right), m-argma{x}_{i=0}^{N_H-1}\left(p_{max}\right(i\left)\right)$

This process is summarized by Figure 2-6.

Figure 2-6 Max Velocity Extension Processing