TIDUF76 Design guide

TIDUF76 June 2024

2.4.7 Vmax Extension

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:

Equation 1.

V_{\max} = \frac{λ}{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

Equation 2.

∆ v_{CurrFrm}

and doppler index of the detected point d_{ind_p} as:

Equation 3.

v (i) = ∆ v_{CurrFrm} \times d_{{ind}_{p}} + k \times 2 V_{\max_{CurrFrm}}, k = i - [\frac{N_{H}}{2}], 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

Equation 4.

∆ v_{PrevFrm}

to get the Doppler index position:

Equation 5.

d_{ind} (i_= round (\frac{v (i)}{∆ 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:

Equation 6.

r_{ind} (i) = round (r_{{ind}_{p}} - v (i) \times T_{frame}), i = 0, 1, . . ., N_{H} - 1

where r_{ind_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:

Equation 7.

{r_{ind} (i), d_{ind} (i)}, 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

Equation 8.

(2 D_{s} + 1) \times (2 R_{s} + 1)

where D_s and R_s are specified by the configuration.

Based on which hypothesis has the largest p_max(i), the corresponding winning hypothesis is chosen:

Equation 9.

p_{\max} (i) = \max_{v_{ind} = v_{ind} (i) - D_{s}}^{v_{ind} (i) + D_{s}} \max_{r_{ind} = r_{ind} (i) - R_{s}}^{r_{ind} (i) + R_{s}} D_{prev} (v_{ind}, r_{ind}), i = 0, 1, . . ., N_{H} - 1

Finally, the actual target velocity $v_{a c t u a l}$ is selected based on the winning hypothesis:

Equation 10.

v_{actual} = v (m), m - {argmax}_{i = 0}^{N_{H} - 1} (p_{\max} (i))

This process is summarized by Figure 2-6.

TIDEP-01034 Max Velocity Extension Processing

Figure 2-6 Max Velocity Extension Processing