Timing

Timing#

Note

The relationships, equations, and constants described here are approximate, not guaranteed, and may change over RSS releases.

Notation#

\(\tau\) - A time duration.

\(f\) - A frequency or rate. Inverse of \(T\).

\(T\) - A period, the time between recurring events. Inverse of \(f\).

\(N\) - A number or amount of something.

Sample duration#

The time to measure one sample \(\tau_\text{sample}\) depends on the configured Profile and PRF according to Table 11 below.

Table 11 Approximate sample durations \(\tau_\text{sample}\) for all profile and PRF \(f_p\) combinations.#
Profile \ PRF	27.7 MHz	20.8 MHz	8.3 MHz	5.3 MHz
1	4.84 µs	6.09 µs	13.59 µs	20.54 µs
2	4.26 µs	5.32 µs	11.66 µs	17.55 µs
3	3.40 µs	4.16 µs	8.78 µs	13.06 µs
4	2.82 µs	3.40 µs	6.86 µs	10.07 µs
5	2.24 µs	2.62 µs	4.93 µs	7.07 µs
6	2.24 µs	2.62 µs	4.93 µs	7.07 µs

Subsweep duration#

The time to measure a single subsweep is

(14)#\[\tau_\text{subsweep} \approx C_\text{subsweep} + N_{a,\text{total}} \cdot N_\text{TX} \cdot \tau_\text{sample}\]

where \(N_{a,\text{total}} = \sum_d \text{HWAAS}(d)\) is the sum of HWAAS values over all distance points in the subsweep (see Signal strength for HWAAS scaling), \(N_\text{TX}\) is the number of active TX antennas, and \(C_\text{subsweep}\) is a fixed overhead (see Table 13).

For constant HWAAS (HWAAS exponent \(e = 0\)): \(N_{a,\text{total}} = N_d \cdot N_a\), where \(N_d\) is num_points and \(N_a\) is hwaas_max.

Sweep duration#

The time to measure a sweep \(\tau_s\) includes all configured subsweeps and the transition from the configured inter_sweep_idle_state.

(15)#\[\tau_s \approx \tau_{S \rightarrow R} + \sum_i \tau_{\text{subsweep},i}\]

where \(\tau_{S \rightarrow R}\) is the sweep transition time from the configured idle state (see Table 12).

Idle state transition times#

Table 12 Approximate sweep transition times \(\tau_{S \rightarrow R}\) per idle state.#
Idle state	\(\tau_{S \rightarrow R}\)
ARMED	\(1.82 \mu\text{s}\)
READY	\(92.8 \mu\text{s}\)

Sweep period#

The sweep period \(T_s\) is the time between the start of two consecutive sweeps in a frame.

If the sweep_rate is not set, the sweep period equals the sweep duration: \(T_s = \tau_s\).

If the sweep rate \(f_s\) is set, the sensor idles in the configured inter_sweep_idle_state between sweeps.

(16)#\[T_s = \frac{1}{f_s} = \tau_s + \tau_{si}\]

where \(\tau_{si}\) is the inter-sweep idle time.

Frame duration#

The time to measure a frame \(\tau_f\) includes all sweeps and the fixed frame overhead.

(17)#\[\tau_f \approx N_s \cdot T_s + C_f\]

where \(N_s\) is the sweeps per frame and \(C_f\) is a fixed overhead (see Table 13).

Note

This formula assumes inter_frame_idle_state equals inter_sweep_idle_state, which is the default. If they differ, the first sweep in each frame transitions from the inter-frame idle state and may take longer than subsequent sweeps.

Frame period#

The frame period \(T_f\) is the time between the start of two consecutive frames. Between frames, the sensor idles in the configured inter_frame_idle_state.

If the frame_rate is not set, the sensor measures as soon as the host commands it to, so in practice \(T_f > \tau_f\) because of host readout and command overhead.

If the frame rate \(f_f\) is set, the sensor idles until the configured period is reached:

(18)#\[T_f = \frac{1}{f_f} = \tau_f + \tau_{fi}\]

where \(\tau_{fi}\) is the inter-frame idle time. The frame period, and thus also the inter-frame idle time, is given by how the host controls the sensor.

Fixed overheads and high speed mode#

The fixed overheads for subsweep (\(C_\text{subsweep}\)) and frame (\(C_f\)) depend on whether high speed mode (HSM) is active.

HSM is activated when all of the following conditions are met:

In HSM there is no separate sweep transition time \(\tau_{S \rightarrow R}\); instead, the idle-state-dependent transition cost is included in the subsweep overhead \(C_\text{subsweep}\). The sweep duration formula therefore reduces to \(\tau_s \approx \tau_\text{subsweep}\).

Table 13 Approximate fixed overhead times.#
Mode	\(C_\text{subsweep}\)	\(C_f\)
Normal (HSM not active)	\(32.6 \mu\text{s}\)	\(4 \mu\text{s}\)
HSM (ARMED)	\(20.4 \mu\text{s}\)	\(4 \mu\text{s}\)
HSM (READY)	\(112.5 \mu\text{s}\)	\(4 \mu\text{s}\)

In normal mode, the idle state affects only the sweep transition time \(\tau_{S \rightarrow R}\) (see Table 12), not \(C_\text{subsweep}\), so a single value for both idle states.

In HSM, the idle state instead affects \(C_\text{subsweep}\) directly, so the table gives a separate value for each configured inter_sweep_idle_state, ARMED and READY.