.. _rdac-a212-timing: Timing ====== .. note:: The relationships, equations, and constants described here are approximate, not guaranteed, and may change over RSS releases. .. seealso:: The :doc:`/resource_calc` in the Exploration Tool estimates timing and power consumption for a given configuration. Notation -------- :math:`\tau` - A time duration. :math:`f` - A frequency or rate. Inverse of :math:`T`. :math:`T` - A period, the time between recurring events. Inverse of :math:`f`. :math:`N` - A number or amount of something. Sample duration --------------- The time to measure one sample :math:`\tau_\text{sample}` depends on the configured :class:`Profile ` and :class:`PRF ` according to :numref:`tab_a212_sample_dur` below. .. _tab_a212_sample_dur: .. table:: Approximate sample durations :math:`\tau_\text{sample}` for all profile and PRF :math:`f_p` combinations. :align: center :widths: auto +----------------+----------+----------+----------+----------+ | 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 .. math:: :label: \tau_\text{subsweep} \approx C_\text{subsweep} + N_{a,\text{total}} \cdot N_\text{TX} \cdot \tau_\text{sample} where :math:`N_{a,\text{total}} = \sum_d \text{HWAAS}(d)` is the sum of HWAAS values over all distance points in the subsweep (see :ref:`rdac-a212-signal-strength` for HWAAS scaling), :math:`N_\text{TX}` is the number of active TX antennas, and :math:`C_\text{subsweep}` is a fixed overhead (see :numref:`tab_a212_fixed_overheads`). For constant HWAAS (HWAAS exponent :math:`e = 0`): :math:`N_{a,\text{total}} = N_d \cdot N_a`, where :math:`N_d` is ``num_points`` and :math:`N_a` is ``hwaas_max``. Sweep duration -------------- The time to measure a sweep :math:`\tau_s` includes all configured subsweeps and the transition from the configured :attr:`~acconeer.exptool.a2.SensorConfig.inter_sweep_idle_state`. .. math:: :label: \tau_s \approx \tau_{S \rightarrow R} + \sum_i \tau_{\text{subsweep},i} where :math:`\tau_{S \rightarrow R}` is the sweep transition time from the configured idle state (see :numref:`tab_a212_transition_times`). Idle state transition times ^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. _tab_a212_transition_times: .. table:: Approximate sweep transition times :math:`\tau_{S \rightarrow R}` per idle state. :align: center :widths: auto +------------+--------------------------------+ | Idle state | :math:`\tau_{S \rightarrow R}` | +============+================================+ | ARMED | :math:`1.82 \mu\text{s}` | +------------+--------------------------------+ | READY | :math:`92.8 \mu\text{s}` | +------------+--------------------------------+ Sweep period ------------ The sweep period :math:`T_s` is the time between the start of two consecutive sweeps in a frame. If the :attr:`~acconeer.exptool.a2.SensorConfig.sweep_rate` is not set, the sweep period equals the sweep duration: :math:`T_s = \tau_s`. If the sweep rate :math:`f_s` is set, the sensor idles in the configured :attr:`~acconeer.exptool.a2.SensorConfig.inter_sweep_idle_state` between sweeps. .. math:: :label: T_s = \frac{1}{f_s} = \tau_s + \tau_{si} where :math:`\tau_{si}` is the inter-sweep idle time. Frame duration -------------- The time to measure a frame :math:`\tau_f` includes all sweeps and the fixed frame overhead. .. math:: :label: \tau_f \approx N_s \cdot T_s + C_f where :math:`N_s` is the sweeps per frame and :math:`C_f` is a fixed overhead (see :numref:`tab_a212_fixed_overheads`). .. note:: This formula assumes :attr:`~acconeer.exptool.a2.SensorConfig.inter_frame_idle_state` equals :attr:`~acconeer.exptool.a2.SensorConfig.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 :math:`T_f` is the time between the start of two consecutive frames. Between frames, the sensor idles in the configured :attr:`~acconeer.exptool.a2.SensorConfig.inter_frame_idle_state`. If the :attr:`~acconeer.exptool.a2.SensorConfig.frame_rate` is not set, the sensor measures as soon as the host commands it to, so in practice :math:`T_f > \tau_f` because of host readout and command overhead. If the frame rate :math:`f_f` is set, the sensor idles until the configured period is reached: .. math:: :label: eq_a212_frame_period T_f = \frac{1}{f_f} = \tau_f + \tau_{fi} where :math:`\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. .. _sec_a212_fixed_overheads: Fixed overheads and high speed mode ------------------------------------ The fixed overheads for subsweep (:math:`C_\text{subsweep}`) and frame (:math:`C_f`) depend on whether high speed mode (HSM) is active. HSM is activated when all of the following conditions are met: - :attr:`~acconeer.exptool.a2.SensorConfig.num_subsweeps`: 1 - :attr:`~acconeer.exptool.a2.SensorConfig.sweeps_per_frame`: > 1 - :attr:`~acconeer.exptool.a2.SensorConfig.jitter_compensation`: False In HSM there is no separate sweep transition time :math:`\tau_{S \rightarrow R}`; instead, the idle-state-dependent transition cost is included in the subsweep overhead :math:`C_\text{subsweep}`. The sweep duration formula therefore reduces to :math:`\tau_s \approx \tau_\text{subsweep}`. .. _tab_a212_fixed_overheads: .. table:: Approximate fixed overhead times. :align: center :widths: auto +----------------------------+--------------------------------------+-----------------------+ | Mode | :math:`C_\text{subsweep}` | :math:`C_f` | +============================+======================================+=======================+ | Normal (HSM not active) | :math:`32.6 \mu\text{s}` | :math:`4 \mu\text{s}` | +----------------------------+--------------------------------------+-----------------------+ | HSM (ARMED) | :math:`20.4 \mu\text{s}` | :math:`4 \mu\text{s}` | +----------------------------+--------------------------------------+-----------------------+ | HSM (READY) | :math:`112.5 \mu\text{s}` | :math:`4 \mu\text{s}` | +----------------------------+--------------------------------------+-----------------------+ In normal mode, the idle state affects only the sweep transition time :math:`\tau_{S \rightarrow R}` (see :numref:`tab_a212_transition_times`), not :math:`C_\text{subsweep}`, so a single value for both idle states. In HSM, the idle state instead affects :math:`C_\text{subsweep}` directly, so the table gives a separate value for each configured :attr:`~acconeer.exptool.a2.SensorConfig.inter_sweep_idle_state`, ARMED and READY.