TI mmWave radar sensors Tutorial 笔记 | Module 4 : Some System Design Topics

本系列为TI(Texas Instruments) mmWave radar sensors 系列视频公开课 的学习笔记。

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FMCW Radars – Module 1 : Range Estimation
FMCW Radars – Module 2 : The Phase of the IF Signal
FMCW Radars – Module 3 : Velocity Estimation
FMCW Radars – Module 4 : Some System Design Topics
FMCW Radars – Module 5 : Angle Estimation

Module 4 Some System Design topics

• Content
  • 2D-FFT Processing
  • Trade-offs involved in designing a frame
  • Radar range equation

之前：

• Range and Velocity Estimation

This Module:

• 结合之前知识，design a transimitted signal $\Rightarrow$ meets the specified requirements (range resolution, max range, velocity resolution, max velocity) $\Rightarrow$ fell the trade-offs

• Radar range equation (maximum distance)

FMCW 2D FFT processing in a nutshell

in a nutshell 简而言之

• 距离、速度估计 (Range-Doppler Heatmap) 流程 如下图

• step 1: ADC data matrix

  • Each row: ADC samples in one chirp
  • Different rows: chirps in one frame

• Step 2: Range FFT

  • Perform on each row

    ✅ resolves objects in range

    ✅ e.g., 两个有阴影的range bin 表示 这两个距离处有物体

    ❗ the x-axis is actually the frequency corresponding to the range FFT bins $\Rightarrow$ 但可以转换为range

• Step 3: Doppler FFT

  • Perform along the columns of the rangeFFT results
  • from the results: can see that the third range bin has two objects at different velocities and
  • the Y axis: $\Rightarrow$ actually the discrete angle of frequencies corresponding to the FFT $\Rightarrow$ proportional to the velocity

2D FFT : Step 2 + Step 3

Note :

In most implementations, the range-FFT is done inline prior to storing the ADC samples into memory

即先range FFT再Doppler FFT, 需要有memory 存储 RangeFFT的中间结果

Mapping requirements to chirp parameters

• Formulas:

  • $v_{max}=\frac{\lambda }{4T_c}$
  • $v_{res}=\frac{\lambda }{2T_f}$
  • $d_{res}=\frac{c}{2B}$
  • $F_{if\_max}=\frac{S2d_{max}}{c}$ (所需要的IF bandwidth)

• Q: Given range resolution ($d_{res}$), max range($d_{max}$), velocity resolution ($v_{res}$), max velocity ($v_{max}$), how to design a frame ?

  • $T_c$ determined using $v_{max}$
  • $B$ determined using $d_{res}$
  • $S$ is determined by $S=B/T_c$
  • $T_f$ (frame time) can be determined using $v_{res}$
  • $\Rightarrow$ 至此，确定了整个frame,如下图

Note:

• However, 还没有用上$F_{if\_max}=\frac{S2d_{max}}{c}$ (所需要的IF bandwidth)

• 通常默认硬件能够提供足够的$F_{if}$ (中频频率)

• In practice, 决定chirp parameters 参数的过程 会更加复杂、more iterative

  • 给定$d_{max}$, the maximum required IF bandwidth might not be supported by the device

    ❗ Since $F_{if\_max}=\frac{S2d_{max}}{c}$, 需要在 $S$ 和$d_{max}$ 进行trade-off

  • The device must be able to generate the required Slope $S$

    ❌ Each device has a limit on the maximum slope of the chirp that the syntesizer can generate

  • Device specific requirements for idle time between adjacent chirps need to be honored

    ❌ Interchirp idle time to allow the synth to ramp down after each chirp (如下图)

  • Device must have sufficient memory to store the range-FFT data for all the chirps in the frame

    ❗ Note that rangeFFT data for all the chirps in the frame must be stored before Doppler-FFT computation can start

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短距雷达 VS 长距雷达

• The product $S\times d_{max}$ is limited by the available IF bandwidth in the device

• Hence as $d_{max}$ increases $\Rightarrow$ $S$ has to be decreased

• Assuming $v_c$固定，即$T_c$ is frozen, then

  • $d_{max}$ increases $\Rightarrow$ $S$ has to be decreased $\Rightarrow$ smaller $B$ $\Rightarrow$ poorer range resolution

• 因此，for a given $T_c$:

  • A short range radar : higher slope and a larger $B$ ( $\Rightarrow$ better resolution)
  • A long range radar : lower slpoe and a smaller chirp bandwidth

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The Radar Rnage Equation

• $P_t$: Output power of device

• Radiated Power Density = $\frac{P_t{G}_{TX}}{4\pi d^2}$ $W/m^2$

  • $G_{TX}$: TX antenna gain $\Rightarrow$ 通常通过 increasing its directivity 实现
  • Concentrating the output power from the device over a narrower field of view

• Power reflected by object:

  • $=\frac{P_t{G}_{TX}\sigma }{4\pi d^2}$

  • where $\sigma$: Radar Cross Section of the Target (RCS)

    ▪ RCS: basically a measure of the target’s ability to reflect radar signals in the direction of the radar receiver

• Power density at RX ant

  • $=\frac{P_t{G}_{TX}\sigma }{(4\pi {)}^2{d}^4}$ $W/m^2$

• Power captured at RX ant

  • $=\frac{P_t{G}_{TX}\sigma A_{RX}}{(4\pi {)}^2{d}^4}$
  • $A_{RX}$ : Effective aperture area of RX antenna $\Rightarrow$ $A_{RX} = \frac{G_{RX} \lambda^2}{4 \pi} $
  • $\Rightarrow$ $=\frac{P_t{G}_{TX}\sigma G_{RX}{\lambda }^2}{(4\pi {)}^3{d}^4}$

• $SNR=\frac{\sigma P_t{G}_{TX}{G}_{RX}{\lambda }^2{T}_{means}}{(4\pi {)}^3{d}^{4}kTF}$

  • $T_{means}$ : Total measurement time ($N{T}_c$)

  • $kT$ : Thermal noise at the receiver

  • $k$ : Boltzman constant

  • $T$ : Antenna temperature

  • Note1: measurement time $T_{meas}\uparrow$ $\Rightarrow$ SNR $\uparrow$

    🚩 Because the signal is deterministic while the noise is random

• There is a minimum SNR (SNR${}_{min}$) required for detecting a target

  • Choice of $SN{R}_{min}$ : trade-off between probability of 漏检 (Missed detections) 和 probability of 虚警 (False alarms) .
  • Typical numbers: $15dB$ ~ $20dB$

• Given a $SN{R}_{min}$, the maximum distance can be computed as:

  • ${\mathrm{d}}_{\max }={\left(\frac{\sigma P_t{G}_{TX}{G}_{RX}{\lambda }^2{T}_{\text{meas }}}{(4\pi {)}^{3}SN{R}_{\min }kTF}\right)}^{\frac{1}{4}}$
  • 其中$T_{meas}$ can be incorporated while designing the tranmit signal
  • Others are decided by hardware

Epilogue

• Two objects equidistant from the radar and with the same velocity relative to the radar
  • How will the range-velocity plot look like?
  • Ans: Single Peak

• How to separate those two objects?
  • Next module: Angle Estimtion