TIDUF89 September   2024

 

  1.   1
  2.   Description
  3.   Resources
  4.   Features
  5.   Applications
  6.   6
  7. 1System Description
    1. 1.1 Detection Theory
    2. 1.2 Multi-Pass Architecture
  8. 2System Overview
    1. 2.1 System Design Theory
      1. 2.1.1 Long Detection Range
        1. 2.1.1.1 Antenna Design for Long Detection Range
        2. 2.1.1.2 SNR Compensation for Long Detection Range
        3. 2.1.1.3 Smart Detection Logic
      2. 2.1.2 Low Power Consumption
        1. 2.1.2.1 Efficient Chirp Design
        2. 2.1.2.2 Deep Sleep Power Modes
        3. 2.1.2.3 Hardware Accelerator
      3. 2.1.3 Low False Alarm Rate
        1. 2.1.3.1 Typical Causes of False Alarms
        2. 2.1.3.2 False Alarms Outside the Detection Zone
        3. 2.1.3.3 False Alarms Within the Detection Zone
        4. 2.1.3.4 Adaptive State Machine
  9. 3Hardware, Software, Testing Requirements, and Test Results
    1. 3.1 Hardware Requirements
    2. 3.2 Software Requirements
    3. 3.3 Test Setup
      1. 3.3.1 Test 1 - Detection Range
      2. 3.3.2 Test 2 - False Alarm Rate
      3. 3.3.3 Test 3 - Power Consumption
    4. 3.4 Test Results
  10. 4Design Files
    1. 4.1 Schematics
    2. 4.2 Bill of Materials
  11. 5Tools and Software
  12. 6Document Support
  13. 7Support Resources
  14. 8Trademarks
  15. 9About the Authors

1.1 Detection Theory

The radar equation found in Programming Chirp Parameters in TI Radar Devices, application note describes the tradeoff between long detection range, low power consumption, and low false alarm rate mathematically.

Equation 1. Rangemax based off SNR= PT×GRX×GTX×c2×σ×N ×TR fc2× 4π3×kT ×NF ×SNRdet4
    PT Tx output power (mW)
    GRx ,GTx RX and TX Antenna gain (linear)
    σ Radar Cross Section of the object (sq. meters)
    N Number of chirps x Number of virtual antennas
    Tr Chirp time (seconds)
    NF Noise figure of the receiver (linear)
    SNRdet Minimum SNR required by the algorithm to detect an object (linear)
    k Boltzmann constant (J/K)
    Tdet Ambient temperature (K)

Pt and Tr are functions of power consumption - as the functions increase, power consumption increases. SNRdet is a function of false alarm rate - as SNRdet increases, false alarm rate decreases. Keeping all the other terms constant, this yields the following relation, that detection range is proportionate to the product of power consumption and false positive rate.

Equation 2. Detection Range ∝ Power Consumption × False Positive Rate

This can also be understood through a broader lens through statistics. A known fact is that the noise of a radar system can be modeled as the magnitude of a complex Gaussian, which is known as a Rayleigh Distribution. If the received signal of a target of interest is modeled as a Gaussian, centered around some non-zero returned power, then the detection threshold for the amount of power returned to the radar system needs to be set somewhere between the two distributions. Detecting whether an object is present or not reduces simply to a hypothesis test of two distributions.


TIDEP-01035 Signal and Noise Power Distributions

Figure 1-1 Signal and Noise Power Distributions

If the detection threshold is set lower, then there can be more false positive alarms (radar wakes up unnecessarily), but fewer false negatives (radar misses a real detection). Conversely, if the detection threshold is set higher, then there can be fewer false positive alarms, but the radar can experience some false negatives. Since the cost of missing a real detection can be quite high for surveillance systems, often the strategy is to make the detection threshold lower, and absorb some of the false alarms in exchange for the reduced likelihood of a missed real detection.