Chronicle on RADAR: Part-2 Vishal Gupta

In the first part of “Chronicle on RADAR”, basic working principle of RADAR, specially pulsed RADAR was explained. It was covered, how RADAR can be explained as transmission and reception of electromagnetic waves via echo location with the help of basic mathematics. Let’s now spend some time on FMCW RADAR and understand it better with more mathematics, equations, and formulae.

FMCW (Frequency Modulated Continuous Wave) technology is a RADAR technique used for distance and velocity measurements. It involves continuous transmission of a signal with a frequency that varies linearly over time. FMCW technology is valuable for applications like automotive RADAR systems, anti-collision systems, industrial sensing for level measurement, and in aerospace for altimetry and navigation due to its ability to provide both range and velocity information simultaneously. However, in advanced driver assistance systems (ADAS) and autonomous vehicles, FMCW RADAR is often integrated with other sensors, such as LIDAR. Sensor integration enhances overall perception and contributes to robust and reliable decision-making. FMCW RADAR can create a Range-Doppler map, combining information about the range and velocity of multiple targets. This mapping is valuable to distinguish between various targets and improving the overall situational awareness. However, owever, HRange-Doppler mapping process may introduce ambiguities in certain situations, especially when targets have similar ranges or velocities. Techniques such as pulse repetition frequency (PRF) optimization are employed to mitigate these ambiguities.

However, there are many associated challenges to this technology. viz.

A.???? Mitigating interference

B.???? Improving sensitivity

C.????? Addressing factors like temperature variations

D.???? Calibration for accurate distance and velocity measurements

E.????? Sensitivity to target reflectivity.

RADAR range equation, which relates transmitted power, target cross-section, and received power, plays a crucial role. Higher reflectivity improves the RADAR's ability to detect and range targets effectively.

Why not a make a CW RADAR: A pure continuous wave (CW) or cosine wave is transmitted by transmitter to its target. Let’s assume that the transmitted signal be:

The return echo from the target will be concentrated at the center frequency. The received signal will be a replica of the transmitted signal but with time delay τ.

In my previous paper it was explained that this time delay will be equal to:

τ = 2*r/c

Where:

·?????? r = Distance to the target

·?????? c = speed of light = 3 X 108 m/ sec

?Hence, the phase difference between the transmitted and received signal (replica of transmitted signal) can be derived as follows:

RADAR receiver measures this time phase difference and use this to calculate the target range as follows:

?There is a small challenge; as phase difference changes will be repeated every signal cycle/ wavelength i.e. 360 degree or 2p, hence, limiting range to time difference (τ) or distance equivalent to 2p at operating frequency of the RADAR.

Therefore, using the above two equations, maximum unambiguous range of the RADAR can be derived as follows:

Practically, at the operating frequencies of RADAR, this value may be too small to use. For e.g., at L-band or 1.5GHz – maximum range will be limited to 100 cm only, hence not useful for any ranging purpose.

Therefore, amplitude or frequency modulated signals for e.g., pulsed, FMCW signals are used to overcome this challenge which was partially covered in my 1st paper. While the pulse modulated RADAR was covered in my 1st paper, we will focus more on understanding principle of FMCW RADAR in this paper. ?FMCW is common in RADAR applications which is typically used for determining the distance as well as speed of target objects. Key applications for FMCW RADAR include for e.g., Short-range detections like speed guns, automotive RADAR, anti-collision RADAR; altimeters; high resolution image RADAR like concealed weapon detection; weather monitoring RADAR and ground surveillance RADAR.

FMCW RADAR system works with a similar phenomenon of a CW RADAR, in which RF energy with known frequency is continuously transmitted and received after getting reflected from targets. FMCW RADAR measures the frequency difference from the transmitted and received signal to calculate the distance. Another advantage of this type of RADAR is that it can also listen while transmitting (unlike a pulsed RADAR) signals and hence, making it useful to detect multiple targets at the same time a typical case of autonomous vehicle.

As was covered earlier, CW RADAR signal detects the reflecting target without providing any information about the object’s distance due to lack of timing stamp required to determine its location. In contrast, FMCW RADAR uses a transmission signal that has been modulated in frequency which allows the varied operating frequency. Further, unlike pulsed RADAR, FMCW RADAR uses CW modulation which can avoid Peak-to-Average Power Ratio (PAPR) in transmission, which simplifies the design process for active RF components.

Simplified block diagram of FMCW RADAR is given below:

?The signal generator generates the required FMCW signal, and the CW signal is modulated with FM waveform.

?The FMCW RADAR transmit a continuous carrier modulated by a periodic function. Since the frequency sweep cannot be continually increased, the periodicity in the modulation is normally utilized for e.g., by using functions such as a saw tooth-wave like linear increasing, decreasing, or triangular wave to provide range data.

The rate of change of frequency for sawtooth waveform is given by following formula:

?The basic principle can be expressed mathematically using the following equation for the transmitted signal:

?Where:

·?????St(t) is the transmitted signal.

·??????A is the amplitude of the signal.

·??????fo ?is the carrier frequency.

·?????f'?is the sweep rate, indicating how fast the frequency changes over time.

·??????t is time.

?The received signal is reflected off a target, resulting in a phase shift proportional to the target's distance. The received signal can be expressed as:

?Where:

- ?Sr(t,τ)is the received signal with a time delay τ.

- τd?is the round-trip time delay

?The rate of change of frequency for triangular waveform is given by following formula:

Here Δf is the difference between the maximum and minimum frequency and fm is the modulating frequency of triangular waveform (fm = 1/To).

τd?is two-way delay which means its relationship with range is given as follows:

Where:

·??????c is the speed of light.

?Instantaneous beat frequency (difference between the transmitted and received frequencies) is given by:

?

Since, slope of the beat frequency vs. time delay is the same with the rate of the FM signal, beat frequency can be related to target range as follows:

?

Pictorially, this can be demonstrated as follows:

?It means:

?FMCW RADAR can also be utilized for velocity measurements. Doppler shift allows FMCW RADAR to determine the velocity of a target moving towards or away from the RADAR system.

The Doppler frequency shift fb is related to the radial velocity v of the target:

??·??????fb ?is the beat frequency or doppler frequency shift.

·?????? v is the radial velocity of the target.

·?????? λ is the wavelength of the RADAR signal.

?The range resolution Δd and velocity resolution Δv in FMCW RADAR are related to the sweep bandwidth B0 and sweep duration T:

and

Where:

·?????? c is the speed of light.

·?????? B0 is the sweep bandwidth.

·?????? T is the sweep duration.

?Above equations highlight the trade-off between range and velocity resolution implicating that a wide bandwidth provides better velocity resolution but compromises range resolution.?? The design of the frequency sweep is crucial for FMCW RADAR performance. The sweep duration, sweep bandwidth, and sweep shape impact the RADAR's range, velocity resolution, and ability to handle various target scenarios.

FMCW has a drawback of creating unreal targets (“ghost targets”), these ghost targets are easily eliminated by measuring the slope of the modulation patterns. This signal also has the additional effect of Doppler frequency where the received signal will be shifted up or down and thus, produces an error in distance measurement. This problem can be eliminated by using different modulation schemes such as modulation with increasing frequency or decreasing frequency. Further, FMCW RADAR offers reduced range as compared to a pulsed RADAR. And at the same time, it is susceptible to interference from other radiating sources.

To summarize, FMCW RADAR technology provides a versatile and efficient way to simultaneously measure the range and velocity of targets. Its applications range from automotive safety to industrial and aerospace applications, with ongoing research focusing on addressing challenges and enhancing performance. FMCW RADAR employs a continuous waveform with a linear frequency sweep. The detection of the beat frequency and subsequent analysis enable the RADAR system to determine both the range and velocity of targets. Practical implementations involve signal processing techniques and considerations for factors like system calibration and noise mitigation. Intricacies of FMCW RADAR technology extend to various technical considerations, signal processing techniques, and integration strategies. The ongoing development and refinement of these aspect contribute to the continued evolution and adoption of FMCW RADAR in diverse applications. An extension of FMCW RADAR, FMICW uses interrupted frequency modulation. This can reduce the RADAR's susceptibility to certain types of interference and provides advantages in specific operational scenarios.

?

?PN: The equations capture the fundamental concepts only and practical implementations may involve many other factors such as signal processing techniques and system calibration. Signal processing techniques, such as Fast Fourier Transform (FFT), are crucial for extracting meaningful information from the received signal. These techniques help identify the beat frequencies, which are then translated into range and velocity measurements.