A complete mmWave radar system includes transmit (TX) and receive (RX) radio frequency (RF) components, analog components such as clocking, and digital components such as analog-to-digital converters (ADCs), microcontrollers (MCUs), and digital signal processors (DSPs). Traditionally, these systems have been implemented as discrete components, increasing power consumption and overall system cost. The complexity and high frequencies have also made system design challenging. To address these challenges, Texas Instruments (TI) has designed a CMOS-based mmWave radar device that integrates TX-RF and RX-RF analog components, such as clocking, with digital components such as ADCs, MCUs, and hardware accelerators.

Cesar Iovescu / Radar Application Manager

Sandeep Rao / Radar Systems Designer

Texas Instruments ( www.ti.com/mmwave)

Millimeter wave (mmWave) is a special type of radar technology that uses short-wave electromagnetic waves. Radar systems send electromagnetic signals to objects in their path and then bounce them back. By capturing the reflected signals, the range, speed, and angle of the object can be determined.

mmWave radar transmits signals using wavelengths in the millimeter range. This is considered a short wavelength in the electromagnetic spectrum, which is one of the advantages of this technology. In fact, the size of system components such as antennas required to process mmWave signals is small. Another advantage of short wavelengths is high accuracy. mmWave systems, which operate at 76–81 GHz (their wavelength is about 4 mm), can detect movements as small as a fraction of a millimeter.

A complete mmWave radar system includes transmit (TX) and receive (RX) radio frequency (RF) components, analog components such as clocking, and digital components such as analog-to-digital converters (ADCs), microcontrollers (MCUs), and digital signal processors (DSPs). Traditionally, these systems have been implemented as discrete components, increasing power consumption and overall system cost. System design has also been challenging due to complexity and high frequencies.

TI Automotive mmWave Sensor

Texas Instruments (TI) has addressed these challenges by designing mmWave radar devices based on complementary metal-oxide-semiconductor (CMOS) that integrate analog components such as TX-RF and RX-RF clocking, along with digital components such as ADCs, MCUs and hardware accelerators. Some families in TI’s mmWave sensor portfolio integrate a digital signal processor (DSP) for additional signal processing capabilities.

TI devices implement a special class of mmWave technology called FMCW (Frequency Modulated Continuous Wave). FMCW radar, as the name suggests, transmits a frequency-modulated signal continuously to measure range, angle, and speed. It is different from existing pulse radar systems that periodically transmit short pulses.

Range measurement

The basic concept of a radar system is to send an electromagnetic signal to an object in its path and then have it reflect back. In the signal used in FMCW radar, the frequency increases in direct proportion to time. This type of signal is also called a chirp. Figure 1 shows a chirp signal with the magnitude (amplitude) as a function of time.

Figure 1 Chirp signal with amplitude as a function of time

Figure 2 shows the same chirp function using frequency as a function of time. This chirp is characterized by its starting frequency (fc), bandwidth (B), and period (Tc). Chirp slope capture frequency change rate.

For example, in the example shown in Figure 2, fc=77GHz, B=4GHz, Tc=40μs, S=100MHz/μs.

Figure 2 Chirp signal using frequency as a function of time

An FMCW radar system transmits a chirp signal and then captures the reflected signal from objects in its path. Figure 3 shows a simplified block diagram of the main RF components of an FMCW radar. Here's how radar works:

Figure 3 FMCW radar block diagram

-The synthesizer generates chirps.

- Chirp sent by the transmitting antenna (TX ant).

-When an object reflects a chirp, the receiving antenna (RX ant) captures it and a reflected chirp is generated.

-The “mixer” combines the RX and TX signals to generate an IF (intermediate frequency) signal.

A frequency mixer is an electronic component that combines two signals to create a new signal with a new frequency.

For two sinusoidal inputs x ₁ and x ₂ (equations 1 and 2)

(1)

(2)

The x _out output has an instantaneous frequency equal to the difference in instantaneous frequencies of the two input sinusoids. The phase of the x _out output is equal to the difference in phases of the two input signals (Equation 3).

(3)



The operation of the frequency mixer can also be understood through the TX and RX chirp frequencies represented as a function of time graphically.

The upper diagram in Figure 4 shows the TX and RX chirps as a function of time for a single detected object. The RX chirp is a time-delayed version of the TX chirp.

Figure 4 IF frequency is a constant frequency.

The time delay (τ) can be calculated mathematically as shown in Equation 4.

(4)

Here, d is the distance to the detected object and c is the speed of light.

To obtain the frequency expressed as a function of time, subtract the two lines shown in the upper section of Figure 4 from the IF signal at the output of the frequency mixer. Since the distance between the two lines is fixed, the IF signal consists of a tone with a constant frequency. Figure 4 shows that this frequency is S _τ . The IF signal is valid only during the time interval where the TX chirp and RX chirp overlap (i.e., the interval between the vertical dotted lines in Figure 4).

The mixer output signal, expressed as a time-scale function, has a constant frequency and is therefore a sine wave.

The initial phase (Φ ₀ ) of the IF signal is the difference between the TX chirp phase and the RX chirp phase at the instantaneous value corresponding to the start of the IF signal (i.e., the instantaneous value represented by the left vertical dotted line in Figure 4). (Equation 5):

(5)

It can also be calculated mathematically as in Equation 6.

(6)

In summary, for an object at distance d from the radar, the IF signal is a sine wave (Equation 7).

(7)

at,

So far we have assumed that the radar detects only one object. Now let us analyze the case where multiple objects are detected. Figure 5 shows three RX chirps received from multiple objects. Each chirp is delayed by a time proportional to the distance to the object. The various RX chirps are converted into multiple IF tones, each with a fixed frequency.

This IF signal, which consists of several tones, must be processed using a Fourier transform to distinguish the various tones. After the Fourier transform process, a frequency spectrum with individual peaks for the various tones is generated, each peak indicating the presence of an object at a certain distance.

Figure 5 Multiple IF tones for multi-object detection

Range resolution

Range resolution is the ability to distinguish between two or more objects. At some point, when two objects are close together, the radar system can no longer distinguish them as separate objects. According to the Fourier transform theory, the resolution can be increased by increasing the length of the IF signal.

Increasing the length of the IF signal requires a proportional increase in bandwidth. Increasing the length of the IF signal produces an IF spectrum with two separate peaks.

Additionally, according to the Fourier transform theory, frequency components separated by a distance of 1/THz or more can be identified through the observation period (T). That is, two IF signal tones can be identified by frequency if the frequencies satisfy the given relationship. Equation 8:

(8)

Here, T _c is the observation interval. thus,

Equation 8 can be expressed as follows:





(Because B=ST _c )

The range resolution (d _Res ) depends only on the bandwidth swept by the chirp (Equation 9).

(9)

Therefore, an FMCW radar with a chirp bandwidth of several GHz will have a range resolution in the order of centimeters (e.g., a chirp bandwidth of 4 GHz translates into a range resolution of 3.75 cm).

Speed measurement

In this section, we will use the phasor representation (distance, angle) for complex numbers.

Velocity measurement using two chirps

To measure velocity, the FMCW radar transmits two chirps at intervals of Tc. By processing each reflected chirp through FFT, the range of the object (range FFT) is detected. The range FFT corresponding to each chirp has peaks at the same location but different phases. This measured phase difference corresponds to the movement of the vTc object.

Figure 6 Velocity measurement using two chirps

The phase difference is obtained using equation 6 as in equation 10.

(10)

We can find the velocity using equation 11.

(11)

This speed measurement is ambiguous because it is based on phase difference. This measurement is unambiguous only if | ΔΦ |<π. Using Equation 11 above, we can mathematically compute

Equation 12 gives the maximum relative velocity (v _max ) measured with two chirps spaced Tc . To increase v _max further, the transmission interval between chirps must be shortened.

(12)







[ The rest of the article will follow next week: Understanding Tricky Millimeter-Wave System Design (Part 2) ]