Frequency-Domain Characteristics in FMCW Radar

Frequency Modulated Continuous Wave (FMCW) radar is a form of radar where the frequency of the transmitted signal is continuously varied at a known rate over a defined time period. The reflected frequency signal is received by the radar and compared. The transceiver generates a signal of linearly increasing frequency for the frequency-sweep period. The signal propagates from the antenna to a static target and back. The value of the received-signal frequency compared to the transmitted-signal frequency is proportional to the propagation range. In addition, advantage of FMCW radar is its ability to adjust the range of frequencies of operation to suit the material and targets under investigation if the antenna has an adequate Pass-band of frequencies. This radar system mixes the wave reflected by a target object and part of the radiated wave to obtain a beat signal that contains distance and speed components. For large scattered, the physical-optics approximation is an efficient method in the frequency domain [1,2]. This physical optics (PO) approximation is initially applied in the frequency-domain with the inverse Fourier transform [3-6]. With FMCW, the high-frequency circuitry for beat signal detection is relatively simple and distance can be directly obtained. By mixing the received FMCW and transmitted FMCW signals, the system obtains a beat signal having a frequency fb. [7] studied the Radar wave propagation characteristics in FMCW by using the frequency domain physical optics. In this paper, we use the frequency-domain physical optics with the inverse Fourier transform [3] and [6]. In addition, we will focus on some numerical results for the frequency-domain.

For a perfectly conducting body, the frequency-domain PO-induced current distribution over the illuminated surface is [8-10]:

The equation (7) describes a linearly increasing FM signal (chirp) at about twice the carrier frequency with a phase shift that is proportional to the delay time To, this term is generally filtered out. Equation (8) describes a beat signal at a fixed frequency

The frequency transfer function H(ω) is defined as

where 𝑉𝑖(𝜔) is the input waveform in frequency domain physical optics, this is just a magnitude of the source.

The output Voltage 𝑉𝑜(𝜔) is calculated from 𝐸𝑝𝑜(𝑅, 𝜔) by considering the receiver antennas as [11-12],

It can be seen that the signal frequency is directly proportional to the time delay time τ , and hence is directly proportional to the round-trip time to the target.

Figures (1-4) represent the relation between the frequency transfer function 𝐻(𝜔) and the angular frequency ω and show the values of the frequency transfer function 𝐻(𝜔) at λ = 1, 2, 3, and 5 respectively. Figures (1-4) show that increasing in the values of the frequency domain transfer function 𝐻(𝜔) due to the increasing in the wavelength λ and the increases in the wavelength λ due to the decay in the frequency. Our series expansion gave good approximations of the field values. The peak in the Figures (3) and (4) at λ = 3 and 5 are small peak compared to the peak in Figures (1) and (2) at λ = ½ and 1. The results represented graphically and illustrated by figures.

We obtained the frequency domain linear system analysis for FMCW which obtained by calculating the integral over the illuminated surface using the free space Green’s function and we use the frequency-domain physical optics with the inverse Fourier transform. We conclude from the present analysis that the increasing in the wavelength λ due to the decay in the frequency, gave the increasing in the values of the frequency transfer function 𝐻(𝜔).

None

No conflict of interest.