## 8 February 2015

Frequency Modulated Continuous Waveform (abbreviated  FMCW) radar differs from pulsed radar in that an electromagnetic signal is continuously transmitted. The frequency of this signal changes over time, generally in a sweep across a set bandwidth. The name chirp is then a signal in which the frequency increases (up-chirp) or decreases (down-chirp) with time. In some sources, the term chirp is used interchangeably with sweep signal, or simply sweep.

A variety of waveforms is possible since the transmitter frequency can slew up and down as follows: sine wave, sawtooth wave, triangle wave and square wave.

 A linear chirp waveform; a sinusoidal wave that increases in frequency linearly over time

Spectrogram of a Linear Chirp. The Spectrogram plot demonstrates the linear rate of change in frequency as a function of time, in this case from 0 to 7 kHz repeating every 2.3 seconds. The intensity of the plot is proportional to the energy content in the signal at the indicated frequency and time ( "LinearChirp" by Spyrogumas - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons)

The difference in frequency between the transmitted and received (reflected) signal is determined by mixing the two signals, producing a new signal which can be measured to determine distance or velocity (the received signal is mixed with the emitted signal and due to the delay caused by the time of flight for the reflected signal, there will be a frequency difference that can be detected as a signal in the low frequency range).

FMCW radar is then an indirect method of distance measurement. The transmitted frequency is modulated between two known values,f1 and f2,and the difference between the transmitted signal and the return echo signal,fd, is measured. This difference frequency is directly proportional to the transit time and hence the distance.

The bandwidth of an FMCW radar is the difference between the start and finish frequency of the linear frequency modulation sweep (sweep width). The amplitude of the FMCW signal is constant across the range of frequencies. A wider bandwidth produces narrower difference frequency ranges for each echo on the frequency spectrum. This leads to better range resolution. The sweep width determines the spatial resolution of the radar: sweeps must be shorter than the time it takes for the signal to travel between the target details; otherwise, the sweeps overlap in the receiver.
The sweep repetition frequency (sweep-rate, sps) determines the maximum unambiguous range to the target. The next (non-coded) sweep cannot be sent until the previous sweep has traveled to the target and back. (Coded sweeps can be sent more frequently because coding can be used to associate responses with their corresponding transmitted sweep.)
Short sweeps with a low repetition rate maximize resolution and unambiguous range and high sweep power maximizes the radar’s range in distance.

Below some measurements of a FMCW OTH-B radar signal, obtained by analyzing the recorderd signal with Signals Analyzer (great software by radioscanner.ru

To approach this kind of transmissions you should run an (at least) 20Khz bandwidth receiver, such an SDR, and record the signal in a .wav file using 48 Khz sample rate value. The analysis is then run off-line, by play-backing the recordered signal.

Synthesized system are not sweeping the frequency continuously, but rather step the frequency with a set of discrete frequency points. Thus, these systems are also called Stepped Frequency Continuous Waveform (abbreviated SFCW) radar. The synthesized signal source assures very precise frequency control, which is important for the accuracy and repeatability of measurements.