Velocity in FMCW Radar

 

1	If a target moves with a certain velocity, its distance changes over successive chirps.
2	As a result, the propagation path of the reflected signal differs from chirp to chirp.
3	This causes a frequency and phase difference in the received signals from the same target across chirps.

 

 

 

 

 

 

1. Signal Flow and Processing

The Doppler FFT is applied along the chirp index axis of the Range FFT output at a fixed range bin,

enabling the estimation of Doppler frequency and target velocity from phase variations over time.

 

 

 

 

 

Phase is different in a range bin across chirps

 

 

 

 

one target

 

 

multi-target

 

 

 

 

 

 

2. Velocity Formula

Velocity is typically calculated by collecting and processing data over one frame

and then estimating the Doppler frequency fdf.

 

Velocity		fd Measured value converted from kd, kd is doppler bin index λ Wave length N Doppler FFT size Tc Chirp to Chirp Interval
Resolution		Frame time limit the resolution between 2 objects   λ Wave length of RF center frequency Tf Frame time
Max Limit		Chirp-to-Chirp interval limit the measurable max velocity   λWave length of RF center frequency Tc Chirp to Chirp Interval

 

 

 

 

 

3. Example report in Radar Sensor SoC

 

구분	필드명	Dword	Bit Range	설명
Header	Fixed Pattern	Dword 0	[31:24]	1010 1010
Header	Reserved	Dword 0	[23]	0
Header	Fixed Pattern	Dword 0	[22:20]	100
Header	DFFT_chirp_index	Dword 0	[19:11]	Chirp sequence number (frame 내, 0부터 시작)
Header	DW_LEN	Dword 0	[10:0]	Doppler FFT data count (0부터 시작)
Data	DFFT_real_data[0]	Dword 1	[31:16]	Doppler FFT real part (signed)
Data	DFFT_imag_data[0]	Dword 1	[15:0]	Doppler FFT imaginary part (signed)
Data	DFFT_real_data[1]	Dword 2	[31:16]	Doppler FFT real part (signed)
Data	DFFT_imag_data[1]	Dword 2	[15:0]	Doppler FFT imaginary part (signed)
Data	DFFT_real_data[n]	Dword …	[31:16]	Doppler FFT real part (signed)
Data	DFFT_imag_data[n]	Dword …	[15:0]	Doppler FFT imaginary part (signed)
Data	DFFT_real_data[m-1]	Dword m	[31:16]	Doppler FFT real part (signed)
Data	DFFT_imag_data[m-1]	Dword m	[15:0]	Doppler FFT imaginary part (signed)
Tail	Check_sum	Dword m+1	[31:16]	Doppler FFT data checksum (low 16bit sum 결과)
Tail	FFT_FRAME_INDEX	Dword m+1	[15:12]	Frame counter (0부터 시작)
Tail	Reserved	Dword m+1	[11:10]	0
Tail	CFG_MSG	Dword m+1	[9:8]	User defined bits
Tail	Fixed Pattern	Dword m+1	[7:0]	0101 0101