Angle In FMCW Radar

 

1	When two or more receiving antennas are spatially arranged, they occupy different physical positions.
2	The propagation path length of the wave may differs for each antenna
3	As a result, the signals received at different antenna positions exhibit phase differences at the same observation time.

 

 

θ  angle of arrival/target direction [degree] d  distance between antennas [m] Δϕ  phase difference between adjacent antennas [rad]

 

 

         

 

 

 

 

1. Signal Flow and Processing

The signals received at different antenna elements exhibit spatial phase differences at the same observation time.

Since the Doppler FFT is a linear operation performed independently on each antenna channel,

the resulting Range–Doppler bins preserve the inter-antenna phase differences, which can be exploited for angle estimation.

 

 

 

                  

2. Example

The phase difference can be calculated from the RD maps generated by the two receive channels (Rx1 and Rx2)

for the same range–Doppler cell.

 

 

Parameter	Symbol	Value	Unit
Chirp Start Freq.	f_chirp_start	24.05	GHz
Chirp Cutoff Freq.	f_chirp_stop	24.25	GHz
Antenna Spacing	d	λ/2	m
Phase of RX1	ϕ1	0.5	rad
Phase of RX2	ϕ2	1.8	rad

 

 

 

 

 

 

 

 

 

 

3. Note

The phase difference information between two receiving channels exists in all output of beat signal, Range FFT, and Doppler FFT.

However, the reliability of phase difference detection is increased as the stage is proceeded.

Therefore, The phase difference estimation is most accurate and stable when performed using the RD map after the Doppler FFT.

Seen with beat signal (Mixer Output) (poor SNR)		Hard to detect phase from a target. All signals are mixed and not seperated
Seen at the Range FFT output (Insufficient SNR yet)		s2 and v3 are seperated by Range bin. But v1, v2, s1 signals are mixed (in same bin)
Seen at the Doppler FFT output (Best SNR)		Furthermore, v1, v2, and s1 are also separated by Doppler, all signals are cleaned.