Horizontal and vertical polarization beamforming in a radar system
Systems and methods involve transmitting both horizontal and vertical polarizations from a radar system. A method includes receiving, using a first antenna of the radar system, first reflected signals with horizontal polarization, and receiving, using a second antenna of the radar system, second reflected signals with vertical polarization. The first reflected signals and the second reflected signals are processed together to obtain one or more angles to respective one or more objects detected by the radar system.
1. A method, comprising:
transmitting both horizontal and vertical polarizations from a radar system;
receiving, using a first antenna of the radar system, first reflected signals with horizontal polarization;
receiving, using a second antenna of the radar system, second reflected signals with vertical polarization;
processing the first reflected signals and the second reflected signals together to obtain one or more azimuth angles to respective one or more objects from the radar system, the one or more angles being obtained by performing processes including beamforming using the first reflected signals and the second reflected signals, wherein the receiving the first reflected signals and the receiving the second reflected signals includes respectively receiving:
y h =Σ m=0 M α(θ m )β m , and
y v =Σ m=0 M α(θ m )γ m , where
M is a number of the first reflected signals and the second reflected signals, α(θ m ) is an array response vector to angle of arrival θ m , and β m and γ m are reflection coefficients, and
the processing the first reflected signals and the second reflected signals includes performing the beamforming to obtain a likelihood indicator P(θ) as:
P (θ)=∥ w θ H y v +w θ H y h ∥ 2 ,
w θ =argmin w ∥w θ H y v +w θ H y h ∥ 2 , and
w θ H α(θ)=1, where
H indicates a conjugate transpose, or
the processing the first reflected signals and the second reflected signals includes performing the beamforming to obtain a likelihood indicator P(θ) as:
P
(
θ
)
=
1
a
H
(
θ
)
(
R
+
σ
I
)
-
1
a
(
θ
)
,
where
R is a sum of autocorrelations of the first reflected signals and the receiving the second reflected signals, σ is a regularization factor, I is an identity matrix, and H indicates a conjugate transpose.
2. The method according to claim 1 , wherein the transmitting both the horizontal and the vertical polarizations includes transmitting a combined signal resulting from feeding a signal both horizontally and vertically to an antenna for transmission.
3. The method according to claim 1 , wherein the transmitting both the horizontal and the vertical polarizations includes transmitting one signal with horizontal polarization and one signal with vertical polarization.
4. The method according to claim 1 , wherein the R is given by:
R=y v y v H +y h y h H .
5. The method according to claim 1 , further comprising selecting a value of the regularization factor σ.
6. The method according to claim 1 , wherein the obtaining the one or more angles includes applying a detection threshold to the likelihood indicator P(θ).
7. The method according to claim 1 , further comprising locating the radar system in a vehicle.
8. A system, comprising:
a radar system configured to transmit both horizontal and vertical polarizations, to receive first reflected signals with horizontal polarization and to receive second reflected signals with vertical polarization; and
a processor configured to process the first reflected signals and the second reflected signals together to obtain one or more azimuth angles to respective one or more objects from the radar system, the processor being configured to obtain the one or more angles by performing processes including beamforming using the first reflected signals and the second reflected signals, wherein the first reflected signals and the second reflected signals are given by:
y h =Σ m=0 M α(θ m )β m , and
y v =Σ m=0 M α(θ m )γ m , where
M is a number of the first reflected signals and the second reflected signals, α(θ m ) is an array response vector to angle of arrival θ m , and β m and γ m are reflection coefficients, and
the processor is configured to perform the beamforming to obtain a likelihood indicator P(θ) as:
P (θ)=∥ w θ H y v +w θ H y h ∥ 2 ,
w θ =argmin w ∥w θ H y v +w θ H y h ∥ 2 , and
w θ H α(θ)=1, where
H indicates a conjugate transpose, or
the processor is configured to perform the beamforming to obtain a likelihood indicator P(θ) as:
P
(
θ
)
=
1
a
H
(
θ
)
(
R
+
σ
I
)
-
1
a
(
θ
)
,
where
R is a sum of autocorrelations of the first reflected signals and the receiving the second reflected signals, σ is a regularization factor, I is an identity matrix, and H indicates a conjugate transpose.
9. The system according to claim 8 , wherein the radar system is configured to transmit a combined signal with both the horizontal and the vertical polarizations based on feeding a signal both horizontally and vertically to an antenna for transmission.
10. The system according to claim 8 , wherein the radar system is configured to transmit one signal with horizontal polarization and one signal with vertical polarization in order to transmit both the horizontal and the vertical polarizations.
11. The system according to claim 8 , wherein the R is given by:
R=y v y v H +y h y h H .
12. The system according to claim 8 , wherein the regularization factor σ is a selected value.
13. The system according to claim 8 , wherein the processor is configured to obtain the one or more angles by applying a detection threshold to the likelihood indicator P(θ).
14. The system according to claim 8 , wherein the radar system is in a vehicle.