In phase (I) and quadrature (Q) imbalance estimation in a radar system
A radar system is provided that includes transmission signal generation circuitry, a transmit channel coupled to the transmission generation circuitry to receive a continuous wave test signal, the transmit channel configurable to output a test signal based on the continuous wave signal in which a phase angle of the test signal is changed in discrete steps within a phase angle range, a receive channel coupled to the transmit channel via a feedback loop to receive the test signal, the receive channel including an in-phase (I) channel and a quadrature (Q) channel, a statistics collection module configured to collect energy measurements of the test signal output by the I channel and the test signal output by the Q channel at each phase angle, and a processor configured to estimate phase and gain imbalance of the I channel and the Q channel based on the collected energy measurements.
1. A system comprising:
a set of transmit paths each configured to couple to a respective antenna, wherein a first transmit path of the set of transmit paths includes a phase shifter configured such that the first transmit path is configured to provide a test signal that includes signal portions at each phase of a set of phases;
a loopback path coupled to the first transmit path;
a set of receive paths each coupled to the loopback path and configured to couple to a respective antenna, wherein each receive path of the set of receive paths is configured to:
receive the test signal;
provide a respective in-phase response to the test signal; and
provide a respective quadrature response to the test signal; and
a control module coupled to the set of receive paths and configured to, for each receive path of the set of receive paths, determine at least one of: a phase imbalance or a gain imbalance for the respective receive path based on the respective in-phase response and the respective quadrature response.
2. The system of claim 1 , wherein the control module is configured to determine the at least one of the phase imbalance or the gain imbalance, for each receive path of the set of receive paths, by:
determining energy peaks of the respective in-phase response; and
determining energy peaks of the respective quadrature response.
3. The system of claim 2 , wherein the control module is configured to:
determine the energy peaks of the respective in-phase response by:
determining coarse peaks from samples of the respective in-phase response; and
performing interpolation around the coarse peaks of the respective in-phase response to determine the energy peaks of the respective in-phase response; and
determine the energy peaks of the respective quadrature response by:
determining coarse peaks from samples of the respective quadrature response; and
performing interpolation around the coarse peaks of the respective quadrature response to determine the energy peaks of the respective quadrature response.
4. The system of claim 2 further comprising a power detector coupled to the first transmit path, wherein the power detector and the control module are configured to:
determine a power of the test signal associated with each of the energy peaks of the respective in-phase response; and
determine a power of the test signal associated with each of the energy peaks of the respective quadrature response.
5. The system of claim 1 , wherein the control module is configured to determine the gain imbalance ({circumflex over (α)}) of a respective one of the set of receive paths based on:
α
^
=
Q
_
p
k
2
γ
Ipk
2
(
θ
Ipk
)
I
_
p
k
2
γ
Qpk
2
(
θ
Qpk
)
wherein Ī pk 2 is an energy of an energy peak in the respective in-phase response; Q pk 2 is an energy of an energy peak in the respective quadrature response; γ Ipk 2 (θ Ipk ) is a power of the test signal associated with the energy peak in the respective in-phase response; and γ Qpk 2 (θ Qpk ) is a power of the test signal associated with the energy peak in the respective in-phase response.
6. The system of claim 1 , wherein the control module is configured to determine the phase imbalance of a respective one of the set of receive paths by:
determining a midpoint phase midway between an energy peak in the respective in-phase response and an energy peak in the respective quadrature response;
determining an energy of the respective in-phase response at the midpoint phase;
determining an energy of the respective quadrature response at the midpoint phase;
determining in-phase and quadrature power of the test signal at the midpoint phase; and
determining the phase imbalance ({circumflex over (Ø)}) based on:
∅
^
=
a
sin
(
Q
_
p
h
2
γ
Ipk
2
(
θ
Qpk
)
Q
_
p
k
2
γ
Qph
2
(
θ
p
h
)
)
-
a
cos
(
I
_
p
h
2
γ
Ipk
2
(
θ
Ipk
)
I
_
p
k
2
γ
Iph
2
(
θ
p
h
)
)
wherein θ ph is the midpoint phase; Ī ph 2 is the energy of the respective in-phase response at the midpoint phase; Q ph 2 is the energy of the respective quadrature response at the midpoint phase; γ Iph 2 (θ ph ) is the in-phase power of the test signal at the midpoint phase; and γ Qph 2 (θ ph ) is the quadrature power of the test signal at the midpoint phase.
7. The system of claim 1 , wherein the first transmit path includes:
a first amplifier that includes an input coupled to receive a reference signal and an output coupled to the phase shifter; and
a second amplifier that includes an input coupled to the phase shifter and an output coupled to the loopback path.
8. The system of claim 7 , wherein each receive path of the set of receive paths includes:
a receiver amplifier that includes an input coupled to receive the test signal and an output configured to provide an amplified test signal; and
a complex mixer that includes a first input coupled to receive the amplified test signal and a second input coupled to receive the reference signal.
9. The system of claim 1 , wherein the loopback path includes an on-off keying modulator coupled between the first transmit path and the set of receive paths.
10. The system of claim 1 , wherein the test signal is a continuous wave signal.
11. A method comprising:
receiving, at a set of receive paths, a test signal that includes a set of signal portions, each having a respective phase that is different from a remainder of the set of signal portions;
receiving, at the set of receive paths, a reference signal;
for each receive path of the set of receive paths, mixing the test signal with the reference signal to generate a respective in-phase response and a respective quadrature response to the test signal; and
for each receive path of the set of receive paths, determining at least one of: a gain imbalance or a phase imbalance of the respective receive path based on the respective in-phase response and the respective quadrature response.
12. The method of claim 11 , wherein the determining of the at least one of: the gain imbalance or the phase imbalance includes:
determining energy peaks of the respective in-phase response; and
determining energy peaks of the respective quadrature response.
13. The method of claim 12 , wherein:
the determining of the energy peaks of the respective in-phase response includes:
determining coarse peaks from samples of the respective in-phase response; and
performing interpolation around the coarse peaks of the respective in-phase response to determine the energy peaks of the respective in-phase response; and
the determining of the energy peaks of the respective quadrature response includes:
determining coarse peaks from samples of the respective quadrature response; and
performing interpolation around the coarse peaks of the respective quadrature response to determine the energy peaks of the respective quadrature response.
14. The method of claim 12 , wherein the determining of the at least one of: the gain imbalance or the phase imbalance includes:
determining a power of the test signal associated with each of the energy peaks of the respective in-phase response; and
determining a power of the test signal associated with each of the energy peaks of the respective quadrature response.
15. The method of claim 11 comprising determining the gain imbalance ({circumflex over (α)}) of each receive path of the set of receive paths based on:
α
^
=
Q
_
p
k
2
γ
Ipk
2
(
θ
Ipk
)
I
_
p
k
2
γ
Qpk
2
(
θ
Qpk
)
wherein Ī pk 2 is an energy of an energy peak in the respective in-phase response; Q pk 2 is an energy of an energy peak in the respective quadrature response; γ Ipk 2 (θ Ipk ) is a power of the test signal associated with the energy peak in the respective in-phase response; and γ Qpk 2 (θ Qpk ) is a power of the test signal associated with the energy peak in the respective in-phase response.
16. The method of claim 11 comprising determining the phase imbalance of each receive path of the set of receive paths by:
determining a midpoint phase midway between an energy peak in the respective in-phase response and an energy peak in the respective quadrature response;
determining an energy of the respective in-phase response at the midpoint phase;
determining an energy of the respective quadrature response at the midpoint phase; and
determining in-phase and quadrature power of the test signal at the midpoint phase, wherein the determining of the phase imbalance ({circumflex over (Ø)}) is based on:
∅
^
=
a
sin
(
Q
_
p
h
2
γ
Ipk
2
(
θ
Qpk
)
Q
_
p
k
2
γ
Qph
2
(
θ
p
h
)
)
-
a
cos
(
I
_
p
h
2
γ
Ipk
2
(
θ
Ipk
)
I
_
p
k
2
γ
Iph
2
(
θ
p
h
)
)
wherein θ ph is the midpoint phase; Ī ph 2 is the energy of the respective in-phase response at the midpoint phase; Q ph 2 is the energy of the respective quadrature response at the midpoint phase; γ Iph 2 (θ ph ) is the in-phase power of the test signal at the midpoint phase; and γ Qph 2 (θ ph ) is the quadrature power of the test signal at the midpoint phase.
17. The method of claim 11 , wherein:
each receive path of the set of receive paths is configured to couple to a respective antenna; and
the test signal is received by each receive path of the set of receive paths via a bypass path that bypasses the respective antenna.
18. The method of claim 11 further comprising generating the test signal by phase shifting the reference signal.
19. The method of claim 11 , wherein the respective phases of the set of signal portions of the test signal are separated by a uniform step size.
20. The method of claim 11 , wherein the test signal is a continuous wave signal.