# US 10,768,291 B2 · Method and system for obtaining angle-doppler signatures in MIMO radars

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- Number: US 10,768,291 B2
- Document ID: US10768291B2
- Status: Granted
- Kind: B2
- Application number: 16/341,269
- Filed: 2017-10-04
- Published: 2019-11-14
- Granted: 2020-09-08
- Earliest claimed: 2016-10-13
- Assignees: Iee International Electronics & Engineering S.A.; Universite Du Luxembourg
- Applicants: Iee International Electronics & Engineering S.A.; Universite Du Luxembourg
- Inventors: Christian Hammes; Yogesh Nijsure; Bjorn Ottersten; Udo Schroder
- Web page: https://patentgrep.com/patent/US10768291B2

## CPC

- G01S 13/343: {using sawtooth modulation}
- G01S 13/42: Simultaneous measurement of distance and other co-ordinates (indirect measurement G01S13/46)
- G01S 13/878: {Combination of several spaced transmitters or receivers of known location for determining the position of a transponder or a reflector (G01S13/874 takes precedence)}
- G01S 13/931: of land vehicles
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES

## Abstract

A method for obtaining an angle-Doppler signature for a target using sparse arrays in multiple-input-multiple-output (MIMO) radar, the MIMO radar including a transmit antenna array, the transmit antenna array being at least one-dimensional (e.g. 2-D, 3-D or 4-D) and having a plurality of antenna elements. The method includes generating transmit signals for transmission by the transmit antenna array, the transmit signals defining at least a first transmit trajectory (e.g. circular) of a phase center within the transmit antenna array, and transmitting the transmit signals using Amplitude Modulation on the transmit antenna array. The method further includes receiving receive signals from the target, the receive signals resulting from the incidence of the transmit signals upon the target, and determining the angle-Doppler signature from the receive signals. The first transmit trajectory is such that, in operation, the phase center undergoes non-linear motion within the transmit antenna array.

## Claims

### Claim 1

A method for obtaining an angle-Doppler signature for a target using multiple-input-multiple-output (MIMO) radar, the MIMO radar including a transmit antenna array, the transmit antenna array being at least one-dimensional and having a plurality of antenna elements, the method comprising:
generating transmit signals for transmission by the transmit antenna array, the transmit signals defining at least a first transmit trajectory of a phase center within the transmit antenna array; and
transmitting the transmit signals using the transmit antenna array;
receiving receive signals from the target, the receive signals resulting from the incidence of the transmit signals upon the target; and
determining the angle-Doppler signature from the receive signals;
wherein the first transmit trajectory is such that, in operation, the phase center undergoes non-linear motion within the transmit antenna array.

### Claim 2 (depends on 1)

The method according to claim 1, wherein the MIMO radar includes a receive antenna array, the receive antenna array being at least one-dimensional and having a plurality of antenna elements, wherein:
receiving the receive signals from the target comprises receiving the receive signals using the receive antenna array; and
the receive signals define at least a first receive trajectory of a phase center within the receive antenna array.

### Claim 3 (depends on 1)

The method according to claim 1, wherein the first transmit trajectory and the first receive trajectory are identical.

### Claim 4 (depends on 1)

The method according to claim 1, wherein the first transmit trajectory and/or the first receive trajectory correspond to an amplitude modulation (AM) of the transmit signals.

### Claim 5 (depends on 4)

The method according to claim 4, wherein the transmit signals are given by
x
⁡
(
t
)
=
w
Tx
⁡
(
t
)
⁢
e
j
⁡
(
ω
0
⁢
t
+
B
T
c
⁢
t
2
)
where the vector wTx(t) represents the AM, ω0 is the carrier angular frequency, B is the chirp bandwidth and Tc the chirp duration.

### Claim 6 (depends on 1)

The method according to claim 1, wherein the receive signals are given by
y
⁡
(
t
)
=
∑
k
=
1
K
⁢
A
k
⁢
e
j
⁢
⁢
ω
Dk
⁢
t
S
k
⁢
w
Tx
⁡
(
t
)
⁢
e
j
⁡
(
ω
0
⁡
(
t
-
r
k
c
0
)
+
B
T
c
⁢
(
t
-
r
k
c
0
)
2
)
where ω0 is the carrier angular frequency, Sk is the MIMO channel matrix, Ak is the k-th target radar cross section, ωDk is the k-th target Doppler shift, K is the total number of targets, rk is the target range, B is the chirp bandwidth, TC is the chirp duration and c0 is the speed of light.

### Claim 7 (depends on 6)

The method according to claim 6, further comprising down mixing the receive signals y(t) to obtain the down-mixed signal yDM(t), given by
y
DM
⁡
(
t
)
=
∑
k
=
1
K
⁢
c
k
⁢
A
k
⁢
e
j
⁢
⁢
ω
Dk
⁢
t
⁢
e
-
j
⁢
⁢
(
2
⁢
Br
k
T
c
⁢
c
0
)
⁢
S
k
⁢
w
tx
⁡
(
t
)
where
c
k
=
e
-
j
⁡
(
ω
0
⁢
r
k
c
0
-
B
T
c
⁢
(
r
k
c
0
)
2
)
and where the vector wTx(t) represents the AM, ω0 is the carrier angular frequency, Sk is the MIMO channel matrix, Ak is the k-th target radar cross section, ωDk is the k-th target Doppler shift, K is the total number of targets, rk is the target range, B is the chirp bandwidth, TC is the chirp duration and C0 is the speed of light.

### Claim 8 (depends on 7)

The method according to claim 7, further comprising transforming the down-mixed signal yDM(t) to the discrete time domain to obtain baseband signals yBB(is), given by
y
BB
⁡
(
i
s
)
=
∑
k
=
1
K
⁢
c
k
⁢
A
k
⁢
e
j
⁢
⁢
ω
Dk
⁢
i
s
⁢
T
s
⁢
e
j
⁡
(
ω
Bk
⁢
i
s
⁢
T
s
)
⁢
S
k
⁢
w
Tx
⁡
(
i
s
⁢
T
s
)
where the vector wTx(t) represents the AM, ω0 is the carrier angular frequency, ωBk is the range corresponding beat frequency with regards to FMCW, Sk is the MIMO channel matrix, Ak is the k-th target radar cross section, ωDk is the k-th target Doppler shift, K is the total number of targets, rk is the target range, and c0 is the speed of light.

### Claim 9 (depends on 8)

The method according to claim 8, further comprising deriving, from the baseband signals yBB(is), a Doppler signature yDS(ic), given by
y
DS
⁡
(
i
c
)
=
∑
k
=
1
K
⁢
c
k
⁢
A
k
⁢
e
j
⁢
⁢
ω
Dk
⁢
i
c
T
c
⁢
S
k
⁢
w
Tx
⁡
(
i
c
⁢
T
c
)
where SkwTx(icTc) is a group factor GTx of the transmit antenna array, given by
G
Tx
⁡
(
i
c
)
=
∑
n
=
1
N
⁢
w
Txn
⁡
(
i
c
⁢
T
c
)
⁢
e
jk
0
⁢
sin
⁡
(
ϕ
k
)
⁢
d
Tx
⁢
n
where dTx is the inter-element spacing of transmit antenna elements, ϕk is the k-th target angle of arrival, the vector wTx(t) represents the AM, wTxn is the n-th element of the amplitude modulation vector wTx, N is the total number of elements within wTx, Sk is the MIMO channel matrix, Ak is the k-th target radar cross section, ωDk is the k-th target Doppler shift, K is the total number of targets, rk is the target range, TC is the chirp duration, and k0 is the free space wave number, and wherein the AM vector wTx comprises the transmit phase center.

### Claim 10 (depends on 9)

The method according to claim 9, wherein the first transmit trajectory and/or a second transmit trajectory are formed using a phase center position xPC defined by
x
PC
⁡
(
i
c
)
=
∂
∂
k
x
⁢
arg
⁡
(
G
Tx
⁡
(
i
c
)
)
where
⁢
⁢
k
x
=
k
0
⁢
sin
⁡
(
ϕ
k
)
and wherein k0 is the free space wave number and GTx is the group factor of the transmit antenna array.

### Claim 11 (depends on 1)

The method according to claim 1, wherein the first transmit trajectory and/or the second transmit trajectory are formed such that the motion of the respective phase center is sinusoidal.

### Claim 12 (depends on 11)

The method according to claim 11, further comprising deriving a Doppler signature yDS(ic) from the receive signals according to
yDS(ic)=ckAkejωDkicTce−jk0 sin(ϕk)x0 sin(ωCPITcic)
where ωCPI is an angular frequency for a coherent processing interval (CPI) and is given by
ω
CPI
=
2
⁢
⁢
π
I
c
⁢
T
c
where
⁢
⁢
c
k
=
e
-
j
⁡
(
ω
0
⁢
r
k
c
0
-
B
T
c
⁢
(
r
k
c
0
)
2
)
and wherein to is the carrier angular frequency, Ak is the k-th target radar cross section, ωDk to is the k-th target Doppler shift, rk is the target range, ϕk is the k-th target angle of arrival, k0 is the free space wave number, x0 is the array size, B is the chirp bandwidth, TC is the chirp duration, and C0 is the speed of light.

### Claim 13 (depends on 1)

The method according to claim 1, wherein determining the angle-Doppler signature from the receive signals comprises using a filter bank wherein every combination of p and q is related to one filter of the filter bank such that each filter is given by
ypq(ic)=ejωDqicTc-jRp sin(ωCPITcic)
where
Rp=pπ
ωDg=qωCPI
where ωCPI is an angular frequency for a coherent processing interval (CPI) and is given by
ω
CPI
=
2
⁢
⁢
π
I
c
⁢
T
c
and wherein rk is the target range, ϕk is the k-th target angle of arrival, k0 is the free space wave number, and TC is the chirp duration.

### Claim 14 (depends on 13)

The method according to claim 13, wherein the output of the filter bank is calculated as
J
^
pq
=
∑
i
c
=
1
I
c
⁢
c
k
⁢
A
k
⁢
e
j
⁡
(
ω
Dk
-
ω
Dq
)
⁢
i
c
⁢
T
c
-
j
⁡
(
R
k
-
R
p
)
⁢
sin
⁡
(
ω
CPI
⁢
T
c
⁢
i
c
)
where
⁢
⁢
R
k
=
sin
⁡
(
ϕ
k
)
⁢
k
0
⁢
x
0
and
⁢
⁢
c
k
=
e
-
j
⁡
(
ω
0
⁢
r
k
c
0
-
B
T
c
⁢
(
r
k
c
0
)
2
)
and wherein Ak is the k-th target radar cross section, ω0 is the carrier angular frequency, ωDk is the k-th target Doppler shift, rk is the target range, ϕk is the k-th target angle of arrival, k0 is the free space wave number, x0 is the array size, B is the chirp bandwidth, TC is the chirp duration and C0 is the speed of light and
ωDq=qωCPI
where ωCPI is an angular frequency for a coherent processing interval (CPI) and is given by
ω
CPI
=
2
⁢
⁢
π
I
c
⁢
T
c
.

### Claim 15 (depends on 14)

The method according to claim 14, further comprising deriving the Doppler from the order of output of the filter bank, preferably from the order of Bessel function in the case of sinusoidal PCM.

### Claim 16 (depends on 14)

The method according to claim 14 further comprising deriving a target angle from the argument of the output of the filter bank.

### Claim 17 (depends on 1)

The method according to claim 1, wherein the at least a first transmit trajectory comprises at least a first transmit trajectory and a second transmit trajectory and/or the at least a first receive trajectory comprises at least a first receive trajectory and a second receive trajectory.

### Claim 18 (depends on 1)

The method according to claim 1, wherein the frequency of the first receive trajectory is different to that of the first transmit trajectory and/or the second receive trajectory is different to that of the second transmit trajectory.

### Claim 19 (depends on 1)

The method according to claim 1, wherein the frequency of the first receive trajectory is half that of the first transmit trajectory and/or the second receive trajectory is half that of the second transmit trajectory.

### Claim 20 (depends on 17)

The method according to claim 17, wherein the first transmit trajectory and the second transmit trajectory have different starting points and/or the first receive trajectory and the second receive trajectory have different starting points.

### Claim 21 (depends on 17)

The method according to claim 17, wherein the first transmit trajectory is one of sine and cosine and the second transmit trajectory is the other of sine and cosine and/or the first receive trajectory is one of sine and cosine and the second receive trajectory is the other of sine and cosine.

### Claim 22 (depends on 1)

The method according to claim 1, wherein the transmit antenna array and the receive antenna array are 2-dimensional or the transmit antenna array and the receive antenna array are 3-dimensional.

### Claim 23 (depends on 1)

The method according to claim 1, wherein determining the Doppler signature from the receive signals comprises determining an angle-Doppler signature yDS(ic) as
y
DS
⁡
(
i
c
)
=
∑
k
=
1
K
⁢
c
k
⁢
A
k
⁢
e
j
⁢
⁢
ω
Dk
⁢
i
c
⁢
T
c
⁢
e
-
jk
0
⁢
sin
⁡
(
ϕ
k
)
⁢
x
PC
⁡
(
i
c
)
where
⁢
⁢
c
k
=
e
-
j
⁡
(
ω
0
⁢
r
k
c
0
-
B
T
c
⁢
(
r
k
c
0
)
2
)
and ω0 is the carrier angular frequency, rk is the target range, B is the chirp bandwidth, C0 is the speed of light, Ak is the k-th target radar cross section, K is the total number of targets, ωDk is the k-th target Doppler shift, Tc is the chirp duration, k0 is the free space wave number, ϕk is the k-th target angle of arrival, xPC(ic) is the phase center trajectory in x-direction.

### Claim 24 (depends on 1)

The method according to claim 1, further comprising determining an argument of angle-Doppler signature YDS(ic) as
φ
k
⁡
(
t
)
=
k
→
k
·
x
→
PC
⁡
(
i
c
)
k
→
k
=
k
0
⁡
(
cos
⁡
(
ϕ
k
)
⁢
cos
⁡
(
θ
k
)
sin
⁡
(
ϕ
k
)
⁢
cos
⁡
(
θ
k
⁢
)
sin
⁡
(
θ
k
)
)
where {right arrow over (x)}PC is the phase center trajectory on a 3 dimension structure, k0 is the free space wave number and ok the k-target angle of arrival;
and discriminating targets based on the determined φk(t).

### Claim 25 (depends on 1)

The method according to claim 1, further comprising determining a Doppler ωDk from
φk(t)={right arrow over (k)}k·{right arrow over (x)}PC(ic)+ωDkt
where {right arrow over (x)}PC is the phase center trajectory on a 3 dimension structure and ωDk is the k-th target Doppler shift;
and discriminating targets based on the determined ωDk.

### Claim 26 (depends on 1)

A system for obtaining an angle-Doppler signature for a target using multiple-input-multiple-output (MIMO) radar, the system comprising
a transmit antenna array, the transmit antenna array being at least one-dimensional and having a plurality of antenna elements; and
processing circuitry, coupled to the transmit antenna array, the processing circuitry being configured to carry out the method of claim 1.

### Claim 27 (depends on 26)

The system according to claim 26, further comprising a receive antenna array coupled to the processing circuitry, the receive antenna array being at least one-dimensional and having a plurality of antenna elements.

### Claim 28 (depends on 1)

A non-transitory computer readable medium storing instructions which, when executed by processing circuitry, perform the method of claim 1.