Orthogonal phase modulation for detection and communication in radar

1. A method of orthogonal modulation of radar waves of a phase-modulated continuous wave radar system by a sequence of numerical communication symbols, the method comprising steps of:

selecting an equidistant bi-phased or multi-phased phase-modulation sequence, wherein members of the sequence are given by complex roots of unity,

phase-modulating the continuous radar wave of the radar system, and

transmitting the orthogonal phase-modulated continuous radar wave towards a scene,

and the method being characterized by the following steps of:

generating a detection sequence (s) by applying an outer coding (H) to the bi-phased or multi-phased phase-modulation sequence,

selecting a communication range (C) in the complex number plane, based on the selected equidistant bi-phased or multi-phased phase-modulation,

generating a communication sequence (c) comprising a plurality of sequence members, wherein the members are natural numbers,

mapping the communication sequence (c) into the communication range (C) by applying an injective mapping function (Γ) to the members of the communication sequence (c),

calculating a numerical product of members of the detection sequence (s) with members of an image of the mapped communication sequence (c),

wherein the step of phase-modulating the continuous radar wave of the radar system is carried out according to the calculated numerical products.

2. The method as claimed in claim 1 , wherein the selected equidistant bi-phased or multi-phased phase-modulation sequence is selected from a group comprising m-sequence, Zadoff-Chu sequence, Legendre sequence or Almost Perfect Autocorrelation Sequence.

3. The method as claimed in claim 1 , wherein the phase-modulated continuous wave radar system is configured to work in a multiple-input and multiple-output configuration, and the step of generating a detection sequence (s) includes applying a Hadamard matrix (H).

4. The method as claimed claim 1 , wherein the injective mapping function (Γ) can be expressed as:

Γ

⁡

(

c

)

=

exp

⁡

(

i

⁢

π

⁡

(

2

⁢

c

-

(

T

+

1

)

)

n

⁡

(

T

+

1

)

)

wherein c denotes the value of a member of the communication sequence (c), n denotes the maximum possible number of different roots of unity for the members of the equidistant bi-phased or multi-phased phase-modulation, and T denotes the maximum value of the members of the communication sequence (c).

5. A method of demodulating phase-modulated continuous radar waves that are orthogonally modulated by a sequence of numerical communication symbols by the method as claimed in claim 1 , wherein the phase-modulated continuous radar waves are directly received, the method comprising steps of:

applying a communication backprojection function Ω to the received phase-modulated continuous radar waves for mapping the numerical communication symbols to the communication range (C), wherein the communication backprojection function Ω can be expressed as:

Ω

⁡

(

c

~

)

=

∑

k

=

0

n

-

1

⁢

χ

⁢

⁢

c

k

⁡

(

c

~

)

⁢

e

-

2

⁢

π

⁢

⁢

i

⁢

k

n

⁢

c

~

,

wherein n denotes the maximum possible number of different roots of unity for the members of the equidistant bi-phased or multi-phased phase-modulation, {tilde over (c)} is an image of a member of the communication sequence (c) in the communication range (C), and χ C k ({tilde over (c)}) is the characteristic function with a value of 1 if the argument lies within the subset C k of the complex unit circle and a value of 0 else, and

extracting the numerical communication symbols by applying the inverse function of the injective mapping function (Γ) to images of the mapped numerical communication symbols in the communication range (C).

6. A method of demodulating phase-modulated continuous radar waves that are orthogonally modulated by a sequence of numerical communication symbols by the method as claimed in claim 1 , wherein the phase-modulated continuous radar waves are received after having been reflected by a target, the method comprising steps of:

applying a detection sequence backprojection function Δ to the received phase-modulated continuous radar waves for projecting all phases lying in a specific subset of the complex unit circle onto a specific complex root of unity that lies within the specific subset, wherein the detection sequence backprojection function Δ can be expressed as:

Δ

⁡

(

c

~

)

=

∑

k

=

0

n

-

1

⁢

χ

⁢

⁢

c

k

⁡

(

c

~

)

⁢

e

2

⁢

π

⁢

⁢

i

⁢

k

n

wherein n denotes the maximum possible number of different roots of unity for the members of the equidistant bi-phased or multi-phased phase-modulation, {tilde over (c)} is an image of a member of the communication sequence (c) in the communication range (C), and χ C k ({tilde over (c)}) is the characteristic function with a value of 1 if the argument lies within the subset C k of the complex unit circle and a value of 0 else, and

applying a phase-modulated continuous wave radar signal processing method to the projected phases.

7. A communication sequence demodulating device for demodulating phase-modulated continuous radar waves that are orthogonally modulated by a sequence of numerical communication symbols by the method as claimed in claim 1 , wherein the phase-modulated continuous waves are directly received, the device comprising:

a radar wave receiving unit that is configured for receiving phase-modulated continuous radar waves, and

a radar signal processing unit that is configured for carrying out a method that comprises the steps of:

applying a communication backproiection function Ω to the received phase-modulated continuous radar waves for mapping the numerical communication symbols to the communication range (C), wherein the communication backproiection function Ω can be expressed as:

Ω

⁡

(

c

~

)

=

∑

k

=

0

n

-

1

⁢

χ

⁢

⁢

c

k

⁡

(

c

~

)

⁢

e

-

2

⁢

π

⁢

⁢

i

⁢

k

n

⁢

c

~

,

wherein n denotes the maximum possible number of different roots of unity for the members of the equidistant bi-phased or multi-phased phase-modulation, {tilde over (c)} is an image of a member of the communication sequence (c) in the communication range (C), and χ C k ({tilde over (c)}) is the characteristic function with a value of 1 if the argument lies within the subset C k of the complex unit circle and a value of 0 else, and

extracting the numerical communication symbols by applying the inverse function of the injective mapping function (Γ) to images of the mapped numerical communication symbols in the communication range (C).

8. A detection sequence backprojection demodulating device for demodulating phase-modulated continuous radar waves that are orthogonally modulated by a sequence of numerical communication symbols by the method as claimed in claim 1 , wherein the phase-modulated continuous waves are received after having been reflected by a target, the device comprising:

a radar wave receiving unit for receiving phase-modulated continuous radar waves, and

a radar signal processing unit that is configured for carrying out a method that comprises the steps of:

applying a detection sequence backproiection function Δ to the received phase-modulated continuous radar waves for projecting all phases lying in a specific subset of the complex unit circle onto a specific complex root of unity that lies within the specific subset, wherein the detection sequence backproiection function Δ can be expressed as:

Δ

⁡

(

c

~

)

=

∑

k

=

0

n

-

1

⁢

χ

⁢

⁢

c

k

⁡

(

c

~

)

⁢

e

2

⁢

π

⁢

⁢

i

⁢

k

n

wherein n denotes the maximum possible number of different roots of unity for the members of the equidistant bi-phased or multi-phased phase-modulation, {tilde over (c)} is an image of a member of the communication sequence (c) in the communication range (C), and χ C k ({tilde over (c)}) is the characteristic function with a value of 1 if the argument lies within the subset C k of the complex unit circle and a value of 0 else, and

applying a phase-modulated continuous wave radar signal processing method to the projected phases.

9. An automotive phase-modulated continuous wave radar system, comprising

a radar wave transmitting unit that is configured to orthogonally modulate phase-modulated continuous radar waves by a sequence of numerical communication symbols by conducting a method as claimed in claim 1 , and to transmit the orthogonal modulated radar waves towards a scene with potential objects to be detected,

a communication sequence demodulating device for demodulating the orthogonal modulated radar waves, wherein the orthogonal modulated radar waves are directly received, the communication sequence demodulating device comprising:

a radar wave receiving unit that is configured for receiving phase-modulated continuous radar waves, and

a radar signal processing unit that is configured for carrying out a method that comprises the steps of:

applying a communication backproiection function Ω to the received phase-modulated continuous radar waves for mapping the numerical communication symbols to the communication range (C), wherein the communication backproiection function Ω can be expressed as:

Ω

⁡

(

c

~

)

=

∑

k

=

0

n

-

1

⁢

χ

⁢

⁢

c

k

⁡

(

c

~

)

⁢

e

-

2

⁢

π

⁢

⁢

i

⁢

k

n

⁢

c

~

,

wherein n denotes the maximum possible number of different roots of unity for the members of the equidistant bi-phased or multi-phased phase-modulation, {tilde over (c)} is an image of a member of the communication sequence (c) in the communication range (C), and χ C k ({tilde over (c)}) is the characteristic function with a value of 1 if the argument lies within the subset C k of the complex unit circle and a value of 0 else, and

extracting the numerical communication symbols by applying the inverse function of the injective mapping function (Γ) to images of the mapped numerical communication symbols in the communication range (C), and

a detection sequence backprojection demodulating device for demodulating the orthogonal modulated radar waves, wherein the orthogonal modulated radar waves are received after having been reflected by a target, the device comprising:

a radar wave receiving unit for receiving phase-modulated continuous radar waves, and

a radar signal processing unit that is configured for carrying out a method that comprises the steps of:

applying a detection sequence backproiection function Δ to the received phase-modulated continuous radar waves for projecting all phases lying in a specific subset of the complex unit circle onto a specific complex root of unity that lies within the specific subset, wherein the detection sequence backproiection function Δ can be expressed as:

Δ

⁡

(

c

~

)

=

∑

k

=

0

n

-

1

⁢

χ

⁢

⁢

c

k

⁡

(

c

~

)

⁢

e

2

⁢

π

⁢

⁢

i

⁢

k

n

wherein n denotes the maximum possible number of different roots of unity for the members of the equidistant bi-phased or multi-phased phase-modulation, {tilde over (c)} is an image of a member of the communication sequence (c) in the communication range (C), and χ C k ({tilde over (c)}) is the characteristic function with a value of 1 if the argument lies within the subset C k of the complex unit circle and a value of 0 else, and

applying a phase-modulated continuous wave radar signal processing method to the projected phases.