In one or more embodiments, the noise correlation level is indicative of a type of noise affecting the radar system. More specifically, the type of noise may be predominantly thermal noise if the noise correlation level is zero or close to zero. Furthermore, the type of noise may be predominantly phase noise if the noise correlation level is significantly greater than zero. Since the noise correlation level may indicate that the type of noise is predominantly thermal noise or phase noise, said level may effectively be used as a parameter to adjust the detector threshold used by the second radar detector stage. Accordingly, the number of false target detections caused by an excess of phase noise may easily be reduced.

Thus, a practical implementation of the presently disclosed radar system may eliminate or at least reduce the number of false positives in a radar target list. The practical implementation may include a first radar detector stage, a noise correlation calculator, and an optimal detector threshold finder followed by a second and final radar detector stage. The first radar detector may be a standard radar detector used to check the presence of a possible target which competes against the system/environmental noise sources. When a target detection has occurred, a digital signal processing method may determine the noise correlation level among channels of the radar system (e.g., a multiple-input multiple-output radar system). This may be carried out by calculating the average correlation matrix of the detected range bins, for all the Doppler components excluding those components at which the target has been detected, for all the radar channels. The calculated correlation level may then be used to adjust the radar detector threshold in order to account for colored noise statistics. After the threshold adjustment the second radar detector stage may use the pre-calculated modified threshold, and the output of the second radar detector stage may either confirm that the target detection is correct or indicate that the target detection is incorrect. Finally, standard processing may be applied after the second radar detector stage in order to obtain the radar target list.

FIG. 5 shows an illustrative embodiment of a method 500 of operating a radar system. The method 500 comprises the following steps. At 502, a first radar detector stage of a radar system detects, using a detector threshold, at least one target through a plurality of receive channels of said radar system. At 504, a noise correlation determination unit of the radar system determines a noise correlation level indicative of noise correlation between the receive channels if the first radar detector stage has detected the target. Furthermore, at 506, a detector threshold adjustment unit of the radar system adjusts the detector threshold in dependence on the noise correlation level determined by the noise correlation determination unit. Finally, at 508, a second radar detector stage of the radar system detects the target using the adjusted detector threshold. As mentioned above, by adjusting the detector threshold in dependence on the noise correlation level between the different receive channels, the number of false target detections caused by an excess of phase noise may be reduced.

FIG. 6 shows an illustrative embodiment of FMCW digital signal processing 600. The acquired raw ADC samples are processed 602 by several stages in a channel-by-channel fashion. First range processing 604 is executed followed by velocity processing 606. Both of these processing stages typically make use of standard windowed fast Fourier transforms (FFTs). The peak detector 608 usually determines the presence of a possible radar target by comparing the amplitude of each range-Doppler bin with a calculated noise-based threshold. This usually takes place after coherent/incoherent combining the signal over multiple antenna channels. After a detection has occurred subsequent MIMO processing 612 and direction-of-arrival (DOA) estimation 614 are performed on all channels 610 with the aim of generating the radar target list.

FIG. 7 shows an illustrative embodiment of the construction of a correlation matrix 700. After a positive radar detection (i.e., an order statistic-CFAR detection) the tested range gate may be used to calculate the correlation of the noise among all the receiver channels. The matrix under test has size N_ch×N_chirps, where N_chis the number of physical receiver channels, while N_chirpsis the number of chirps contained in the radar frame. The correlation coefficient is a measure of the linear dependency among the variables of which the correlation should be calculated. If, for the sake of simplicity, only four channels are considered, the correlation coefficient can be calculated as shown in equation 9.

ρ
⁡
(

ch
1

,
 

ch
2

,
 

ch
3

,
 

ch
4

)

=

cov
⁢

(

ch
1

,

ch
2

,

ch
3

,

ch
4

)

σ
⁡
(

ch
1

)

⁢

σ
⁡
(

ch
2

)

⁢

σ
⁡
(

ch
3

)

⁢

σ
⁡
(

ch
4

)

(

Eq
.

9

)

In equation 9, the term cov(·) represents the covariance of x and y, while σ (·) defines the standard deviation of x and y, respectively. Given the fact that each variable is directly correlated to itself, the correlation coefficient matrix may be expressed as shown in equation 10.

R
=

(

1

ρ
⁡
(

ch
1

,

ch
2

)

ρ
⁡
(

ch
1

,

ch
3

)

ρ
⁡
(

ch
1

,

ch
4

)

ρ
⁡
(

ch
2

,

ch
1

)

1

ρ
⁡
(

ch
2

,

ch
3

)

ρ
⁡
(

ch
2

,
4

)

ρ
⁡
(

ch
3

,

ch
1

)

ρ
⁡
(

ch
3

,

ch
2

)

1

ρ
⁡
(

ch
3

,

ch
4

)

ρ
⁡
(

ch
4

,

ch
1

)

ρ
⁡
(

ch
4

,

ch
2

)

ρ
⁡
(

ch
4

,

ch
3

)

1

)

(

Eq
.

10

)

Averaging the non-diagonal elements of the correlation matrix gives a measure of the average correlation level experienced by all the channels in that particular range gate. The maximum correlation level (assuming that all channel noise is perfectly correlated) is then N²_ch− N_ch. In the example the maximum correlation level is 12.

FIG. 8 shows an illustrative embodiment of a calculated correlation factor 800. The underlying assumption is that the correlation coefficient is calculated for each individual range gate, even if no target detection has occurred. When the correlation level is close to zero the thermal noise is the noise source that dominates the system, while every other value greater than zero and lower than a maximum correlation level (targets) expresses an excess of phase noise that may lead to false or missed detections. The calculated normalized correlation factor may be used to adjust the threshold of the radar detector in order to account for the excess of correlated noise. For a particular range gate k (k=1 . . . N_samples), the modified threshold may be calculated as shown in equation 11. In equation 11, THLD_krepresents the threshold, THLD_{adj_k}represents the modified threshold, and nCF_krepresents the normalized correlation factor. It is noted that normalization is performed by scaling the correlation factor by the number of non-diagonal elements of the correlation coefficient matrix. For example, if there are four transmitters (NTx=4) and four receivers (NRx=4), then the scaling factor is NTx*NRx-NTx=4*4−4=12.

THLD_{adj_k}=THLD_k+nCF_k (Eq. 11)

FIG. 9 shows an illustrative embodiment of a detector threshold adjustment 900. In particular, an example is shown of the effectiveness of the presently disclosed radar system and corresponding operation method. More specifically, the left part of FIG. 9 shows that an excess of phase noise is present, while the right part shows a comparison between the default threshold (THLD) 902 calculated under the assumption of uncorrelated noise and an adjusted threshold (THLD_adj) 904, wherein the latter has been adjusted in dependence on a determined noise correlation level.

FIG. 10 shows an illustrative embodiment of an adaptive radar detection process. The radar detector 1002 searches for power values above a pre-determined threshold for all the Doppler bins, for a given range gate k. If no detections have occurred (“Detection absent”) the range gate k+1 will be analyzed. If a detection is has occurred (“Detection present”) the normalized correlation factor is calculated 1004 according to equation 12. In equation 12, NTx represents the number of transmitters, NRx represents the number of receivers, and Non-Diagonal(R) represents the non-diagonal elements of the correlation coefficient matrix. The threshold will be modified 1006 accordingly with the calculated normalized correlation factor. The radar detector 1002 is then re-evaluated with the modified threshold (i.e., with the adjusted threshold). Thus, in this example the same radar detector 1002 is used to execute both the first radar detector stage and the second radar detector stage, with different thresholds being applied. However, the skilled person will appreciate that in principle also different radar detectors (i.e., different devices or units) may be used to execute the first radar detector stage and the second radar detector stage. If no detections have occurred (“Detection absent”) the range gate k+1 will be analyzed, and the previous detection will be discarded. If a detection has occurred (“Detection present”) the next steps in the radar processing chain are executed, in particular MIMO decoding and DOA processing/estimation 1010.

n
⁢
C
⁢

F
k

=

Non
-

Diagonal
(
R
)

NTx
*
NRx

-
NTx

(

Eq
.

12

)

As mentioned above, the radar system may further comprise a plurality of transmit channels, wherein the noise correlation level determined by the noise correlation determination unit is also indicative of the noise correlation between said transmit channels. Thus, the MIMO operation may be included in the process as well. In that case, the amount of correlation that can also be experienced by the different transmit channels may be taken into account as well, and the correlation coefficient matrix may be expressed as shown in equation 13.

R
=

(

1

ρ
⁡
(

ch
1

,

ch
2

)

ρ
⁡
(

ch
1

,

ch
3

)

ρ
⁡
(

ch
1

,

ch
4

)

ρ
⁡
(

ch
2

,

ch
1

)

1

ρ
⁡
(

ch
2

,

ch
3

)

ρ
⁡
(

ch
2

,
4

)

ρ
⁡
(

ch
3

,

ch
1

)

ρ
⁡
(

ch
3

,

ch
2

)

1

ρ
⁡
(

ch
3

,

ch
4

)

ρ
⁡
(

ch
4

,

ch
1

)

ρ
⁡
(

ch
4

,

ch
2

)

ρ
⁡
(

ch
4

,

ch
3

)