Antenna selection in radar systems based on multiple detection objects and multi-step planning

Abstract

A radar system includes antenna elements and receive channels. An adaptive switch couples receive channels to a subset of the antenna elements as selected antenna elements. The selected antenna elements receive reflected signals from objects reflections, and each receive channel outputs a digital signal based on the reflected signals from the coupled selected antenna elements. A controller processes the digital signals from each receive channel to estimate a direction to each object and to produce candidate configurations of the switch. Evaluating the candidate configurations includes performing a multi-step evaluation using a decision tree rooted at each candidate configuration and checking accuracy of an output at a last step of the decision tree to select a selected candidate configuration based on the accuracy. The switch is configured according to the selected candidate configuration before receiving reflected signals of a next iteration.

Description

TECHNICAL FIELD

[0001] The subject disclosure relates to antenna selection in a radar system based on multiple detected objects and multi-step planning. BACKGROUND

[0002] Vehicles (e.g., cars, trucks, construction equipment, agricultural equipment, automated factory equipment) increasingly include sensors to acquire information about the vehicle and its surroundings. This information, for example, helps with semi-automated and automated operation of the vehicle. Exemplary sensors include cameras, light detection and ranging (lidar) systems, and radio detection and ranging (radar) systems. A multiple-input multiple-output (MIMO) radar system has multiple transmit antenna elements and multiple receive antenna elements. The number of transmit and receive channels can be less than the number of transmit and receive antenna elements. It is desirable to provide antenna selection in a radar system based on multiple detected objects and multi-step planning. SUMMARY

[0003] In one exemplary embodiment, a method includes configuring an adaptive switch to couple a plurality of receive channels to a subset of a plurality of antenna elements as selected antenna elements, and receiving reflected signals with the selected antenna elements. The method also includes processing each reflected signal received at each selected antenna element at a respective one of the plurality of receive channels to obtain a digital signal at each of the plurality of receive channels, and processing the digital signal from each of the plurality of receive channels to estimate a direction of arrival (DOA) of each object detected based on the reflected signals. A set of candidate configurations of the adaptive switch is generated for evaluation based on the DOA of each object. Evaluating the set of candidate configurations of the adaptive switch includes performing a multi-step evaluation using a decision tree, where each of the set of candidate configurations is taken as a root, and accuracy of an output is checked at a last step of the decision tree. A selected candidate configuration is selected from the set of candidate configurations of the adaptive switch based on accuracy obtained with each of the set of candidate configurations taken as a root of the decision tree. The adaptive switch is configured according to the selected candidate configuration of the set of candidate configurations of the adaptive switch before receiving reflected signals for a next iteration.

[0004] In addition to one or more of the features described herein, processing each reflected signal includes amplifying, mixing, and performing an analog-to-digital conversion on each reflected signal.

[0005] In addition to one or more of the features described herein, estimating the direction of arrival of each object includes performing an iterative process to detect two or more objects.

[0006] In addition to one or more of the features described herein, performing the iterative process includes detecting and removing the object of the two or more objects that causes the strongest reflection before removing the object before the next iteration.

[0007] In addition to one or more of the features described herein, the method further includes generating the set of candidate configurations from a set of initial configurations. Evaluating the set of initial configurations of the adaptive switch to obtain the candidate configurations is based on a DOA of each object, including determining a Bobrovski-Zakai bound (BZB) of each object.

[0008] In addition to one or more of the features described herein, determining the BZB of each object is based on implementing a Metropolis-Hastings (MH) algorithm to simulate each object.

[0009] In addition to one or more of the features described herein, the method further includes fixing all but one of the plurality of receive channels coupled to all but one of the subset of the plurality of antenna elements to leave one unfixed receive channel, and generating the set of initial configurations by sequentially coupling one unfixed receive channel to each of the plurality of antenna elements that is not coupled to all but one of the plurality of receive channels.

[0010] In addition to one or more of the features described herein, evaluating the candidate configurations by performing the multi-step evaluation using the decision tree includes using each candidate configuration as a root of the decision tree to grow a sub-tree at each step of the multi-step evaluation.

[0011] In addition to one or more of the features described herein, using the decision tree includes growing each sub-tree based on random switching.

[0012] In addition to one or more of the features described herein, selecting the selected candidate configuration is based on aggregating error statistics and computing a root mean square error (RMSE) at a last step of the multi-step evaluation to select a corresponding root as the selected candidate configuration.

[0013] In another example embodiment, a radar system includes a plurality of antenna elements and a plurality of receive channels. Each receive channel includes an analog-to-digital converter (ADC) to output a digital signal. The radar system includes an adaptive switch to couple the plurality of receive channels to a subset of the plurality of antenna elements as selected antenna elements. The selected antenna elements receive reflected signals resulting from transmitted signals transmitted by the radar system being reflected by a plurality of objects, and each of the plurality of receive channels outputs a digital signal based on the reflected signals from the selected antenna elements coupled thereto. A controller processes the digital signals from each of the plurality of receive channels to estimate a direction of arrival (DOA) of each object detected based on the reflected signals, and generates a set of candidate configurations of the adaptive switch to be evaluated based on the DOA of each object. Evaluating the set of candidate configurations of the adaptive switch includes performing a multi-step evaluation using a decision tree, where each of the set of candidate configurations is a root, and accuracy of an output is checked at a last step of the decision tree. The controller also selects a selected candidate configuration from the set of candidate configurations of the adaptive switch based on accuracy obtained with each of the set of candidate configurations as a root of the decision tree, and configures the adaptive switch according to the selected candidate configuration of the set of candidate configurations of the adaptive switch prior to receiving reflected signals for a next iteration.

[0014] Each of the plurality of receive channels further includes an amplifier and a mixer, in addition to one or more features described herein.

[0015] The controller estimates the DOA of each object based on performing an iterative process to detect two or more objects, in addition to one or more features described herein.

[0016] The iterative process includes detecting and removing an object of the two or more objects that causes a strongest reflection, and then removing the object prior to a next iteration, in addition to one or more features described herein.

[0017] The controller generates the set of candidate configurations from a set of initial configurations, and evaluates the set of initial configurations of the adaptive switch to obtain the set of candidate configurations based on the DOA of each object by determining a Bobrovski-Zakai boundary (BZB) of each object, in addition to one or more features described herein.

[0018] The controller determines the BZB of each object based on implementing a Metropolis-Hastings (MH) algorithm to simulate each object, in addition to one or more features described herein.

[0019] In addition to one or more of the features described herein, the controller fixes all but one of the plurality of receive channels coupled to all but one of the subset of the plurality of antenna elements to leave one unfixed receive channel and generates an initial set of configurations by sequentially coupling one unfixed receive channel to each of the plurality of antenna elements that is not coupled to all but one of the plurality of receive channels.

[0020] In addition to one or more of the features described herein, the controller evaluates the set of candidate configurations by performing a multi-step evaluation using a decision tree that grows a sub-tree at each step of the multi-step evaluation by using each of the set of candidate configurations as a root of the decision tree.

[0021] In addition to one or more of the features described herein, the controller uses the decision tree by growing each sub-tree based on random switching.

[0022] In addition to one or more of the features described herein, the controller selects the selected candidate configuration based on aggregating error statistics and computing a root mean square error (RMSE) at a last step of the multi-step evaluation to select a corresponding root as the selected candidate configuration.

[0023] The above features and advantages and other features and advantages of the present disclosure are readily apparent from the following detailed description when taken in connection with the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0024] Other features, aspects, and details of the present disclosure can be described in or apparent from the following detailed description, which is to be taken in connection with the accompanying drawings.

[0025] Figure 1 is a block diagram of a vehicle according to one or more embodiments that employs antenna selection based on a plurality of detected objects and a multi-step plan in a radar system;

[0026] Figure 2 is a block diagram of an exemplary receive portion of a radar system according to one or more embodiments that performs antenna selection based on a plurality of detected objects and a multi-step plan; and

[0027] Figure 3 is a flowchart of a method of determining a switch matrix for a given transmit and receive iteration of a radar system according to one or more embodiments. DETAILED DESCRIPTION

[0028] As previously mentioned, multiple types of sensors can be used in a vehicle. Certain applications require a higher angular resolution than others. Angular resolution refers to the angular accuracy from a point on the vehicle (i.e., direction of arrival, DOA) to an object. For example, autonomous driving applications require a higher angular resolution than other applications because the information obtained by the sensors about the objects surrounding the autonomous vehicle is critical for the proper operation of the autonomous vehicle. The data density provided by a lidar system helps to obtain the necessary angular resolution. However, a lidar system is more expensive than, for example, a radar system and the cost is prohibitive in consumer applications. A suite of several (e.g., three to seven) radar systems can also achieve the necessary angular resolution but can also prove to be cost prohibitive.

[0029] Embodiments of the systems and methods detailed herein relate to antenna selection in a radar system based on multiple detected objects and a multi-step planning. For high resolution imaging radars, a radar system with a large aperture array (i.e., a large number of antenna elements) is desirable, but the transmit and receive channels to acquire and initially process the signals received by the antenna elements can be cost prohibitive. Thus, as detailed, the number of transmit and receive channels is less than the full set of antenna elements and a switching scheme is used to couple a set of transmit and receive channels to a subset of the available antenna elements. According to one or more embodiments, the switching is based on a multi-step planning and also takes into account scenarios where multiple objects are detected. Multi-step planning means that a decision tree is used to consider the accuracy of the DOAs obtained for each switching scenario after more than one transmit and receive cycle. Thus, the given switching scenario selected for the next step (i.e., the next transmit and receive cycle) is based on the accuracy resulting from multiple steps of the decision tree.

[0030] According to exemplary embodiments, Figure 1 is a block diagram of a vehicle 100 employing antenna selection in a radar system 110 based on multiple detected objects 150a, 150b (generally referred to as 150) and a multi-step planning. Figure 1 The exemplary vehicle 100 shown is an automobile 101. The vehicle 100 includes a radar system 110 having a transmit portion 105, a receive portion 115, and a radar controller 120. For example, the radar system 110 can be a multiple-input multiple-output radar system. The vehicle 100 can include one or more other sensors 140 (e.g., cameras, lidar systems) to obtain information about the objects 150 or the vehicle 100 itself. The transmit portion 105 of the radar system 110 emits a transmit signal 106 and the receive portion 115 of the radar system 110 receives a reflected signal 116. The reflected signal 116 is a portion of the transmit signal 106 that is reflected by an object 150 in the field of view of the radar system 110. Reference is made to Figure 2 The receive portion 115 is described in further detail.

[0031] The controller 130 can obtain information from the radar system 110 and one or more other sensors 140. The controller 130 can control semi-automated or automated operation of the vehicle 100 based on this information. The antenna selection detailed herein can be performed by the radar controller 120 alone or in conjunction with the controller 130. The radar controller 120 and the controller 130 can comprise processing circuitry, which can include an application-specific integrated circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group), and a memory that executes one or more software or firmware programs, a combinational logic circuit, and / or other suitable components that provide the described functionality.

[0032] Figure 2 is a block diagram of an exemplary receive portion 115 of a radar system 110 that performs antenna selection based on a plurality of detected objects 150 and a multi-step plan, in accordance with one or more embodiments. The receive portion 115 includes receive antenna elements 210-1 through 210-N (generally referred to as 210). The receive portion 115 also includes receive channels 230-1 through 230-M (generally referred to as 230). As shown for receive channel 230-1, each receive channel 230 generally includes an RF amplifier 231 that amplifies a received radio frequency (RF) signal (i.e., a portion of the received reflections 116 detected by the corresponding receive antenna element 210). A mixer 232 converts the received RF signal to an intermediate frequency (IF) signal, which is amplified by an IF amplifier 233. An analog-to-digital converter (ADC) 234 provides a digitized signal to a controller (i.e., the radar controller 120 and / or the controller 130) for processing.

[0033] The number N of receive antenna elements 210 is greater than the number M of receive channels 230. Accordingly, an adaptive switch 220 couples some or all of the M receive channels 230 to a respective subset of the N receive antenna elements 210 at a given time. For purposes of explanation, it is assumed that M receive antenna elements 210 corresponding to M receive channels 230 (rather than fewer than M receive channels 230) are selected in each transmit and receive iteration of the radar system 110. The selection of receive antenna elements 210 to be operated is based on an adaptive switch 220, which can be implemented, for example, in the form of a switch matrix G. The switch matrix G can be updated by processing of the radar controller 120 or the controller 130, as described in further detail with reference to Figure 3 The switch matrix G is provided in view of any number of detected objects 150 and in accordance with a multi-step plan, as previously described.

[0034] Figure 3is a flowchart of a method 300 of determining a switch matrix G for a given transmit and receive iteration of a radar system 110 according to one or more embodiments. At block 310, the process includes obtaining and sampling a reflected signal 116 with a receive antenna element 210 selected according to a switch matrix G K-1 set for a most recent transmit and receive iteration K-1, where iteration is k = 1,..., K-1. At block 320, a DOA of each object 150 detected based on the reflected signal 116 received at iteration K-1 is estimated.

[0035] At block 330, a process is performed to generate a set of candidate switch matrices {G K} from which a switch matrix G K will be selected for use in a next transmit and receive iteration K. At block 340, a multi-step planning is performed with the set of candidate switch matrices {G K}. For example, a decision tree is developed in which each candidate of the set of candidate switch matrices {G K} serves as a root. At block 350, the root (i.e., the candidate of the set of candidate switch matrices {G K} associated with a best sub-tree is selected as the switch matrix G K for the next transmit and receive iteration K. The best sub-tree refers to a sub-tree that produces the most accurate DOA estimates at a last level of the decision tree. Each of these processes will be further detailed.

[0036] At block 310, the process includes obtaining and sampling a reflected signal 116 at iteration (K-1). Each receive antenna element 210 selected according to a switch matrix G K-1 at iteration (K-1) obtains a portion of the reflected signal 116 (i.e., a received signal) and provides the received signal to a corresponding receive channel 230. A baseband model or vector of the received signal using M of the N receive antenna elements 210 and obtaining J samples is given by:

[0037]

[0038] The index K refers to a transmit and receive iteration (e.g., (K-1)), and the index j refers to samples 1 through J. In Equation 1, A is an array of steering vectors each steering vector corresponds to a direction of a received signal to a receive antenna element 210 that obtains a portion of the reflected signal 116. Steering vectors with higher power suggest an estimate of a DOA. One known multiple signal classification (MUSIC) algorithm is a frequency estimation method for distinguishing closely spaced objects 150 that uses steering vectors in DOA estimation, as detailed with reference to block 320.

[0039] The signal sequence s in Equation 1 jk and noise sequence υ jk are independent of each other and have a covariance matrix:

[0040] cov(s jk )=R s (Equation 2)

[0041]

[0042] The signal covariance matrix is ​​Rs in Equation 2. In Equation 3, the identity matrix I M The size is M, where M is the number of receive channels 230, and the square of the QIE noise is considered to be known. At the Kth iteration the vector x jk (e.g., k-1 iterations) to form the observation matrix X k =[x 1k ,...,x Jk ]. Therefore, the current and past observation matrices [X1,...,X K-1 ] is available in box 310.

[0043] At block 320 , the angle relative to each detected object 150 is estimated. The DOA estimation algorithm (e.g., DOA estimation) includes an iterative process in which the object 150 associated with the current strongest signal is detected and then removed to facilitate detection of the object 150 associated with the next strongest signal. This is referred to as the CLEAN algorithm. As previously mentioned, DOA estimation also uses the MUSIC algorithm for detection classification. Therefore, using MUSIC-CLEAN, the MUSIC algorithm is used to estimate the DOA of the object 150 associated with the strongest signal at each iteration according to the CLEAN algorithm.

[0044] At each iteration k, J samples are clustered to construct the covariance matrix:

[0045]

[0046] In Equation 4, H represents the Hermitian transpose. The DOA of the object 150 associated with the strongest signal is Estimated as cumulative MUSIC 1,k＝1,...,K-1 The MUSIC algorithm is cumulatively used over K-1 iterations to estimate the DOA of the object 150 with the strongest signal. In the exemplary case of only two objects 150, the estimate of the DOA of the weak object 150 is obtained by subtracting the contribution of the strong object 150 from the received signal spectrum, and is given by:

[0047]

[0048] The singular value decomposition (svd) in equation 5 produces singular value vectors.

[0049]

[0050]

[0051]

[0052] DOA of object 150 associated with weak signals is estimated as the cumulative MUSIC 2,k＝1,...,K-1 in response to the pattern. That is, the DOA of the object 150 with weaker signals is estimated cumulatively using the MUSIC algorithm in K-1 iterations According to an exemplary case, the object is the only other object 150.

[0053] At block 330, the process includes generating a set of candidate switch matrices {G K The complete set of candidates would include every possible combination of M receive antenna elements 210 out of the complete set of N receive antenna elements 210. However, rather than evaluating every combination of M out of N receive antenna elements 210, a set of initial combinations is first evaluated, as detailed, to select the set of candidate switch matrices {G K} at block 330. For the candidate switch matrices {G K} a decision tree is generated (at block 340) to ultimately select the next M receive antenna elements 210 (at block 350) that will be defined by the switch matrix G K

[0054] ​At block 330, initial combinations are generated by fixing the receive antenna elements 210 corresponding to all but one of the M receive channels 230 (i.e., for M-1 receive channels 230). Then, each of the (N-M-1) remaining receive antenna elements 210 is added to the fixed set in turn to generate each initial combination. According to an exemplary embodiment, fixing can mean preserving (i.e., the receive antenna elements 210 corresponding to M-1 receive channels 230 are preserved from the previous iteration). According to an example for explanatory purposes, M=3 and N=5, such that there are three receive channels 230 and five receive antenna elements 210 A1, A2, A3, A4, and A5. Assuming A3 and A5 are fixed as the receive antenna elements 210 for two receive channels 230, then each of A1, A2, and A4 is added to A3 and A5 to generate initial combinations. That is, A1, A3, and A5 are one initial combination of receive antenna elements 210, A2, A3, A5 are a second initial combination of receive antenna elements 210, and A4, A3, and A5 are a third initial combination of receive antenna elements 210.

[0055] Continuing with the process at block 330, after the initial combinations of receive antenna elements 210 are generated, a set of candidate switch matrices {G K} is generated that represents a subset of the initial combinations of receive antenna elements 210. The criterion for evaluating the initial candidates is the Bobrovski-Zakai Bound (BZB). The Metropolis-Hastings (MH) algorithm is used to simulate the objects 150 for detection. Specifically, the MH algorithm is used twice to generate one-dimensional samples where i = 1, 2 in the exemplary case of two objects 150. When i = 1, the parameters of the strong object 150 and the covariance matrix of equation 9 (below) are used. When i = 2, the parameters of the weak object 150 and the covariance matrix of equation 10 (below) are used.

[0056] For each n, where n is the index of the number of objects 150, the BZB is evaluated on the DOA estimation error. For the typical case of two objects, the BZB is combined with the CLEAN algorithm for a two-step BZB-CLEAN bound estimation. In the first step, the BZB is derived for the strong object 150 (i.e., the object 150 corresponding to the stronger signal) by subtracting the contribution of the weak object 150. Then, in the second step, the BZB is derived for the weak object 150 by subtracting the contribution of the strong object 150. In each step, the covariance matrix is obtained:

[0057]

[0058]

[0059] That is, for each initial combination of receive antenna elements 210, the covariance matrix of each equation 9 and 10 is used to obtain BZB1 and BZB2, respectively. BZB1 and BZB2 are evaluated independently, such that only candidates with high scores for both BZB1 and BZB2 are of interest. A predetermined number of initial combinations with the highest {BZB1, BZB2} can be retained, or all initial combinations with {BZB1, BZB2} exceeding a predetermined threshold can be retained as candidate switch matrices {G K}.

[0060] The process at block 330 can be repeated by fixing the receive antenna elements 210 corresponding to all but a different one of the M receive channels 230 for each iteration. Once candidate switch matrices {G K} specifying an initial candidate subset of receive antenna elements 210 are obtained, a multi-step planning process is performed at block 340. Each candidate switch matrix from the set of candidate switch matrices {G K} is located at the root level of a decision tree. Sub-trees (i.e., additional levels) are grown by random switch growth. That is, a random combination of the M receive antenna elements 210 is the next level of the decision tree. After a decision tree of a predetermined depth is developed, the final level is evaluated based on aggregated error statistics and computing the root mean square error (RMSE) for each combination of each sub-tree. The sub-tree with the smallest RMSE is traced back to its root to select one of the candidate switch matrices {G K} at block 350.

[0061] While the foregoing disclosure has been described in reference to exemplary embodiments, it will be understood by those skilled in the art that various changes can be made and equivalents can be substituted for elements thereof without departing from the scope thereof. In addition, many modifications can be made to adapt a particular situation or material to the teachings of the disclosure without departing from the central scope thereof. Therefore, it is intended that the disclosure not be limited to the particular embodiment disclosed, but will include all embodiments falling within the scope of the disclosure.

Claims

1. A method of antenna selection in a radar system based on a plurality of detected objects and a multi-step planning, comprising: configuring an adaptive switch to couple a plurality of receive channels to a subset of a plurality of antenna elements as selected antenna elements; receiving reflected signals with the selected antenna elements; processing each reflected signal received on each selected antenna element on a corresponding one of the plurality of receive channels to obtain a digital signal on each of the plurality of receive channels; processing the digital signals from each of the plurality of receive channels to estimate a direction of arrival (DOA) of each object detected based on the reflected signals; generating a set of candidate configurations of the adaptive switch to be evaluated from a set of initial configurations based on the direction of arrival of each object, wherein evaluating the set of initial configurations of the adaptive switch to obtain the set of candidate configurations is based on the direction of arrival to each object, including determining a Bobrovski-Zakai boundary (BZB) to each object, wherein evaluating the set of candidate configurations of the adaptive switch includes performing a multi-step evaluation using a decision tree, and checking accuracy of an output of a last step in the decision tree, wherein each of the set of candidate configurations is taken as a root; selecting a selected candidate configuration from the set of candidate configurations of the adaptive switch based on accuracy obtained with each of the set of candidate configurations as a root of the decision tree; and configuring the adaptive switch according to the selected candidate configuration of the set of candidate configurations of the adaptive switch prior to receiving reflected signals for a next iteration.

2. The method of claim 1, wherein processing each reflected signal includes amplifying, mixing, and performing an analog-to-digital conversion on each reflected signal.

3. The method of claim 1, wherein estimating the direction of arrival of each object includes performing an iterative process to detect two or more objects, and performing the iterative process includes detecting and removing an object of the two or more objects that causes a strongest reflection, and then removing the object prior to a next iteration.

4. The method of claim 1, further comprising fixing all but one of the plurality of receive channels coupled to all but one of the subset of the plurality of antenna elements to leave one unfixed receive channel, and generating the set of initial configurations by sequentially coupling one unfixed receive channel to all but one of the plurality of antenna elements, wherein determining the BZB to each object is based on implementing a Metropolis-Hastings (MH) algorithm to simulate each object.

5. The method of claim 1, wherein evaluating the set of candidate configurations by performing a multi-step evaluation using a decision tree comprises using each candidate configuration of the set of candidate configurations as a root of a decision tree to grow a sub-tree at each step of the multi-step evaluation, using the decision tree comprises growing each sub-tree based on random switching, and selecting the selected candidate configuration selects a respective root as the selected candidate configuration based on aggregating error statistics and computing a root mean square error (RMSE) at a last step of the multi-step evaluation.

6. A radar system comprising: a plurality of antenna elements; a plurality of receive channels, each receive channel comprising an analog-to-digital converter (ADC) to output a digital signal; an adaptive switch configured to couple the plurality of receive channels to a subset of the plurality of antenna elements as selected antenna elements, wherein the selected antenna elements are configured to receive reflected signals resulting from a plurality of objects reflecting a transmitted signal transmitted by the radar system, and each of the plurality of receive channels is configured to output a digital signal based on the reflected signals from the selected antenna elements coupled thereto; and a controller configured to process the digital signals from each of the plurality of receive channels to estimate a direction of arrival (DOA) for each object detected based on the reflected signals, to generate a set of candidate configurations for the adaptive switch to be evaluated from a set of initial configurations, and to evaluate the set of initial configurations for the adaptive switch to obtain the set of candidate configurations based on the direction of arrival for each object by determining a Bobrovski-Zakai boundary (BZB) for each object, wherein evaluating the set of candidate configurations for the adaptive switch comprises performing a multi-step evaluation using a decision tree, and checking accuracy of an output at a last step of the decision tree, wherein each of the set of candidate configurations is a root, to select a selected candidate configuration from the set of candidate configurations for the adaptive switch based on accuracy obtained with each of the set of candidate configurations as a root of the decision tree, and to configure the adaptive switch according to the selected candidate configuration of the set of candidate configurations for the adaptive switch prior to receiving reflected signals for a next iteration.

7. The radar system of claim 6, wherein each of the plurality of receive channels further comprises an amplifier and a mixer.

8. The radar system of claim 6, wherein the controller is configured to estimate the direction of arrival for each object based on performing an iterative process to detect two or more objects, and the iterative process comprises detecting and removing an object of the two or more objects that causes a strongest reflection, and then removing that object prior to a next iteration.

9. The radar system of claim 6, wherein, The controller is configured to determine the BZB for each object by simulating each object based on implementing a Metropolis-Hastings (MH) algorithm, and fixing all but one of the receive channels coupled to all but one of the subset of the plurality of antenna elements, leaving one unfixed receive channel, and generating a set of initial configurations by sequentially coupling one unfixed receive channel to each of the plurality of antenna elements that is not coupled to all but one of the plurality of receive channels.

10. The radar system of claim 6, wherein the controller is configured to evaluate the set of candidate configurations by using a decision tree by using each of the set of candidate configurations as a root of the decision tree to perform a multi-step evaluation by growing a sub-tree at each step of the multi-step evaluation, using the decision tree by growing each sub-tree based on random switching, and selecting the selected candidate configuration based on aggregated error statistics and computing a root mean square error (RMSE) at a last step of the multi-step evaluation to select a corresponding root as the selected candidate configuration.

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