Multichannel Repeater for Coherent Radar Networks Enabling High-Resolution Radar Imaging

Coherent radar networks allow for spanning very large apertures that include all sensors with their subapertures in the network, resulting in very good angular resolution. However, as a radar network typically has a sparse array, its performance depends on the flexibility of the antenna and network node placement. Thus, in this work, a new type of radar network is presented, allowing for a highly flexible network and array design and providing an excellent performance in direction-of-arrival (DoA) estimation. This is reached by using multichannel repeaters (MCRs) in combination with a single multiple-input multiple-output (MIMO) radar. The multichannel repeaters (MCRs) receives the radar’s signal via a line-of-sight path, and then re- transmits it via multiple transmit channels, each with a dedicated mixer used for multiplexing. To show the feasibility and the performance of this concept, a 77- $\mathrm { \text {G} \text {Hz} }$ radar network consisting of a digital $4\,\, \times 4$ multiple-input multiple-output (MIMO) radar and two four-channel MCRs is presented. It is designed following network array design recommendations mathematically derived in this work and combined with an adapted signal processing and network-based direction-of-arrival (DoA) estimation. The high performance of the system is demonstrated not only via systematic measurements in an anechoic chamber, but also in various automotive scenarios including multiple road users.


I. INTRODUCTION
D RIVEN by the advances in autonomous driving, recent research shows a rapid development in the imaging capacities of radars.This not only includes the measurement of range and radial velocity, but also an improved estimation of the angle of the target [1], [2].This is accomplished by expanding the virtual aperture of the radar either by increasing the number of transmit (Tx) and receive (Rx) channels or by designing a network of cooperative radar sensors.
Recent publications discuss multiple-input multiple-output (MIMO) radars with more than 100 [3], [4], [5] or even up to 1700 [6] virtual channels, typically achieved by using a radar frontend with multiple transceiver chips.While these approaches show a high performance in terms of radar imaging, they also lead to large, inflexible hardware designs, as all channels must be placed on a single printed circuit board (PCB).Thus, often the capabilities of MIMO radars are not limited due to technical reasons, but due to limitations in placement and available space, which is especially true for automotive applications [5].
With the radar network approach, this drawback can be overcome.As multiple cooperative radars are combined, the number of channels per radar and thus their size can be reduced.The benefits of radar networks are most significant when coherency is established [2], [7], i.e. when phase coherency is achieved between signals from different radar nodes.Then, a bistatic evaluation is possible without performance degradation caused by phase noise as in incoherent networks [8], [9].Furthermore, the signals of several nodes can be combined for phase coherent direction-of-arrival (DoA) estimation and thus the additional radars in the network lead to the same benefit as additional channels on a MIMO radar.
While first efforts in coherent radar networks mainly include widely distributed multistatic radar systems [7], [10], [11] and coherent multistatic synthetic aperture radars (SARs) [12], [13], [14], recently these systems became a competitor of massive MIMO systems as they allow to build up extended apertures for DoA estimation.However, the approaches differ in system and array design as well as in their way of achieving coherency.An overview is given in Table I.
In [15], a system is proposed where a reference clock is shared among multiple frequency modulated continuous wave (FMCW) radars.Based on this low-frequency coupling, a coherent DoA estimation including the use of the bistatic signals is possible.However, a distribution network for the reference clock is necessary, and additional phase noise generated by each radar's phase-locked loop (PLL) and voltage-controlled oscillator (VCO) cannot be eliminated.The work in [16] shows that coherent DoA estimation is possible in an uncoupled radar network, but it still suffers from a phasenoise-induced performance loss.
In [17] and [18], radar-repeater networks are introduced for FMCW as well as digital orthogonal frequency-division multiplexing (OFDM) radars.These networks consist of a single radar and several repeaters.The repeaters receive the radar's Tx signal reflected at the target.Then, they modulate and re-transmit the signal.After a second reflection at the target, the bistatic signal is received and evaluated by the radar.This type of network will be referred to as a symmetric-path radar-repeater network from here on.The repeaters do not down-convert the signal, thus, all mono-and bistatic signals are fully coherent and can be directly used for DoA estimation.Since no connection between the network nodes is necessary, these networks are highly flexible.However, due to the double reflection at the target, they suffer from high path losses for the bistatic signals.
In [19] and [20], the coherency in a network of FMCW radars is achieved by sharing a trigger and a clock, thus leading to a low-frequency coupled setup.Coherent signal processing is achieved by estimating and correcting the phase offset algorithmically.Two different approaches are presented for the exploitation of the network.In [19], all mono-and bistatic virtual apertures are combined, leading to a virtual network array (VNA) consisting of four uniform linear array (ULA) subapertures.While this results in a very large network aperture, due to the combination of several ULAs with gaps in between, it suffers from a high sidelobe level (SLL).In contrast, in [20], only the bistatic arrays are combined to a single ULA.This way, the SLL is massively reduced, but at the expense of highly reduced aperture size compared to the use of the full network.Thus the potential of the network in terms of angular resolution is not fully exploited.
When analyzing the relationship between array and position of the network nodes, the resulting VNA, and the networkbased DoA estimation, it is shown that for a proper DoA estimation a radar network allowing for a flexible VNA design is crucial.This is not possible with the networks presented in [15], [16], and in [19], [20], as the bistatic subarrays will always be in the middle of the two monostatic subarrays.
Thus, in this work, a new architecture for coherent radar networks is proposed.It uses a combination of a radar with a new type of repeater node.Instead of feeding the repeater via a reflection at the targets as proposed in [17] and [18], it is fed by a direct line-of-sight (LoS) between radar and repeater.This way, the bistatic path losses are drastically reduced, while the advantages of flexible low-cost repeater nodes remain.This new system architecture is combined with a new repeater design, a so-called multichannel repeater (MCR).Each MCR consists of one Rx antenna, after which the signal is split up into multiple independent modulated Tx channels.This way, multiple Tx antennas per repeater are used, leading to an improved VNA.Using the MCR concept, a radar network is designed.It consists of two fourchannel MCRs and a 77 GHz 4 × 4 MIMO OFDM radar.The virtual aperture of the network has a size of 239 λ/2, which, according to the Rayleigh criterion [1], leads to a theoretical target separability of 0.584 • in azimuth, while an SLL of −6.8 dB before compressed sensing (CS) is achieved.The network is combined with an adapted signal processing.Its high DoA estimation and imaging performance are not only systematically evaluated in an anechoic chamber, but also successfully in practical scenarios.
The article is structured as follows.At first, the concept of the VNA and considerations regarding the design of a radar network's array are introduced in Section II.This is followed by a detailed description of the proposed radar network concept and signal processing in Section III.The network-based DoA estimation is explained in Section IV.Then, Section V describes the design of the 77-GHz system, including the design of the MCR and the network setup.Finally, Section VI provides a detailed evaluation of the proposed system based on measurements.

II. NETWORK ARRAY DESIGN
The virtual array of a single MIMO radar is calculated based on the spatial convolution of the Tx antenna positions and the Rx antenna positions of the radar [21], [22].To extend this model to the VNA, the various nodes, i.e. the sensors in the network, and their positions have to be taken into account.

A. Virtual Network Array
A VNA is the virtual array of the entire network and thus determines the sampling of the phase values used for the network-based DoA estimation.It is defined based on a spatial grid, which typically is a λ/2-grid.The position of each of the N nw network nodes is described by the vector d nw ∈R N nw .Each kth element d nw [k] equals the position in the spatial grid of the first virtual antenna of the kth node.Furthermore, each node has its own subarray, describing the positions of the node's N sub virtual antennas in the spatial grid as d sub,k ∈R N sub , k = 1, 2, . . ., N nw .The VNA is then calculated by which equals a spatial convolution of the position of each node with the virtual antenna positions in their respective subarray.
The notation is shown in Fig. 1 using the example of a network with three subarrays, each consisting of four virtual antennas.

B. Analysis
As the VNA typically is a sparse array with several subarrays in blocks and gaps in between, it very likely exhibits an ambiguity function [23] with a high SLL.This problem exists in previous works like [17], [18], and [19].In this section, the relationship between the VNA design and the SLL is analyzed and design recommendations are derived.
In the following, a simple network consisting of N nw nodes with identical subarrays of size l sub and antennas in a λ/2-grid is considered, leading to a normalized subarray size of For ULA-subarrays, L sub = N sub − 1 applies.For sparse subarrays, additionally the empty antenna positions within the subarray have to be taken into account.
A DoA estimation based on the Fourier transform [24] is assumed.A target at angle θ introduces a phase progression along the virtual antenna elements in the VNA with an angular frequency of equaling the phase offset between adjacent virtual antennas in the grid.This phase progression now is sampled by a VNA consisting of N nw subarrays.Each subarray is described by a subarray function w(x) equaling the antenna positions in the subarray as a window function centered at the position d nw [k] + l sub /2.The subarray function w(x) may account for the gaps in sparse subarrays as well as for an optional subarray tapering.In case of an non-tapered ULA-subarray, w(x) equals a rectangular function rect(x).The Fourier transform of the angle-dependent phase progression sampled by the VNA, the so-called steering vector γ(x), thus equals the angular spectrum ( ) as in ( 4) and ( 5), shown at the bottom of the page.
Three factors determine the Fourier transform and thus target separability and SLL: the subarray function w(x), the size l sub of the subarrays, and the positions of the subarrays d nw [k].Their influence on the SLL can be shown by the example of a simple network of two non-tapered ULA-subapertures [w(x) = rect(x)], which was used, e.g., in [17] and [18].Assuming d nw [1] = 0, N nw = 2, and W ( ) = si( ), (5) simplifies to ( ) 1 + e −j d nw [2] .
The DoA estimation is then based on the absolute value of the Fourier transform.With 1 + e −j d nw [2]  = 2 cos( d nw [2]) + 2 (7) the absolute value of the angular spectrum becomes The sinc function si( (l sub /2)) equals the angular spectrum when only using one subarray and no network.Due to the multiplication with (2 cos( d nw [2]) + 2) 1/2 , the main lobe becomes narrower with increasing d nw [2], which increases the target separability.However, also the SLL is significantly increased.Fig. 2(a) shows the example of a VNA with a size of 239 λ/2 consisting of two ULA subarrays with N sub = 16 virtual antennas each.A DoA estimation is simulated for a target at 0 • .The SLL equals −0.1 dB, which makes this exemplary VNA barely usable.

C. Interpretation
The previous analysis has clearly shown that an array consisting of two ULA subapertures does not lead to a satisfactory Steering vector: node position network (5) Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.imaging performance.Therefore, recommendations for the design of radar networks are derived in the following.1) By using at least three subarrays, the multiplication with the term (2 cos( d nw [2]) + 2) 1/2 can be avoided.Instead, (5) includes a sum of several exponential terms, each containing the respective node position.When using proper distances between the subarrays, the exponential terms may sum up destructively at the sidelobes.This becomes obvious when comparing the examples in Fig. 2(a) and (b), where the SLL is improved from −0.1 to −2 dB by adding a third subarray at a position between the other two.The position of the middle node is crucial, thus the one resulting in the lowest SLL is chosen.2) With the use of a sparse subaperture, the relation between the subaperture size l sub and the size of the gaps in between can be improved.This can be clearly seen when comparing the examples in Fig. 2(b) and (c).Again, three subarrays with 16 virtual antennas each are used, but they are sparse with a size of l sub = 65 λ/2.This way, the SLL is further reduced to −6.8 dB. 3) When choosing the distances between the subarrays, the trade-off between the size of the VNA and the SLL has to be considered.4) Subarray tapering may not be helpful when using small subarrays, as the loss of power at the outer virtual antenna elements can decrease the performance.Using, for example, a Hann window for each subarray in Fig. 2(b) increases the SLL to −0.7 dB.

III. NETWORK CONCEPT
To provide a high-resolution network-based DoA estimation with a low SLL, a network that allows to create a VNA according to the recommendations proposed in Section II is needed.Thus, a concept for a coherent radar network allowing for a highly flexible array design while providing a good link budget is presented.

A. System Concept
The proposed radar network uses a single radar in combination with a new type of repeater, the so-called MCR.In contrast to the repeater presented in [17] and [18], the MCR receives its input signal from the radar via a direct LoS, as illustrated in Fig. 3, forming a so-called triangular path configuration.The receive signal of the MCR is then distributed to the MCRs different Tx channels.Each channel has its own mixer, which is fed with a modulation signal in the kilohertz region.This way, each channel can be modulated by a different frequency, which allows for a multiplexing of the signals.Due to the low modulation frequency, no significant phase noise is added.
The bistatic signals from the MCR are then transmitted into the channel, and, after a reflection at the targets, are received by all radar Rx channels.The virtual subarray of an MCR can therefore be calculated by a convolution of the MCRs transmit channel positions and the radar Rx array.Principally, the system concept allows for an arbitrary number of MCR, only restricted by the condition, that a good LoS between the radar and each MCR can be established.Also the number of channels per repeater is not restricted by the concept.However, the multiplexing strategy must be considered.

B. Multiplexing
By using an OFDM radar, a straightforward multiplexing based on subcarrier interleaving is made possible [25].The OFDM signal consists of N orthogonal subcarriers in a frequency spacing of f and M OFDM-symbols [26], [27].To assure the orthogonality of the subcarriers, each OFDM symbol has the length T = 1/ f .In each OFDM symbol, each subcarrier is modulated by a complex modulation symbol d Tx .These modulation symbols can be combined to Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.a matrix D Tx ∈ C N ×M .For further details regarding OFDM radar signal processing, it is referred to [28].
To enable multiplexing at the radar transmitter, for each radar Tx channel k, an individual modulation matrix D k Tx is used.In the case of frequency-division multiplexing (FDM), as in this work, they differ in the subcarriers used for the respective transmitter.The repeater Tx channels are then included in the modulation by leaving empty subcarriers in the radar's Tx signals, which the repeater are using for their transmit signal.Analogously to [18], the modulation frequency of each repeater channel k is thus an integer multiple of the subcarrier spacing.To assure orthogonality, h k must be different for each channel.Furthermore, in the radar Tx signal, there must remain empty subcarriers leaving room for the MCR signals.When using double-sideband (DSB) mixers in the MCR, both the upper and lower sidebands of each repeater channel must be considered.Furthermore, for the recovery of the phase of the modulation signal, a repeater Tx channel must transmit onto two different subcarriers, which is explained in detail in Section IV-A.If multiple modulation signals are derived from the same signal source and thus are aligned in phase, which, e.g., can be the case for all channels on the same repeater, this is only necessary for one channel per signal source.Overall, while in the channel all subcarriers are fully occupied, an OFDM signal sparse in subcarrier direction is transmitted at each Tx antenna of the radar or an MCR, which ensures orthogonality between the different signals from different Tx antennas.In Fig. 4, the subcarrier assignment is exemplarily shown for a network consisting of a radar with four transmitters and two four-channel repeaters with singlesideband (SSB) mixers.
In general, considering a network of a radar with N Tx,radar transmitters and N MCR repeaters with N Tx,MCR channels each and one modulation signal source per repeater, only every n Tx th channel is used for the same Tx channel, which A drawback of this multiplexing strategy is that the unambiguous range is reduced by the factor n Tx .However, in [29], other multiplexing techniques with a lower reduction of unambiguous range are presented for symmetric-path radar-repeater networks, which could also be adapted for the MCR network proposed here.

C. Signal Processing
Analogously to standard OFDM radar signal processing [28], at first, the sampled Rx signal is reshaped to a matrix containing one OFDM symbol per column and the cyclic prefix (CP) is removed.The CP is the guard interval included in the transmit signal before every OFDM symbol [28].By performing a column-wise fast Fourier transform (FFT), the matrix is transformed into the symbol domain receive matrix In the next step, the different mono-and bistatic channels are separated and the transmit symbols are removed.The receive signal initially contains all signals from all Tx channels in the network.To evaluate a specific one, only the correct subcarriers assigned to this signal must be evaluated.For the monostatic signal, this is done straightforward by an element-wise multiplication (⊙) of the receive matrix D Rx with the complex conjugate (denoted as (•) * ) of the transmit matrix D k Tx by As D k Tx includes zeros on all subcarriers not used by kth transmit channel, only the wanted subcarriers are evaluated.Afterwards, the complex radar image I for the monostatic channels is calculated by performing a row-wise FFT and a column-wise inverse fast Fourier transform (IFFT) [28].
In case of the bistatic channels, the frequency shifts by the repeaters have to be considered.This is done by at first shifting the transmit matrix of the LoS channel D LoS Tx by the modulation factor h = f mod / f in subcarrier direction.This shifted matrix is defined as D LoS Tx (h).Then, analogously to (11), the division matrix D bi Div (h) of the respective bistatic signal is calculated by Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
In the example in Fig. 4 as well as in the network presented in Section V, Tx4 is used for the LoS.In this case, it holds that D LoS Tx (0) = D 4 Tx .Afterwards, the phase shift induced by the modulation signal during each cyclic prefix is corrected by means of a correction vector [18] κ(h) = e −j2π hT CP /T , e −j4π hT CP /T , . . ., e −jM2π hT CP /T .(13) For the correction, every mth column of D bi Div (h) is multiplied by the mth element of κ(h).For further details, it is referred to [18, Sec.III.B].Then, analogously to the monostatic evaluation, the bistatic radar image I (h) can be calculated by performing a row-wise FFT and a column-wise IFFT.

D. Comparison to Symmetric Path Radar-Repeater Networks
In the following, a short overview over the differences between the triangular-path repeater network using MCR proposed in this work and the symmetric path radar-repeater network from [17] and [18] is given.
1) Path Loss: For the MCR, the path loss between the MCR Tx and the radar Rx approximately equals the path loss of a monostatic radar and can be estimated using the radar equation.Additionally, loss caused by the LoS path with length d LoS has to be considered, which leads to an MCR Rx power of where P Tx,LoS is the LoS Tx power of the radar, G ant,LoS the antenna gain of the LoS antennas, and λ the wavelength of the radio frequency (RF) carrier.With a sufficient repeater gain, this loss can be compensated, achieving the same detection range as with monostatic radars.In contrast, using a symmetric path radar-repeater network, both the path from the radar to the repeater and back contain a reflection at the targets.This leads to a 1/R 8 dependency of the path loss considering point targets.The networks from [17] and [18] are therefore only suitable for short-range applications.
2) Array Design: In this work, each MCR provides an additional array of Tx antennas, creating a virtual subarray which can be calculated by the spatial convolution of the MCR's Tx array and the radar's Rx array.If required, the Tx array of each MCR can be individually designed, leading to a high flexibility.In contrast, each single-channel repeater leads to a repetition of the radar's virtual array in the VNA for the symmetric-path radar-repeater network from [17] and [18].
3) Hardware Complexity: In [17] and [18], less hardware components are needed per virtual antenna added by a repeater in comparison to the MCR proposed in this work.Hence, a symmetric-path radar-repeater network leads to a potentially lower hardware complexity and power consumption.However, the hardware complexity of an MCR network still is much lower than that of a network of multiple radar sensors.
4) Risk of Ghost Targets: In the symmetric-path radar repeater network, the signal is also reflected at different targets on the way from the radar to the repeater and the way back.This leads to ghost targets [30].In a triangular-path repeater network as the one proposed in this work, these ghost targets do not occur.

IV. NETWORK-BASED DOA ESTIMATION
When using a coherent radar network, the DoA estimation is based on a sparse VNA consisting of several subarrays.Thus, the DoA estimation as known for MIMO radars [22], [31] has to be adapted.In this section, the different steps of the network-based DoA estimation are explained in detail.While the first step, the phase reconstruction, has to be done exclusively in radar-repeater networks, the other steps are independent of the network architecture.

A. Phase Reconstruction
As radar and MCR are not synchronized, the phase of the modulation signal at t = 0 s, which is defined as the start of the radar Tx signal, is not known.Thus, a reconstruction and compensation is necessary to retrieve full phase coherency.The modulation signal of the kth MCR channel can be described by where A k is the signal amplitude and t < 0 is the point in time closest to t = 0 s where it holds arg(y mod,k ( t)) = 0 [18].The unknown modulation phase then is defined as Assuming that the different modulation frequencies of one MCR are synchronized, the modulation phases of its channels have a fixed relation H k = f mod,k / f mod,0 .Assuming channel k = 0 has the lowest modulation frequency, each modulation phase φ mod,k can be calculated based on φ mod,0 as This simplifies the phase reconstruction, as only one modulation phase per MCR has to be reconstructed.As described in [18] and [32], the reconstruction of φ mod,0 can be determined by modulating the same MCR channel with a two-tone signal.By modulating channel 0 with f mod,0 and f mod,II,0 = b f mod,0 , b > 1, the modulation phase can be determined by where φ Rp,II,0 = arg(a II,0 ) and φ Rp,0 = arg(a 0 ) are the phases measured over the reflection at the same target on the different modulation frequencies.Alternatively, the direct coupling between MCR Tx and radar Rx can be used.Calculating with complex numbers, this equals z mod,0 = e jφ mod,0 = (b−1) a II,0 a 0 (19) and is unambiguous for 1 < b ≤ 2.
When using an OFDM radar, it thus makes sense to modulate the first channel of each MCR onto two neighboring subcarriers.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

B. Combination of the Subarrays
By performing the signal evaluation described in Section III-C, for each virtual channel of the VNA a complex range-Doppler (Rv) matrix I is generated.In order to perform a DoA estimation, for each target, the phases of all channels have to be combined correctly.However, different aspect angles of the network nodes result in range-angle coupling [15] and differences in the radial velocity of each node [33], which have to be considered when identifying the target peaks.Furthermore, the range induced by the LoS and the delay inside an MCR has to be considered, and a discrepancy in the modulation frequency may lead to a velocity offset.
After correctly identifying the target peaks, the complex subarray steering vectors can be combined to a network steering vector γ according to the VNA.In this work, no subarray tapering is used.All elements in γ thus are normalized to have the same amplitude.

C. Zero Padding
When having a VNA consisting of multiple subarrays and gaps in between, it results in a block-wise sampling structure as described in (7).In this case, wrong results may occur due to sampling errors when performing an FFT-based DoA without extending the steering vector via zero padding (ZP).The effect is most grave in the case of ULA subarrays with large gaps in between, as, for example, in the VNAs shown in Fig. 2(a) and (b), which is shown in Fig. 5.
It can be explained at the example of a VNA with two ULA subarrays using (7) and (8).Considering the Nyquist-Shannon theorem [34], the term cos( d nw [2]) is free from aliasing, if the resolution in the Fourier domain is smaller than (2d nw [2]) −1 .Thus, using a λ/2-grid, the steering vector γ needs to have a length of 2d nw [2](2/λ) elements.
Although the effect is reduced when using more and sparse subarrays, to avoid this error, ZP is also recommended for other VNA.In the general case of N nw subapertures, the length of γ is should be larger than 2d nw [N nw ](2/λ), with the N nw th subaperture having the largest d nw .In practice, an even larger ZP is favorable for further interpolation.In this work, the steering vector is extended to more than eight times its length.

D. FFT-Based DoA Estimation Using Compressed Sensing
Before the final steps of the DoA estimation, the steering vectors are corrected based on a calibration, e.g., a calibration with a target at 0 • .Furthermore, a near field correction as proposed in [15] and [35] is applied.
Then, due to the sparsity of the VNA, the DoA estimation itself is performed using a CS algorithm in combination with a Fourier transform [24], [36].This way, the sparse elements in the steering vector are reconstructed and sidelobes as well as artifacts are reduced.In this work, an iterative method with adaptive thresholding (IMAT) [37] is used since this algorithm combines well with ZP.
V. SYSTEM DESIGN Based on the proposed network concept, a system at 77-GHz is designed.It uses the OFDM-radar demonstrator presented in [38] and two four-channel MCRs.

A. Multichannel Repeater
The MCRs are designed using Rogers 3003G2 substrate PCBs and GaAs monolithic microwave integrated circuits (MMICs) from UMS.A block diagram and a photograph are presented in Fig. 6.The Rx antenna is connected via a waveguide-to-microstrip transition.Then, the signal is split into four different signals for the four channels of the repeater.Each channel includes an UMS CHM2179b98F DSB mixer.Additionally, before each power divider and after the mixer, UMS CHA2080-98F variable gain amplifiers (VGAs) are used to compensate the losses of the LoS path, the microstrip lines, and the mixer, leading to a total of seven amplifiers.As Tx antennas, an eight-element patch antenna array is used.The Tx antennas are placed in a λ/2-grid.The Tx array of the MCR is identical to the Tx array of the radar and can be found in Table II.

B. Radar
The radar consists of a 4×4 77-GHz frontend and a digital backend based on a Xilinx RFSoC [39].Baseband signals are generated and processed by eight digital-to-analog converters (DACs) and analog-to-digital converters (ADCs) each, with two per channel used for in-phase and quadrature components.Each baseband signal is sampled with 1 GSa/s, which allows for a signal bandwidth of about 400 MHz.Further details can be found in [38].
The same eight-element patch arrays as on the MCRs are used as radar antennas and placed as specified in Table II.The signal of the fourth Tx channel is split by a power divider and feeds the radar transmit antenna as well as a waveguide antenna used for the LoS path to the MCRs.

C. Network Design
The proposed network consists of three nodes, the radar and two MCRs.As shown in Fig. 7, the MCRs are mounted in a distance of 100 λ/2 and 175 λ/2.This leads to a network   aperture with a size of 239 consisting of three sparse subapertures, each with a size of 65 λ/2.The VNA is the same as depicted in Fig. 2(c), with the colors of the network nodes in Fig. 7 matching the colors of the corresponding subarrays in the VNA.It has to be mentioned that the network nodes are offset only along the x-axis, but not in yor z-direction (see Fig. 7 for the axis definition).

D. Multiplexing
The used multiplexing pattern is depicted in Fig. 8.The first three subcarriers are used by Tx1, Tx2, and Tx3.Then, there are nine subcarriers used by the lower sidebands (LSBs) of MCR2 and MCR1, followed by Tx4, which in this work is connected to a regular Tx antenna as well as to the LoS antenna.Above the subcarrier of Tx4, there are nine subcarriers for the upper sidebands (USBs) of both MCRs.This pattern is then repeated 187 times, which results in a total of N = 4114 subcarriers.The modulation frequencies of the MCRs are listed in Table III.As all modulation signals for both repeaters are generated using the same multichannel

VI. MEASUREMENTS AND EVALUATION
Using the proposed radar network, measurements for evaluation and verification of the system are performed.This includes a systematical evaluation of the radar networks performance based on measurements in an anechoic chamber as well as radar imaging of automotive scenarios.The OFDM parameters are presented in Table IV.All measurements are calibrated using a copper pole with a diameter of 27 mm placed at boresight (θ = 0 • ).

A. Sidelobe Level
For a validation of the SLL, a measurement using the same copper pole as for calibration but placed at θ GT = −3 • in a range of R = 3.5 m is performed.Fig. 9 shows the DoA estimation result of this scenario.The theoretical SLL of −6.8 dB from Fig. 2(c) is matched.Thus, this low sidelobe level is achieved not only theoretically but also practically.
In contrast, using only the radar and hence a single subarray, the sidelobe level is increased to −3.4 dB.Additionally, the 3 dB width of the radar's main lobe is 1.72 • .Using the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

B. Target Separability
The target separability is evaluated based on measurements of two aluminum poles with 12 mm diameter at a range of R = 3.5 m.They are measured at different separations x in steps of 1 cm.The results in Fig. 10 include network-based DoA estimations with and without CS as well as DoA estimations using the radar only.
The theoretical target separability based on Rayleigh criterion [1] equals θ NW = 0.584 • .In measurements, this separability is not reached, as targets with a difference in angle of θ GT = 0.66 • are not separable.However, as shown in Fig. 10(a), at the next measured angle difference θ GT = 0.82 • they are.Thus, the measured target separability is slightly higher than the Rayleigh criterion, which is to be expected, as the Rayleigh criterion represents a theoretical minimum.Yet, it is much lower than the target separability of the radar only, which is 2.15 • according to the Rayleigh criterion.Fig. 10(b) and (c) shows the results of similar measurements with pole spacings of θ GT = 0.99 • and θ GT = 1.15 • , respectively.While in all three DoA estimations in Fig. 10, the targets can be separated successfully, the deviation between the ground-truth (GT) spacing and the measurement result differs.In Fig. 10(c), the error is only 0.03 • , well within the accuracy of the scenario setup, in Fig. 10(a) and (b) it is at about 0.2 • .However, since in a Fourier transform two closely spaced peaks influence each other depending on their phase [40], at a target spacing close to the network's separability, an error is to be expected.

C. Automotive Scenarios
In order to verify the performance of the radar network in practical scenarios, measurements with automotive targets including a car, a pedestrian, a bicycle, and a motorcycle are performed.In the evaluation, at first an Rv-image is created, where for the range evaluation, a zero padding to more than eight times the initial length is used.Then, a bird-view image Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
is created, where for every range cell, a network-based DoA estimation using CS is performed for the velocity bin with the highest power.
The measurement scenarios shown in Fig. 11 include a small number of road users, which are imaged very detailed due to the high angular resolution of the network.Fig. 11(a) shows a scenario with a car and a pedestrian.Multiple reflection points at the corners and the license plate of the car as well as both legs of the pedestrian are visible.A high number of features can be seen especially in Fig. 11(b), where both fork tubes of the bicycle as well as the left leg of the cyclist are visible.Fig. 11(c) shows a motorcycle approaching the radar with 3.5 m s −1 .Multiple features like the crash bar can be observed.
Fig. 12 visualizes the measurement results of difficult scenarios with multiple road users close to each other.Furthermore, a comparison of the network-based DoA estimation and a DoA estimation using only the radar's 4 × 4 array is shown.In Fig. 12(a) and (b), the scenario includes a car, a pedestrian, and a bicycle, all at a similar distance between 4 m and 5 m.Despite the combination of a weak pedestrian next to a strongly reflecting car, in both cases, all road users are visible in detail when using the radar network.In contrast, in Fig. 12(a), the pedestrian is not detected when using only the radar.Also, additional features like different reflection points at the front of the bicycle are only detected by the network.
In the very dense scenario in Fig. 12(b), where there is a road user every 0.5 m, still all targets are well detectable using the network.However, some features especially of the bicycle are lost compared to Fig. 11(b).In contrast, using the radar only, far less details and reflection points are visible, and the pedestrian as well as the cyclist are harder to detect.
In Fig. 12(c), a bicycle and a motorcycle are placed handlebar to handlebar.Using the radar network, the motorcycle is visible with a high level of details.Also the bicycle still is detected, despite the strong target directly next to it.With the radar only, both targets are detectable, but just as single peaks.
By the measurements in Fig. 12, it thus is verified that using the radar network weak targets can be detected next to strong ones, separated only by the DoA estimation.This is of special importance, as in automotive scenarios weak targets typically include the most vulnerable road users.

VII. CONCLUSION
To show the potential of coherent radar networks, a network system is proposed allowing for a flexible design of the VNA while providing a good link budget.It is based on a digital radar accompanied by two MCR, leading to three network nodes and thus three subapertures.With a VNA designed based on the proposed recommendations for network array design, a high target separability is reached while maintaining a low SLL.The measurement results not only show the high target separability of the network-based DoA estimation, but also its applicability in automotive scenarios.With the high angular resolution, a very detailed image of the traffic scenario and the different road users is created.Furthermore, the ability to detect weak targets next to strong ones exclusively based on the DoA estimation is demonstrated.All in all, the results show the high potential of network-based radar imaging using a well-designed radar network.

ACRONYMS
In the following, an overview over the most important acronyms is given.

Fig. 1 .
Fig. 1.VNA of a network consisting of three subarrays with four virtual antennas each.

Fig. 2 .
Fig. 2. Simulation results for a DoA estimation of a target at 0 • using different VNA without subarray tapering.Different colors in the VNAs represent different subarrays.(a) VNA with two 16-element ULA subarrays.(b) VNA with three 16-element ULA subarrays.(c) VNA with three 16-element sparse subarrays.

Fig. 3 .
Fig.3.Concept of a triangular-path radar-repeater network using MCR, exemplarily shown for a network with one four-channel MCR.

Fig. 4 .
Fig. 4. Subcarrier assignment exemplarily shown for a network consisting of a radar with four transmitters and two four-channel MCRs with SSB mixers.The pattern is repeated.

Fig. 5 .
Fig. 5. Comparison of the DoA estimation results of a target at 5 • with ZP to eight times the array size and without ZP.The network with two 16-element ULA subarrays from Fig. 2(a) is simulated.

Fig. 8 .
Fig. 8. Subcarrier assignment as used in the presented radar repeater network.Channel MCR1-1 modulates onto two different subcarriers to enable phase reconstruction as explained in Section IV-A.The pattern is repeated 187 times.arbitrary waveform generator (AWG), the modulation signals of MCR1 and MCR2 are synchronized and MCR2 thus does not need a channel modulating onto two subcarriers.

Fig. 9 .
Fig. 9. DoA estimation of a single pole at θ GT = −3 • .With the network aperture, a SLL of −6.8 dB can be reached, equaling the theoretical performance as shown in Fig. 2(c).

Fig. 11 .
Fig. 11.Measurements of static and dynamic low density automotive scenarios.The measurement results are shown as bird's view, the DoA estimation is performed based on the whole network using CS.The measurement scenarios include (a) a car and a pedestrian at [0, 4] m; (b) a bicycle at boresight, fork at [0, 5] m; (c) a motorcycle approaching at 3.5 m/s.

TABLE I RADAR
NETWORKS WITH COHERENT DOA ESTIMATION

TABLE III MODULATION
FREQUENCIES OF THE REPEATER CHANNELS