Enhancing mmWave Radar Sensing Using a Phased-MIMO Architecture

Millimeter-wave (mmWave) radar has become instrumental in diverse consumer applications. Yet current radar architectures face major limitations. While full-MIMO structures are feature-rich, their cost and complexity rise rapidly with more antennas. Phased-MIMO radars promise enhanced scalability by combining large phased arrays with a small number of RF chains. Nevertheless, the phased-MIMO research thus far primarily relies on simulation or theoretical analysis. In this paper, we introduce HybRadar, a novel programmable phased-MIMO radar platform to address this experimental gap. HybRadar repurposes the phased arrays on a low-cost 802.11ad radio to create a scalable low-cost array of phased subarrays. It further incorporates transmit/receive front-end, control channel, and hardware synchronization mechanisms to enable a modular phased-MIMO system. By extending recent MIMO array synthesis models, we optimize the placement of phased subarrays to maximize the spatial resolution. Our prototype validation and case studies confirm the capability and versatility of HybRadar.


INTRODUCTION
For decades, millimeter-wave (mmWave) radars have played a crucial role in aviation, defense, and meteorology applications.With advances in RF hardware, they are also becoming vital in consumergrade applications such as automotive perception [20,45,46,68], wearable/mobile and contactless health monitoring [2,17,18,26,55], low-power activity and location tracking in smart spaces [84], etc.These applications are projected for an exponential market penetration [15].Unlike optical sensors like cameras and LIDAR, mmWave radars maintain functionality even in adverse weather and poor lighting conditions, making them particularly attractive for emerging domains, e.g., surveillance and autonomous driving.
However, consumer-grade mmWave radars currently lag behind their military-grade counterparts in spatial resolution, mostly offering only single-point ranging or tracking [24].This roots from a combination of factors including cost, power consumption, and form-factor constraints.While the range resolution of a radar depends on its signal bandwidth which is often xed for a given spectrum band, the angular resolution of a radar hinges upon its e ective antenna aperture [49] which varies widely and proportionally to the number of antenna elements.
Current mmWave radars predominantly adopt a full-MIMO structure wherein each RF chain is singularly linked to a passive antenna.This enables exible array processing within both the transmit path and the receive path.However, the inherent hardware complexity of the MIMO architecture hinders the scalability of the number of physical antennas.Adding an extra antenna necessitates a full RF chain, comprised of data converters, mixers, and lters, coupled with clock distribution and heat dissipation problems, among others.The cost, complexity, size, and power consumption become increasingly daunting as the system scales [52].
Phased array radars represent a contrasting approach, where multiple antennas are connected to a single RF chain through phase shifters.While more cost-e ective, phased arrays only support analog beamforming with limited phase/amplitude resolution.It requires multiple beam scans to cover wide angles, hindering realtime operation.
In the past decade, phased-MIMO radar, also referred to as subarray MIMO radar, has been explored [21,22,75] to strike a balance between the above two paradigms, as illustrated in Fig. 1.The phased-MIMO radar concept was developed concurrently with the hybrid beamforming in communication systems [38].Both adopt an array of subarray antenna architecture, where each RF chain can be connected to a phased array.Such subarray architecture is considered the optimal way of scaling up the number of antenna elements and hence the radar can provide close-to-LIDAR-level spatial resolution, and supreme target detectablilty, under the hardware  complexity and cost constraints of commodity devices.The potential of phased-MIMO already emerged in automotive and health sensing [53,75], and is likely to propagate to many other wireless sensing use cases such as computer-human interaction [30].
However, the degree of freedom in phased-MIMO radar sensing remains largely underexplored.Examples include waveform con guration, beam pattern (codebook) design, phased array geometry, baseband processing algorithms, etc. Existing work either employs numerical analysis [22] or simulation [21] which misrepresents the elusive environmental factors, or resorts to emulation using MIMO radar with a limited number of antenna elements (e.g., 3 × 4 [75]) which underrates the scalability of phased-MIMO.
In this paper, we introduce HybRadar, a programmable phased-MIMO radar platform with a scalable array of subarray architecture.HybRadar supports digital beamforming through multiple RF chains, each of which is connected to a 32-element phased array.This design enables the platform to scale easily in multiples of 32 simply by adding more RF chains and phased arrays.More importantly, we can exibly recon gure the phased array beam patterns and the subarray layout, and implement any phased-MIMO baseband processing algorithms.
Inspired by the mmWave software radio in [82], we repurpose a commercial-of-the-shelf 802.11ad radio, hijack the control channel to its phased arrays, and redesign the data channel so that the phased arrays can be used to transmit/receive radar signals.We have realized both software radar that supports arbitrary radar waveform and the cost-e cient analog FMCW radar.To optimize the sensing performance of HybRadar, we make a set of design choices unique to the array of subarray setup, including (i) synchronization between the phased array control channel and FMCW synthesizer channel; (ii) designing the transmitting and receiving paths for high-frequency FMCW chirp generation and mixing; (iii) ensuring easy scalability towards many RF chains and antenna elements.In addition, we extend the concept of the virtual array in MIMO radar systems [49], and propose a sparse subarray layout, which achieves superior angular resolution even with a small number of phased arrays.
We have conducted comprehensive experiments to demonstrate HybRadar's capabilities and a rm the e ectiveness of our design in terms of time/phase synchronization, multi-chain scalability, power budget, etc. Remarkably, HybRadar achieves an angular resolution of 2.46 • using only 2Tx and 2Rx RF chains (64×64 antenna elements).To further illustrate the practical applications of Hyb-Radar, we have performed two case studies: high-resolution 3D point cloud generation and compressive radar beam scanning.We rst demonstrate that HybRadar can be used to generate accurate,  dense 3D point clouds, similar to high-end imaging radar, even with a limited 2Tx-2Rx setup.We then design a compressive scanning codebook, which can use a small fraction of the available beams to achieve similar or even better angular accuracy than evenly spaced beam patterns.In summary, the key contributions of this work are: (i) The design and implementation of HybRadar, the rst mmWave radar experimental platform that embodies a scalable array of subarray architecture.We intend to make HybRadar's hardware opensource and available to the research community.
(ii) The exploration of the distinctive bene ts of phased-MIMO radars, particularly the development of a sparse subarray layout that delivers superior spatial resolution.
(iii) The experimental validation of HybRadar's architecture and performance, along with case studies in point cloud imaging and compressed beam scanning, demonstrating the versatility of the platform.Our mmWave radar system is built upon the 3 software-de ned radio (SDR) platform, which modi es a COTS 802.11ad radio (Airde Sparrow+) by integrating a custom "bridge board" for arbitrary waveform transmission.

SOFTWARE DEFINED RADAR
Digital radar.Digital radar on the 3 platform is realized by directly inputting a radar waveform into the baseband.This approach o ers signi cant waveform design exibility, proving crucial for various research applications, including advanced radar waveform design and the fusion of sensing with communication.
Synthesizing a wideband radar signal (4 GHz) necessitates highend baseband processing units (BPUs) such as Xilinx RFSoC [73].Interfacing the RFSoC with the 3 front-end requires a specially designed adapter board.The default XM500 [74] board does not support full bandwidth across all 8 ADC/DAC channels.Therefore, we designed a new adapter board to fully utilize all channels, shown in Fig. 2(a).We have also incorporated baseband ampli ers with adjustable gain to accommodate the wide range of radar-re ected signal strengths, ensuring compatibility with the ADCs' input range.
In our preliminary experiments using digital radar, we measure a corner re ector with a radar cross-section (RCS) of 12 dBsm at a distance of 2.5 m.We generate a −2 to 2 GHz FMCW chirp signal with a duration of 90 µs at the baseband using two DAC channels (I/Q).Subsequent Tx/Rx correlation is performed to detect the targets.Although the Tx/Rx phased array is spaced by 7 cm, we observe a strong direct-path leakage signal.However, by activating additional Tx/Rx antennas and employing beamforming, we observe a suppression of this leakage and an improvement in the SNR of the target, as shown in Fig. 2(b).
Despite its successful implementation, digital radar faces two main limitations: (i) High cost: utilizing the Xilinx RFSoC incurs a signi cant expense, approximately 11k USD.(ii) Complex signal processing: real-time sampling, correlation, and data management on an FPGA adds considerable complexity to system evaluation and development.
Analog radar.In contrast, the analog radar implementation replaces the "bridge board" with an "FMCW radar front-end" board, employing a voltage-controlled oscillator (VCO) and phase-locked loop (PLL) for wideband chirp signal generation.Table 1 outlines the key design di erences between digital and analog radar.Given the cost-e ectiveness and straightforward digital signal processing of the analog approach, the remainder of this paper will focus predominantly on the design, development, and evaluation of the analog radar system.

RADAR HARDWARE DESIGN
In this section, we delve into the architecture and key hardware design choices of the analog radar.The hardware is highly modular.Each module comprises 3 main components: the FMCW chirp synthesizer, the radar front-end PCB, and the phased-array module (PAM), as shown in Fig. 3(a).We have designed the synchronization mechanisms across the time, phase/frequency and control channel, so that HybRadar can scale its antenna aperture as more modules are added.Within each module, the FMCW chirp synthesizer generates a 13-17 GHz frequency sweeping signal that is connected to the radar front-end PCB.The chirp signal is subsequently upconverted into the 58-62 GHz mmWave band by the PAM originating from a COTS 802.11ad radio.The front-end PCB performs chirp signal ampli cation, distribution, and FMCW dechirping, and produces the beat signals that are sampled by the ADCs.The resulting baseband signals can be processed in real-time using an FPGA-based BPU (such as USRP [14] or RFSoC [73]).

Phased Array Module
We retro t the PAM from a COTS 802.11ad radio (Air de Spar-row+ 1 ) and design the control/data interfaces to repurpose it for our phased-MIMO radar.Each of the phased arrays follows a 6×6 uniform planar array (UPA) layout with 4 inactive corner elements. 1Now discontinued, but can be replaced with Microtik wAP 60Gx3 [33].
The beamformer inside the PAM provides 2-bit phase and 1-bit amplitude control, supporting a codebook size of 128, i.e., 128 di erent beam patterns.
Following a similar architecture as in 3 [82], we disconnect the network interface card (NIC) which is originally connected to the PAMs, and implant a custom-designed radar front-end board in between, as shown in Fig. 3(a).We use an external control FPGA to reproduce the PAM control commands to facilitate real-time control and synchronization.We use a triplexer on the radar frontend board to combine the chirp signal, the control signal (118 MHz), the LO signal (7.56 GHz), and the power supply and feed into the PAM together.Since these signals range from 118 MHz to 17 GHz, we select a wideband 4-way splitter, Minicircuits EP4RKU+ [37], to implement the triplexer.To avoid impedance mismatch, a 50 Ω resistor connects the unused port on the splitter to the ground.
To enable phased-MIMO, the phased array beam scanning must be synchronized with the radar waveform, i.e., the beginning of an FMCW chirp needs to be aligned with the start of a new beam pattern.To this end, we use the BPU-an NI USRP N210-to create a synchronization anchor.When the BPU starts sampling the signal, it sends a trigger signal through its GPIO PIN to the chirp synthesizer and the control FPGA.Upon receiving the trigger signal, the chirp synthesizer starts producing chirps, and the control FPGA sends the PAM the enabling and beam scanning commands.The interval of the beam scanning commands is set using a counter on the FPGA to ensure that it aligns with the duration of the chirps.Our experiments verify this design perfectly aligns the chirp synthesis with beam switching (Sec.5).

Transmitting Path Design
We generate the frequency sweeping radar chirps using a frequency synthesizer (ADF4159 [3]) and a VCO (HMC587 [4]).A PLL is designed with ADF4159 and HMC587 to produce a linear, low-phase noise chirp signal, as shown in Fig. 4. ADF4159 can be programmed through a simple 3-wire interface and therefore the chirps with di erent parameters (such as duration, slope, frequency range, etc.) can be synthesized.A graphic user interface provided by Analog Devices is used to con gure the chirp synthesizer.Alternatively, the controlling commands can be sent by FPGA for real-time conguration.
As HMC587 can only support a frequency range of 5-10 GHz, we adopt a 2-stage chirp synthesizer design to meet the desired IF frequency of HybRadar.Speci cally, we rst generate a 6.5-8.5 GHz chirp signal and subsequently add a frequency doubler (HMC814 [5]) to double the frequency to 13-17 GHz.The original signal is not completely eliminated by the frequency doubler, and the resulting leakage may cause interfering harmonics.We thus add a high-pass lter XHF-143M+ [35] at the following stage to further attenuate the 6.5-8.5 GHz signal.
To perform the Tx-Rx mixing required by an FMCW radar, another copy of the chirp signal is needed.We thus add a power splitter (Minicircuit EP2RKU+ [34]) to split the chirp signal along 2 ways, one to the Tx PAM, and the other to the Rx mixer.Eventually, the Tx PAM upconverts the chirp signal to the mmWave band and emits a 58-62 GHz chirp.

Receiving Path Design
The transmitted FMCW signals are re ected by the objects in the environment and received by the Rx PAM, which subsequently downconverts the signals back to 13-17 GHz.The output signals from the Rx PAM are just a replica of the Tx chirp but with time delays proportional to the range of the re ecting objects.Afterward, the Tx-Rx chirp mixing produces the beat signal that embodies the range information.
The receiving path of the radar front-end board comprises 3 components: the high-pass lter (HPF), the ampli er (AMP), and the mixer.The HPF prevents the 7.56 GHz LO signal from entering the receiving path because otherwise the LO signal, typically stronger than the Rx chirp signal, may saturate the Rx ampli ers.We select XHF-143 [35] as the HPF which features a cuto frequency of 11 GHz, imposing around 30 dB attenuation on the 7.5 GHz signal with a negligible impact on the 13-17 GHz chirp.In addition, XHF143 is also a re ectionless lter that exhibits a 50 Ω impedance at the stopband, which does not cause any impedance mismatch for the LO and command signal at the triplexer ports, thus ensuring signal integrity.
Although the Rx chirp signal has already been ampli ed in the Rx PAM, it su ers attenuation from various sources, such as cables, connectors, triplexers, and transmission lines.Therefore, it is essential to amplify the Rx chirp signal before it enters the mixer to maintain a decent SNR.We use Minicircuits AVA-183A+ [36] as the Rx ampli er because it supports a wide bandwidth of 5-18 GHz which covers the desired 13-17 GHz chirp bandwidth.Moreover, AVA-183A+ features a ±1.2 dB gain atness which ensures a at frequency response of our wideband chirp signal.We cascade 2 AVA-183A+ to obtain a su ciently strong Rx chirp signal.
We use HMC8191 [6] as the mixer which supports a wide bandwidth of 6 GHz-26.5 GHz to perform dechirping and produce the baseband beat signal.Notably, HMC8191 is an I/Q mixer that produces two signals, IF1 and IF2, which are 90 • out of phase.I/Q mixer structure is often adopted in FMCW radar design because it cancels half of the noise signal and achieves a 3 dB SNR gain [47].I/Q samples also facilitate the baseband signal processing since the phase of each sample is directly available.In addition, since HMC8191 is a passive mixer and requires a high signal drive power of 18 dBm, we add another AVA183A+ ampli er between the Tx chirp diplexer and the mixer.

Baseband Circuit Design
After the dechirping process, the beat signal containing essential sensing information is produced.The beat signal bandwidth (∼10s MHz) is much narrower than the chirp (4 GHz), which relaxes the ADC sampling rate and simpli es baseband processing.
The baseband circuit achieves two functions: direct path image ltering and baseband signal ampli cation.As the radar transmits and receives signals, the Tx signal can propagate to the Rx antennas, causing a direct-path leakage signal.Due to the close proximity between the Tx and Rx antennas, the leakage signal results in a strong close-to-DC image in the baseband signal spectrum.Therefore, an HPF is designed to suppress the low-frequency interference which can improve the linearity of the baseband ampli er.
We determine the cuto frequency of the HPF by identifying the near-zero peak of the baseband spectrum when no real target is present.The cuto sharpness of the lter is of top design priority, as the HPF should aim to suppress only the direct path image but not other frequency components corresponding to close-by real radar targets.We, therefore, opt for Chebyshev HPF as it exhibits a sharp cuto transition region.More speci cally, we design a 5th-order Chebyshev lter with discrete LC components.
The strength of the re ected radar signal can vary signi cantly due to di erent environments.To fully exploit the dynamic range of the ADC, we employ a variable gain ampli er (VGA) at the baseband.When the signal is strong and ADC clipping is observed, the VGA gain should be tuned down.Otherwise, it should be maximized to detect weak re ecting objects.We use the TI LMH6882 [58] as the baseband VGA to allow for controllable ampli cation.LMH6882 is a 2-channel programmable gain ampli er with a gain range of 6 dB to 26 dB.The gain can be con gured manually using mechanical switches.

Expanding to Multiple RF Chains
The 1Tx-1Rx module design can easily be expanded to multi-TXmulti-RX by stacking multiple instances of the FMCW radar frontend board, as shown in Fig. 3

PHASED-SUBARRAY LAYOUT AND SIGNAL PROCESSING
Using classical FFT processing [7], the baseband signals of an FMCW radar can be decoupled into multiple range bins.Within each range bin, we can obtain a 2D channel matrix H, comprised of the radar backscatter channel from each Tx antenna element to each Rx antenna element.A direction of arrival (DoA) spectrum can be further extracted from H, from which we can estimate the relative angles of targets.For full-MIMO arrays, W and W can be considered as identity matrices, and the radar channel matrix H is directly obtained from a single radar snapshot.Contrarily, a phased array, due to its inherent analog beamforming component, can only obtain the weighted summation of H. Consequently, a phased array needs to make multiple radar snapshots with varying Tx/Rx beam patterns to recover H.

Radar Channel Estimation
Exhaustive beam scanning.The baseline method scans at least a full set of beams [81].For example, rstly, the Tx PAM is xed to beam #1 while the Rx PAM iterates from beam #1 to # ; then similarly, Tx PAM xes to beam #2, #3 ... # , while the Rx PAM scans all the beams.Orthogonal beam sets, such as discrete Fourier Transform (DFT) based beam sets, are commonly employed to ensure full rankness of Eq. ( 1).H can then be e ectively estimated by solving Eq. (1) using the Least Squared (LS) method.
Compressive sensing (CS).CS-based channel estimation methods [12,39] utilize the inherent sparsity of the mmWave channel [57] and require signi cantly fewer observations than to estimate H.With a judiciously designed codebook (i.e.W and W ) and sparse recovery algorithms, H can be e ectively estimated even when Eq. ( 1) is underdetermined.A case study in Sec.6 demonstrates a compressive beam scanning method, reducing the number of observations to 1/8-1/4.
Sensing time and max velocity.During one complete scan, the radar channel needs to be approximately unchanged.Based on the wireless channel coherence time model [48], the target's maximum velocity supported by the radar can be approximated.
Here denotes the wavelength, is the chirp duration, and is the number of snapshots.
The maximum velocity a phased array radar supports grows inversely with the number of beam scans.A phased-MIMO system comprises multiple independent phased subarrays and requires fewer snapshots than a phased-array system, striking a tradeo between system complexity and sensing time.

Optimizing Subarray Layout
Optimal antenna placement in full-MIMO radar systems is a wellexplored area.However, the phased-MIMO architecture introduces additional constraints on antenna locations, necessitating further investigation.This section delves into the optimal arrangement of phased subarrays to create virtual arrays with an expansive antenna aperture, thereby achieving enhanced spatial resolution.

Sum
Co-array (SCA) Design.The SCA [25] is a type of virtual array widely employed in active radar sensing where the Tx and Rx elements are coherent and co-located.SCA construction involves determining the spatial summation of Tx-Rx element pairs within a physical sensor array.This process e ectively transforms the physical array into a con guration comprising a singular Tx element alongside a virtualized Rx array.This transformation is predicated on the principle that the summation of spatial locations mirrors the cumulative phase of the wavefront, a relationship depicted in Fig. 6.An SCA can be constructed by performing spatial convolution of the Tx array and Rx array [49].In the case of both the Tx array and Rx array being a × UPA, an SCA of (2 − 1) × (2 − 1) can be constructed.The Tx/Rx array in HybRadar is a 6×6 UPA with antennas on the 4 corners disabled.Thus, the corresponding SCA is an 11×11 UPA with 3 elements missing on each corner, as illustrated in Fig. 7. Notably, due to the close spacing of the antennas within the same phased array, a large portion of Tx-Rx pairs synthesize a virtual antenna at the same location, resulting in redundant channel information.
With multiple Tx and Rx phased-arrays, an even larger SCA can be synthesized.To maximize the SCA, the location of the PAMs should be designed to minimize overlapping elements in the virtual array.Since each Tx-Rx phased-array pair synthesizes a (2 − Rx1 Rx2 Rx3 Rx4

Tx1
Tx2 Tx3 v1 Virtual Array r1 r2 r3 r4 Figure 9: Illustration of the DCA.The di erences of the locations mirror the phase di erences of the wavefront.Element v6 is missing since 5 can not be found in the phase di erences.
Level-1 Level-2 1) × (2 − 1) virtual UPA, if Tx and Rx PAMs are placed on a horizontal line to achieve angular resolution on the azimuth plane, the spacing between the phased arrays should satisfy: or alternatively, = (2 − 1) and = .Consequently, the size of the virtual SCA: The e ective aperture can thus be scaled by multi-folds in comparison to an unspaced placement of the phased arrays.An example is shown in Fig. 8.

Di erence Co-array (DCA) Design.
The DCA is primarily employed in passive sensing scenarios, such as radio astronomy or passive radar systems, where an array of co-located sensors receive signals from uncontrolled, unknown sources.The DCA operates independently from the SCA and can further expand the virtual array's dimensions beyond what the SCA o ers.The construction of a DCA involves calculating the spatial location di erences between element pairs within an Rx physical array.The construction is based on the principle that the di erence of the spatial locations mirrors the di erence of the phases of the wavefront at the sensors, which can be found by determining the signal vector's autocorrelation [44].
Figure 11: DCSC with nested subarrays.The light blue squares represent the virtual antennas from the SCA.Rx subarrays keep the same geometry as the DCA shown in Fig. 10.Tx2 makes a second copy of the virtual array on the right side.
In classical DCA theory, the signal sources must be assumed to be uncorrelated.In the context of active radar sensing, the "sources" correspond to the re ections from the radar targets, which are originally from the same Tx source.The assumption holds only when the multiple targets experience random yet uncorrelated small displacement over time (e.g., random vibration caused by wind).Since HybRadar operates at 60 GHz mmWave band, the maximum displacement only needs to be around 2.5 mm to cause a phase shift of 2 and randomize the complex radar channel.Notably even if the assumption does not hold, DCA can still be e ectively utitlized through techniques like spatial smoothing [10].
To employ DCA in HybRadar, we propose a subarray placement strategy to maximize the aperture of the DCA.This is challenging because given the number of antennas on a straight line, the optimal locations and corresponding DCA size cannot be computed in any closed-form [31].Consequently, many suboptimal but trackable array geometries have been proposed for DCA synthesis [42,43,66].However, these methods only deal with the element placement in traditional antenna arrays, whereas HybRadar comprises subarrays that constrain the locations of their antenna elements.
We extend the idea of nested array [42], and propose a 2-level nested array of subarrays (NAS) for HybRadar, as shown in Fig. 10.The proposed NAS comprises a level-1 array of 1 subarrays with spacing 1 and a level-2 array of 2 subarrays with spacing 2 , where Notably, the spacing between the rst level-2 subarray and the last level-1 subarray is also 1 .In the level-1 subarray, the spacing (2 − 1) ensures that the "holes" between the -th and ( − 1)-th subarrays can be lled by nding the di erence set between the -th subarray with the 1st subarray.In the level-2 subarray, the spacing is related to the number of level-1 subarrays 1 , and the "holes" between the -th and ( − 1)-th subarrays can be lled by nding the di erence set between the -th subarray with all the level-1 subarrays.The total number of virtual antennas Therefore, given the total number of phased arrays , the goal is to maximize under the constraint that 1 + 2 = .For example, with = 4 Rx phased arrays and = 6 element on one dimension of the phased array, it can be found through an exhaustive search over a few combinations that when 1 = 2, 2 = 2, the dimension of the virtual array is maximized, i.e., = 61.

Di erence Co-array of Sum Co-array (DCSC) Design.
The SCA and the DCA can be combined to synthesize a DCSC with even a large aperture [9].Based on the analysis in Sec.4.2.1, 1 Tx and 1 Rx phased array can be equivalently seen as one single Tx antenna and a (2 − 1) × (2 − 1) Rx phased array.Similarly, when there are 2 Tx phased arrays, 2 copies of (2 − 1) × (2 − 1) are synthesized.Following the principle, we employ the idea of SCA to create multiple copies of the NAS.Speci cally, the Rx phased arrays follow the same 2-level nested array geometry as in Eq. ( 5) but with ′ = 2 − 1.Since each Tx phased array adds another copy of the NAS in Fig. 9, a new Tx PAM should be placed in a location such that the rst subarray of the new NAS has the same level-2 spacing with the last subarray of the previous NAS, as shown in Fig. 11.Therefore, the Tx PAMs should follow a uniform spacing given by: Thus, the size of the nal virtual array scales up to:

HARDWARE PERFORMANCE EVALUATION
In this section, we conduct microbenchmarks to verify HybRadar's hardware design and virtual array synthesis methods.Time synchronization across subsystems.As mentioned in Sec.3.1, the BPU, chirp synthesizer, control FPGA and the PAMs need to be fully synchronized.To verify this, we use an oscilloscope to measure the triggering signal from the BPU, the chirp complete signal from the ADF4159 evaluation board, and the PAM controlling signal from the FPGA.As typical chirp durations for commercial automotive FMCW radars are in the order of 10s of µs [59], we set the chirp duration to be 90 µs with a 10 µs inter-chirp idle period.The chirp idle period is inserted to mitigate the noise introduced when the chirp is reset to the starting sweep frequency [59].Fig. 12 shows that once triggered, the FPGA sends commands right at the time when one chirp synthesis is complete, and this happens with a period of 100 µs as expected.The PAM responds to the commands after a delay of 170 ns, and the exact start-up timing can be found in [82].In the current prototype, the clock of the FPGA is not synchronized with the rest of the system, causing a slight time o set for each chirp.Through measurement, we the accumulated time o set after sending 10k chirps is 1.5 µs.However, the beam switching command does not need to be perfectly synchronized; it only needs to be issued during the inter-chirp idle time (10 µs) so that the beam pattern is aligned with each chirp.For long-time continuous radar sensing applications, the BPU can always send repeated triggering signals to regain synchronization.The experiment veri es HybRadar's subsystems are synchronized and that each beam scan is aligned with each FMCW chirp.Multi-channel calibration.HybRadar requires a one-time calibration to compensate for the phase/amplitude variations across di erent Tx-Rx pairs.We follow a common MIMO radar calibration procedure to perform calibration for a representative 2Tx-2Rx Hyb-Radar setup.We put a trihedral corner re ector at a distance of 7.5 m at the boresight as a reference target, and enable each Tx-Rx PAM pair to sense the target with a xed beam.We perform range FFTs (with zero-padding to improve accuracy) and identify the range bins with the highest amplitude.We then compare the phase/amplitude di erences and compute the complex calibration vector.
To show the e ectiveness of the calibration, we move the corner re ector to a di erent location and perform range and angular analysis.If the calibration factors are not applied, the angular spectrum exhibits multiple strong lobes (Fig. 13(a)) due to the phase o set among the Tx-Rx pairs.Once compensated, the split lobes are eliminated (Fig. 13(b)), which veri es the e ectiveness of the calibration across RF chains and PAMs.
Angular resolution with multiple Tx-Rx PAMs.To evaluate the e ectiveness of sparse array synthesis for HybRadar, we conduct experiments measuring angular resolution across di erent co-array setups.We place 2 identical trihedral corner re ectors in front of the radar at around 7.5 m and gradually reduce the separation between the targets until they become undistinguishable in the angular spectrum.The theoretical angular resolution for beamforming-based DoA estimation is described by ≈ 0.89 cos [56].Here the antenna spacing = 0.58 , is the number of antennas, and is the target angle relative to the antenna array.Without loss of generality, we only measure the horizontal angular resolution.
In our rst experiment, we employ the SCA con guration with varying numbers of Tx/Rx PAMs, i.e. 1Tx-1Rx, 1Tx-2Rx, 1Tx-3Rx, and 2Tx-2Rx.The spacing between the Rx PAMs is designed to be 11 , aligning with Eq. ( 3).Also from Eq. ( 3 4).As a prototype HybRadar, we only fabricated 2 Rx chains.So we emulate the 3rd Rx-chain by repositioning a PAM and combining the data from 2 measurements.Fig. 14(a) shows that the angular resolution improves as the number of PAMs increases, although it falls short of the theoretical value due to practical limitations such as PAM spacing tolerance, corner re ector size, and SNR.
In our second experiment, we measure the angular resolution with the DCSC setup in Fig. 11 with varying numbers of PAMs, including 1Tx-1Rx, 1Tx-2Rx, and 2Tx-2Rx.Based on Sec.4.2.3, for 1Tx-1Rx, the virtual array is the same as an SCA.For 1Tx-2Rx, the DCSC reduces to 1 = 1, 2 = 1, = 1.For 2Tx-2Rx, 1 = 1, 2 = 1, = 2.According to Eq. ( 8), the horizontal dimension of the virtual array is (11,32,95), respectively, which corresponds to a theoretical value of 8.98 • , 3.09 • , and 1.04 • .The result in Fig. 14(b) a rms that the DCSC con guration o ers an improvement in angular resolution with the same number of Tx/Rx chains.Notably, there remains a gap between the measured resolution to the theoretical resolution.Apart from the measurement error mentioned above, the gap also stems from the unsatis ed assumption of uncorrelated sources (Sec.4.2.2) in practical experiments.
Table 2 compares HybRadar with 2Tx-2Rx setup with the stateof-the-art (SOTA) mmWave radar systems.The angular resolution is measured using a similar setup described above employing SCA only.For the 1D horizontal-only case, with only 4 RF chains, Hyb-Radar achieves a better angular resolution than VTRIG-74.TI mmWCAS achieves a superior resolution, but it cannot achieve 2D resolution simultaneously due to its antenna layout.In the 2D case, HybRadar achieves a comparable angular resolution with VTRIG-74 with only 1/10 of the RF chain count which implies a much lower system complexity, cost, and power budget.However, with a similar number of virtual elements, HybRadar requires 10-20 times more snapshots than VTRIG-74, which increases the sensing time and compromises its sensing ability for moving targets (Eq.( 2)).
Radar link budget analysis.The capability of a radar to detect a target is fundamentally linked to the SNR of the received signals, which follows the well-known radar equation [56]: Here, represents the radar cross section (RCS) of the target.Extracted from the datasheet from Air de [1], the single-chain transmission power = 6 dBm, and the gain of each antenna element = 5 dBi.and denote the respective Tx/Rx array gains, which grow proportionally with the number of active antennas.Other factors include the carrier wavelength = 5 mm, the target's distance , the Boltzmann constant = 1.38 × 10 −23 J/K, and , the temperature measured in Kelvin.The noise bandwidth in FMCW radar = 1/ where = 90 µs is the chirp duration in our experiments.The receiver's noise factor = 8.5 dB is determined by the PAM's RF character.
We de ne the maximum detection range as the distance when the SNR falls below a pre-speci ed threshold, which in turn depends on the desired detection accuracy [56].For example, the required SNR to detect a target with a probability of 0.9 and a false detection rate of 10 −3 is 11 dB [56].To characterize the and , we place a corner re ector at the boresight of the radar and sense the target with an incrementally growing count of active antennas.The phase shifters in the beamformers are con gured to Tx/Rx boresight beams.Fig. 15(a) shows an SNR augmentation of approximately 25 dB, when all the Tx and Rx antennas are active, relative to a singular Tx and Rx antenna con guration.Correspondingly, Fig. 15(b) exhibits the maximum detection range receiving a boost of around 20 to 25 meters as the antenna count increases.The result substantiates the e ectiveness of the antenna array in elevating target detectability.
We further measure the SNR of common radar targets at a xed range with multiple Rx PAMs and then follow Eq. ( 9) to estimate the link budget.The Rx PAMs are placed on a 2×2 array with all the antennas enabled.As a prototype with only 2 Rx chains, the 2×2 array is a virtual array emulated using 2 Tx PAMs through time division following the SCA principle (Sec.4.2.1).
Table 3 shows that even with the 1Tx-1Rx setup, most common objects can be detected at a range > 12 m.Human does not re ect radar waves as strongly as other objects but the detection range is su cient for short-range indoor applications.The maximum detection range can further increase with more Rx channels.The impact of multiple Tx PAMs is similar, and therefore not further evaluated.Notably, due to practical factors such as calibration residual and radar channel diversity across the PAMs, the SNR gain from coherent combining does not simply increase linearly.This demonstrates the capability of HybRadar as a research platform for short to mid range phased-MIMO radar experiments.
We note that, theoretically, the phased array beam patterns manifest only in the radar's far-eld.For example, for a 1 Tx and 4 adjacent Rx arrays, this is around 5.5 m following the far eld model [40], still well within the detection range of HybRadar.For even larger array of subarray geometries, the far-eld may exceed the detection range.However, note that the far-eld model is only an approximation.Even within the near-eld, the beam patterns' mainlobes still dominate, albeit distorted and hence reducing the e ective array aperture from the theoretical maximum.System cost.The cost breakdown of HybRadar is detailed in Table 4, which reveals that the cost of the RF front-end of the digital and analog radar are similar.However, the need for wideband baseband processing in digital radars leads to a noticeable increase in overall system cost.Despite its prototype status, HybRadar's cost is comparable to start-of-the-art radar systems, as indicated in Table 5. Replacing the USRP N210 with a low-end FPGA and a low sampling-rate multi-channel ADC (20 MHz is su cient) could substantially reduce the cost.Moreover, integrating the FMCW front-end board and the chirp synthesizer into ICs can further improve cost e ciency.

CASE STUDIES 6.1 3D Point Cloud Generation
In this section, we showcase the capability of HybRadar in synthesizing high-resolution 3D radar point cloud images.
Hardware setup.Illustrated in Fig. 17(a), our setup incorporates 2 Tx PAMs aligned vertically and 2 Rx PAMs in a horizontal layout, both maintaining a central gap of 11 .We employ the SCA array synthesis (Sec.4.2.1) which is suitable for stationary targets (Sec.4.2.2).With a 1Tx-1Rx combination, we obtain an 11×11 virtual array, equating to an angular resolution of 8.98 • across both axes.In contrast, the 2Tx-2Rx amalgamation yields a 22×22 virtual array, re ning the angular resolution to 4.49 • .This con guration is appropriate when imaging precision is of equal importance in both dimensions.The 2 Tx PAMs operate in a time division manner while the Rx PAMs remain constantly active.
The chirp bandwidth is maximized to 4 GHz to achieve a negrained range resolution of 3.75 cm.Following a similar con guration to commercial FMCW radar [59], the chirp duration and the inter-chirp idle duration are respectively set to 90 µs and 10 µs.
Phased-MIMO radar 3D point cloud work ow.Our procedure for 3D radar imaging using HybRadar is depicted in Fig. 16.We follow the exhaustive beam-scanning approach detailed in Sec.4.1.Considering each PAM as a 6×6 UPA, the steering matrix is generated using the Kronecker product of two 6×6 DFT matrices [70,76], resulting in a dimension of 36×36.Factoring in 4 inactive corner antennas, the actual dimensions reduce to 36×32.After scanning 36×36 chirps, the observation matrix Y (Eq.( 1)) is acquired after performing the range FFTs.For each relevant range bin, the channel matrix H can be subsequently obtained by performing LS estimation.Next, employing the SCA principle, a 22×22 virtual array is derived.The missing elements in the virtual array caused by the 4 inactive corner antennas are lled with zeros.
Subsequently, the MUSIC algorithm [51] is employed on the virtual array to discern the DoA of re ective points.The steering vector used in MUSIC aligns with the angle de nition in Fig. 17(b).In active radar sensing, since target-re ected signals are coherent, we employ spatial smoothing [54,69] for enhanced MUSIC output.For the 1Tx-1Rx PAM setting, we use the redundancy in the phased array radar channel and perform joint transmitter smoothing as in [79].For the 2Tx-2Rx arrangement, with missing central elements due to the inactive corner antennas, spatial smoothing is executed over the 4 individual 11×11 virtual arrays, each corresponding to a Tx-Rx pair.Upon obtaining the MUSIC pseudo-spectrum, a pre-de ned threshold lters out valid (range-angle) data points, culminating in the nal 3D point cloud.
Experimental results for 3D point cloud generation.We choose a human subject to showcase the imaging performance, under 3 hardware setups: (a) 1 single Tx antenna + 1 Rx PAM; (b) 1 Tx PAM + 1 Rx PAM; and (c) 2 Tx PAMs + 2 Rx PAMs.The corresponding virtual array sizes are 6×6, 11×11, and 22×22, respectively.Fig. 18 shows the front and top view of the subjects with di erent postures.Setup (a) possesses the smallest virtual array size and does not have any redundant channels, resulting in a poor SNR, sparse point cloud, and lots of ghost points.Employing 2 PAMs in setup (b), the contour of the subjects becomes distinguishable and ghost points are mitigated.Setup (c) quadruple the number of observations compared with (b).With the spatial diversity o ered by the extra Tx-Rx channels, more details of the subject can be distinguished, and the point cloud shape highly resembles the ground truth.Multiple Tx-Rx PAMs allow for more degrees of freedom for spatial smoothing, e ectively suppressing the noise and ghost points.
The result highlights the phased-MIMO radar's capability to generate high-resolution point clouds.The employed exhaustive scanning method necessitates the scanning of 2,592 beams (36×36×2) for each scanning session.Due to the long scanning time, the method is best suited for scenarios where the targets exhibit minimal movement such as detailed environmental mapping.

Compressive Radar Beam Sensing
As discussed in Sec.4.1, a phased-MIMO radar with large phasedsubarrays requires a signi cantly longer sensing time than a full-MIMO radar, which makes real-time sensing cumbersome.CS [12], which has already found applicability in fast beam alignment for mmWave communication devices [11,16,27,28,39,71], emerges as a potential solution for e cient radar sensing as well.In this case study, we demonstrate a quick scanning method for phased-MIMO radar using CS.
Problem formulation.CS radar channel estimation utilizes the mmWave channel sparsity to reduce the number of beams.The sparsity indicates that there only exists a few directions where the Tx signal is re ected into Rx.Mathematically, it means the beamspace matrix X, de ned as the 2D-DFT of H, has only a few non-zero elements.Eq. ( 1) can be reformulated into the standard CS framework [12,29] as Here y ∈ C ×1 represents the vectorized observation matrix Y; Q ∈ C × is the sensing matrix derived from W and W ; x ∈ C ×1 stands for the sparse beamspace vector transformed from the original channel matrix H and v ∈ C ×1 denotes the noise vector.With limited beam scans, Eq. ( 10) is underdetermined ( < ).Sparse recovery techniques like orthogonal matching pursuit (OMP) [65] and sparse Bayesian learning (SBL) [64] are commonly used to solve for x utilizing its sparsity.The estimated beamspace vector x can then be transformed back to the original channel matrix H.
Codebook design for compressive beam scanning.Considering the unique phased-MIMO architecture of HybRadar, we propose a custom CS codebook design.The design of the codebook for CS aims to minimize the total coherence of the sensing matrix Q [13], a measure of correlation among beam patterns.Considering the optimal codebook form provided in [29,78] and HybRadar's The construction results in a full codebook with a size equal to the number of Tx-Rx antenna pairs.We subsequently select a subset of the complete codebook for compressed radar beam scanning.To enhance robustness, the selection of beams follows two empirical principles: full spatial coverage and inter-beam overlap.Additionally, other beam sets like the DFT matrix-based codebook [76] and the random codebook are generated to serve as benchmarks.Typical beam shapes are displayed in Fig. 19.
Experimental results for compressed radar beam scanning.To validate the e ciency and e cacy of the proposed CS-based radar beam scanning, we implement and use it to detect a target (corner re ector) randomly placed at 40 positions (between 1.7 m and 7.1 m from the radar).Fig. 20(a) presents the angular accuracy and error rate with an increased number of Rx PAMs.An angular estimation error is declared when the estimated angle deviates from the ground truth by over 10 • .We compare di erent CS methods against a baseline LS method, which requires transmission across all possible 32×32 beam pairs.As expected, with the same beam scanning time, the angular accuracy improves with the number of Rx PAMs.Notably, the simpler, greedy algorithm, OMP, does not match up to the more intricate ℓ 1 -minimization-based SBL approach [72], underscoring the trade-o between computational simplicity and performance.
Fig. 20(b) contrasts the angular accuracy against the count of scanned beam pairs.Our designed codebook achieves commendable performance with just a quarter of the beam pairs in full-MIMO.Contrarily, the randomly selected DFT codebook exhibits subpar performance.Its primary setback is the narrow concentration of each beam, causing the chosen beams to inadequately span the entire space with minimal overlap.The random codebook, on the other hand, exhibits an overly broad beam pattern, that leads to a reduced SNR, thus lagging behind our designed codebook in performance.
The CS algorithm can be further optimized by incorperating two factors.(1) The co-located Tx/Rx antennas result in identical AoA and AoD in radar sensing, which provides additional prior knowledge.(2) The current virtual array design introduces redundancy (Sec.4.2.1) that could be optimized to reduce the number of beam scans.Addressing these issues could drastically boost sensing speed, enabling phased-MIMO radars to operate in highly-dynamic environments such as autonomous driving and drone navigation.

DISCUSSION
Scaling towards a massive phased-MIMO radar.Our present hardware con guration supports a maximum of 4Tx and 4Rx channels, restricted by the NIC's 8 LO ports (Sec.3.1).A potential route to system expansion involves substituting the NIC with an external clock synthesizer (e.g.TI LMX2595 [63]).To supply LO to more than 8 channels, a clock distribution network comprising splitters and ampli ers needs to be designed, ensuring phase coherence and su cient power delivery.The FPGA embedded within the system can handle all the PAM command signals, and custom sources can provide DC power supply.
The limited bene t of Tx phased array.In practical applications, since the Tx power is regulated by maximum e ective isotropic radiated power (EIRP), which necessitates power adjustments during beamforming, the Tx phased array provides no SNR gain.In addition, due to the close antenna spacing, employing phased arrays on both Tx and Rx results in numerous overlapping elements in the virtual array.It provides limited improvement of angular resolution while greatly increasing the sensing time (Sec.4.1).Therefore, a better design tradeo might be employing phased-MIMO on the Rx side while maintaining full-MIMO on the Tx side.HybRadar can realize this setup by enabling only one antenna on the Tx phased array.

Figure 2 :
Figure 2: The implementation of digital radar.
Scaling HybRadar to multiple chains.

Figure 5 :
Figure 5: (a) HybRadar with a 2Tx-2Rx setup.The chirp synthesizer and the control FPGA can be further integrated to reduce form factor.(b) Radar front-end PCB.(c) PAM mounting structure.multipleradar channels, the chirp, LO, and command signals on di erent channels should be synchronized.We use an RF splitter (EP4RKU+[37], same as in Sec.3.1) to create multiple identical copies of the chirp signal and feed them into the stacked FMCW radar front-end boards.Notably, the RF splitter causes phase unbalance among the di erent output ports.For the 13-17 GHz chirp signal, the maximum phase unbalance is 5.3 •[37].Moreover, the cable or PCB traces are not perfectly length-matched which also introduces phase o sets.Nonetheless, these phase o sets are timeinvariant, because either the chirps or the LO are synthesized from the same clock source.Therefore, calibration can be performed and phase o sets compensated using standard MIMO radar calibration techniques[8].Fig. 5(a) portraits an example 2Tx-2Rx HybRadar setup, where two of the radar front-end boards (Fig. 5(b)) are stacked.We have also designed several di erent PAM mounting structures that allow for customized subarray location (shown in both Fig. 5(c) and 5(a)).
Consider a setup withTx antennas and Rx antennas and Tx beams combined with Rx beams (totaling scans).The observed radar channel matrix Y is expressed as:Y = W H HW + N.(1)Here,W = [u 1 , u 2 , . . ., u ] and W = [v 1 , v 2 , . . ., v ]represent the Tx and Rx beamforming weight vectors respectively, where u ∈ C ×1 and v ∈ C ×1 .N denotes noise.HybRadar's beamformer features a 2-bit phase (0, /2, and 3 /2) and 1-bit amplitude (on/o ) (Sec.3.1).Due to the length di erence of the feedline, each antenna has an extra xed phase o set, which can be obtained through a standard one-time calibration [82].The effective W and W in real experiments can therefore be calculated accordingly.
SCA with increased PAM count.

Figure 14 :
Figure 14: Angular resolution measurement result.the2Tx-2Rx setup.With such a con guration, the size of the virtual array is =(11,22,33,44) following Eq.(4).As a prototype HybRadar, we only fabricated 2 Rx chains.So we emulate the 3rd Rx-chain by repositioning a PAM and combining the data from 2 measurements.Fig.14(a)shows that the angular resolution improves as the number of PAMs increases, although it falls short of the theoretical value due to practical limitations such as PAM spacing tolerance, corner re ector size, and SNR.In our second experiment, we measure the angular resolution with the DCSC setup in Fig.11with varying numbers of PAMs, including 1Tx-1Rx, 1Tx-2Rx, and 2Tx-2Rx.Based on Sec.4.2.3, for 1Tx-1Rx, the virtual array is the same as an SCA.For 1Tx-2Rx, the DCSC reduces to1 = 1, 2 = 1, = 1.For 2Tx-2Rx, 1 = 1, 2 = 1, = 2.According to Eq. (8), the horizontal dimension of the virtual array is(11,32, 95), respectively, which corresponds to a theoretical value of 8.98 • , 3.09 • , and 1.04 • .The result in Fig.14(b) a rms that the DCSC con guration o ers an improvement in angular resolution with the same number of Tx/Rx chains.Notably, there remains a gap between the measured resolution to the theoretical resolution.Apart from the measurement error mentioned above, the gap also stems from the unsatis ed assumption of uncorrelated sources (Sec.4.2.2) in practical experiments.Table2compares HybRadar with 2Tx-2Rx setup with the stateof-the-art (SOTA) mmWave radar systems.The angular resolution is measured using a similar setup described above employing SCA only.For the 1D horizontal-only case, with only 4 RF chains, Hyb-Radar achieves a better angular resolution than VTRIG-74.TI mmWCAS achieves a superior resolution, but it cannot achieve 2D resolution simultaneously due to its antenna layout.In the 2D case, HybRadar achieves a comparable angular resolution with VTRIG-74 with only 1/10 of the RF chain count which implies a much lower system complexity, cost, and power budget.However, with a similar number of virtual elements, HybRadar requires 10-20 times more snapshots than VTRIG-74, which increases the sensing time and compromises its sensing ability for moving targets (Eq.(2)).Radar link budget analysis.The capability of a radar to detect a target is fundamentally linked to the SNR of the received signals, which follows the well-known radar equation[56]:

Figure 15 :
Figure 15: The array gain with the increasing number of Tx/Rx antennas.

Table 3 :
Detection range of common objects.