Joint Radar and Communication Design: Applications, Stateoftheart, and the Road Ahead
Abstract
For the sake of enhancing the exploitation of the permanently allocated, but potentially underutilized spectral resources, sharing the frequency bands between radar and communication systems has attracted substantial attention. More explicitly, there is increasing demand for sharing both the frequency band and the hardware platform between these two functionalities, but naturally, its success critically hinges on highquality joint sensing and communications. In this paper, we firstly overview the application scenarios and the research progress in the area of communication and radar spectrum sharing, with particular emphasis on: 1) Radarcommunication coexistence; 2) Dualfunctional radarcommunication (DFRC) systems. In the remainder of the paper, we propose a novel transceiver architecture and frame structure for a DFRC base station (BS) operating in the millimeter wave (mmWave) band, using the hybrid analogdigital (HAD) beamforming technique. We assume that the BS is serving a multiantenna aided user equipment (UE) operating in a mmWave channel, which in the meantime actively detects multiple targets. Note that part of the targets also play the role of scatterers for the communication signal. Given this framework, we then propose a novel scheme for joint target search and communication channel estimation relying on the omnidirectional pilot signals generated by the HAD structure. Given a fullydigital communication precoder and a desired radar transmit beampattern, we propose to design the analog and digital precoders under nonconvex constantmodulus (CM) and power constraints, such that the BS can formulate narrow beams towards all the targets, while preequalizing the impact of the communication channel. Furthermore, we design an HAD receiver that can simultaneously process signals from the UE and echo waves from the targets. By tracking the angular variation of the targets, we show that it is possible to recover the target echoes and mitigate the potential interference imposed on the UE signals by invoking the successive interference cancellation (SIC) technique, even when the radar and communication signals share the equivalent signaltonoise ratio (SNR). The feasibility and the efficiency of the proposed approaches in realizing DFRC are verified via numerical simulations. Finally, our discussions are summarized by overviewing the open problems in the research field of CRSS.
I Introduction
Ia Background
Given the plethora of connected devices and services, frequency spectrum is becoming increasingly congested with the rapid growth of the wireless communication industry. As a consequence, the auction price of the available wireless spectrum has experienced a sharp rise during recent years. For example, since 2015, mobile network operators in the UK have been required to pay a combined annual total of £80.3 million for the 900 MHz and £119.3 million for the 1800 MHz band, employed for voice and data services using a mix of 2/3/4G technologies[1]. Meanwhile in Germany, the regulator Bundesnetzagentur revealed that the total in the auction of 4 frequency bands for mobile network operators exceeded €5 billion[2]. The US Federal Communications Commission (FCC) completed its first 5G auction, with a sale of 28 GHz spectrum licences raising $702 million[3]. By 2025, the number of connected devices worldwide is predicted to be 75 billion [4], which further emphasizes impending need for extra spectral resources. In view of this, network providers are seeking opportunities to reuse spectrum currently restricted to other applications. The radar bands are among at the best candidates to be shared with various communication systems due to the large chunks of spectrum available at radar frequencies [5].
Radar has been developed for decades since its birth in the first half of the 20th century. Modern radar systems are deployed worldwide, with a variety of applications including traffic control, geophysical monitoring, weather observation as well as surveillance for defense and security. Below 10 GHz, a large portion of spectral resources has been primarily allocated to radar, but at the current stateoftheart new cohabitation options with wireless communication systems, e.g. 5G NR, LTE and WiFi[5]. At the higher frequencies such as the mmWave band, the communication and radar platforms are also expected to achieve harmonic coexistence or even beneficial cooperation in the forthcoming 5G network and beyond. Nevertheless, with the allocation of the available frequency bands to the above wireless technologies, the interference in the radar bands is on the rise, and has raised concerns both from governmental and military organizations for the safeguarding of critical radar operations [6, 7, 8, 9, 10]. To this end, research efforts are well underway to address the issue of communication and radar spectrum sharing (CRSS).
In general, there are two main research directions in CRSS: 1) Radarcommunication coexistence (RCC) and 2) Dualfunctional RadarCommunication (DFRC) system design [11]. By considering the coexistence of individual radar and communication systems, the first category of research aims for developing efficient interference management techniques, so that the two systems can operate without unduly interfering with each other. On the other hand, DFRC techniques focus on designing joint systems that can simultaneously perform wireless communication and remote sensing. The joint design benefits both sensing and signalling operations, decongests the RF environment, and allows a single hardware platform for both functionalities. This type of work has been extended to numerous novel applications, including vehicular networks, indoor positioning and secrecy communications [12, 13, 14].
Below we present existing, or potential application scenarios of CRSS from both civilian and military perspectives.
AoA  Angle of Arrival 

AoD  Angle of Departure 
ATC  Air Traffic Control 
AV  Autonomous Vehicle 
BS  Base Station 
CM  Constant Modulus 
CRSS  Communication and Radar Spectrum Sharing 
CRB  CramérRao Bound 
CSI  Channel State Information 
DL  Downlink 
DP  Downlink Pilot 
DFRC  Dualfunctional RadarCommunication 
GNSS  Global Navigation Satellitebased Systems 
GP  Guard Period 
HAD  Hybrid AnalogDigital Beamforming 
ICSI  Interference Channel State Information 
LTE  LongTerm Evolution 
LPI  Lowprobability of Intercept 
LoS  LineofSight 
MIMO  MultiInputMultiOutput 
mmWave  Millimeter Wave 
mMIMO  Massive MIMO 
MUI  Multiuser Interference 
MUMIMO  Multiuser MIMO 
NR  New Radio 
NSP  Nullspace Projection 
NLoS  Non LineofSight 
PRF  Pulse Repetition Frequency 
PRI  Pulse Repetition Interval 
RCC  RadarCommunication Coexistence 
RCS  Radar Cross Section 
RF  Radio Frequency 
RFID  Radio Frequency Identification 
SIC  Successive Interference Cancellation 
SINR  SignaltoInterferenceplusNoise Ratio 
SNR  SignaltoNoise Ratio 
SVD  Singular Value Decomposition 
TDD  Timedivision Duplex 
UAV  Unmanned Areial Vehicle 
UE  User Equippment 
UL  Uplink 
UP  Uplink Pilot 
V2X  VehicletoEverything 
WPS  WiFi Positioning System 
IB Civilian Applications
1) Coexistence of individual radar and wireless systems
As discussed above, CRSS has originally been motivated by the need for the coexistence of radar and commercial wireless systems. Next, we provide examples of coexisting systems in various bands.

Lband (12 GHz): This band is primarily used for longrange airsurveillance radars, such as Air Traffic Control (ATC) radar, which transmits highpower pulses with broad bandwidth. The same band, however, is also used by 5G NR and FDDLTE cellular systems as well as the Global Navigation Satellite System (GNSS) both in their downlink (DL) and uplink (UL) [15].

Sband (24 GHz): This band is typically used for airborne early warning radars at considerably higher transmit power[16]. Some longrange weather radars also operate in this band due to moderate weather effects in heavy precipitation [5]. Communication systems present in this band include 802.11b/g/n/ax/y WLAN networks, 3.5 GHz TDDLTE and 5G NR [17].

Cband (48 GHz): This band is very sensitive to weather patterns. Therefore, it is assigned to most types of weather radars for locating light/medium rain [5]. On the same band operate radars used for battlefield/ground surveillance and vessel traffic service (VTS)[5]. Wireless systems in this band mainly include WLAN networks, such as 802.11a/h/j/n/p/ac/ax [18].

MmWave band (30300 GHz)^{1}^{1}1Typically, communication systems operated close to 30GHz (e.g. 28GHz) are also referred as mmWave systems.: This band is conventionally used by automotive radars for collision detection and avoidance, as well as by highresolution imaging radars [19]. However, it is bound to become busier, as there is a huge interest raised by the wireless community concerning mmWave communications, which are soon to be finalized as part of the 5G NR standard [20]. Currently, the mmWave band is also exploited by the 802.11ad/ay WLAN protocols [18].
Among the above coexistence cases, the most urgent issues arise due to interference between base stations and ATC radars [15]. Early in 2012, a report pointed out that airport radar could delay the deployment of LTE in Southeast England, especially at the main London gateways [21]. In the forthcoming 5G network, the same problem still remains to be resolved. For reasons of clarity, we summarize the above coexistence cases in TABLE II.
Frequency Band  Radar Systems  Communication Systems  

Lband (12GHz)  Longrange surveillance radar, ATC radar  LTE, 5G NR  
Sband (24GHz) 



Cband (48GHz) 

IEEE 802.11a/h/j/n/p/ac/ax WLAN  
MmWave band (30300GHz)  Automotive radar, highresolution imaging radar  IEEE 802.11ad/ay WLAN, 5G NR 
2) 5G mmWave localization for vehicular networks
In nextgeneration autonomous vehicle (AV) networks, vehicletoeverything (V2X) communication will require lowlatency Gbps data rates; while general communications can deal with hundreds of ms delays, AVcontrolled critical applications require delays of the order of tens of ms [12]. In the same scenario, radar sensing should be able to provide robust, highresolution obstacle detection on the order of a centimeter. At the time of writing, vehicular localization and networking schemes are mostly built upon GNSS or default standards such as dedicated shortrange communication (DSRC)[22] and the D2D mode of LTEA [19]. While these approaches do readily provide basic V2X functionalities, they are unable to fulfill the demanding requirements mentioned above. As an example, the 4G cellular system provides the localization information at an accuracy on the order of 10m, at a latency often in excess of 1s, and is thus far from ensuring driving safety [12].
It is envisioned that the forthcoming 5G technology, exploiting both massive MIMO antenna arrays and the mmWave spectrum, will be able to address the future AV network requirements [23, 24]. The large bandwidth available in the mmWave band would not only enable higher data rates, but would also significantly improve range resolution. Furthermore, largescale antenna arrays are capable of formulating “thumbtacklike” beams that accurately point to the directions of interest; this could compensate for the pathloss encountered by mmWave signals, while potentially enhancing the angle of arrival (AoA) estimation accuracy. More importantly, as the mmWave channel is characterized by having only a few multipath components, there is far less clutter interference imposed on target echoes than that of the rich scattering channel encountered in the sub6GHz band, which is thus beneficial for localization of vehicles [12].
For all advantages mentioned in Sec. IA, it would make sense to equip vehicle or road infrastructure sensors with joint radar and communication functionalities. While the current DFRC system has considered sensors with dual functionality, those were mainly for the lower frequency bands, and cannot be easily extended to the V2X scenario. However, several problems need to be investigated in that context, such as specific mmWave channel models and constraints.
3) WiFi based indoor localization and activity recognition
Indoor positioning technologies represent a rapidly growing market, and thus are attracting significant research interest [13, 25]. While the GNSS is eminently suitable for outdoor localizations, its performance degrades drastically in an indoor environment. To address the above issue, WiFi based positioning system (WPS) constitutes promising solutions, as a benefit of their low cost and ubiquitous deployment, while requiring no additional hardware [13]. Essentially, WPS can be viewed as a type of passive radar, which locates the target based on the received signals sent by the user equipment (UE). In general, the UE is localized based on the estimation of its time of arrival (ToA) and AoA parameters. Alternatively, the localization information can also be obtained by measuring the received signal strength (RSS) and by exploiting its fingerprint properties (frequency response, signal strength regarding the I/Q channel, etc.), which are then associated with a possible location in a premeasured fingerprint database [26, 27].
To gain more detailed information concerning the target such as the human behavior, the receiver can process the signal reflected/scattered by the human body, based on specific transmitted signals. This system is more similar to a bistatic radar than to conventional WPS. The microDoppler shift caused by human activities can be further extracted from the channel state information (CSI) of the WiFi, and analyzed for recognizing human actions [28, 29]. Potential applications of such techniques go far beyond the conventional indoor localization scenarios, which include healthcare for elderly people, contextual awareness, antiterrorism actions and InternetofThings (IoT) for smart homes [30, 28, 31]. It is worth highlighting that a similar idea has been recently applied by the Soli project as part of the Google Advanced Technology and Projects (ATAP), where a mmWave radar chip is sophistically designed for fingergesture recognition by exploiting the microDoppler signatures, hence enabling touchless humanmachine interaction [32].
The above technology can be viewed as a particular radar/sensing functionality incorporated into a WiFi communication system, which again falls into the area of DFRC. Consequently, sophisticated joint signal processing approaches need to be developed for realizing simultaneous localization and communications.
4) Unmanned aerial vehicle (UAV) communication and sensing
UAVs have been proposed as aerial base stations to a range of datademanding scenarios such as concerts, football games, disasters and emergency scenarios[33]. It is worth noting that in all of these applications, communication and sensing are a pair of essential functionalities. In contrast to the commonlyused camera sensor on the typical UAV platforms which are sensitive to environmental conditions, such as light intensity and weather, radio sensing is more robust and could thus be incorporated into allweather services. Additionally, radio sensing could be adopted in drone clusters for formation flight and collision avoidance [34]. While both communication and sensing techniques have been individually investigated over the past few years, the dualfunctional design aspect remains widely unexplored for UAVs. By the shared exploitation of the hardware between sensors and transceivers, the payload on the UAV is minimized, which increases its mobility/flexibility, while reducing the power consumption [35].
5) Others
Apart from the aforementioned research contributions, there are also a number of interesting scenarios, where CRSS based techniques could find employment, which include but are not limited to:

Radio Frequency Identification (RFID): A typical RFID system consists of a reader, reader antenna array and tags. Tags can either be passive or active depending on whether they carry batteries. To perform the identification, the reader firstly transmits an interrogation signal to the tag, which is modulated by the tag and then reflected back to the reader, giving a unique signature generated by the particular variation of the tag’s antenna load [36]. The RFID based sensing is carried out by establishing a cooperative communication link between the reader and the tag. Hence this combines radar and communication techniques to a certain degree.

Medical sensors: To monitor the health conditions of patients, biosensors may be embedded in the human body. As these sensors support only lowpower sensing relying on their very limited computational capability, the measured raw data has to be transmitted to an external device for further processing. The most reliable solution for joint sensing and communication is yet to be explored in that scenario [37]. This, however, requires more interdisciplinary approaches.

Radar as a relay: In contrast to classic wireless communications, most of radar waveforms are highpowered and strongly directional. These properties make the radar a suitable communication relay, which can amplify and forward weak communication signals to remote users [38]. Again, joint radar and communication relaying can play a significant role here.
IC Military Applications
1) Multifunction RF systems
The development of shipborne and airborne RF systems, including communication, electronic warfare (EW) and radar, has historically been isolated from each other. The independent growth of these subsystems led to significant increase in the volume and weight of the combat platform, as well as in the size of the antenna array. This results in a larger radar crosssection (RCS) and a consequently increased detectability by adversaries. Moreover, the addition of such subsystems will inevitably cause electromagnetic compatibility issues, which may impose serious mutual interference on the existing subsystems. To address these problems, the Advanced Multifunction Radio Frequency Concept (AMRFC) project was launched by the Defense Advanced Research Projects Agency (DARPA) in 2005, whose aim was to design integrated RF systems capable of simultaneously supporting multiple functions mentioned above[39, 40]. In 2009, the Office of Naval Research (ONR) sponsored a followup project namely the Integrated Topside (InTop) program [41], with one of its goals to further develop wideband RF components and antenna arrays for multifunction RF systems based on the outcome of AMRFC.
Clearly, the fusion of the radar and the communication subsystems is at the core of the above research. By realizing this, a dedicated project named as “Shared Spectrum Access for Radar and Communications (SSPARC)” was funded by the DARPA in 2013, and was further proceeded into the second phase in 2015 [8]. The purpose of this project is to release part of the sub6GHz spectrum which is currently allocated to radar systems for shared use by radar and wireless communications. By doing so, SSPARC aims for sharing the radar spectrum not only with military communications, but also with civilian wireless systems, which is closely related to the coexistence cases discussed in Sec. IB.
2) Military UAV applications
In addition to the civilian aspect mentioned above, UAVs have also been considered as an attractive solution to a variety of military missions that require high mobility, flexibility and covertness. Such tasks include search and rescue, surveillance and reconnaissance as well as electronic countermeasures [42, 43, 44], all of which need both sensing and communication operations. Similar to its civilian counterpart, the integration of the two functionalities could significantly reduce the payload as well as the RCS of the UAV platform.
On the other hand, UAVs can also be a threat to both infrastructures and people, as it might be used to carry out both physical and cyber attacks. Moreover, even civilian UAVs can impose unintentional but serious danger if they fly into restricted areas [45]. To detect and track unauthorized UAVs, various techniques such as radar, camera and acoustic sensors have been employed. Nevertheless, a dedicated equipment specifically conceived for sensing UAVs could be expensive to deploy [46]. Therefore, there is a growing demand to utilize existing communication systems, such as cellular BSs, to monitor unauthorized UAVs while offering wireless services to authorized UEs, which needs no substantial extra hardware and thus reduces the cost [47]. By modifying BSs for acting as lowpower radars, the future Ultra Dense Network (UDN) having a large number of cooperative micro BSs can be exploited as the urban air defense system, which provides early warning of the incoming threats.
Civilian Applications 



Military Applications 

3) Radarassisted lowprobabilityofintercept (LPI) communication
The need for covert/secrecy communication has emerged in many defenserelated applications, where sensitive information such as the locations of critical facilities should be protected during the transmission. The probability of intercept is thus defined as a key performance metric for secrecy communications. Conventionally, LPI is achieved by frequency/time hopping or spreadspectrum methods, which require vast time and frequency resources [48, 49]. From a CRSS viewpoint, however, a more costefficient approach would be to embed the communication signal into radar echo waves to mask the data transmission [14, 50, 51].
A general model for the above scenario is composed by a RF tag/transponder within a collection of scattered targets and a radar transceiver. To elaborate briefly, the radar firstly emits a probing waveform, which is captured by the RF tag on its way to the targets. The tag then remodulates the radar signal with communication information and sends it back to the radar, which is naturally embedded in the reflected radar returns [14]. The communication waveform should be appropriately designed by controlling its transmit power and the correlation/similarity with the radar waveform. As such, the communication signal can be hard to recognize at the adversary’s side, since it hides itself behind the random clutters and echoes. Nevertheless, it can be easily decoded at the radar by exploiting some a priori knowledge [50]. Accordingly, a number of performance tradeoffs among radar sensing, communication rate and information confidentiality can be achieved by welldesigned waveforms and advanced signal processing techniques.
4) Passive radar
From a broader viewpoint, passive radar, which exploits scattered signals gleaned from noncooperative communication systems, could be classified as a special type of CRSS technology. Such illumination sources can be television signals, cellular BSs and digital video/audio broadcasting (DVB/DAB) [52]. To detect a target, the passive radar firstly receives a reference signal transmitted from a direct LoS path (usually referred as “reference channel”) from the above external TXs. In the meantime, it listens to the scattered counterpart of the same reference signal that is reflected by potential targets (referred as “surveillance channel”) [53]. Note that these scattered signals contain target information similarly to the case of active radars. As a consequence, the related target parameters can be estimated by computing the correlation between signals gleaned from the two channels.
The passive radar is known to be difficult to locate or be interfered, since it remains silent when detecting targets, and hence it is advantageous for covert operations. Furthermore, it requires no extra time/frequency resources, leading to a cost that is significantly lower than that of its conventional active counterparts. For this reason, it has been termed “green radar” [53]. Nonetheless, it may suffer from poor reliability due to the facts that the signal used is not specifically tailored for target detection, and that the transmit source is typically not under the control of the passive radar [53]. To further improve the detection probability while guaranteeing a satisfactory communication performance, joint waveform designs and resource allocation approaches could be developed by invoking CRSS techniques [54].
For clarity, we summarize the aforementioned application scenarios of CRSS technologies in TABLE III.
Ii Literature Review
In this section, we review the recent research progress in the area of CRSS. We will firstly introduce the coexistence approaches for individual radar and communication systems, and then the family of the dualfunctional radarcommunication system designs.
Iia RadarCommunication Coexistence (RCC)
1) Opportunistic spectrum access
From the perspective of cognitive radio, a straightforward approach is the socalled opportunistic spectrum access, in which the radar is regarded as the primary user (PU) of the spectrum, whereas the communication system plays the role of the secondary user (SU). Such methods typically require the SU to sense the spectrum, by which a transmission opportunity is obtained when the spectrum is unoccupied. To avoid imposing interference on the radar, the communication system has to control its power to ensure that the radar’s interferencetonoise ratio (INR) does not become excessive [55]. A similar approach has been adopted in [56] for the coexistence of a rotating radar and a cellular BS. In this scenario, the mainlobe of the radar antenna array rotates periodically to search for potential targets. The BS is thus allowed to transmit only when it is in the sidelobe of the radar. Under this framework, the minimum distance between the two systems is determined given the tolerable INR level, and the communication performance is also analyzed in terms of the DL data rate.
Although being easily implemented in realistic scenarios, the above approaches are unable to fully exploit the shared use of the spectrum. This is because the communication system can only operate under certain circumstances, namely when the radar is not occupying the frequency and the spatial resources. Additionally, the above contributions do not easily extend to facilitate coexistence with MIMO radar. Unlike conventional radars, the MIMO radar transmits omnidirectional waveforms to search for unknown targets across the whole space, and formulates directional beams to track known targets of interest [57, 58]. Consequently, it is hard for the BS to identify the sidelobes of the MIMO radar, since the radar beampattern may change randomly along with the movement of the targets. Therefore, more powerful techniques such as transmit precoding design are required to cancel the mutual interference.
2) Interference channel estimation
Before designing a transmit precoder, the interference channel state information (ICSI), i.e. the information on the channel where the mutual interference signals propagate, should be firstly obtained. Conventionally, this information is obtained by exploiting the received pilot signals received from the BS at the radar, which might consume extra computational and signaling resources [59]. As another option, the authors of [60] proposed to build a dedicated control center connected to both systems via wireless or backhaul links, which would carry out all the coordinations including ICSI estimation and transmit precoding design. In cases where the radar has priority, such a control center would be part of the radar [59]. However, such a method would involve significant overhead. A novel channel estimation approach has been proposed in [61] by exploiting the radar probing waveform as the pilot signal, where the radar is oblivious to the operation of the communication system. Since the radar randomly changes its operational mode from searching to tracking, the BS has to firstly identify the working modes of the radar by hypothesis testing methods, and then estimate the channel.
3) Closedform precoder design
After estimating the interference channel, the precoder can be designed at either the radar or the communication’s side. Similar to the zeroforcing (ZF) precoding of classic MIMO communication, a simple idea is the socalled nullspace projection (NSP) [62], which typically requires the radar to have the knowledge of the ICSI. In the NSP scheme, the radar firstly obtains the right singular vectors of the interference channel matrix by singular value decomposition (SVD), and then constructs an NSP precoder relying on those vectors associated with the null space of the channel. The precoded radar signal is projected onto the nullspace of the channel, so that the interference power received at the BS is strictly zero. However, such a precoder might lead to serious performance losses of the MIMO radar, for example by eroding the spatial orthogonality of the searching waveform. To cope with this issue, the authors of [63] designed a carefully adjusted threshold for the singular values of the channel matrix and then formulated a relaxed NSP precoder by the right singular vectors associated with singular values that are smaller than the threshold. By doing so, the radar performance can be improved at the cost of increasing the interference power received at the BS.
Despite the abovementioned benefits, there are still a number of drawbacks in NSP based approaches. For instance, the interference power can not be exactly controlled, since it is proportional to the singular values of the random channel. Additionally, since the target’s response might fall into the row space of the communication channel matrix, it will be zeroforced by the NSP precoder and as a consequence, be missed by the radar. Fortunately, these disadvantages could be overcome by use of convex optimization techniques, which optimize the performance of both systems under controllable constraints.
4) Optimization based designs
Pioneering effort on optimization based beamforming/signaling for the RCC is the work in [64], where the coexistence of a pointtopoint (P2P) MIMO communication system and a MatrixCompletion MIMO (MCMIMO) radar is considered. As a computationally efficient modification of the MIMO radar, the MCMIMO radar typically employs a subsampling matrix to sample the receive signal matrix of the target echoes, and approximately recovers the target information using the matrix completion algorithm [64]. The random subsampling at the radar receive antennas modulates the interference channel, and increases its null space. This gives the opportunity to the communication system to design its precoding scheme so that it minimizes the interference caused to the radar. In [64], the covariance matrix of the communication signal and the subsampling matrix of the MCMIMO radar are jointly optimized, subject to power and capacity constraints. The corresponding optimization problem is solved via Lagrangian dual decomposition and alternating minimization methods. By taking realistic constraints into consideration, the authors further introduce signaldependent clutter into the coexistence scenario in [60], which has to be reduced to maximize the effective SINR of the radar while guaranteeing the communication performance. It has been also pointed out in [60] that while the interference imposed by the communication system onto the radar is persistent, the interference inflicted by the radar upon the communication link is intermittent. By realizing this, the authors of [65] have considered the coexistence issues of a communication system and a pulsed radar, and quantified the communication rate as the weighted sum of the rates with and without the radar interference, which is named as the compound rate. The authors then formulate an optimization problem to maximize the rate subject to power and radar SINR constraints. It is worth noting that this problem can be solved in closedform when the radar interference satisfies certain conditions.
To address the coexistence problem of the MIMO radar and the multiuser MIMO (MUMIMO) communication system, the authors of [66] have proposed a robust beamforming design at the MIMO BS when the ICSI between the radar and the communication system is imperfectly known. An optimization problem is formulated for maximizing the detection probability of the radar, while guaranteeing the power budget of the BS and the SINR of the DL users. Cui et al. [67] have further proposed an interference alignment based transmit precoding design with special emphasis on the degree of freedom (DoF), under the scenario where multiple communication users coexist with multiple radar users. More recently, a constructive interference based beamforming design has been proposed for the coexistence scenario [68], where the known DL multiuser interference (MUI) is utilized for enhancing the useful signal power. As a result, the SINR of the DL users is significantly improved compared to that of [66] given the same transmit power budget. We refer readers to [69] for more details on the topic of interference exploitation.
5) Receiver designs
We end this section by briefly reviewing the receiver designs conceived for the coexistence of radar and communications. The aim of such a receiver is to estimate the target parameters in the presence of the communication interference, or to demodulate the communication data while cancelling the radar interference, depending on which side it belongs to. To the best of our knowledge, most of the existing research is focused on the second type, i.e., on the design of receivers for communication systems.
In [70], the authors consider a spectrum sharing scenario in which a communication receiver coexists with a set of radar/sensing systems. In contrast to the cooperative scenarios discussed in the relevant literature [62, 64, 60], the authors of [70] assume that the only information available at the communication system is that the interfering waveforms impinging from the radars fall into the subspace of a known dictionary. Given the sparse properties of both the radar interference and the communication demodulation errors, several optimization algorithms have been conceived for simultaneously estimating the radar interference, whilst demodulating the communication symbols based on compressed sensing (CS) techniques. It is shown that the associated optimization problems can be efficiently solved via nonconvex factorization and conjugate gradient methods.
In a typical coexistence scenario, the communication system periodically receives radar interfering pulses having high amplitudes and short durations, which implies that a narrowband communication receiver experiences radar interference as an approximately constantamplitude additive signal. Due to the slow variation of the radar parameters, this amplitude can be accurately estimated. Nevertheless, the phase shift of the interfering signal is sensitive to the propagation delay, thus is difficult to obtain. In [71], the authors exploit the assumption that the amplitude of the radar interference is known to the communication receiver, whereas the phase shift is unknown and uniformly distributed on . With the presence of the interfering signal receiving from the radar, a pair of communicationrelated issues have been studied. The first one is how to formulate the optimal decision region on a given constellation based on the maximum likelihood (ML) criterion. The second one, on the other hand, is how to design selfadaptive constellations that optimize certain metrics, namely the communication rate and the symbol error rate (SER). It is observed via numerical simulations that the optimal constellation tends to a concentric hexagon shape for lowpower radar interference and to an unequallyspaced pulse amplitude modulation (PAM) shape for the highpower counterpart.
IiB Dualfunctional RadarCommunication (DFRC) System
1) Information theory for the DFRC
It is wellunderstood that the radar works in a way that is fundamentally different from classic communication systems. Specifically, the communication takes place between two or more cooperative transceivers. By contrast, radar systems send probing signals to uncooperative targets, and infer useful information contained in the target echoes. To some degree, the process of radar target probing may be deemed as similar to the communication channel estimation, with the probing waveforms acting as the pilot symbols. For designing a DFRC system, one can unify radar and communication principles by invoking information theory, which may reveal fundamental performance bounds of the dualfunctional systems [72].
In a communication system, the transmitted symbols are drawn from a discrete constellation that is known to both TX and RX, which enables the use of bit rate as a performance metric for the communication. By contrast, the useful information for radar is not in the probing waveform but rather in the echo wave reflected by the target, which is however not drawn from a finitecardinality alphabet [38]. Drawing parallels from information theory, one way to measure the radar information rate is to view each resolution unit of the radar as a “constellation point”, as each unit can accommodate a distinguishable pointlike target. In [73], the “channel capacity” of the radar is defined as the number of distinguishable targets, which is the maximum information that can be contained in the echo wave.
In addition to the above definition, the authors of [72] have considered the mutual information between the radar and the target. Intuitively, the variance of the noise imposed on the echo wave represents the uncertainty of the target information, and can be measured by the entropy of the echo. From an information theoretical viewpoint, the radar cancels part of the uncertainty by estimating the target parameters, where the remaining part is lowerbounded by the CramérRao Bound (CRB), which can be viewed as the minimum variance achievable of the estimated parameter [74]. In light of this methodology, the authors of [72] consider a singleantenna DFRC receiver, which can process the target echo wave and the UL communication signal simultaneously. Such a channel can be viewed as a special multiaccess (MAC) channel, where the target is considered as a virtual communication user. An estimation rate is defined as the information metric for the radar in [72]. By invoking the analytical framework of the communicationonly MAC channel, the tradeoff between radar and communication performances is analyzed under different multiaccess strategies. In [75], an integrated metric is proposed for the DFRC receiver, which is the weighted sum of the estimation and communication rates. More recently, this approach has been generalized to the multiantenna DFRC system in [76]. While the performance bounds of the DFRC systems have been specified by the above contributions, the design of DFRC waveforms is still an open problem.
2) Temporal and spectral processing
In the early 1960s, the pioneering treatise [77] proposed to modulate communication bits onto radar pulses by the classical pulse interval modulation (PIM), which shows that one can design dualfunctional waveforms by embedding useful information into radar signals. By realizing this, the authors of [78, 79] proposed to modulate chirp signals with communication bit sequences, where 0 and 1 are differentiated by exploiting the quasiorthogonality of the up and down chirp waveforms. Likewise, the pseudorandom codes can also be used both as the probing signal and the information carrier [80]. A simpler approach is proposed in [81] under a timedivision framework, where the radar and the communication signals are transmitted in different time slots and thus do not interfere with each other.
In addition to the above approaches where the DFRC waveforms are designed from the groundup, a more convenient option would be to employ the existing communication signals for target detection. In this spirit, the classic Orthogonal Frequency Division Multiplexing (OFDM) signal is considered as a promising candidate [82]. In [83], the authors proposed to transmit OFDM communication signals for vehicle detection. The impact of the random data can be eliminated by simple elementwise division between the transmitted OFDM symbols and the received echoes. In contrast to its singlecarrier counterpart, the OFDM approach of [83] employs the fast Fourier transform (FFT) and the inverse FFT (IFFT) for Doppler and range processing, respectively, which obtains the velocity and the range parameters in a decoupled manner. It is also possible to replace the sinusoidal subcarrier in the OFDM as the chirp signal [84]. Accordingly, the fractional Fourier transform (FrFT) [85], which is built upon orthogonal chirp basis, is used to process the target return.
The above contributions have mainly investigated temporal and spectral processing for designing DFRC waveforms, while paying little information to the beneficial aspects of spatial processing. In what follows, we review the research progress in the design of MIMO DFRC systems.
3) Spatial processing
Inspired by the spacedivision multiple access (SDMA) concept of MIMO communications, a straightforward MIMO DFRC scheme is to detect the target in the mainlobe of the radar antenna array, while transmitting useful information in the sidelobe. One can simply modulate the sidelobe level using amplitude shift keying (ASK), where different powers represent different communication symbols [86]. Similarly, classic phase shift keying (PSK) could also be applied for representing the bits as the phases of the signals received at the angle of the sidelobe [87]. Accordingly, multiuser communication can be implemented by varying the sidelobes at multiple angles. To avoid any undue performanceloss of the radar, beampattern invariance based approaches have been studied in [88], where the communication symbols are embedded by shuffling the transmitted waveforms across the antenna array. In this case, the information is embedded into the permutation matrices.
In the above methods, a communication symbol is usually embedded into either a single or several radar pulses, which results in a low data rate that is tied to the pulse repetition frequency (PRF) of the radar, hence it is limited to the order of kbps. Moreover, the sidelobe embedding schemes can only work when the communication receiver benefits from a lineofsight (LoS) channel. This is because for a multipath channel, the received symbol will be seriously distorted by the dispersed signals arriving from NonLoS (NLoS) paths, where all the sidelobe and the mainlobe power may contribute. To this end, the authors of [89] proposed several beamforming designs to enable joint MIMO radar transmission and MUMIMO communication, in which the communication signal was exploited for target detection, hence it would not affect the DL data rate. The joint beamforming matrix is optimized to approach an ideal radar beampattern, while guaranteeing the DL SINR and the power budget. To conceive the constantmodulus (CM) waveform design for DFRC systems, the recent contributions [90, 91] proposed to minimize the DL multiuser interference (MUI) subject to specific radar waveform similarity and CM constraints. An efficient branchandbound (BnB) algorithm has been designed for solving the nonconvex optimization problem, which finds the global optimum in tens of iterations.
IiC Limitations of the Existing Works
Although there is a rich literature on various aspects of both RCC and DFRC scenarios, prior research mainly considers the applications in sub6GHz band. To address the explosive growth of wireless devices and services, the forthcoming 5G network aims at an ambitious 1000fold increase in capacity by exploiting the large bandwidth available in the mmWave band. In the meantime, it is expected that the mmWave BS will be equipped with beneficial sensing capability, which may find employment in a variety of scenarios such as vehicletoeverything (V2X) communications. Dualfunctional radarcommunication in mmWave systems is a new and promising research area. Recent treatises [92, 93, 94] propose to invoke the radar function to support V2X communications based on the IEEE 802.11ad WLAN protocol, which operates in the 60GHz band. As the WLAN standard is typically indoor based and employs smallscale antenna arrays, it can only support shortrange sensing at the order of tens of meters. To overcome these drawbacks, the largescale antenna arrays have to be exploited, which can compensate the high pathloss imposed on mmWave signals. Moreover, the high DoFs of massive antennas make it viable to support joint sensing and communication tasks. In order to reduce the hardware complexity and the associated costs, the maturing hybrid analogdigital (HAD) beamforming structure is typically used in such systems [95, 96], which requires much fewer RF chains than the fully digital transceivers. While the authors of [97] have presented analog beamforming designs for smallscale MIMO DFRC, little attention has been paid to HAD based massive MIMO (mMIMO) DFRC systems, which might be more practical, whilst maintaining compatibility with 5G mmWave applications.
IiD Main Contributions of Our Work
In this paper, we propose a novel architecture for a DFRC system operating in the mmWave band. We consider a mMIMO mmWave BS that serves a multiantenna UE while detecting multiple targets, where part of the targets are also the scatterers in the communication channel. To reduce the number of RF chains, an HAD beamformer is employed for both transmission and reception at the BS. We propose a novel DFRC frame structure that complies with stateoftheart timedivision duplex (TDD) protocols, which can be split into three stages for unifying similar radar and communication operations, namely 1) radar target search and communication channel estimation, 2) radar transmit beamforming and downlink communication and 3) radar target tracking and uplink communication. In each stage, we propose joint signal processing approaches that can fulfill both target detection and communication tasks via invoking hybrid beamforming. To be specific, in Stage 1, we estimate the AoAs of all the potential targets and the communication channel parameters by using both DL and UL pilots. Based on the estimation results, we propose in Stage 2 a novel joint HAD transmit beamforming design that can formulate directional beams towards the angles of interest, while equalizing the communication channel. Finally, in Stage 3 we track the angular variation by simultaneously processing the echoes of the targets while decoding the UL signal transmitted from the UE. Below we boldly and crisply summarize our contributions:

A novel mmWave mMIMO DFRC architecture that can simultaneously detect targets while communicating with the UE;

A novel TDD frame structure capable of unifying radar and communication operations;

A joint signal processing strategy that can search for unknown targets while estimating the communication channel;

A joint HAD beamforming design that formulates directional beams towards targets of interest while equalizing the influence of the channel;

A joint receiver design that can simultaneously track the variation of the targets while decoding the UL communication signals.
The remainder of this paper is organized as follows. Section III introduces the system model, Section IV proposes the basic framework of the DFRC system, Sections VVII consider the signal processing schemes for Stages 1, 2 and 3, respectively, Section VIII provides numerical results. Finally, Section IX concludes the paper and identifies a number of future research directions.
Notation: Unless otherwise specified, matrices are denoted by bold uppercase letters (i.e., ), vectors are represented by bold lowercase letters (i.e., ), and scalars are denoted by normal font (i.e., ). Subscripts indicate the location of the entry in the matrices or vectors (i.e., denotes the th entry of , and denote the ith row and the jth column of , respectively). , , , and stand for trace, transpose, Hermitian transpose, complex conjugate and pseudoinverse, respectively. and denote the norm and the Frobenius norm respectively.
Iii System Model
We consider an antenna massive MIMO DFRC BS that communicates with an antenna UE while detecting multiple targets. The system operates in TDD mode, and both BS and UE are assumed to be equipped with uniform linear arrays (ULA). To reduce the number of RF chains, the BS employs a fullyconnected hybrid analogdigital beamforming structure with RF chains, where . Since the size of the antenna array at the UE is typically much smaller than at the BS, we assume that the UE adopts fully digital beamforming structure.
We show a generic DFRC scenario in Fig. 1, where a collection of scatterers/radar targets are randomly distributed within the communication/sensing environment, which are yet to be detected by the BS. While all targets reflect back the echo wave to the BS, not all of them contribute to communication scattering paths between the BS and the UE. Recent literature on mmWave channel modeling has shown that the scattering model describes well the mmWave communication channel, which typically has a small number of scattered paths. We assume that only out of scatterers are resolvable in the communication channel, and that . Therefore, the rank of the communication channel is , which suggests that the channel can support up to independent data streams to be transmitted simultaneously. For convenience, both and are assumed to be known to the BS.
Remark 1: From a radar perspective, not all targets are of interest. Obstacles such as trees and buildings, are unwanted reflectors and are commonly referred to as “clutter” in the radar literature. Clutter interference can be avoided by not radiating or receiving in the corresponding directions. However, some of the clutter might come from significant scatterers in the communication channel (as shown by red triangles in Fig. 1). Therefore, for the purpose of estimating the channel parameters, it might still be necessary to beamform towards those scatterers. This is distinctly different from a pure radar target detection scenario. For convenience, we will not distinguish these two types of targets, and only identify the communication paths within the collection of all the targets, which will be discussed in detail in Sec. V.
Remark 2: There might also exist targets that are neither significant scatterers in the communication channel nor of any interest to the DFRC BS. For notational convenience and following most of the seminal literature in the area [59, 62, 64, 66, 68, 98], we will not discuss such targets in detail and simply incorporate the generated interference in the noise term.
While the hybrid beamforming technique is popular in mmWave mMIMO communications, it can be useful in the radar area as well. In fact, the HAD structure has already been exploited to design a type of novel radar system referred to as “phasedMIMO radar” [99], which is a compromise between the phasedarray radar and the MIMO radar. There has been a long debate in the radar community on which type of radar has better performance since the birth of the MIMO radar concept in 2004 [100, 101]. To be specific, the MIMO radar transmits independent waveforms by each antenna by employing a fully digital beamformer, whereas the phasedarray radar transmits via each antenna the phaseshifted counterpart of a benchmark signal, which indicates that there are multiple phase shifters and antennas but only a single RF chain used by the phasedarray radar. By exploiting higher degreesoffreedom (DoFs) and waveform diversity, the MIMO radar achieves higher detection probability at the cost of increasing the computational overhead and the hardware complexity [57, 58]. Moreover, due to the noncoherent combination of the received signals, the receive SINR of the MIMO radar is lower than that of its phasedarray counterpart [99]. It is against this background that the phasedMIMO radar has been proposed. By partitioning the antenna array into several subarrays [102], the phasedMIMO radar transmits individual digital signals by each RF chain, but performs coherent analog combination at each subarray, which is expected to strike a favorable performance tradeoff between both types of radars. Given the similarities between the HAD communication and the phasedMIMO radar, we consider their combination in the proposed DFRC system.
Iiia Radar Model
Let be a probing signal matrix sent by the BS, which is composed by snapshots along the fasttime axis. The echo wave reflected by the targets received at the BS can be expressed as
(1) 
where denotes the complexvalued reflection coefficient of the kth target, is the kth target’s azimuth angle, with being the steering vector of the transmit antenna array, finally represents the noise plus interference, with the variance . In the case of ULA, the steering vector can be written in the form
(2) 
where and denote the antenna spacing and the signal wavelength. Without loss of generality, we set . Following the standard assumptions in the literature [103, 98, 58], the signal model in (1) is assumed to be obtained in a particular rangeDoppler bin of interest, for which the range and the Doppler parameters are omitted in the model.
By arranging the steering vectors into a steering matrix , the reflected signal model in (1) can be equivalently recast as
(3) 
where , .
IiiB MmWave Communication Model
Let be a DL signal matrix sent from the BS to the UE, the received signal model at the UE can be formulated as
(4) 
where denotes the noise with the variance of , and is the narrowband mmWave communication channel, which is assumed constant throughout the duration , and can be expressed as follows by use of the extended SalehValenzuela model [104, 105]
(5) 
where and denote the complex scattering coefficient, the Angle of Arrival (AoA) and the Angle of Departure (AoD) of the lth scattering path, and
(6) 
represents the steering vector of the UE’s antenna array. Note that the scatterers of the communication channel are also part of the targets being detected by the BS. From the perspective of the UE, the AoDs belong to the set of AoAs of radar targets seen from the BS. We assume, without loss of generality, that . The received signal can be therefore rearranged as
(7) 
where
(8) 
Given the reciprocity of the TDD channel, the UL communication model can be accordingly expressed as
(9) 
where denotes the UL communication signal, and represents the noise having the variance of .
It can be observed in the model of (5) and (9) that the mmWave communication channel has an intrinsic geometric structure, which makes it equivalent to a bistatic radar channel [106], where the radar’s TX and RX antennas are widely separated instead of being collocated as in the monostatic case of (1). Accordingly, the scatterers act as known or unknown radar targets, depending on whether the channel has been estimated. Note that such equivalences do not hold for channels modeled by stochastic distributions, e.g., Rayleigh distribution, which contain little information about the geometric environment over which the communication takes place.
Iv The Dualfunctional RadarCommunication Framework
We further reveal some important insights by taking a closer look at both the radar and the communication models.
Remark 3: The aim of the communication is to decode data from the noisy signal under the knowledge of the channel state information. On the other hand, the radar acquires the geometric information of targets by sending a known probing signal. This indicates that, radar target detection is more similar to the channel estimation process rather than to the data communication itself.
Remark 4: Radar detection can also be viewed as a special communication scenario, where the targets unwillingly transmit their geometric information to the radar. Therefore, the radar targets may act as virtual communication users that communicate with the radar in an uncooperative manner.
Inspired by the above remarks, we propose the following mmWave DFRC framework, which aims for unifying radar and communication operations by joint signal processing, and can be generally split into the following three stages:
1) Radar target search and communication channel estimation
When the radar has no a priori knowledge about targets, the initial step is to search for potential targets in the whole angular domain. Similarly, when no channel information is available at the communication system, the CSI has to be estimated before any useful information can be decoded at the receiver. Note that both operations require a signal with beneficial auto and crosscorrelation properties in order to extract the target parameters or the scattering characteristics of the channel. Hence, it is natural to combine the two operations into a joint process. More specifically, in our case, the BS first sends omnidirectional DL pilots (DP), and then estimates the AoAs of all K targets in . The UE also receives the probing waveform through L scattering paths, based on which it estimates AoDs in , and sends back UL pilots (UP) to the BS. By exploiting the reciprocity of the DL and the UL channels, the BS is able to identify those targets which also play the role of scatterers in the communication link. We propose a joint solution for this operation in Sec. V.
2) Radar transmit beamforming and downlink communication
After the first stage, the BS will have the estimate of for all the targets. Nevertheless, the estimate of is only available at the UE. The BS then formulates directional DL beams towards the angles of the targets of interest by designing a joint sensingcommunication beamformer, and obtains more accurate observations. In the meantime, the joint beamformer designed aims for preequalizing the communication channel effects, so that the data can be correctly decoded at the UE. We propose and detail a joint solution for this operation in Sec. VI.
3) Radar target tracking and uplink communication
After Stage 2, the BS may receive both the target echoes and the UL signals, based on which it tracks the variation of target parameters while decoding the UL data transmitted from the UE. As we have discussed above, the targets can be viewed as virtual UEs that passively transmit their geometric parameters to the BS by reflecting the probing signal. In this spirit, we design sophisticated receive signal processing approaches to jointly fulfill both requirements, i.e., target parameter estimation and data decoding. We propose and detail a joint solution for this operation in Sec. VII.
As shown in Fig. 2, a specifically tailored frame structure is designed to coordinate the above DFRC operations based on a typical TDD protocol. In Stage 1, the BS transmits omnidirectional waveforms to search for targets and to estimate the communication channel, and then receives both the echoes from the targets and the UP from the UE. Since all the targets/scatterers are distributed in between the BS and the UE, and that the echoes are reflected instantaneously after hitting the targets, the roundtrip from the BS to the targets/scatterers is typically shorter than that from the BS to the UE given the processing delay of the UL communication. For this reason, we assume that the target echoes are always received ahead of the UL transmission. It is worth noting that a guard period^{2}^{2}2Note that the GP is typically used in TDD protocols such as TDDLTE. (GP) is required between DP and UP to avoid the interference between UP and target echoes [107]. The GP should be long enough to cover the longest roundtrip delay plus the length of the DP. In addition, the UP is designed to be much shorter than the DP to further avoid collision of the received signals. In Stage 2, the BS transmits DL data while formulating directional beams towards all the directions in based on the measurements in Stage 1. In Stage 3, the BS receives both the echoes and the UL data, based on which it tracks the variation of the targets while decoding the UL information. Here we reserve a shorter GP between DL and UL operations to guarantee a high UL data rate. As the UL data sequences are much longer than the UP in Stage 1, collision between the echo wave and the data is inevitable. To this end, we propose a successive interference cancellation (SIC) approach [108] at Stage 3 to mitigate the interference from the targets, which will be discussed in Sec. VII. It can be noted from above that the BS indeed acts as a pulsing radar that repeatedly transmits pulses and receives both echoes and UL signals. Following the standard radar literature, we term a transmitreceive cycle as a pulse repetition interval (PRI).
In what follows, we will design signal processing strategies for the above three stages, respectively.
V Stage 1: Radar Target Search and Communication Channel Estimation
In this section, we first introduce a novel pilot signal generation method for the purpose of joint target search and CSI acquisition, and then propose parameter estimation approaches at both the BS and the UE.
Va Pilot Signal Generation Using Hybrid Structure
Given a DP signal matrix , it is wellknown in the field of channel estimation that the optimal performance can be achieved if its covariance matrix satisfies
(10) 
where is the total transmit power. It can be seen from above that the optimal pilot signal transmitted on each antenna should be spatially orthogonal. Similar investigations in the MIMO radar literature have also revealed that, the CRB of target parameter estimation can be minimized by the use of orthogonal waveforms [58], in which case the spatial beampattern can be written as
(11) 
which is an omnidirectional beampattern. Naturally, such a beampattern transmits equivalent power at each angle, and will hence search for targets over the whole angular domain.
At a first glance, it seems that any orthogonal waveform can be used for both radar target search and channel estimation. Nevertheless, there are still some radarspecific requirements that the probing waveform should satisfy. For instance, waveforms having large timebandwidth product (TBP) are preferred by the radar, as it offers performance improvement in both the range resolution and the maximum detectable range. To this end, we propose to employ orthogonal linear frequency modulation (LFM) signals, which are commonly used MIMO radar waveforms. According to [109], the th entry of a orthogonal LFM waveform matrix can be defined as
(12) 
It can be readily proven that (12) satisfies the orthogonality property (10). Next, we consider to generate such a waveform matrix by invoking the HAD array. Let us denote the baseband signal matrix by , and the analog precoding matrix with unitmodulus entries by . The problem is to design both and , such that
(13) 
Due to the nonconvex unitmodulus constraints imposed on , it is difficult to solve the above equation directly. We therefore propose a construction method in the following.
For the signal transmitted on the nth antenna, note that as per (12), the following equation holds true for any adjacent timeslots
(14) 
By introducing the notation of
(15) 
(16) 
it follows that
(17) 
where denotes the tth column of .
In order to generate , we consider a simple strategy where the analog beamforming matrix changes on a timeslot basis, in which case the following two equations should be satisfied
(18a)  
(18b) 
where denotes the analog beamforming matrix at the tth timeslot. Therefore, it is sufficient to let
(19a)  
(19b) 
Furthermore, noting that , we can simply choose
(20) 
where denotes the allone vector. By the above method, the analog beamforming matrix and the baseband signal can be generated at each timeslot in a recursive manner. One can thus generate the LFM waveform in (12) for target search and channel estimation.
VB Parameter Estimation
After transmitting the waveform using the HAD architecture, the BS receives the signals reflected from the targets, which can be expressed as
(21) 
Then, the signal after analog combination can be accordingly expressed by
(22) 
where is the analog combination matrix having unitmodulus entries, is the equivalent receive steering vector, and . Since no a priori knowledge about the AoAs is available at this stage, there is no preference on the choice of the analog beamformer. To this end, we assume that each entry of is randomly drawn from the unit circle.
To estimate the angles, we invoke the classic MUltiple SIgnal Classification (MUSIC) algorithm, which is known to have high angle resolution [110]. Nevertheless, the conventional MUSIC approach requires the processing of multiple receptions of the reflected pulses. Typically, the number of such observations should be larger than the size of the antenna array, which is not realistic in the case of massive MIMO. Therefore, we propose a modification of the MUSIC algorithm where we estimate the AoAs using a single pulse. Let . The eq. (22) can be equivalently recast as
(23) 
Note the fact that when is sufficiently large. By recalling (10), the covariance matrix of (23) is given by
(24) 
where . Following the standard MUSIC algorithm, the eigenvalue decomposition of (24) is formulated as
(25) 
where and contain eigenvectors, which span the signal and the noise subspaces, respectively. It then follows that
(26) 
which suggests that are orthogonal to . The MUSIC spectrum can be thus formulated as
(27) 
By finding the K largest peaks of (27), we can readily locate the AoAs of the K targets.
The next step is to estimate associated with each AoA. Since the estimated angle is now available, we employ the Angle and Phase EStimation (APES) algorithm of [98, 111] to obtain an estimated with superior accuracy. Given each estimated , the APES technique aims at solving the following optimization problem [98]
(28) 
where is the weighting vector. Following [98], the optimal of (28) can be expressed as
(29) 
where
(30) 
Accordingly, the kth complex amplitude can be estimated by
(31) 
We then estimate the angle parameters at the UE, where the received signal matrix at the UE can be formulated as
(32) 
Similarly, the UE estimates by the MUSIC algorithm, and obtains the estimated angles .
VC Identifying Communication Channel Paths from Targets
While the BS has the knowledge of all the AoAs of targets, it still remains for us to distinguish which targets contribute to the scattering paths in the communication channel. In other words, the BS has to separate from . Also, the BS still has to estimate for each scattering path, as this is not equivalent to the reflection coefficient .
With the estimated at hand, the UE formulates the following transmit beamformer
(33) 
which aims for zeroforcing the steering matrix . Following the frame structure proposed in Sec. IV, the UE then sends a very short UP to the BS by using . Without loss of generality, we assume that the UP is an identity matrix . If is perfectly estimated, the signal received at the BS is
(34) 
To identify , the BS formulates the new analog combiner with K RF chains being activated, where the kth row of is given as
(35) 
After analog combination, the BS picks the specific entries having the largest moduli from , which are generated by the signal arriving from L AoAs of the communication channel. By doing so, the BS can identify .
Finally, we rebuild the steering matrix , and estimate the scattering coefficients by the simple leastsquares (LS) estimation. For clarity, we summarize the target search/channel estimation process in Algorithm 1.
Vi Stage 2: Radar Transmit Beamforming and Downlink Communication
In this section, we propose a novel joint transmit beamforming design at the BS for both target detection and DL communication by invoking the HAD structure. For supporting the radar functionality, we formulate directional beams towards the targets of interest to obtain more accurate observations. For the communication aspect, on the other hand, we equalize the channel.
Via Problem Formulation
Our goal is to design the analog and the digital beamforming matrices and to jointly approach the ideal radar and communication beamformers. Recalling that , the communication channel matrix has a rank of , which supports a maximum of independent data streams to be transmitted simultaneously. Nevertheless, we use a digital beamformer with larger size since we have to formulate extra beams towards the radar targets. In addition, the proposed method requires to have a full rank of . Accordingly, K RF chains are activated, leading to an analog beamformer. The signal vector received at the UE can therefore be expressed as
(36) 
where denotes the noise vector with variance , denotes the transmit signal vector, which can be further decomposed as
(37) 
where and are statistically independent of each other. Each entry of is assumed to follow a standard Gaussian distribution. Note that while both and are exploited for radar target detection, only is exploited for DL communication whereas contains no useful information, as the communication channel only supports transmission of L independent data streams .
Note that a pseudo inverse is unobtainable for the channel since neither nor is invertible. Therefore, both transmit and receive beamformings are required for equalizing the channel. By introducing , the channel can be equivalently expressed as . Noting that both and have a full rank of , and that they have been estimated at the BS and the UE respectively, we can formulate the corresponding zeroforcing (ZF) beamformers as
(38) 
While can be implemented as a fullydigital beamformer at the UE, can only be approximately approached by the hybrid array at the BS. In the meantime, the beamformer designed should also steer the beams towards all the K targets. Note that this is equivalent to designing the covariance matrix of the transmit signal, which is formulated as
(39) 
In what follows, we propose a lowcomplexity approach to the design of both and .
ViB Lowcomplexity Approach for DFRC Hybrid Beamforming Design
Based on the discussions above, a straightforward approach is to formulate each column of based on the steering vector associated with all the K angles, yielding
(40) 
Nevertheless, the above does not guarantee having a desired transmit beampattern, which also depends on . From (11) and (39), it becomes plausible that the transmit beampattern is solely dependent on if is an unitary matrix. To this end, we consider the following optimization problem by fixing as (40), yielding
(41) 
where is defined in (38), and is an auxiliary matrix that is to be designed later. The scaling factor ensures satisfying the total transmit power budget of . To be specific, the problem (41) aims at approximating the fullydigital ZF beamformer by using the first columns of while keeping the orthogonality of .
We can readily solve problem (41) by obtaining its global optimum despite the nonconvex constraint in . Based on [112, 90], problem (41) can be classified as an orthogonal Procrustes problem (OPP), whose optimal solution can be formulated in closedform as
(42) 
where
(43) 
is the singular value decomposition (SVD) of .
ViC Spectral Efficiency Evaluation
It can be noted that the above design is capable of guaranteeing the formulation of K narrow beams towards radar targets. To show this, we write the transmit beampattern as
(44) 
When is sufficient large, will be much smaller than for any , and thus a peak only appears if .
We then evaluate the performance of the communication by computing the spectral efficiency (SE). Let us firstly split the designed beamforming matrix as
(45) 
where By recalling (37), and multiplying (36) with , the postprocessing signal vector at the UE can be formulated by
(46) 
where stands for the average received power. The second term of (46) is the interference imposed on the UE as it contains no useful information. The spectral efficiency is therefore given as
(47) 
where is the covariance matrix of the interference plus noise, which is
(48) 
ViD Interference Reduction
The enhancement of SE requires addressing the interference term in (46). It can be observed that the interference power is mainly determined by , which is designed to approach in the optimization problem (41). Hence, the choice of is key to the hybrid beamforming design.
HBFNull Design: As an intuitive method, one may choose as a nullspace projection (NSP) matrix, such that . This can be realized by firstly performing the SVD of , and then choosing the right singular vectors associated with zero singular values as the columns of . By doing so, the solution of (41) will satisfy that and thus .
HBFOpt Design: To further mitigate the interference, we consider another option by letting . While it is impossible to approach zero by multiplying the right side of with any unitary matrix, we show that such a method brings significant benefits by proving the following proposition.
Proposition 1.
The interference can be completely eliminated by solving (41) upon letting .
Proof.
See Appendix. ∎
The intuition behind the HBFOpt method is simple. Based on (42) and (45), is obtained by letting all the nonzero singular values of be 1. As a result, is an approximation of . By letting , belongs to the nullspace of , and thus belongs to the nullspace of given the pseudoinverse structure of . Therefore, the interference of is zeroforced.
Vii Stage 3: Radar Target Tracking and Uplink Communication
After the joint transmission of radar and communication signals, the BS receives both the echo wave from the targets and the communication data from the UE. In this section, we propose a novel approach for joint radar target tracking and UL communication by relying on the knowledge of the previously estimated channel and target parameters.
Viia Receive Signal Model
According to the frame structure designed in Fig. 2, the signal received at the BS may fall into 2 categories: 1) Nonoverlapped radar echo and UL communication signal and 2) overlapped signals. Since in the nonoverlapped case both signals are interferencefree, they can be readily processed using the conventional approaches. We therefore focus our attention on the overlapped case, where the radar and communication signals are partially interfering with each other.
We show a generic model of the overlapped case in Fig. 3, where the overlapped period is marked as black. The received signal can be expressed as
(49) 
where denotes the noninterfered part of the radar echo wave, represents the mixture of the echo wave and the communication signal received from the UE with being the length of the overlapping period, and finally stands for the noninterfered part of the UE signal with being the length of the UL frame. It can be readily seen that .
By using the same notations from the previous sections, the above three signal matrices can be expressed as
(50) 
(51) 
(52) 
where , and contain the AoAs of all the K targets, the AoAs and the AoDs of the UL channel (which are the AoDs and the AoAs of the DL channel, respectively) estimated in the last PRI, , and represent accordingly the variations in these angles in the current PRI. Furthermore, contains the complex reflection coefficients of all the K targets, while contains the complex scattering coefficients of L communication paths. Referring to (50) and (52), and are the noninterfered parts of the radar and communication signals, while and are the signals in the overlapped period, and finally denote the Gaussian noise matrices.
To track the targets, the current AoAs and AoDs have to be estimated based on the previously estimated angles. As the angles are slowly varying as compared to the movement of the targets, we assume that these variations are relatively small. In contrast to the AoAs and AoDs, we assume that both and are random realizations that are independent of those of the last PRI, and hence have to be estimated again. Furthermore, we denote the transmitted signal in the PRI as
(53) 
which has been precoded by and designed in Stage 2, where generates K beams towards the estimated AoAs in . Finally, the UL communication signal is given by
(54) 
which has been precoded at the UE by in (33) with the knowledge of the previously estimated . Note that both and are assumed to be Gaussian distributed following the previous assumptions. For the sake of convenience, we employ the assumption that the BS can reliably identify the beginning of . This can be realized by inserting synchronization sequences at the beginning of the . The designed sequences should be orthogonal to the radar signal , such that the interference of the echo wave can be mitigated at the synchronization stage^{3}^{3}3Note that such synchronization sequences can be easily formulated as the nullspace projection matrix of the radar signal. Nevertheless, the data sequences that contain information from the UE are unlikely to be orthogonal to the radar signal. Hence, we still need to mitigate the radar interference when processing the communication signal after synchronization..
In what follows, we propose approaches for both target tracking and UL signal processing.
ViiB Target Tracking
After receiving , the first step is analog combination, which gives us
(55) 
where we activate all RF chains to formulate an analog combination matrix . To exploit the knowledge of the estimated angles in , the first K rows of (which represent the phase shifters linked with the first K RF chains) are set as
(56) 
which indicates that the receive beams are pointing to the previously estimated AoAs. The phase shifters in the remaining RF chains are randomly set, thus for creating redundant observations of the received data in order to improve the estimation accuracy.
An important fact that can be observed from (50)(52) is that the mutual interference signal in (51) will not degrade the AoA estimation performance. Instead, it may provide benefits in estimating some of the AoAs. This is because the BS receives both the echo waves and the communication signals from the angles in . As a result, the signal associated with these angles may have higher power than that associated with others, hence leading to better estimation performance.
Given the small variations in the AoAs, one may search in the small intervals within each instead of searching the whole angular domain. We therefore propose to apply the MUSIC algorithm to for estimating the AoAs. For each , we search for peaks in the MUSIC spectrum (27) within , where is the maximum angular variation of the targets.
ViiC Uplink Communication
In this subsection, we propose a promising technique for estimating the remaining target parameters and decode the communication signals. Since is not interfered by the communication signal, it can be used to estimate the target reflection coefficients . With the estimated AoAs at hand, one can apply the APES approach to obtain an estimate of , i.e., for each angle.
The communication signal can then be recovered by the SIC approach. Given the estimated parameters and , the target reflections can be reconstructed as
(57) 
where denotes the estimated variations of AoAs. Note that by multiplying , the matrix has been mapped to a lowerdimensional space having the size of . Therefore, one can only recover the communication signal after lowcomplexity analog combination. By subtracting the radar signal estimated, the interfered communication signal in can be estimated as
(58) 
Based on the above, the whole UL signal after analog combination can be expressed as
(59) 
Since the UL signal has been precoded by (33) at the UE, the steering matrix has been eliminated with limited errors. The BS can simply obtain the estimates of the pathlosses by the LS approach with the help of the known synchronization sequence, and construct a baseband ZF beamformer by computing the following pseudoinverse