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operations [6]–[10]. To this end, research efforts are well TABLE I underway to address the issue of communication and radar LISTOF ACRONYMS spectrum sharing (CRSS). AoA Angle of Arrival In general, there are two main research directions in CRSS: AoD Angle of Departure 1) Radar-communication coexistence (RCC) and 2) Dual- ATC Air Traffic Control functional Radar-Communication (DFRC) system design [11]. AV Autonomous Vehicle By considering the coexistence of individual radar and com- BS Base Station munication systems, the first category of research aims for CM Constant Modulus developing efficient interference management techniques, so CRSS Communication and Radar Spectrum Sharing that the two systems can operate without unduly interfering CRB Cram´er-Rao Bound with each other. On the other hand, DFRC techniques focus CSI Channel State Information on designing joint systems that can simultaneously perform DL Downlink wireless communication and remote sensing. The joint design DP Downlink Pilot benefits both sensing and signalling operations, decongests DFRC Dual-functional Radar-Communication the RF environment, and allows a single hardware platform GNSS Global Navigation Satellite-based Systems for both functionalities. This type of work has been extended GP Guard Period to numerous novel applications, including vehicular networks, HAD Hybrid Analog-Digital Beamforming indoor positioning and secrecy communications [12]–[14]. ICSI Interference Channel State Information Below we present existing, or potential application scenarios LTE Long-Term Evolution of CRSS from both civilian and military perspectives. LPI Low-probability of Intercept LoS Line-of-Sight B. Civilian Applications MIMO Multi-Input-Multi-Output mmWave Millimeter Wave 1) Coexistence of individual radar and wireless systems mMIMO Massive MIMO As discussed above, CRSS has originally been motivated by MUI Multi-user Interference the need for the coexistence of radar and commercial wireless MU-MIMO Multi-user MIMO systems. Next, we provide examples of coexisting systems in NR New Radio various bands. NSP Null-space Projection • L-band (1-2 GHz): This band is primarily used for long- NLoS Non Line-of-Sight range air-surveillance radars, such as Air Traffic Control PRF Pulse Repetition Frequency (ATC) radar, which transmits high-power pulses with PRI Pulse Repetition Interval broad bandwidth. The same band, however, is also used RCC Radar-Communication Coexistence by 5G NR and FDD-LTE cellular systems as well as the RCS Radar Cross Section Global Navigation Satellite System (GNSS) both in their RF Radio Frequency downlink (DL) and uplink (UL) [15]. RFID Radio Frequency Identification • S-band (2-4 GHz): This band is typically used for air- SIC Successive Interference Cancellation borne early warning radars at considerably higher trans- SINR Signal-to-Interference-plus-Noise Ratio mit power [16]. Some long-range weather radars also SNR Signal-to-Noise Ratio operate in this band due to moderate weather effects in SVD Singular Value Decomposition heavy precipitation [5]. Communication systems present TDD Time-division Duplex in this band include 802.11b/g/n/ax/y WLAN networks, UAV Unmanned Areial Vehicle 3.5 GHz TDD-LTE and 5G NR [17]. UE User Equippment • C-band (4-8 GHz): This band is very sensitive to weather UL Uplink patterns. Therefore, it is assigned to most types of UP Uplink Pilot weather radars for locating light/medium rain [5]. On V2X Vehicle-to-Everything the same band operate radars used for battlefield/ground WPS WiFi Positioning System 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]. the mmWave band is also exploited by the 802.11ad/ay 1 • MmWave band (30-300 GHz) : This band is convention- WLAN protocols [18]. ally used by automotive radars for collision detection Among the above coexistence cases, the most urgent issues and avoidance, as well as by high-resolution imaging arise due to interference between base stations and ATC radars radars [19]. However, it is bound to become busier, as [15]. Early in 2012, a report pointed out that airport radar could there is a huge interest raised by the wireless community delay the deployment of LTE in Southeast England, especially concerning mmWave communications, which are soon to at the main London gateways [21]. In the forthcoming 5G be finalized as part of the 5G NR standard [20]. Currently, network, the same problem still remains to be resolved. For 1Typically, communication systems operated close to 30GHz (e.g. 28GHz) reasons of clarity, we summarize the above coexistence cases are also referred as mmWave systems. in TABLE II. 3

TABLE II RADAR-COMMUNICATIONCOEXISTENCECASES

Frequency Band Radar Systems Communication Systems L-band (1-2GHz) Long-range surveillance radar, ATC radar LTE, 5G NR Moderate-range surveillance radar, ATC radar, IEEE 802.11b/g/n/ax/y WLAN, S-band (2-4GHz) airborne early warning radar LTE, 5G NR Weather radar, ground surveillance radar, C-band (4-8GHz) IEEE 802.11a/h/j/n/p/ac/ax WLAN vessel traffic service radar MmWave band (30-300GHz) Automotive radar, high-resolution imaging radar IEEE 802.11ad/ay WLAN, 5G NR

2) 5G mmWave localization for vehicular networks door environment. To address the above issue, Wi-Fi based In next-generation autonomous vehicle (AV) networks, positioning system (WPS) constitutes promising solutions, as vehicle-to-everything (V2X) communication will require low- a benefit of their low cost and ubiquitous deployment, while latency Gbps data rates; while general communications can requiring no additional hardware [13]. Essentially, WPS can deal with hundreds of ms delays, AV-controlled critical appli- be viewed as a type of passive radar, which locates the target cations require delays of the order of tens of ms [12]. In the based on the received signals sent by the user equipment (UE). same scenario, radar sensing should be able to provide robust, In general, the UE is localized based on the estimation of its high-resolution obstacle detection on the order of a centimeter. time of arrival (ToA) and AoA parameters. Alternatively, the At the time of writing, vehicular localization and networking localization information can also be obtained by measuring the schemes are mostly built upon GNSS or default standards such received signal strength (RSS) and by exploiting its fingerprint as dedicated short-range communication (DSRC) [22] and the properties (frequency response, signal strength regarding the D2D mode of LTE-A [19]. While these approaches do readily I/Q channel, etc.), which are then associated with a possible provide basic V2X functionalities, they are unable to fulfill the location in a pre-measured fingerprint database [26], [27]. demanding requirements mentioned above. As an example, the To gain more detailed information concerning the target 4G cellular system provides the localization information at an such as the human behavior, the receiver can process the accuracy on the order of 10m, at a latency often in excess of signal reflected/scattered by the human body, based on specific 1s, and is thus far from ensuring driving safety [12]. transmitted signals. This system is more similar to a bistatic It is envisioned that the forthcoming 5G technology, ex- radar than to conventional WPS. The micro-Doppler shift ploiting both massive MIMO antenna arrays and the mmWave caused by human activities can be further extracted from the spectrum, will be able to address the future AV network channel state information (CSI) of the Wi-Fi, and analyzed requirements [23], [24]. The large bandwidth available in the for recognizing human actions [28], [29]. Potential appli- mmWave band would not only enable higher data rates, but cations of such techniques go far beyond the conventional would also significantly improve range resolution. Further- indoor localization scenarios, which include health-care for more, large-scale antenna arrays are capable of formulating elderly people, contextual awareness, anti-terrorism actions “thumbtack-like” beams that accurately point to the directions and Internet-of-Things (IoT) for smart homes [28], [30], [31]. of interest; this could compensate for the path-loss encountered It is worth highlighting that a similar idea has been recently by mmWave signals, while potentially enhancing the angle applied by the Soli project as part of the Google Advanced of arrival (AoA) estimation accuracy. More importantly, as Technology and Projects (ATAP), where a mmWave radar the mmWave channel is characterized by having only a few chip is sophistically designed for finger-gesture recognition multipath components, there is far less clutter interference by exploiting the micro-Doppler signatures, hence enabling imposed on target echoes than that of the rich scattering touchless human-machine interaction [32]. channel encountered in the sub-6GHz band, which is thus The above technology can be viewed as a particular beneficial for localization of vehicles [12]. radar/sensing functionality incorporated into a Wi-Fi commu- For all advantages mentioned in Sec. I-A, it would make nication system, which again falls into the area of DFRC. sense to equip vehicle or road infrastructure sensors with joint Consequently, sophisticated joint signal processing approaches radar and communication functionalities. While the current need to be developed for realizing simultaneous localization DFRC system has considered sensors with dual functionality, and communications. those were mainly for the lower frequency bands, and cannot 4) Unmanned aerial vehicle (UAV) communication and be easily extended to the V2X scenario. However, several sensing problems need to be investigated in that context, such as UAVs have been proposed as aerial base stations to a range specific mmWave channel models and constraints. of data-demanding scenarios such as concerts, football games, 3) Wi-Fi based indoor localization and activity recognition disasters and emergency scenarios [33]. It is worth noting that Indoor positioning technologies represent a rapidly growing in all of these applications, communication and sensing are a market, and thus are attracting significant research interest pair of essential functionalities. In contrast to the commonly- [13], [25]. While the GNSS is eminently suitable for outdoor used camera sensor on the typical UAV platforms which are localizations, its performance degrades drastically in an in- sensitive to environmental conditions, such as light intensity 4 and weather, radio sensing is more robust and could thus Multi-function Radio Frequency Concept (AMRFC) project be incorporated into all-weather services. Additionally, radio was launched by the Defense Advanced Research Projects sensing could be adopted in drone clusters for formation flight Agency (DARPA) in 2005, whose aim was to design integrated and collision avoidance [34]. While both communication and RF systems capable of simultaneously supporting multiple sensing techniques have been individually investigated over functions mentioned above [39], [40]. In 2009, the Office of the past few years, the dual-functional design aspect remains Naval Research (ONR) sponsored a follow-up project namely widely unexplored for UAVs. By the shared exploitation of the Integrated Topside (InTop) program [41], with one of its the hardware between sensors and transceivers, the payload on goals to further develop wideband RF components and antenna the UAV is minimized, which increases its mobility/flexibility, arrays for multi-function RF systems based on the outcome of while reducing the power consumption [35]. AMRFC. 5) Others Clearly, the fusion of the radar and the communication Apart from the aforementioned research contributions, there subsystems is at the core of the above research. By realizing are also a number of interesting scenarios, where CRSS based this, a dedicated project named as “Shared Spectrum Access techniques could find employment, which include but are not for Radar and Communications (SSPARC)” was funded by the limited to: DARPA in 2013, and was further proceeded into the second • Radio Frequency Identification (RFID): A typical RFID phase in 2015 [8]. The purpose of this project is to release part system consists of a reader, reader antenna array and tags. of the sub-6GHz spectrum which is currently allocated to radar Tags can either be passive or active depending on whether systems for shared use by radar and wireless communications. they carry batteries. To perform the identification, the By doing so, SSPARC aims for sharing the radar spectrum reader firstly transmits an interrogation signal to the tag, not only with military communications, but also with civilian which is modulated by the tag and then reflected back wireless systems, which is closely related to the coexistence to the reader, giving a unique signature generated by cases discussed in Sec. I-B. the particular variation of the tag’s antenna load [36]. 2) Military UAV applications The RFID based sensing is carried out by establishing a In addition to the civilian aspect mentioned above, UAVs cooperative communication link between the reader and have also been considered as an attractive solution to a variety the tag. Hence this combines radar and communication of military missions that require high mobility, flexibility and techniques to a certain degree. covertness. Such tasks include search and rescue, surveillance • Medical sensors: To monitor the health conditions of and reconnaissance as well as electronic countermeasures patients, bio-sensors may be embedded in the human [42]–[44], all of which need both sensing and communication body. As these sensors support only low-power sensing operations. Similar to its civilian counterpart, the integration of relying on their very limited computational capability, the two functionalities could significantly reduce the payload the measured raw data has to be transmitted to an as well as the RCS of the UAV platform. external device for further processing. The most reliable On the other hand, UAVs can also be a threat to both solution for joint sensing and communication is yet to infrastructures and people, as it might be used to carry out be explored in that scenario [37]. This, however, requires both physical and cyber attacks. Moreover, even civilian UAVs more interdisciplinary approaches. can impose unintentional but serious danger if they fly into • Radar as a relay: In contrast to classic wireless com- restricted areas [45]. To detect and track unauthorized UAVs, munications, most of radar waveforms are high-powered various techniques such as radar, camera and acoustic sensors and strongly directional. These properties make the radar have been employed. Nevertheless, a dedicated equipment a suitable communication relay, which can amplify and specifically conceived for sensing UAVs could be expensive to forward weak communication signals to remote users deploy [46]. Therefore, there is a growing demand to utilize [38]. Again, joint radar and communication relaying can existing communication systems, such as cellular BSs, to play a significant role here. 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 low- C. Military Applications power radars, the future Ultra Dense Network (UDN) having 1) Multi-function RF systems a large number of cooperative micro BSs can be exploited as The development of shipborne and airborne RF systems, the urban air defense system, which provides early warning of including communication, electronic warfare (EW) and radar, the incoming threats. has historically been isolated from each other. The independent 3) Radar-assisted low-probability-of-intercept (LPI) com- growth of these sub-systems led to significant increase in munication the volume and weight of the combat platform, as well as The need for covert/secrecy communication has emerged in in the size of the antenna array. This results in a larger many defense-related applications, where sensitive information radar cross-section (RCS) and a consequently increased de- such as the locations of critical facilities should be protected tectability by adversaries. Moreover, the addition of such sub- during the transmission. The probability of intercept is thus systems will inevitably cause electromagnetic compatibility defined as a key performance metric for secrecy communi- issues, which may impose serious mutual interference on the cations. Conventionally, LPI is achieved by frequency/time existing subsystems. To address these problems, the Advanced hopping or spread-spectrum methods, which require vast time 5

TABLE III munication performance, joint waveform designs and resource APPLICATIONS OF THE CRSS TECHNOLOGY allocation approaches could be developed by invoking CRSS techniques [54]. Radar-comms coexistence, V2X network, Civilian Applications WiFi localization, UAV comms and sensing, For clarity, we summarize the aforementioned application RFID, Medical sensors, Radar relay, etc. scenarios of CRSS technologies in TABLE III. Multi-function RF system, LPI comms, Military Applications UAV comms and sensing, Passive radar, etc. II. LITERATURE REVIEW In this section, we review the recent research progress in the area of CRSS. We will firstly introduce the coexistence ap- and frequency resources [48], [49]. From a CRSS viewpoint, proaches for individual radar and communication systems, and however, a more cost-efficient approach would be to embed then the family of the dual-functional radar-communication the communication signal into radar echo waves to mask the system designs. 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 A. Radar-Communication Coexistence (RCC) and a radar transceiver. To elaborate briefly, the radar firstly 1) Opportunistic spectrum access emits a probing waveform, which is captured by the RF tag From the perspective of cognitive radio, a straightforward on its way to the targets. The tag then remodulates the radar approach is the so-called opportunistic spectrum access, in signal with communication information and sends it back which the radar is regarded as the primary user (PU) of to the radar, which is naturally embedded in the reflected the spectrum, whereas the communication system plays the radar returns [14]. The communication waveform should be role of the secondary user (SU). Such methods typically appropriately designed by controlling its transmit power and require the SU to sense the spectrum, by which a transmission the correlation/similarity with the radar waveform. As such, opportunity is obtained when the spectrum is unoccupied. To the communication signal can be hard to recognize at the avoid imposing interference on the radar, the communication adversary’s side, since it hides itself behind the random clutters system has to control its power to ensure that the radar’s and echoes. Nevertheless, it can be easily decoded at the radar interference-to-noise ratio (INR) does not become excessive by exploiting some a priori knowledge [50]. Accordingly, [55]. A similar approach has been adopted in [56] for the a number of performance trade-offs among radar sensing, coexistence of a rotating radar and a cellular BS. In this communication rate and information confidentiality can be scenario, the mainlobe of the radar antenna array rotates achieved by well-designed waveforms and advanced signal periodically to search for potential targets. The BS is thus processing techniques. allowed to transmit only when it is in the sidelobe of the 4) Passive radar radar. Under this framework, the minimum distance between From a broader viewpoint, passive radar, which exploits the two systems is determined given the tolerable INR level, scattered signals gleaned from non-cooperative communi- and the communication performance is also analyzed in terms cation systems, could be classified as a special type of of the DL data rate. CRSS technology. Such illumination sources can be television Although being easily implemented in realistic scenarios, signals, cellular BSs and digital video/audio broadcasting the above approaches are unable to fully exploit the shared use (DVB/DAB) [52]. To detect a target, the passive radar firstly of the spectrum. This is because the communication system receives a reference signal transmitted from a direct LoS can only operate under certain circumstances, namely when the path (usually referred as “reference channel”) from the above radar is not occupying the frequency and the spatial resources. external TXs. In the meantime, it listens to the scattered Additionally, the above contributions do not easily extend to counterpart of the same reference signal that is reflected facilitate coexistence with MIMO radar. Unlike conventional by potential targets (referred as “surveillance channel”) [53]. radars, the MIMO radar transmits omnidirectional waveforms Note that these scattered signals contain target information to search for unknown targets across the whole space, and similarly to the case of active radars. As a consequence, the formulates directional beams to track known targets of interest related target parameters can be estimated by computing the [57], [58]. Consequently, it is hard for the BS to identify the correlation between signals gleaned from the two channels. sidelobes of the MIMO radar, since the radar beampattern The passive radar is known to be difficult to locate or be may change randomly along with the movement of the targets. interfered, since it remains silent when detecting targets, and Therefore, more powerful techniques such as transmit precod- hence it is advantageous for covert operations. Furthermore, it ing design are required to cancel the mutual interference. requires no extra time/frequency resources, leading to a cost 2) Interference channel estimation that is significantly lower than that of its conventional active Before designing a transmit precoder, the interference chan- counterparts. For this reason, it has been termed “green radar” nel state information (ICSI), i.e. the information on the channel [53]. Nonetheless, it may suffer from poor reliability due to the where the mutual interference signals propagate, should be facts that the signal used is not specifically tailored for target firstly obtained. Conventionally, this information is obtained detection, and that the transmit source is typically not under by exploiting the received pilot signals received from the BS the control of the passive radar [53]. To further improve the at the radar, which might consume extra computational and detection probability while guaranteeing a satisfactory com- signaling resources [59]. As another option, the authors of [60] 6 proposed to build a dedicated control center connected to both gives the opportunity to the communication system to design systems via wireless or backhaul links, which would carry out its precoding scheme so that it minimizes the interference all the coordinations including ICSI estimation and transmit caused to the radar. In [64], the covariance matrix of the precoding design. In cases where the radar has priority, such communication signal and the sub-sampling matrix of the a control center would be part of the radar [59]. However, such MC-MIMO radar are jointly optimized, subject to power and a method would involve significant overhead. A novel channel capacity constraints. The corresponding optimization problem estimation approach has been proposed in [61] by exploiting is solved via Lagrangian dual decomposition and alternating the radar probing waveform as the pilot signal, where the radar minimization methods. By taking realistic constraints into is oblivious to the operation of the communication system. consideration, the authors further introduce signal-dependent Since the radar randomly changes its operational mode from clutter into the coexistence scenario in [60], which has to be searching to tracking, the BS has to firstly identify the working reduced to maximize the effective SINR of the radar while modes of the radar by hypothesis testing methods, and then guaranteeing the communication performance. It has been also estimate the channel. pointed out in [60] that while the interference imposed by 3) Closed-form precoder design the communication system onto the radar is persistent, the After estimating the interference channel, the precoder can interference inflicted by the radar upon the communication be designed at either the radar or the communication’s side. link is intermittent. By realizing this, the authors of [65] Similar to the zero-forcing (ZF) precoding of classic MIMO have considered the coexistence issues of a communication communication, a simple idea is the so-called null-space pro- system and a pulsed radar, and quantified the communication jection (NSP) [62], which typically requires the radar to have rate as the weighted sum of the rates with and without the the knowledge of the ICSI. In the NSP scheme, the radar firstly radar interference, which is named as the compound rate. The obtains the right singular vectors of the interference channel authors then formulate an optimization problem to maximize matrix by singular value decomposition (SVD), and then the rate subject to power and radar SINR constraints. It is constructs an NSP precoder relying on those vectors associated worth noting that this problem can be solved in closed-form with the null space of the channel. The precoded radar signal when the radar interference satisfies certain conditions. is projected onto the null-space of the channel, so that the To address the coexistence problem of the MIMO radar and interference power received at the BS is strictly zero. However, the multi-user MIMO (MU-MIMO) communication system, such a precoder might lead to serious performance losses of the the authors of [66] have proposed a robust beamforming design MIMO radar, for example by eroding the spatial orthogonality at the MIMO BS when the ICSI between the radar and the of the searching waveform. To cope with this issue, the authors communication system is imperfectly known. An optimization of [63] designed a carefully adjusted threshold for the singular problem is formulated for maximizing the detection probabil- values of the channel matrix and then formulated a relaxed ity of the radar, while guaranteeing the power budget of the NSP precoder by the right singular vectors associated with BS and the SINR of the DL users. Cui et al. [67] have further singular values that are smaller than the threshold. By doing proposed an interference alignment based transmit precoding so, the radar performance can be improved at the cost of design with special emphasis on the degree of freedom (DoF), increasing the interference power received at the BS. under the scenario where multiple communication users coex- Despite the above-mentioned benefits, there are still a ist with multiple radar users. More recently, a constructive number of drawbacks in NSP based approaches. For instance, interference based beamforming design has been proposed for the interference power can not be exactly controlled, since it the coexistence scenario [68], where the known DL multi-user is proportional to the singular values of the random channel. interference (MUI) is utilized for enhancing the useful signal Additionally, since the target’s response might fall into the power. As a result, the SINR of the DL users is significantly row space of the communication channel matrix, it will be improved compared to that of [66] given the same transmit zero-forced by the NSP precoder and as a consequence, be power budget. We refer readers to [69] for more details on the missed by the radar. Fortunately, these disadvantages could be topic of interference exploitation. overcome by use of convex optimization techniques, which 5) Receiver designs optimize the performance of both systems under controllable We end this section by briefly reviewing the receiver designs constraints. conceived for the coexistence of radar and communications. 4) Optimization based designs The aim of such a receiver is to estimate the target param- Pioneering effort on optimization based beamform- eters in the presence of the communication interference, or ing/signaling for the RCC is the work in [64], where the to demodulate the communication data while cancelling the coexistence of a point-to-point (P2P) MIMO communication radar interference, depending on which side it belongs to. To system and a Matrix-Completion MIMO (MC-MIMO) radar the best of our knowledge, most of the existing research is is considered. As a computationally efficient modification of focused on the second type, i.e., on the design of receivers for the MIMO radar, the MC-MIMO radar typically employs communication systems. a sub-sampling matrix to sample the receive signal matrix In [70], the authors consider a spectrum sharing scenario of the target echoes, and approximately recovers the target in which a communication receiver coexists with a set of information using the matrix completion algorithm [64]. The radar/sensing systems. In contrast to the cooperative scenarios random sub-sampling at the radar receive antennas modulates discussed in the relevant literature [60], [62], [64], the authors the interference channel, and increases its null space. This of [70] assume that the only information available at the com- 7 munication system is that the interfering waveforms impinging rate is to view each resolution unit of the radar as a “constel- from the radars fall into the subspace of a known dictionary. lation point”, as each unit can accommodate a distinguishable Given the sparse properties of both the radar interference and point-like target. In [73], the “channel capacity” of the radar the communication demodulation errors, several optimization is defined as the number of distinguishable targets, which is algorithms have been conceived for simultaneously estimating the maximum information that can be contained in the echo the radar interference, whilst demodulating the communication wave. symbols based on compressed sensing (CS) techniques. It In addition to the above definition, the authors of [72] is shown that the associated optimization problems can be have considered the mutual information between the radar efficiently solved via non-convex factorization and conjugate and the target. Intuitively, the variance of the noise imposed gradient methods. on the echo wave represents the uncertainty of the target In a typical coexistence scenario, the communication sys- information, and can be measured by the entropy of the echo. tem periodically receives radar interfering pulses having high From an information theoretical viewpoint, the radar cancels amplitudes and short durations, which implies that a narrow- part of the uncertainty by estimating the target parameters, band communication receiver experiences radar interference where the remaining part is lower-bounded by the Cram´er-Rao as an approximately constant-amplitude additive signal. Due Bound (CRB), which can be viewed as the minimum variance to the slow variation of the radar parameters, this amplitude achievable of the estimated parameter [74]. In light of this can be accurately estimated. Nevertheless, the phase shift of methodology, the authors of [72] consider a single-antenna the interfering signal is sensitive to the propagation delay, DFRC receiver, which can process the target echo wave and thus is difficult to obtain. In [71], the authors exploit the the UL communication signal simultaneously. Such a channel assumption that the amplitude of the radar interference is can be viewed as a special multi-access (MAC) channel, known to the communication receiver, whereas the phase shift where the target is considered as a virtual communication user. is unknown and uniformly distributed on [0, 2π]. With the An estimation rate is defined as the information metric for presence of the interfering signal receiving from the radar, the radar in [72]. By invoking the analytical framework of a pair of communication-related issues have been studied. the communication-only MAC channel, the trade-off between The first one is how to formulate the optimal decision region radar and communication performances is analyzed under on a given constellation based on the maximum likelihood different multi-access strategies. In [75], an integrated metric (ML) criterion. The second one, on the other hand, is how is proposed for the DFRC receiver, which is the weighted to design self-adaptive constellations that optimize certain sum of the estimation and communication rates. More recently, metrics, namely the communication rate and the symbol error this approach has been generalized to the multi-antenna DFRC rate (SER). It is observed via numerical simulations that the system in [76]. While the performance bounds of the DFRC optimal constellation tends to a concentric hexagon shape systems have been specified by the above contributions, the for low-power radar interference and to an unequally-spaced design of DFRC waveforms is still an open problem. pulse amplitude modulation (PAM) shape for the high-power 2) Temporal and spectral processing counterpart. 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 B. Dual-functional Radar-Communication (DFRC) System one can design dual-functional waveforms by embedding 1) Information theory for the DFRC useful information into radar signals. By realizing this, the It is well-understood that the radar works in a way that is authors of [78], [79] proposed to modulate chirp signals with fundamentally different from classic communication systems. communication bit sequences, where 0 and 1 are differentiated Specifically, the communication takes place between two or by exploiting the quasi-orthogonality of the up and down chirp more cooperative transceivers. By contrast, radar systems send waveforms. Likewise, the pseudo-random codes can also be probing signals to uncooperative targets, and infer useful used both as the probing signal and the information carrier information contained in the target echoes. To some degree, [80]. A simpler approach is proposed in [81] under a time- the process of radar target probing may be deemed as similar division framework, where the radar and the communication to the communication channel estimation, with the probing signals are transmitted in different time slots and thus do not waveforms acting as the pilot symbols. For designing a DFRC interfere with each other. system, one can unify radar and communication principles by In addition to the above approaches where the DFRC wave- invoking information theory, which may reveal fundamental forms are designed from the ground-up, a more convenient performance bounds of the dual-functional systems [72]. option would be to employ the existing communication signals In a communication system, the transmitted symbols are for target detection. In this spirit, the classic Orthogonal drawn from a discrete constellation that is known to both TX Frequency Division Multiplexing (OFDM) signal is considered and RX, which enables the use of bit rate as a performance as a promising candidate [82]. In [83], the authors proposed metric for the communication. By contrast, the useful informa- to transmit OFDM communication signals for vehicle detec- tion for radar is not in the probing waveform but rather in the tion. The impact of the random data can be eliminated by echo wave reflected by the target, which is however not drawn simple element-wise division between the transmitted OFDM from a finite-cardinality alphabet [38]. Drawing parallels from symbols and the received echoes. In contrast to its single- information theory, one way to measure the radar information carrier counterpart, the OFDM approach of [83] employs the 8 fast Fourier transform (FFT) and the inverse FFT (IFFT) for the applications in sub-6GHz band. To address the explosive Doppler and range processing, respectively, which obtains the growth of wireless devices and services, the forthcoming 5G velocity and the range parameters in a decoupled manner. It is network aims at an ambitious 1000-fold increase in capacity also possible to replace the sinusoidal subcarrier in the OFDM by exploiting the large bandwidth available in the mmWave as the chirp signal [84]. Accordingly, the fractional Fourier band. In the meantime, it is expected that the mmWave BS transform (FrFT) [85], which is built upon orthogonal chirp will be equipped with beneficial sensing capability, which may basis, is used to process the target return. find employment in a variety of scenarios such as vehicle- The above contributions have mainly investigated temporal to-everything (V2X) communications. Dual-functional radar- and spectral processing for designing DFRC waveforms, while communication in mmWave systems is a new and promising paying little information to the beneficial aspects of spatial research area. Recent treatises [92]–[94] propose to invoke processing. In what follows, we review the research progress the radar function to support V2X communications based in the design of MIMO DFRC systems. on the IEEE 802.11ad WLAN protocol, which operates in 3) Spatial processing the 60GHz band. As the WLAN standard is typically indoor Inspired by the space-division multiple access (SDMA) based and employs small-scale antenna arrays, it can only concept of MIMO communications, a straightforward MIMO support short-range sensing at the order of tens of meters. DFRC scheme is to detect the target in the mainlobe of the To overcome these drawbacks, the large-scale antenna arrays radar antenna array, while transmitting useful information in have to be exploited, which can compensate the high path- the sidelobe. One can simply modulate the sidelobe level using loss imposed on mmWave signals. Moreover, the high DoFs amplitude shift keying (ASK), where different powers repre- of massive antennas make it viable to support joint sensing sent different communication symbols [86]. Similarly, classic and communication tasks. In order to reduce the hardware phase shift keying (PSK) could also be applied for representing complexity and the associated costs, the maturing hybrid the bits as the phases of the signals received at the angle of the analog-digital (HAD) beamforming structure is typically used sidelobe [87]. Accordingly, multi-user communication can be in such systems [95], [96], which requires much fewer RF implemented by varying the sidelobes at multiple angles. To chains than the fully digital transceivers. While the authors of avoid any undue performance-loss of the radar, beampattern [97] have presented analog beamforming designs for small- invariance based approaches have been studied in [88], where scale MIMO DFRC, little attention has been paid to HAD the communication symbols are embedded by shuffling the based massive MIMO (mMIMO) DFRC systems, which might transmitted waveforms across the antenna array. In this case, be more practical, whilst maintaining compatibility with 5G the information is embedded into the permutation matrices. mmWave applications. 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 D. Main Contributions of Our Work frequency (PRF) of the radar, hence it is limited to the In this paper, we propose a novel architecture for a order of kbps. Moreover, the sidelobe embedding schemes can DFRC system operating in the mmWave band. We consider a only work when the communication receiver benefits from a mMIMO mmWave BS that serves a multi-antenna UE while line-of-sight (LoS) channel. This is because for a multi-path detecting multiple targets, where part of the targets are also channel, the received symbol will be seriously distorted by the the scatterers in the communication channel. To reduce the dispersed signals arriving from Non-LoS (NLoS) paths, where number of RF chains, an HAD beamformer is employed for all the sidelobe and the mainlobe power may contribute. To both transmission and reception at the BS. We propose a this end, the authors of [89] proposed several beamforming novel DFRC frame structure that complies with state-of-the- designs to enable joint MIMO radar transmission and MU- art time-division duplex (TDD) protocols, which can be split MIMO communication, in which the communication signal into three stages for unifying similar radar and communication was exploited for target detection, hence it would not affect operations, namely 1) radar target search and communica- the DL data rate. The joint beamforming matrix is optimized tion channel estimation, 2) radar transmit beamforming and to approach an ideal radar beampattern, while guaranteeing downlink communication and 3) radar target tracking and the DL SINR and the power budget. To conceive the constant- uplink communication. In each stage, we propose joint signal modulus (CM) waveform design for DFRC systems, the recent processing approaches that can fulfill both target detection contributions [90], [91] proposed to minimize the DL multi- and communication tasks via invoking hybrid beamforming. user interference (MUI) subject to specific radar waveform To be specific, in Stage 1, we estimate the AoAs of all the similarity and CM constraints. An efficient branch-and-bound potential targets and the communication channel parametersby (BnB) algorithm has been designed for solving the non-convex using both DL and UL pilots. Based on the estimation results, optimization problem, which finds the global optimum in tens we propose in Stage 2 a novel joint HAD transmit beam- of iterations. forming 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 C. Limitations of the Existing Works by simultaneously processing the echoes of the targets while Although there is a rich literature on various aspects of both decoding the UL signal transmitted from the UE. Below we RCC and DFRC scenarios, prior research mainly considers boldly and crisply summarize our contributions: 9

• A novel mmWave mMIMO DFRC architecture that can

simultaneously detect targets while communicating with ,QWHUHVWHGWDUJHWV the UE; 8QLQWHUHVWHGWDUJHWV UE • A novel TDD frame structure capable of unifying radar N and communication operations; r • A joint signal processing strategy that can search for unknown targets while estimating the communication channel; • A joint HAD beamforming design that formulates direc- L tional beams towards targets of interest while equalizing N the influence of the channel; t • A joint receiver design that can simultaneously track the variation of the targets while decoding the UL commu- nication signals. 'XDO IXQFWLRQDO 6FDWWHUHUVLQWKH The remainder of this paper is organized as follows. Section UDGDUFRPPV%6 FRPPVFKDQQHO III introduces the system model, Section IV proposes the basic Fig. 1. MmWave dual-functional radar-communication scenario. framework of the DFRC system, Sections V-VII 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 to be transmitted simultaneously. For convenience, both K and directions. L are assumed to be known to the BS. Notation: Unless otherwise specified, matrices are denoted Remark 1: From a radar perspective, not all targets are by bold uppercase letters (i.e., H), vectors are represented of interest. Obstacles such as trees and buildings, are un- by bold lowercase letters (i.e., α), and scalars are denoted wanted reflectors and are commonly referred to as “clutter” by normal font (i.e., θ). Subscripts indicate the location of in the radar literature. Clutter interference can be avoided the entry in the matrices or vectors (i.e., FRF (i, j) denotes by not radiating or receiving in the corresponding directions. the (i, j)th entry of FRF , FRF (i, :) and FRF (:, j) denote However, some of the clutter might come from significant the ith row and the jth column of FRF , respectively). tr ( ), scatterers in the communication channel (as shown by red T H ∗ † · ( ) , ( ) , ( ) and ( ) stand for trace, transpose, Hermitian triangles in Fig. 1). Therefore, for the purpose of estimating transpose,· · complex· conjugate· and pseudo-inverse, respectively. the channel parameters, it might still be necessary to beamform towards those scatterers. This is distinctly different froma pure and F denote the l2 norm and the Frobenius norm k·krespectively.k·k 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, III. SYSTEM MODEL which will be discussed in detail in Sec. V. We consider an Nt-antenna massive MIMO DFRC BS Remark 2: There might also exist targets that are neither that communicates with an Nr-antenna UE while detecting significant scatterers in the communication channel nor of multiple targets. The system operates in TDD mode, and both any interest to the DFRC BS. For notational convenience and BS and UE are assumed to be equipped with uniform linear following most of the seminal literature in the area [59], [62], arrays (ULA). To reduce the number of RF chains, the BS [64], [66], [68], [98], we will not discuss such targets in detail employs a fully-connected hybrid analog-digital beamforming and simply incorporate the generated interference in the noise structure with NRF RF chains, where NRF Nt. Since the term. size of the antenna array at the UE is typically≤ much smaller While the hybrid beamforming technique is popular in than at the BS, we assume that the UE adopts fully digital mmWave mMIMO communications, it can be useful in the beamforming structure. radar area as well. In fact, the HAD structure has already We show a generic DFRC scenario in Fig. 1, where a col- been exploited to design a type of novel radar system referred lection of K scatterers/radar targets are randomly distributed to as “phased-MIMO radar” [99], which is a compromise within the communication/sensing environment, which are yet between the phased-array radar and the MIMO radar. There to be detected by the BS. While all targets reflect back the echo has been a long debate in the radar community on which type wave to the BS, not all of them contribute to communication of radar has better performance since the birth of the MIMO scattering paths between the BS and the UE. Recent literature radar concept in 2004 [100], [101]. To be specific, the MIMO on mmWave channel modeling has shown that the scattering radar transmits independent waveforms by each antenna by model describes well the mmWave communication channel, employing a fully digital beamformer, whereas the phased- which typically has a small number of scattered paths. We array radar transmits via each antenna the phase-shifted coun- assume that only L out of K scatterers are resolvable in the terpart of a benchmark signal, which indicates that there are communication channel, and that L Nr Nt. Therefore, multiple phase shifters and antennas but only a single RF chain the rank of the communication channel≤ is L≤, which suggests used by the phased-array radar. By exploiting higher degrees- that the channel can support up to L independent data streams of-freedom (DoFs) and waveform diversity, the MIMO radar 10 achieves higher detection probability at the cost of increasing duration T , and can be expressed as follows by use of the the computational overhead and the hardware complexity [57], extended Saleh-Valenzuela model [104], [105] [58]. Moreover, due to the non-coherent combination of the L received signals, the receive SINR of the MIMO radar is lower T H = βlb (φl) a (ϕl) , (5) than that of its phased-array counterpart [99]. It is against this l=1 background that the phased-MIMO radar has been proposed. X where β , φ and ϕ denote the complex scattering coefficient, By partitioning the antenna array into several sub-arrays [102], l l l the Angle of Arrival (AoA) and the Angle of Departure (AoD) the phased-MIMO radar transmits individual digital signals of the lth scattering path, and by each RF chain, but performs coherent analog combination at each sub-array, which is expected to strike a favorable 2π 2π T b (φ)= 1,ej λ d sin(φ), ..., ej λ d(Nr−1) sin(φ) CNr×1 performance tradeoff between both types of radars. Given the ∈ (6) similarities between the HAD communication and the phased- h i represents the steering vector of the UE’s antenna array. MIMO radar, we consider their combination in the proposed Note that the scatterers of the communication channel are DFRC system. also part of the targets being detected by the BS. From the perspective of the UE, the AoDs ϕl, l belong to the set of ∀ A. Radar Model AoAs Θ= θ1, ..., θK of radar targets seen from the BS. We assume, without{ loss of} generality, that ϕ = θ ,l = 1, ..., L. Let X CNt×T be a probing signal matrix sent by the l l r The received signal can be therefore re-arranged as BS, which∈ is composed by T snapshots along the fast-time T axis. The echo wave reflected by the targets received at the YDL = B (Φ) diag (β) A (Θ1) XDL + NDL, (7) BS can be expressed as where K T B (Φ) = [b (φ1) , ..., b (φL)] , A (Θ1) = [a (θ1) , ..., a (θL)] Yecho = αka (θk)a (θk) Xr + Z, (1) T k=1 β = [β1, ..., βL] , Φ = [φ1, ..., φL] , Θ1 = θ1, ..., θL Θ. X { }⊆ (8) where αk denotes the complex-valued reflection coefficient of Given the reciprocity of the TDD channel, the UL communi- the kth target, θk is the kth target’s azimuth angle, with a (θ) cation model can be accordingly expressed as being the steering vector of the transmit antenna array, finally Nt×T T Z C represents the noise plus interference, with the YUL = A (Θ1) diag (β) B (Φ) XUL + NUL, (9) ∈ 2 variance σr . In the case of ULA, the steering vector can be Nr×T where XUL C denotes the UL communication signal, written in the form ∈ Nt×T and NUL C represents the noise having the variance 2π 2π T 2 ∈ a (θ)= 1,ej λ d sin(θ), ..., ej λ d(Nt−1) sin(θ) CNt×1, of σUL. ∈ It can be observed in the model of (5) and (9) that the (2) h i mmWave communication channel has an intrinsic geometric where d and λ denote the antenna spacing and the signal structure, which makes it equivalent to a bi-static radar channel wavelength. Without loss of generality, we set d = λ/2. [106], where the radar’s TX and RX antennas are widely sepa- Following the standard assumptions in the literature [58], [98], rated instead of being collocated as in the mono-static case of [103], the signal model in (1) is assumed to be obtained in a (1). Accordingly, the scatterers act as known or unknown radar particular range-Doppler bin of interest, for which the range targets, depending on whether the channel has been estimated. and the Doppler parameters are omitted in the model. Note that such equivalences do not hold for channels modeled By arranging the steering vectors into a steering matrix by stochastic distributions, e.g., Rayleigh distribution, which A (Θ) = [a (θ ) , ..., a (θ )], the reflected signal model in (1) 1 K contain little information about the geometric environment can be equivalently recast as over which the communication takes place. T Yecho = A (Θ) diag (α) A (Θ) Xr + Z, (3) HE UAL FUNCTIONAL ADAR OMMUNICATION T IV. T D - R -C where α = [α , ..., αK ] , Θ= θ ,θ , ..., θK . 1 { 1 2 } FRAMEWORK We further reveal some important insights by taking a closer B. MmWave Communication Model look at both the radar and the communication models. Remark 3: The aim of the communication is to decode data Let X CNt×T be a DL signal matrix sent from the DL from the noisy signal under the knowledge of the channel BS to the UE,∈ the received signal model at the UE can be state information. On the other hand, the radar acquires the formulated as geometric information of targets by sending a known probing signal. This indicates that, radar target detection is more YDL = HXDL + NDL, (4) similar to the channel estimation process rather than to the Nr×T where NDL C denotes the noise with the variance of data communication itself. 2 ∈ CNr×Nt σDL, and H is the narrowband mmWave commu- Remark 4: Radar detection can also be viewed as a spe- nication channel,∈ which is assumed constant throughout the cial communication scenario, where the targets unwillingly 11

PRI 1 PRI 2 PRI 3

Comms : DP GP UP DD GP UD DD GP UD

Radar

Echo : Radar transmit Radar transmit Radar target searching and Radar target tracking and Radar target tracking and beamforming beamforming comms channel estimation uplink comms uplink comms and downlink and downlink (Stage 1) (Stage 3) (Stage 3) comms comms (Stage 2) (Stage 2)

DP Downlink Pilots DD Downlink Data GP Guard Period

UP Uplink Pilots UD Uplink Data

Fig. 2. Frame structure of the DFRC system. transmit their geometric information to the radar. Therefore, After Stage 2, the BS may receive both the target echoes the radar targets may act as virtual communication users that and the UL signals, based on which it tracks the variation communicate with the radar in an uncooperative manner. of target parameters while decoding the UL data transmitted Inspired by the above remarks, we propose the following from the UE. As we have discussed above, the targets can be mmWave DFRC framework, which aims for unifying radar viewed as virtual UEs that passively transmit their geometric and communication operations by joint signal processing, and parameters to the BS by reflecting the probing signal. In can be generally split into the following three stages: this spirit, we design sophisticated receive signal processing 1) Radar target search and communication channel estima- approaches to jointly fulfill both requirements, i.e., target tion parameter estimation and data decoding. We propose and detail When the radar has no a priori knowledge about targets, a joint solution for this operation in Sec. VII. the initial step is to search for potential targets in the whole As shown in Fig. 2, a specifically tailored frame structure angular domain. Similarly, when no channel information is is designed to coordinate the above DFRC operations based available at the communication system, the CSI has to be on a typical TDD protocol. In Stage 1, the BS transmits estimated before any useful information can be decoded at omnidirectional waveforms to search for targets and to es- the receiver. Note that both operations require a signal with timate the communication channel, and then receives both beneficial auto- and cross-correlation properties in order to the echoes from the targets and the UP from the UE. Since extract the target parameters or the scattering characteristics of all the targets/scatterers are distributed in between the BS the channel. Hence, it is natural to combine the two operations and the UE, and that the echoes are reflected instantaneously into a joint process. More specifically, in our case, the BS after hitting the targets, the round-trip from the BS to the first sends omnidirectional DL pilots (DP), and then estimates targets/scatterers is typically shorter than that from the BS to the AoAs of all K targets in Θ. The UE also receives the the UE given the processing delay of the UL communication. probing waveform through L scattering paths, based on which For this reason, we assume that the target echoes are always it estimates L AoDs in Φ, and sends back UL pilots (UP) received ahead of the UL transmission. It is worth noting that to the BS. By exploiting the reciprocity of the DL and the a guard period2 (GP) is required between DP and UP to avoid UL channels, the BS is able to identify those targets which the interference between UP and target echoes [107]. The GP also play the role of scatterers in the communication link. We should be long enough to cover the longest round-trip delay propose a joint solution for this operation in Sec. V. plus the length of the DP. In addition, the UP is designed to 2) Radar transmit beamforming and downlink communica- be much shorter than the DP to further avoid collision of the tion received signals. In Stage 2, the BS transmits DL data while After the first stage, the BS will have the estimate of Θ formulating directional beams towards all the directions in Θ for all the targets. Nevertheless, the estimate of Φ is only based on the measurements in Stage 1. In Stage 3, the BS available at the UE. The BS then formulates directional DL receives both the echoes and the UL data, based on which beams towards the angles of the targets of interest by designing it tracks the variation of the targets while decoding the UL a joint sensing-communication beamformer, and obtains more information. Here we reserve a shorter GP between DL and UL accurate observations. In the meantime, the joint beamformer operations to guarantee a high UL data rate. As the UL data designed aims for pre-equalizing the communication channel sequences are much longer than the UP in Stage 1, collision effects, so that the data can be correctly decoded at the UE. between the echo wave and the data is inevitable. To this We propose and detail a joint solution for this operation in end, we propose a successive interference cancellation (SIC) Sec. VI. 3) Radar target tracking and uplink communication 2Note that the GP is typically used in TDD protocols such as TDD-LTE. 12 approach [108] at Stage 3 to mitigate the interference from Due to the non-convex unit-modulus constraints imposed on the targets, which will be discussed in Sec. VII. It can be FRF , it is difficult to solve the above equation directly. We noted from above that the BS indeed acts as a pulsing radar therefore propose a construction method in the following. that repeatedly transmits pulses and receives both echoes and For the signal transmitted on the nth antenna, note that as UL signals. Following the standard radar literature, we terma per (12), the following equation holds true for any adjacent transmit-receive cycle as a pulse repetition interval (PRI). time-slots

In what follows, we will design signal processing strategies SDP (n,t + 1) j2πn jπ (2t 1) = exp exp − . (14) for the above three stages, respectively. S (n,t) T T DP     By introducing the notation of V. STAGE 1: RADAR TARGET SEARCH AND COMMUNICATION CHANNEL ESTIMATION j2πn jπ (2t 1) u = exp , v = exp − , (15) n T t T In this section, we first introduce a novel pilot signal gen-     eration method for the purpose of joint target search and CSI u T acquisition, and then propose parameter estimation approaches = [u1,u2, ..., uNt ] , (16) at both the BS and the UE. it follows that

SDP (:,t + 1) = diag (u) SDP (:,t) vt, t, (17) A. Pilot Signal Generation Using Hybrid Structure ∀ Nt×T where SDP (:,t) denotes the tth column of SDP . Given a DP signal matrix SDP C , it is well-known in the field of channel estimation that∈ the optimal performance In order to generate SDP , we consider a simple strategy can be achieved if its covariance matrix satisfies where the analog beamforming matrix changes on a time-slot basis, in which case the following two equations should be 1 H P Rs = SDP SDP = INt , (10) satisfied T Nt F1 S S (18a) where P is the total transmit power. It can be seen from RF BB (:, 1) = 0 (:, 1) , t+1 t above that the optimal pilot signal transmitted on each antenna FRF SBB (:,t + 1) = diag (u) FRF SBB (:,t) vt, (18b) should be spatially orthogonal. Similar investigations in the t where FRF denotes the analog beamforming matrix at the tth MIMO radar literature have also revealed that, the CRB of time-slot. Therefore, it is sufficient to let target parameter estimation can be minimized by the use of orthogonal waveforms [58], in which case the spatial Ft+1 = diag (u) Ft , t, (19a) RF RF ∀ beampattern can be written as SBB (:,t +1) = SBB (:,t) vt, t. (19b) ∀ T ∗ d (θ)= a (θ) Rsa (θ)= P, θ, (11) Furthermore, noting that S 1 , we can ∀ DP (:, 1) = P/Nt Nt simply choose which is an omnidirectional beampattern. Naturally, such a p beampattern transmits equivalent power at each angle, and will 1 T P hence search for targets over the whole angular domain. FRF = 1Nt 1NRF , SBB (:, 1) = 1NRF , t, (20) N 2 N ∀ At a first glance, it seems that any orthogonal waveform can s RF t be used for both radar target search and channel estimation. where 1N denotes the N 1 all-one vector. By the above × Nevertheless, there are still some radar-specific requirements method, the analog beamforming matrix and the baseband that the probing waveform should satisfy. For instance, wave- signal can be generated at each time-slot in a recursive manner. forms having large time-bandwidth product (TBP) are pre- One can thus generate the LFM waveform in (12) for target ferred by the radar, as it offers performance improvement in search and channel estimation. both the range resolution and the maximum detectable range. To this end, we propose to employ orthogonal linear frequency B. Parameter Estimation modulation (LFM) signals, which are commonly used MIMO After transmitting the waveform SDP using the HAD archi- radar waveforms. According to [109], the (n,t)th entry of a tecture, the BS receives the signals reflected from the targets, orthogonal LFM waveform matrix can be defined as which can be expressed as P j2πn (t 1) jπ(t 1)2 K SDP (n,t)= exp − exp − . Y = α a (θ )aT (θ ) S + Z. (21) Nt T T ! echo k k k DP r   k (12) X=1 It can be readily proven that (12) satisfies the orthogonality Then, the signal after analog combination can be accordingly property (10). Next, we consider to generate such a waveform expressed by matrix by invoking the HAD array. Let us denote the baseband K CNRF ×T T signal matrix by SBB , and the analog precoding Y˜ echo = αkWRF a (θk)a (θk) SDP + WRF Z ∈ Nt×NRF matrix with unit-modulus entries by FRF C . The k ∈ X=1 (22) problem is to design both FRF and SBB, such that K T = αk˜a (θk)a (θk) SDP + Z˜, F S = S . (13) RF BB DP k X=1 13

NRF ×Nt NRF ×1 where WRF C is the analog combination matrix where wk C is the weighting vector. Following [98], ∈ NRF ×1 ∈ having unit-modulus entries, ˜a (θ) = WRF a (θ) C the optimal wk of (28) can be expressed as ∈ is the equivalent receive steering vector, and Z˜ = WRF Z. −1 ˆ Since no a priori knowledge about the AoAs is available at Q ˜a θk wk = , (29) this stage, there is no preference on the choice of the analog H −1  ˜a θˆk Q ˜a θˆk beamformer. To this end, we assume that each entry of WRF is randomly drawn from the unit circle. where     To estimate the angles, we invoke the classic MUltiple 1 H ∗ T H SIgnal Classification (MUSIC) algorithm, which is known to Q = R ˜ Y˜ echoS a θˆk a θˆk SDP Y˜ . Y − T 2P DP echo have high angle resolution [110]. Nevertheless, the conven-     (30) tional MUSIC approach requires the processing of multiple Accordingly, the kth complex amplitude can be estimated by receptions of the reflected pulses. Typically, the number of 1 such observations should be larger than the size of the antenna αˆ = wH Y˜ SH a∗ θˆ . (31) k T P k echo DP k array, which is not realistic in the case of massive MIMO.   Therefore, we propose a modification of the MUSIC algo- rithm where we estimate the AoAs using a single pulse. Let We then estimate the angle parameters at the UE, where the ˜ received signal matrix at the UE can be formulated as A (Θ) = [˜a (θ1) , ..., ˜a (θK )]. The eq. (22) can be equivalently recast as L T T YDL = βlb (φl) a (ϕl) SDP + NDL. (32) Y˜ echo = A˜ (Θ) diag (α) A (Θ) SDP + Z˜. (23) l=1 1 H X Note the fact that WRF W INRF when Nt is Nt RF Similarly, the UE estimates Φ by the MUSIC algorithm, and sufficiently large. By recalling (10), the≈ covariance matrix of obtains the estimated angles Φ=ˆ φˆ , ..., φˆ . (23) is given by 1 L n o 1 ˜ ˜ H P ˜ ˜ H 1 ˜˜H RY˜ = YechoYecho = A (Θ) RsA (Θ) + ZZ T Nt T C. Identifying Communication Channel Paths from Targets P ˜ ˜ H 2 H While the BS has the knowledge of all the AoAs of targets, = A (Θ) RsA (Θ) + σr WRF WRF Nt it still remains for us to distinguish which targets contribute P ˜ ˜ H 2 to the scattering paths in the communication channel. In other A (Θ) RsA (Θ) + σr NtINRF , , ≈ Nt words, the BS has to separate Θ1 from Θ2 Θ Θ1. Also, (24) \ the BS still has to estimate βl for each scattering path, as this where R α AT A∗ α∗ . Following s = diag ( ) (Θ) (Θ) diag ( ) is not equivalent to the reflection coefficient αl. the standard MUSIC algorithm, the eigenvalue decomposition With the estimated Φˆ at hand, the UE formulates the of (24) is formulated as following transmit beamformer H Σs Us −1 R = [U , U ] , (25) ∗ ˆ T ˆ ∗ ˆ CNr×L Y˜ s n Σ H FUE = B Φ B Φ B Φ , (33) n " Un # ∈         NRF ×K NRF ×(NRF −K) which aims for zero-forcing the steering matrix B . Fol- where Us C and Un C contain (Φ) eigenvectors,∈ which span the signal∈ and the noise subspaces, lowing the frame structure proposed in Sec. IV, the UE then respectively. It then follows that sends a very short UP to the BS by using FUE. Without loss of generality, we assume that the UP is an identity matrix I . ˜ ˜ L span A (Θ) = span (Us) , span A (Θ) span (Un) , If is perfectly estimated, the signal received at the BS is ⊥ Φ     (26) T YUL = A (Θ1) diag (β) B (Φ) FUE IL + NUL which suggests that ˜a (θk) , k are orthogonal to Un. The ∀ (34) MUSIC spectrum can be thus formulated as = A (Θ1) diag (β)+ NUL. 1 To identify Θ1, the BS formulates the new analog combiner PMUSIC (θ)= . (27) H H K×Nt ˜a (θ) UnUn ˜a (θ) GRF C with K RF chains being activated, where the ∈ By finding the K largest peaks of (27), we can readily locate kth row of GRF is given as the AoAs of the K targets. H GRF (k, :) = a θˆk , k. (35) The next step is to estimate αk associated with each AoA. ∀ Since the estimated angle ˆ is now available, we employ θk After analog combination, the BS picks the specific L entries the Angle and Phase EStimation (APES) algorithm of [98], having the L largest moduli from GRF yUL, which are gener- [111] to obtain an estimated αk with superior accuracy. Given ated by the signal arriving from L AoAs of the communication each estimated ˆ , the APES technique aims at solving the θk channel. By doing so, the BS can identify Θ . following optimization problem [98] 1 Finally, we rebuild the steering matrix A Θˆ 1 , and es- 2 H T min w Y˜ α a θˆ S timate the scattering coefficients βl, l by the simple least- w k echo k k 0   k ,αk − (28) squares (LS) estimation. For clarity, we∀ summarize the target   w H ˜a ˆ s.t. k θ =1, search/channel estimation process in Algorithm 1.   14

Algorithm 1 Stage 1: Radar Target Search and Communica- that both H˜ and B (Φ) have a full rank of L, and that they tion Channel Estimation have been estimated at the BS and the UE respectively, we can Step 1: BS sends DP to search targets and estimate the formulate the corresponding zero-forcing (ZF) beamformers as channel. −1 H H Step 2: BS receives the echo wave from targets, and FBS = H˜ H˜ H˜ , estimates Θ and α using MUSIC and APES. (38) H  −1 H Step 3: UE receives DP, and estimates Φ using MUSIC. WUE = B (Φ) B (Φ) B (Φ) . Step 4: UE formulates the ZF beamformer based on (33), While WUE can be implemented as
a fully-digital beam- and transmits UP. former at the UE, FBS can only be approximately approached Step 5: BS receives the UP, identifies the communication by the hybrid array at the BS. In the meantime, the beamformer paths by the analog combiner (35), and estimates β using FD = FRF FBB designed should also steer the beams towards the LS estimator. all the K targets. Note that this is equivalent to designing the covariance matrix of the transmit signal, which is formulated as VI. STAGE 2: RADAR TRANSMIT BEAMFORMING AND E H H E H H Rs = FDss FD = FD ss FD DOWNLINK COMMUNICATION H H (39) = FRF FBBFBBFRF
.
In this section, we propose a novel joint transmit beam- forming design at the BS for both target detection and DL In what follows, we propose a low-complexity approach to the communication by invoking the HAD structure. For supporting design of both FRF and FBB. the radar functionality, we formulate directional beams towards the targets of interest to obtain more accurate observations. For B. Low-complexity Approach for DFRC Hybrid Beamforming the communication aspect, on the other hand, we equalize the Design channel. Based on the discussions above, a straightforward approach is to formulate each column of FRF based on the steering A. Problem Formulation vector associated with all the K angles, yielding Our goal is to design the analog and the digital beamforming ∗ FRF (:,i)= a (θi) , i. (40) matrices FRF and FBB to jointly approach the ideal radar ∀ and communication beamformers. Recalling that L Nr Nevertheless, the above FRF does not guarantee having a ≤ ≤ Nt, the communication channel matrix H has a rank of L, desired transmit beampattern, which also depends on FBB. which supports a maximum of L independent data streams to From (11) and (39), it becomes plausible that the transmit be transmitted simultaneously. Nevertheless, we use a digital beampattern is solely dependent on FRF if FBB is an unitary K×K beamformer with larger size FBB C since we have to matrix. To this end, we consider the following optimization ∈ formulate extra beams towards the radar targets. In addition, problem by fixing FRF as (40), yielding the proposed method requires FBB to have a full rank of K. 2 min FRF FBB [FBS, Faux] F Accordingly, K RF chains are activated, leading to an Nt K FBB k − k × (41) analog beamformer. The signal vector received at the UE can H P s.t. FBBFBB = IK , therefore be expressed as KNt

T Nt×L yDL = B (Φ) diag (β) A (Θ1) FRF FBB s + nDL, (36) where FBS C is defined in (38), and Faux CNt×(K−L) is∈ an auxiliary matrix that is to be designed∈ n 2 s where DL denotes the noise vector with variance σDL, later. The scaling factor P ensures satisfying the total CK×1 denotes the transmit signal vector, which can be further∈ KNt transmit power budget of F F 2 . To be specific, decomposed as RF BB F = P the problem (41) aims atk approximatingk the fully-digital ZF s1 s = , (37) beamformer FBS by using the first L columns of FD while s " 2# keeping the orthogonality of FBB. We can readily solve problem (41) by obtaining its global where s CL×1 and s C(K−L)×1 are statistically inde- 1 2 optimum despite the non-convex constraint in F . Based on pendent of∈ each other. Each∈ entry of s is assumed to follow a BB [90], [112], problem (41) can be classified as an orthogonal standard Gaussian distribution. Note that while both s and s 1 2 Procrustes problem (OPP), whose optimal solution can be are exploited for radar target detection, only s is exploited for 1 formulated in closed-form as DL communication whereas s2 contains no useful information, as the communication channel only supports transmission of P F = U˜ V˜ H , (42) L independent data streams . BB KN r t Note that a pseudo inverse is unobtainable for the channel where H H H since neither HH nor H H is invertible. Therefore, both H H U˜ Σ˜V˜ = F [FBS, Faux] (43) transmit and receive beamformings are required for equalizing RF ˜ T the channel. By introducing H , diag (β) A (Θ1), the chan- is the singular value decomposition (SVD) of ˜ H nel H can be equivalently expressed as H = B (Φ) H. Noting FRF [FBS, Faux]. 15

C. Spectral Efficiency Evaluation Reflection Coefficient Estimation SIC Data Decoding It can be noted that the above design is capable of guar- anteeing the formulation of K narrow beams towards radar targets. To show this, we write the transmit beampattern as Radar Echo UL Data P d (θ)= aT (θ) F FH a∗ (θ) KN RF RF t Yecho ,1 Ym YUL ,2 K P 2 T ∗ 2 AoA Tracking  Nt + a (θ) a (θk) ,θ = θi Θ, i, KNt   ∈ ∀  k=1 =  Xk=6 i Fig. 3. Overlapped receive signal model.     K   P 2 aT a∗ (θ) (θk) ,θ / Θ. ˜  KNt ∈ HFRF FBB,2 0 and thus HFRF FBB,2 0.  k=1 ≈ ≈  X (44) HBF-Opt Design: To further mitigate the interference, we  T ∗ 2 When Nt is sufficient large, a (θi) a (θk) will be much consider another option by letting Faux = 0. While it is im- 2 smaller than N for any i = k, and thus a peak only appears possible to approach zero by multiplying the right side of FRF t 6 if θ Θ. with any unitary matrix, we show that such a method brings We∈ then evaluate the performance of the communication by significant benefits by proving the following proposition. computing the spectral efficiency (SE). Let us firstly split the Proposition 1. The interference can be completely eliminated designed beamforming matrix as by solving (41) upon letting Faux = 0. FD = FRF FBB = FRF [FBB,1, FBB,2] , (45) Proof. See Appendix.  K×L K×(K−L) where FBB, C , FBB, C . By recalling 1 ∈ 2 ∈ The intuition behind the HBF-Opt method is simple. Based (37), and multiplying (36) with WUE, the post-processing on (42) and (45), FBB,1 is obtained by letting all the non-zero signal vector at the UE can be formulated by H singular values of FRF FBS be 1. As a result, FRF FBB,1 is an F F 0 F ˜yDL = √ρWUE HFRF FBBs + WUE n approximation of BS. By letting aux = , BB,2 belongs H to the null-space of FRF FBS, and thus belongs to the null- = √ρWUEHFRF FBB,1s1 + √ρWUEHFRF FBB,2s2 space of HFRF given the pseudo-inverse structure of FBS. Useful Signal Interference Therefore, the interference of s2 is zero-forced. |+WUEnDL{z. } | {z } (46) VII. STAGE 3: RADAR TARGET TRACKING AND UPLINK where ρ stands for the average received power. The second COMMUNICATION term of (46) is the interference imposed on the UE as it After the joint transmission of radar and communication contains no useful information. The spectral efficiency is signals, the BS receives both the echo wave from the targets therefore given as and the communication data from the UE. In this section, we ρ −1 propose a novel approach for joint radar target tracking and UL IL + Rin WUEHFRF FBB,1 RDL = log det L , (47) communication by relying on the knowledge of the previously  H H H H  FBB,1FRF H WUE estimated channel and target parameters. ×   where Rin is the covariance matrix of the interference plus noise, which is A. Receive Signal Model H H H H According to the frame structure designed in Fig. 2, the Rin = ρWUEHFRF FBB,2FBB,2FRF H WUE (48) signal received at the BS may fall into 2 categories: 1) Non- 2W WH +σc UE UE. overlapped radar echo and UL communication signal and 2) overlapped signals. Since in the non-overlapped case both sig- D. Interference Reduction nals are interference-free, they can be readily processed using The enhancement of SE requires addressing the interference the conventional approaches. We therefore focus our attention term in (46). It can be observed that the interference power on the overlapped case, where the radar and communication is mainly determined by FRF FBB,2, which is designed to signals are partially interfering with each other. approach Faux in the optimization problem (41). Hence, the We show a generic model of the overlapped case in Fig. 3, choice of Faux is key to the hybrid beamforming design. where the overlapped period is marked as black. The received HBF-Null Design: As an intuitive method, one may choose signal can be expressed as

Faux as a null-space projection (NSP) matrix, such that Nt×T0 Y0 = [Yecho,1, Ym, YUL,2] C , (49) HF˜ aux = 0. This can be realized by firstly performing ∈ ˜ Nt×(T −∆T ) the SVD of H, and then choosing the right singular vec- where Yecho,1 C denotes the non-interfered part ∈ Nt×∆T tors associated with zero singular values as the columns of of the radar echo wave, Ym C represents the mixture ∈ Faux. By doing so, the solution of (41) will satisfy that of the echo wave and the communication signal received 16 from the UE with ∆T being the length of the overlapping synchronization stage3. Nt×(Tc−∆T ) period, and finally YUL, C stands for the non- In what follows, we propose approaches for both target 2 ∈ interfered part of the UE signal with Tc being the length of tracking and UL signal processing. the UL frame. It can be readily seen that T = T + Tc ∆T . 0 − By using the same notations from the previous sections, the B. Target Tracking above three signal matrices can be expressed as After receiving Y0, the first step is analog combination, T which gives us Yecho,1 = A Θ+∆Θˆ diag (α˜) A Θ+∆Θˆ Xr,1 +Z1, ˜     (50) Y0 = WRF Y0 NRF ×T0 = [WRF Yecho, , WRF Ym, WRF YUL, ] C , 1 2 ∈ Ym = Yecho,2 + YUL,1 (55) ˆ T ˆ where we activate all NRF RF chains to formulate an analog = A Θ+∆Θ diag (α˜) A Θ+∆Θ Xr,2 NRF ×Nt combination matrix WRF C . To exploit the knowl- ∈   ˜ T  edge of the estimated angles in Θˆ , the first K rows of W +A Θˆ 1 + ∆Θ1 diag β B Φ+∆Φˆ XUL,1 + Zm, RF (51) (which represent the phase shifters linked with the first K RF       chains) are set as

T H Y = A Θˆ + ∆Θ diag β˜ B Φ+∆Φˆ X WRF (k, :) = a θˆk , k, (56) UL,2 1 1 UL,2 ∀ +Z2,       which indicates that the receive beams  are pointing to the (52) previously estimated AoAs. The phase shifters in the remain- where Θˆ , Θˆ Θˆ and Φˆ contain the AoAs of all the K targets, 1 ⊆ ing RF chains are randomly set, thus for creating redundant the AoAs and the AoDs of the UL channel (which are the observations of the received data in order to improve the AoDs and the AoAs of the DL channel, respectively) estimated estimation accuracy. in the last PRI, ∆Θ, ∆Θ1 and ∆Φ represent accordingly the An important fact that can be observed from (50)-(52) is that variations in these angles in the current PRI. Furthermore, the mutual interference signal in (51) will not degrade the AoA α˜ contains the complex reflection coefficients of all the K estimation performance. Instead, it may provide benefits in ˜ targets, while β contains the complex scattering coefficients estimating some of the AoAs. This is because the BS receives of L communication paths. Referring to (50) and (52), Xr,1 both the echo waves and the communication signals from the and XUL, are the non-interfered parts of the radar and 2 angles in Θ1 + ∆Θ1. As a result, the signal associated with communication signals, while Xr,2 and XUL,1 are the signals these angles may have higher power than that associated with in the overlapped period, and finally Z1, Zm, Z2 denote the others, hence leading to better estimation performance. Gaussian noise matrices. Given the small variations in the AoAs, one may search To track the targets, the current AoAs and AoDs have to in the small intervals within each θˆk, k instead of searching be estimated based on the previously estimated angles. As the the whole angular domain. We therefore∀ propose to apply the angles are slowly varying as compared to the movement of the ˜ MUSIC algorithm to Y0 for estimating the AoAs. For each targets, we assume that these variations are relatively small. In θˆk, we search for peaks in the MUSIC spectrum (27) within contrast to the AoAs and AoDs, we assume that both α˜ and θˆk ∆ , θˆk + ∆ , where ∆ is the maximum an- β˜ are random realizations that are independent of those of the − max max max gular variation of the targets. last PRI, and hence have to be estimated again. Furthermore, h i we denote the transmitted signal in the PRI as C. Uplink Communication CNt×T Xr = [Xr,1, Xr,2] , (53) In this subsection, we propose a promising technique for ∈ estimating the remaining target parameters and decode the which has been precoded by F and F designed in Stage RF BB communication signals. Since Yecho,1 is not interfered by the 2, where FRF generates K beams towards the estimated AoAs communication signal, it can be used to estimate the target ˆ in Θ. Finally, the UL communication signal is given by reflection coefficients α˜. With the estimated AoAs at hand, one can apply the APES approach to obtain an estimate of Nr×Tc XUL = [XUL,1, XUL,2] C , (54) ˆ ∈ α˜k, i.e., α˜k for each angle. The communication signal can then be recovered by the SIC which has been precoded at the UE by FUE in (33) with the X ˆ approach. Given the estimated parameters and r, the target knowledge of the previously estimated Φ. Note that both Xr reflections can be reconstructed as and XUL are assumed to be Gaussian distributed following T the previous assumptions. For the sake of convenience, we Yˆ echo = A Θˆ + ∆Θˆ diag α˜ˆ A Θˆ + ∆Θˆ Xr, (57) employ the assumption that the BS can reliably identify the       3 beginning of XUL. This can be realized by inserting synchro- Note that such synchronization sequences can be easily formulated as the null-space projection matrix of the radar signal. Nevertheless, the data nization sequences at the beginning of the XUL. The designed sequences that contain information from the UE are unlikely to be orthogonal sequences should be orthogonal to the radar signal Xr, such to the radar signal. Hence, we still need to mitigate the radar interference that the interference of the echo wave can be mitigated at the when processing the communication signal after synchronization. 17 where ∆Θˆ denotes the estimated variations of AoAs. Note that Fortunately, the above interference will only be active during by multiplying WRF , the Nt T matrix Y has been mapped the first ∆T symbols, in which case the spectral efficiency can × 0 0 to a lower-dimensional space having the size of NRF T0. be given by Therefore, one can only recover the communication signal× ρ −1 after low-complexity analog combination. By subtracting the IL + Rin WBBWRF HFUE R1 = log det L , (62) radar signal estimated, the interfered communication signal in  H H H H  FUEH WRF WBB Ym can be estimated as × where   ˆ WRF YUL,1 = WRF Ym 1 H 2 H H T (58) Rin = WBBWRF YresYres + σULINt WRF WBB WRF A Θˆ + ∆Θˆ diag α˜ˆ A Θˆ + ∆Θˆ Xr,2. ∆T −   (63)       Based on the above, the whole UL signal after analog combi- is the covariance matrix of the interference plus noise, and nation can be expressed as ρ is the average received power. During the interference-free period having a length of Tc ∆T , the spectral efficiency can ˆ ˆ − WRF YUL = WRF YUL,1, WRF YUL,2 . (59) be expressed as h i ρ H H † Since the UL signal has been precoded by (33) at the UE, IL + 2 WRF WBB HFUE LσUL T R2 = log det . (64) the steering matrix B Φ+∆Φˆ has been eliminated with  H H H H
 FUEH WRF WBB limited errors. The BS can simply obtain the estimates of × The overall UL SE can be computed as the weighted summa- the path-losses β˜ˆ by the LS approach with the help of the tion of R and R , which is known synchronization sequence, and construct a baseband 1 2 ZF beamformer by computing the following pseudo-inverse ∆T Tc ∆T RUL = R1 + − R2. (65) Tc Tc ˆ † WBB = WRF A Θˆ 1 + ∆Θˆ 1 diag β˜ . (60) VIII. NUMERICAL RESULTS      In this section, we provide numerical results to validate the Upon multiplying WRF Yˆ UL by WBB, the communication symbols can be finally decoded. For clarity, we summarize performance of the proposed DFRC framework. Without loss the signal processing procedures of Stage 3 in Algorithm 2. of generality, the BS is assumed to be equipped with Nt = 64 antennas and NRF = 16 RF chains, which communicates with Algorithm 2 Stage 3: Radar Target Tracking and UL Com- a UE having Nr = 10 antennas. Unless otherwise specified, munication we assume that the BS is detecting K = 8 targets, wherein Step 1: BS receives both target echoes and UL signals that L = 4 of them act as the scatterers in the communication are partially overlapped with each other. channel. Unless otherwise specified, all the AoAs and AoDs are randomly drawn from the interval of [ 90◦, 90◦], which Step 2: BS formulates an analog combiner WRF based on − estimated Θˆ in the last PRI. has been uniformly split into 180 slices. All the reflection and Step 3: BS estimates the reflection coefficients and the the scattering coefficients are assumed to obey the standard angular variation ∆Θ by searching in a small interval within complex Gaussian distribution. each θˆk Θˆ . ∈ Step 4: BS recovers the radar echoes based on the estimates A. Radar Target Search and Channel Estimation from Step 3, and removes the radar interference in the We first show the performance of Stage 1 in Figs. 4-6 overlapped part of the received signal. with the aid of target search and channel estimation results. Step 5: BS formulates a ZF beamformer to equalize the More specifically, in Fig. 4, we show the target estimation communication channel, and decodes the UL data. performance for a single channel realization at SNR = 10dB for both DL and UP. We use a 64 100 LFM signal matrix as the DP, and a 4 4 identity matrix× as the UP. We compare the estimated results× to the true values for both Θ and Φ. It D. Spectral Efficiency Evaluation can be seen that the proposed MUSIC-APES and MUSIC-LS We round off this section by proposing a performance metric algorithms obtain accurate estimates of all the targets/scatterers for the UL communication. While the estimated radar inter- at both the BS and the UE. It is worth highlighting that ◦ ference has been subtracted from Ym, there will still be some the MUSIC-APES has a superior angular resolution of 2 , ◦ ◦ residual interference potentially degrading the communication which accurately differentiates the angle pairs [ 26 , 24 ] ◦ ◦ − − performance. The residual interference can be expressed as and [25 , 27 ]. We then consider another example in Fig. 5 at SNR =0dB, T Yres = A Θ+∆Θˆ diag (α˜) A Θ+∆Θˆ Xr,2 where there are two targets close to each other at the angles of [ 38◦, 37◦]. In this case, the BS fails to identify the target ˆ  ˆ  ˆ T ˆ  ˆ  Nt×∆T − −◦ A Θ + ∆Θ diag α˜ A Θ + ∆Θ Xr,2 C . at 38 despite that it successfully estimates all the other − ∈ −       (61) 7 targets. Furthermore, the UE makes a wrong estimation 18

Estimation of 2 2 MUSIC-APES Estimation True Value 1.5 -2 1

Amplitude 0.5 -6 0 -90 -60 -30 0 30 60 90 Comms channel, SNR = 0dB Angle (deg) Comms channel, SNR = 10dB -10

Estimation of NMSE (dB) Comms channel, SNR = 20dB 2 MUSIC-LS Estimation Radar channel, SNR = 0dB True Value 1.5 Radar channel, SNR = 10dB -14 Radar channel, SNR = 20dB 1

Amplitude 0.5 -18 10 20 30 40 50 60 70 80 90 100 0 -90 -60 -30 0 30 60 90 Pilots Length Angle (deg) Fig. 6. Estimation NMSE of both radar and communication channel.

Fig. 4. Angle estimation performance for Case 1 by using (27) and (31), SNR = 10dB, T = 100. 40 FD-ZF Estimation of 35 HBF-Opt 2 MUSIC-APES Estimation HBF-Null True Value 30 1.5 Unresolvable 1 25 AoAs Perfect CSI

Amplitude 0.5 20

0 15 -90 -60 -30 0 30 60 90 Estimated Angle (deg) CSI 10 Estimation of 1.5 Spectral Efficiency (bps/Hz) MUSIC-LS Estimation 5 True Value Error 1 Estimations 0 -30 -20 -10 0 10 20 0.5 Amplitude SNR (dB)

0 Fig. 7. Spectral efficiency of the DL communication by using (47). -90 -60 -30 0 30 60 90 Angle (deg) better than that of the communication channel. This is because Fig. 5. Angle estimation performance for Case 2 by using (27) and (31), the BS employs 64 antennas to estimate the AoAs, while the = 0 T = 100 SNR dB, . UE only has 10 antennas. In addition, the length of the UP has to be very short (in our case it is fixed as L =4) given the frame structure we proposed in Fig. 2, which might lead to at the angle of φ = 23◦ with an error of 1◦. As a result, 3 estimation errors in β. We will show in the next subsection that the estimations of the scattering coefficients β and β show 3 4 fortunately the overall communication performance is good, large errors compared to the true values. This suggests that despite the estimation errors in Stage 1. when the targets are too close to each other, the accumulated angular estimation errors will have an impact on the estimation performance of the path coefficients. Nevertheless, since most B. Radar Transmit Beamforming and Downlink Communica- of the angles are accurately estimated, the communication tion performance will only be marginally affected. Figs. 7-9 characterize the performance of Stage 2 in terms In Fig. 6, we show the normalized mean-squared error of the SE of the DL communication, the transmit beampattern (NMSE) of both the radar and communication channels upon and the number of the targets. In Fig. 7, we show the SE varying the SNR and the DP length by averaging 8000 versus SNR of both perfect CSI and estimated CSI cases, random channel realizations. It can be observed that the NMSE where ‘FD-ZF’ denotes fully digital ZF beamforming, ‘HBF- decreases in general with the growth of both parameters. Note Opt’ and ‘HBF-Null’ represent the hybrid beamforming de- that the estimation performance of the radar channel is far signs proposed in Sec. VI-D with Faux being zero and NSP 19

20 40 ZF Beamformer DFRC Beamformer

10 35

0 30

-10 FD-ZF, perfect CSI FD-ZF, estimated CSI 25 Beampattern (dBi) HBF-Opt, perfect CSI -20 Spectral Efficiency (bps/Hz) HBF-Opt, estimated CSI HBF-Null, perfect CSI HBF-Null, estimated CSI 20 8 9 10 11 12 13 14 15 -30 -90 -60 -30 0 30 60 90 Number of Targets Angle (deg) Fig. 9. Tradeoff between the spectral efficiency and the number of targets, SNR = 20dB. Fig. 8. Transmit beampatterns for the communication-only ZF beamformer and the proposed DFRC beamformers.

50 FD-ZF, perfect CSI matrices, respectively. There are slight SE performance-losses FD-ZF, estimated CSI for the cases with estimated CSI, which suggests that the HBF-ZF, zero interference, estimated CSI proposed channel estimation method guarantees a satisfac- 40 HBF-ZF-SIC, estimated CSI tory communication performance. Furthermore, we see that HBF-ZF, no SIC, estimated CSI in both the perfect and estimated CSI cases, the HBF-Opt 30 design outperforms the HBF-Null design by approaching the performance of the fully digital ZF beamformer, which verifies our derivation on interference reduction. 20 Fig. 8 shows the transmit beampattern for both the communication-only ZF beamformer and for the HBF beam- formers designed for the DFRC system proposed. While Spectral Efficiency (bps/Hz) 10 the HBF-Opt and the HBF-Null designs employ different unitary matrices as F , the resultant beampatterns are the BB 0 same since they use the same FRF . It can be seen that the -30 -20 -10 0 10 20 30 ZF beamformer only formulates beams towards 4 scatterers SNR (dB) in the communication channel, and thus fails to track the extra 4 targets. By contrast, the proposed DFRC beamformer Fig. 10. Spectral efficiency of the UL communication by using (65), 30% overlapped ratio. successfully generates 8 beams towards all the 8 targets. To explicitly illustrate the performance tradeoff between radar and communication, we show in Fig. 9 the DL spectral of the previous PRI are perfectly known, based on which efficiency by varying the number of targets at SNR = 20dB, the DFRC system tracks the variation of the angles in the where we fix the number of scatterers in the communication current PRI, while performing UL communications. As the channel as L = 4, and increase the total number of targets angle parameters typically vary slowly in realistic scenarios, from K = 8 to 15. Since illuminating more targets requires we assume without loss of generality that the variation of each more transmit power, less power is allocated to beams towards ◦ angle is less than ∆max =1 at each PRI, which is reasonable AoAs of the communication scatterers, leading to a reduced for a PRI of a few of milliseconds. The DL and UL frame SINR. As a result, the DL SE decreases upon increasing the lengths are set as 140. The communication signal and the target number of targets. Again, the SE of the HBF-Opt design is echo wave are overlapped with each other, and share the same larger than that of the HBF-Null design. It is also interesting SNR. While it is known that the equivalent SNR scenario is to observe the reduced SE of the fully digital ZF beamformer the worst case for the SIC-based approaches, we will show using estimated CSI, as the channel estimation becomes inac- next that our method can still achieve good performance. curate owing to the newly added targets. Fig. 10 shows the UL SE performance of the proposed approach in Sec. VII. It is noteworthy that by using the SIC C. Radar Target Tracking and Uplink Communication method proposed, the SE of the communication significantly Finally, we provide results for Stage 3 in Figs. 10-13, where increases compared to the cases with full radar echo interfer- we assume that the angle parameters of all the 8 targets ence in the overlapped period. Fig. 11 further illustrates the 20

40 2 ° Tracking Error for , = 2 max ° Tracking Error for , = 2 max ° Tracking Error for , = 1 max 30 1.5 ° Tracking Error for , = 1 max

20 1 RMSE (deg)

FD-ZF, perfect CSI 0.5 10 FD-ZF,estimated CSI

Spectral Efficiency (bps/Hz) HBF-ZF, zero interference, estimated CSI HBF-ZF-SIC, estimated CSI HBF-ZF, no SIC, estimated CSI 0 0 10 20 30 40 50 60 70 80 90 -30 -20 -10 0 10 20 30 Overlapped Ratio (%) SNR (dB) Fig. 13. Angle tracking RMSE vs. SNR. Fig. 11. Tradeoff between the spectral efficiency and the overlapped ratio, SNR = 20dB.

and the AoDs Φ of the scattering paths at SNR = 20dB Tracking Tracking − 90 40 for both target echoes and the communication signals. Note Markers: True Value Markers: True Value that the angles in Θ are estimated at the BS using both the Lines: Tracked Value Lines: Tracked Value target echoes and the UL signals, while the angles in Φ are 60 Target 1 20 Target/Path 1 estimated at the UE. It can be seen that all the angles can be Target 2 accurately tracked with slight tracking errors despite the low 30 0 Target 3 SNR, which verifies again the effectiveness of the proposed method. Similar results are observed in Fig. 13, where we 0 Target 4 -20 show the root-mean-squared-error (RMSE) of the proposed Target/Path 2 target tracking approach versus the SNR. It is shown that the Target 5 Angle (deg) Angle (deg) ◦ -30 -40 RMSE for all the estimations is less than 1 at most of the Target 6 Target/Path 3 ◦ ◦ SNR values for both ∆max =1 and 2 .

-60 Target 7 -60 Target/Path 4 ONCLUSION AND UTURE ESEARCH Target 8 IX. C F R -90 -80 A. Summary of the Proposed Approaches 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 No. of PRI No. of PRI In this paper, we have reviewed the application scenarios and recent research progress in the area of communication Fig. 12. Angle tracking performance at the BS and the UE, SNR = −20dB. and radar spectrum sharing (CRSS). We have proposed a novel dual-functional radar-communication (DFRC) system architec- ture that operates in the mmWave band, and is equipped with UL SE performance given the increased overlapped period a massive MIMO antenna array and a hybrid analog-digital ∆T , where the overlapping ratio is defined as ∆T/T . We see beamforming structure. We have further designed a novel TDD that the SE becomes worse for longer overlapped period, in frame structure that can unify the radar and communication which case the interference of the radar echo is not cancelled operations into 3 stages, namely 1) radar target search and thoroughly, and the residual interference power may have a channel estimation, 2) radar transmit beamforming and DL grave impact on the UL communication performance. When communication and 3) radar target tracking and UL communi- the overlapped period is short, the performance gain obtained cation. Accordingly, we have proposed joint signal processing by the SIC approach is marginal since the interference from strategies for each stage. In Stage 1, we aim for estimating the radar echo is small enough. On the other hand, when the the communication channel and searching for potential targets overlapped ratio is greater than 90%, the BS fails to recover the using orthogonal LFM signals generated by the HAD structure, radar signal, and thus is unable to cancel the interference by while identifying the communication paths from the radar using the SIC, which also leads to modest performance gain. targets. In Stage 2, we have designed both analog and digital Nevertheless, in most overlapping cases, the SIC approach precoders for generating directional beams towards all the works well by considerably improving the SE. targets and scatterers, while pre-equalizing the impact of the In Fig. 12, we evaluate the performance of the proposed communication channel. Finally in Stage 3, we have proposed target tracking approach, where we compare the tracking a joint scheme for tracking the angular variation of all the results and the true variation for the AoAs Θ of the targets targets, while decoding the UL communication signals by 21 using the SIC approach. Simulation results have been provided and communication systems [117], the DL DFRC channel to validate the proposed approaches, showing the feasibility needs further investigations. Here the key point is to view the of realizing both radar and communication functionalities on radar targets as virtual energy receivers, and hence the DFRC a single mmWave BS. transmission can be seen as the allocation of information and energy resources in the NLoS and LoS channels. From a higher-level perspective, one can also view the radar target B. Future Works as a relay, which receives the probing waveform and forwards While a number of contributions have been made to- it back to the radar, with its own parameter information being wards radar-communication coexistence and joint radar- embedded in the echo wave. As such, the target detection communication systems, the topic remains to be further ex- problem can be analyzed using the information theory of the plored within a broader range of constraints and scenarios. To relay channel, where a number of information metrics can this end, we list in the following a number of future research be defined. It is believed that such analysis could help us to directions in the area. understand the intrinsic nature of the DFRC systems, and point 1) Learning based CRSS us to the essential system design criteria. A key challenge for CRSS is to distinguish between the echoes from targets and communication signals from users APPENDIX in the presence of noise and interference. In addition to PROOF OF PROPOSITION 1 the proposed joint receiver design for the mmWave system H considered, it is also viable to apply machine learning (ML) Let us denote the SVD of FRF FBS as based approaches, such as the independent component analysis Σ˜ H ˜ ˜ s ˜ (ICA) algorithm, for signal classification in more generic FRF FBS = Us, Un Vs, (66) scenarios, given the independent statistical characteristics of " 0 # h i the two kinds of signals. A recent example can be found in ˜ CK×L ˜ CL×L [70] where the compressed sensing (CS) approach is employed where Us and Vs contain the left and right singular∈ vectors associated∈ with non-zero singular values, for joint parameter estimation and symbol demodulation. It is K×(K−L) and U˜ n C contains the left singular vectors expected that by using advanced ML based techniques, the ∈ receiver design for CRSS can be well-addressed. corresponding to zero singular values. We then compute the 2) Security issues optimal solution of (41) when Faux = 0. Note that Recent CRSS research raised security and privacy concerns. ˜ ˜ H ˜ ˜ Σs Vs By sharing the spectrum with communication systems, the FRF [FBS, Faux]= Us, Un , 0 V˜ n military radar may unintentionally give away vital information h i   (67) to commercial users, or even worse, to the adversary eaves- H which is the SVD of FRF [FBS, Faux] for Faux = 0, where droppers. To this end, physical layer security must be consid- V˜ n is an arbitrary (K L) (K L) unitary matrix. The ered in the CRSS scenarios, where a possible method is that optimal solution to problem− (41)× can− therefore be obtained in radar actively transmits artificial noise (AN) to the adversary the form target to contaminate the eavesdropping, while formulating ˜ desired beampatterns. In the meantime, the communication P ˜ ˜ Vs FBB = Us, Un ˜ performance also has to be guaranteed. Accordingly, a number KNt Vn r h i   (68) of performance trade-offs involving the radar detection and es- P ˜ ˜ ˜ ˜ timation performance, the communication rate and the secrecy = UsVs, UnVn . KNt rate remain to be studied. Some initial works on this topic can r h i be found in [113]–[115]. It follows that 3) DFRC for V2X P ˜ ˜ P ˜ ˜ FBB,1 = UsVs, FBB,2 = UnVn. (69) As an important application scenario of the DFRC system, KNt KNt vehicular networks have recently drawn much attention from r r It can be readily verified that F is indeed a unitary matrix both industry and academia, where joint sensing and commu- BB that satisfies the constraint in (41). Furthermore, we have nications at the mmWave band is required. While the proposed approaches in this paper focus on mmWave cellular systems, H H P ˜ H ˜ H H it can be extended to V2X applications with the consideration FBB,2FRF FBS = Vn Un FRF FBS = 0, (70) KNt of specific channel models for vehicle-to-vehicle (V2V) and r vehicle-to-infrastructure (V2I) scenarios. Again, such schemes which suggests that call for the design of novel beamforming/signaling approaches −1 H ˜ ˜ H ˜ [92], [93], [116]. FBSFRF FBB,2 = HH HFRF FBB,2 = 0. (71) 4) Information theory aspects   ˜ ˜ H To gain more in-depth insight into DFRC systems, infor- By multiplying the above equation with B (Φ)HH , we have mation theoretical analysis is indispensable for revealing the ˜ B (Φ) HFRF FBB,2 = HFRF FBB,2 = 0. (72) fundamental performance limit. While existing contributions have considered the DFRC UL [72] as well as coexisting radar This completes the proof. 22

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