An Overview of Signal Processing Techniques for Joint Communication and Radar Sensing
J. Andrew Zhang, Fan Liu, Christos Masouros, Robert W. Heath Jr., Zhiyong Feng, Le Zheng, Athina Petropulu
11 An Overview of Signal Processing Techniques forJoint Communication and Radar Sensing
J. Andrew Zhang,
Senior Member, IEEE , Fan Liu,
Member, IEEE ,Christos Masouros,
Senior Member, IEEE , Robert W. Heath Jr.,
Fellow, IEEE ,Zhiyong Feng,
Senior Member, IEEE , Le Zheng,
Member, IEEE , Athina Petropulu,
Fellow, IEEE
Abstract —Joint communication and radar sensing (JCR) rep-resents an emerging research field aiming to integrate the abovetwo functionalities into a single system, sharing a majorityof hardware and signal processing modules and, in a typicalcase, sharing a single transmitted signal. It is recognised asa key approach in significantly improving spectrum efficiency,reducing device size, cost and power consumption, and improvingperformance thanks to potential close cooperation of the twofunctions. Advanced signal processing techniques are critical formaking the integration efficient, from transmission signal designto receiver processing. This paper provides a comprehensiveoverview of JCR systems from the signal processing perspective,with a focus on state-of-the-art. A balanced coverage on bothtransmitter and receiver is provided for three types of JCRsystems, communication-centric, radar-centric, and joint designand optimization.
Index Terms —Dual-function Radar-Communications(DFRC), RadCom, Joint Radar-Communications (JRC),Joint Communications-Radar (JCR), Joint Communication andRadio/Radar sensing (JCAS).
I. I
NTRODUCTION
A. Background
Wireless communication and radar sensing (C&R) havebeen advancing in parallel yet with limited intersections fordecades. They share many commonalities in terms of signalprocessing algorithms, devices and, to a certain extent, systemarchitecture. They can also potentially share the spectrum.These have recently motivated significant research interests inthe coexistence, cooperation, and joint design (or co-design)of the two systems [1]–[13].The coexistence of C&R systems has been extensivelystudied in the past decade, with a focus on developing ef-ficient interference management techniques so that the twoindividually deployed systems can operate smoothly withoutinterfering with each other [3], [6], [14]–[18]. Although C&Rsystems may be co-located and even physically integrated,they transmit two different signals overlapped in time and/orfrequency domains. They operate cooperatively to minimizeinterference to each other. Great research efforts have beendevoted to mutual interference cancellation in this case, using,
J. A. Zhang is with the University of Technology Sydney, Aus-tralia. Email: [email protected]; F. Liu, the corresponding author,is with Southern University of Science and Technology, China. Email:[email protected]; C. Masouros is with University College London, UK.Email: [email protected]; R. W. Heath Jr. is with the North Carolina StateUniversity, USA. Email: [email protected]; Z. Feng is with Beijing Uni-versity of Posts and Telecommunications, China. Email: [email protected];L. Zheng is with the Aptiv Company, USA. Email: [email protected];A. Petropulu is with The State University of New Jersey, USA. Email:[email protected]. for example, beamforming (BF) design in [18] and cooperativespectrum sharing in [17]. However, effective interference can-cellation typically has stringent requirements on the mobilityof nodes and information exchange between them. The spectralefficiency improvement is hence limited in practice.The joint design of colocated C&R systems considers theintegration of these two functions in one system. The initialconcept may be traced back to 1960s [19], and the researchhad been primarily on multimode or multi-function militaryradars until 2010s. Recently, we are witnessing a boominginterest from both academia and industry on the joint system,thanks to its great potentials in emerging defence applicationsand more recently in a range of Smart Cities applicationssuch as intelligent vehicular networks [20], [21] and moregeneral, the Internet of Things (IoT) [5]. Where there is arecognised congestion of sensors and transceivers, integratingthe two systems in one can achieve reduced device size, powerconsumption, and cost, lead to more efficient radio spectrumusage, and is expected to significantly expand the capabilitiesand performance of both communication and radar sensing.The integration may be classified into the following twoclasses: (1) The two functions are physically integrated inone system, but they use two sets of dedicated hardwarecomponents, and/or two different waveforms, superimposed orseparated in time, frequency or spatial domains [2]; (2) Thetwo functions are more firmly integrated by sharing the ma-jority of hardware components and are delivered by the samewaveform, which is designed to optimize both communicationand radar performance [7], [8], [12]. The first class represents aloose integration and may only achieve limited benefits such asreduction in signalling overheads and removal of interference[12]. The second class is a step change beyond collocation,and is the main focus of this paper.Based on the design priorities and the underlying signal andsystems, current joint C&R systems may be classified into thefollowing three categories: • Communication-centric design . In this class, radar sens-ing is an add on to a communication system, wherethe design priority is on communications. The aim ofsuch design is to exploit communication waveform toextract radar information through target echoes. Enhance-ments to hardware and algorithms are required to supportradar sensing. Possible enhancements to communicationstandards may be introduced to enable better reuse ofthe communication waveform for radar sensing purposes.In this design, the communication performance can belargely unaffected, however, the sensing performance maybe scenario-dependent and difficult-to-tune; a r X i v : . [ ee ss . SP ] F e b • Radar-centric design . Conversely, such approaches aimat modulating or introducing information signalling inknown radar waveform. Since the radar signalling re-mains largely unaltered, the resulting approaches benefitfrom a near optimal radar performance. The main draw-back of such approaches is the limited data rates achieved.Some performance loss may be tolerated by the radar toenable better communication functionality; and • Joint design and Optimization . This class encompassessystems that are jointly designed from the start, to offera tunable trade-off between C&R performance. Suchsystems may not be limited by any of the existingcommunication or radar standards.Owing to the significant differences between traditional C&Rsystems, the design problems in these three categories arequite different. In the first two categories, the design andresearch focus is typically on how to realize the secondaryradar (communication) function based on the signal formatsof the primary communication (radar) system, in a way thatdoes not significantly affect the primary system. The lastcategory considers the joint design and optimization of thesignal waveform, system, and network architecture, with aflexible tradeoff achievable between C&R.These categories of joint systems have been receiving strongand growing research interest, with results having been re-ported under various names, such as Radar-communications(RadCom) [1], joint radar (and) communications (JRC) [7],[9], [11], joint communication (and) radar (JCR) [20], [22],joint communication and radar/radio sensing (JCAS) [23],[24], and dual-function(al) radar communications (DFRC) [4],[10], [25], [26]. The first three typically refer to a generaljoint system and can be used interchangeably. Sometimes JRCand JCR are used to differentiate between radar-centric andcommunication-centric designs. The term JCAS is introducedto stress the evolution of radar towards more general radiosensing applications of communication-centric joint systems.These sensing applications go beyond localization, trackingand object recognition of traditional radar functions, suchas human behaviour recognition and atmosphere monitoringusing radio signals [5]. DFRC is specifically used for jointsystems with a shared, single transmitted waveform. It hasbeen widely used for radar-centric joint systems [4], [8], andhas also been recently used for communication-centric systems[10], [25]. In the rest of this paper, we use the term JCR torefer to a general joint system, and use the term DFRC to referto joint systems with a shared single transmit waveform.
B. Contributions and Structure of this Paper
There exist some excellent overview articles on JCR, par-ticularly on system and signal modelling. For example, [1]provides a foundational review of signal models for basicsingle carrier and multicarrier JCR systems; [3], [6], [11] coverC&R systems from coexistence, cooperation, to co-design; [4],[8] survey radar-centric DFRC systems, with a focus on signalembedding; [7] delivers an excellent review on the evolutionof JCR systems and their potential applications; [12] providesan overview on mobile network JCR systems; [9], [10], [13] overview millimeter-wave JCR systems for automotivenetworks, providing detailed signal models. However, the topicof receiver signal processing, which is critical for the viabilityand performance of the JCR systems, has not been adequatelycovered by the aforementioned literature.The objective of this paper is to provide a comprehensiveoverview on JCR from the signal processing perspective, withbalanced coverage on both transmitter and receiver. For eachof the first two categories of JCR designs, we review mainsystems and typical signal models, and then discuss criticalsignal processing techniques at the receiver. For the thirdcategory, we provide a detailed overview of joint design andoptimization techniques. To reduce the overlap with existingarticles, we also focus on more recent technologies. Thedetailed structure of the rest of this paper is as follows. • Section II describes the signal and channel models oftypical C&R systems, separately. Via comparing thesemodels, we disclose the connections and differencesbetween C&R, which are very important for the under-standing and development of JCR technologies; • Section III provides a review on communication-centricJCR technologies. We first introduce two main JCRsystems based on 802.11ad and mobile networks, andthen discuss signal processing technologies on sensingparameter estimation, resolution of clock asynchrony, andsensing assisted communications; • Section IV reviews radar-centric JCR technologies. Well-known information embedding technologies are first sum-marized, and the recent promising technology of indexmodulation (IM) is elaborated, with reference to severalemerging radar systems. We then describe signal recep-tion and processing techniques for communications, in-cluding information demodulation and channel estimationfor IM. Codebook design for IM is also discussed; • A detailed review of joint design and optimizationtechnologies for JCR is provided in Section V. Thesetechnologies include waveform optimization via spatialprecoding, multibeam optimization for analog array, andsignal optimization in other domains. With these tech-nologies, balanced performance between C&R can beachieved as desired; and • Concluding remarks are provided in Section VI.
Notations: C denotes the set of complex numbers. ( · ) H , ( · ) ∗ , ( · ) T denote the Hermitian transpose, conjugate, andtranspose of a matrix or vector. n ! denotes n factorial and C nk = n ! / ( k !( n − k )!) denotes the binomial coefficient. (cid:98) x (cid:99) rounds towards negative infinity. { x m } , m = 1 , . . . , M denotes a column vector with elements x , . . . , x M .II. S YSTEM AND S IGNAL M ODELS
In this section, we describe some typical C&R systemsand their signal models. Since these systems and models aregenerally well known in respective areas, we only provide briefdescriptions as necessary to illustrate the JCR technologies.The basic pulsed radar, continuous-wave radar, and commu-nication systems are illustrated in Fig. 1. We first present abeamspace channel model that can be used for both C&R. We Tx RxLO Pulse n Pulse n+1
Pulsed Radar
Packet n Packet n+1
Preamble
Data payload
Communications
Tx Rx Tx Rx
Node A Node B Tx Continuous-wave Radar
BPF Rx time freq PRITransmitted chirp signal timeBeat freq PRIOutput0 Fig. 1. Illustration of basic pulsed radar, continuous-wave radar, and com-munication systems. Tx: transmitter; Rx: Receiver; BPF: bandpass filter; PRI:Pulse repetition interval. then describe signal models for C&R separately, and highlightthe differences between them. Signal models for JCR will bedescribed in later sections, based on the models presented here.For the simplicity of notation, we assume the total transmittedpower of all systems is , unless noted otherwise.We consider a general system with Q ≥ nodes and eachnode has a uniform linear antenna array (ULA). Let B denotethe total signal bandwidth. For MIMO-OFDM systems, B isdivided into N subcarriers and the subcarrier interval is f = B/N . The OFDM symbol period is T s = T + T cp where T = N/B and T cp is the period of cyclic prefix.In this section, for the clarity of illustration, we describethe signal models with reference to a general transmitter andreceiver without indexing them. Later, when these models needto be differentiated for different nodes, we will add a subscriptof the node index to the variables in the models. A. Beam-space Channel Models
Let the angle-of-departure (AoD) and angle-of-arrival(AoA) of a multipath be θ (cid:96) and φ (cid:96) , (cid:96) ∈ [1 , L ] , respectively.Assume a planar wave-front in signal propagation. The arraysteering/response vector of a ULA is given by a ( M, α ) = [1 , e j πd/λ sin( α ) , · · · , e j ( M − πd/λ sin( α ) ] T , where M is the number of antennas, λ is the wavelength, d is the interval of antennas, and α is either AoD or AoA.For M T transmitting and M R receiving antennas, the M R × M T time-domain baseband channel matrix at time t can berepresented as H ( t ) = L (cid:88) (cid:96) =1 b (cid:96) δ ( t − τ (cid:96) − τ o ( t )) e j π ( f D,(cid:96) + f o ( t )) t · a ( M R , φ (cid:96) ) a T ( M T , θ (cid:96) ) , (1)where for the (cid:96) -th multipath, b (cid:96) is its amplitude of complexvalue, accounting for both signal attenuation and initial phasedifference; τ (cid:96) is the propagation delay; f D,(cid:96) is the associatedDoppler frequency; and τ o ( t ) and f o ( t ) denote the potential time-varying timing offset and carrier frequency offset (CFO)due to possibly unlocked clocks between transmitter andreceiver, respectively. Here, we ignore the “beam squint” effectin BF and assume b (cid:96) is frequency independent.Equation (1) represents a general channel model that can beused for both C&R, although the physical meaning and namesof these parameters are slightly different. Our descriptionabove is mainly based on the terminologies in communica-tions. For radar sensing, { τ (cid:96) , f D,(cid:96) , φ (cid:96) , θ (cid:96) , b (cid:96) } are the sensingparameters to be estimated. These parameters can be used todetermine a target/reflector’s spatial and moving information.In particular, φ (cid:96) and θ (cid:96) are the AoA and AoD of the target inrelation to the receiving and transmitting ULA, resepctively; τ (cid:96) = R (cid:96) /c and f D,(cid:96) = v (cid:96) f c /c where R (cid:96) is the signalpropagation distance, c is the speed of light, v (cid:96) is the radialvelocity of the reflector, and f c is the carrier frequency; and b (cid:96) is related to the radar cross-section (RCS) and materialproperty of the target. We define a coherent processing interval(CPI) when all these parameters remain almost unchanged.The length of CPI depends on the mobility of objects in thechannels and is typically a few milliseconds when objectsmove at speeds of tens of meters per second.For a broadband OFDM system, the frequency-domainchannel matrix at the n -th subcarrier corresponding to (1) is ˜ H n ( t ) = L (cid:88) (cid:96) =1 b (cid:96) e − j πn ( τ (cid:96) + τ o ( t )) f e j π ( f D,(cid:96) + f o ( t )) t · a ( M R , φ (cid:96) ) a T ( M T , θ (cid:96) ) , (2)where we have approximated the slightly varying phases dueto Doppler frequency and CFO over one OFDM block as aconstant value. For the k -th OFDM symbol with t = kT s , wedenote ˜ H n,k = ˜ H n ( t ) t = kT s .Note that for communications, we generally only need toknow the composite values of the matrix H ( t ) or ˜ H n ( t ) . Theycan typically be obtained by directly estimating channel coef-ficients, or for OFDM, directly estimating at some subcarriersand obtaining the rest via interpolation. For radar sensing,however, the system needs to resolve the detailed channelstructure and estimate the sensing parameters. Note that thisbeam-space channel model is also widely used in millimeterwave (mmWave) communication systems.When the oscillator clocks of the transmitter and receiverare not locked/synchronized, both the timing offset τ o ( t ) andCFO f o ( t ) are nonzero. The values of τ o ( t ) can also be fasttime-varying in terms of ranging due to crystal oscillator’sinstability, while CFO changes relatively slower. For example,for a typical clock stability of parts-per-million (PPM), theaccumulated maximal variation of τ o ( t ) over millisecondcan be nanoseconds, which translates to a ranging errorof meters. For communications, these offsets are generallynot a big problem, as τ o ( t ) can be absorbed into channelestimates after synchronization, and f o ( t ) can be estimated andcompensated. Their residual values become relatively smallcompared to the baseband signal parameters. However, forradar sensing, when these offsets are unknown to the receiver,they can cause ambiguity in range and speed estimation, and become obstacles for processing signals across packetscoherently. B. Basic Communication Systems and Signals
We consider a node transmitting M S spatial streams with M T ≥ M S antennas. The description here is with referenceto a single user MIMO system, and it will be extended tomultiuser MIMO later.
1) Single Carrier MIMO:
For a general single carrier (SC)MIMO system, we can represent the baseband signal vectorat time t from the transmitter as x ( t ) = Ps ( t ) , (3)where P is the spatial precoding matrix of size M T × M S andis typically fixed over a packet, and s ( t ) are the data vector of M S × . The symbols s ( t ) can be either the directly modulatedconstellation points that are unknown to the receiver, or knownpilots. In the case of spread spectrum signals, each elementin s ( t ) can be the product of a pseudo-random code and theconstellation point (or pilot).For a narrowband system, after propagating over the channel H ( t ) , the received signals are given by y ( t ) = H ( t ) (cid:126) x ( t ) + z ( t ) , (4)where (cid:126) denotes convolution, and z ( t ) is the AWGN.
2) MIMO-OFDM:
For a MIMO-OFDM system, the base-band transmitting signals at subcarrier n in the k -th OFDMsymbol over all antennas can be represented as ˜ x n,k = P n,k s n,k , (5)where these variables are similarly defined as those in (3),but could have different values for different subcarriers. Inthe case of MIMO-OFDMA, each node may be allocated to aresource block occupying groups of the antennas, subcarriers,and OFDM symbols, that are typically non-overlapping. Theseblocks can be discontinuous and irregular in these domains,which can cause significant challenges in sensing parameterestimation, as will be discussed in Section III-C.After propagating over the channel, the received frequency-domain baseband signals at subcarrier n over all antennas aregiven by ˜ y n,k = ˜ H n,k ˜ x n,k + ˜ z n,k , (6)where ˜ z n,k is the AWGN. C. MIMO Radar Signals and Systems
In a MIMO radar, the waveforms transmitted from differentantennas are typically orthogonal, and the waveform can beeither pulsed or continuous waveforms. The MIMO radarbaseband waveform at a transmitter with M T antennas canbe expressed as x R ( t ) = M T (cid:88) m =1 w m ψ m ( t ) = W ψ ( t ) , (7)where x R ( t ) = { x R,m ( t ) } , m = 1 , . . . , M T with x R,m ( t ) being the signal at the m -th antenna, ψ m ( t ) is the basic radar waveform, w m is the M T × precoding/BF vector, and W = [ w , · · · , w M T ] and ψ ( t ) = { ψ m ( t ) } , m = 1 , · · · , M T .Note that in radar, the peak to average power ratio (PAPR) ofthe transmitted signal is typically required to be very low,so that high power efficiency can be achieved. Thus W istypically an identity matrix.The basic waveforms ψ m ( t ) can be any set of signals thatare orthogonal in either one or multiple domains of time,frequency, space, and code. It can also take any waveformof pulsed and continuous-wave radars [27], [28]. In pulsedradar systems, short pulses of large bandwidth are transmittedeither individually or in a group, followed by a silent periodfor receiving the echoes of the pulses, as can be seen from Fig.1. Continuous-wave radars transmit waveforms continuously,typically scanning over a large range of frequencies. In bothsystems, the waveforms are typically non-modulated.Referring to the channel model in (1), τ o ( t ) and f o ( t ) arezeros for radar since the clocks for transmitter and receiverare typically locked. With the transmitting signal in (7), thereceived noise-free radar signal is given by y R ( t ) = M T (cid:88) m =1 L (cid:88) (cid:96) =1 b (cid:96) ψ m ( t − τ (cid:96) ) e j πf D,(cid:96) t · a ( M R , φ (cid:96) ) a T ( M T , θ (cid:96) ) w m , (8)Applying matched filtering with ψ m (cid:48) ( t ) to y R ( t ) , we obtain r m ( t ) = L (cid:88) (cid:96) =1 b (cid:96) ρ m ( t − τ (cid:96) ) e j πf D,(cid:96) t a ( M R , φ (cid:96) ) a T ( M T , θ (cid:96) ) w m , where ρ m ( t ) is the non-zero output of the matched filteringof ψ m ( t ) when m = m (cid:48) , as all other outputs for m (cid:54) = m (cid:48) arezeros.Assume that ρ m ( t ) = ρ ( t ) is the same for all m ∈ [1 , M T ] .Staking all r m ( t ) , m = 1 , · · · , M T to a matrix, we get R ( t ) = L (cid:88) (cid:96) =1 b (cid:96) ρ ( t − τ (cid:96) ) e j πf D,(cid:96) t a ( M R , φ (cid:96) ) a T ( M T , θ (cid:96) ) W . When W is an identity matrix (if not, multiplying both sideswith W − ), we can vectorize R ( t ) and getvec ( R ( t )) = L (cid:88) (cid:96) =1 b (cid:96) ρ ( t − τ (cid:96) ) e j πf D,(cid:96) t a ( M R , φ (cid:96) ) ⊗ a T ( M T , θ (cid:96) ) , where ⊗ denotes the Kronecker product.In MIMO radars, particularly mono-static radars, the an-tenna intervals of transmitter and receiver, d T and d R , aretypically set as d T = M T d R or d R = M T d T . Then when φ (cid:96) = θ (cid:96) , which is generally true for a monostatic radar, wehave a ( M R , φ (cid:96) ) ⊗ a T ( M T , θ (cid:96) ) = a ( M R M T , φ (cid:96) ) . This enablesa MIMO radar to achieve the spatial resolution correspondingto a virtual ULA with M T M R antennas [28]. Note that theincreased aperture of the virtual array is only meaningful when φ (cid:96) is related to θ (cid:96) in some way, although φ (cid:96) = θ (cid:96) is not anecessary condition.In this paper, we mainly consider the following emergingMIMO radars, which have not been widely implemented inpractice, but have great potentials for realizing JCR systemswith balanced C&R performance.
1) MIMO-OFDM Radar:
In a MIMO-OFDM radar, thewaveform ψ m ( t ) is in the form of time-domain OFDM signals.Without considering the cyclic prefix, the baseband signal of ψ m ( t ) can be represented as ψ m ( t ) = (cid:88) n ∈S m ˜ w m,n e j πnf t g ( t − kT ) , (9)where S m is the set of used subcarriers, g ( t ) is a windowingfunction, and ˜ w m,n can be a complex variable combiningorthogonal coding, subcarrier-dependent spatial precoding/BF,and/or other processing such as PAPR reduction.To achieve orthogonality, S m s are typically selected to beorthogonal for different m . The set of subcarriers can beallocated in various forms, such as the interleaved pattern[29], and nonequidistant subcarrier interleaving [30]. Differentallocations may lead to different signal properties and ambi-guity functions. Alternatively, the orthogonality may also beachieved over time domain via the use of orthogonal codes,while different antennas share the subcarriers.MIMO-OFDM signals for radar are very similar to those forcommunications, except that they are typically non-modulatedand/or orthogonal across antennas. Hence MIMO-OFDM sig-nals are excellent options for JCR systems. In particular,the training sequence in the preamble of MIMO-OFDMcommunication systems holds the desired characteristic oforthogonality, and can be directly used for radar sensing.
2) Frequency-Hopping MIMO Radar and Frequency AgileRadar:
The frequency-hopping (FH) MIMO radar [31] andthe frequency agile radar (FAR) [32], as well as its extensionsto multicarrier [33], all use the FH technologies - the totalbandwidth is divided into many subbands, only a subset ofsubbands are used at a time, and the subset at each antennarandomly varies over time. FH can be implemented in eitherfast time or slow time, and in the form of either pulse orcontinuous-wave. We consider pulsed fast FH here, i.e., thesignals are continuously transmitted with frequencies beingchanged rapidly and in multiple times over a PRI, followedby a silent period. Using FH leads to major advantages such asbetter security, and lower implementation cost by avoiding theuse of costly instantaneous wideband components, while withnegligible degradation in sensing performance, compared tousing full bandwidth signals. FH-MIMO radar and FAR and itsvariants differ in how the frequencies are used at each antenna.Next, we briefly present their signal models, using notationssimilar to those for OFDM: B for the radar bandwidth, N forthe number of sub-bands, and T for the hop duration.In a FAR, all antennas use one common frequency at ahop, and a BF weight is applied to each antenna so that thearray forms steerable beam [32]. The basic concept of FAR isextended to multi-subband signaling in [33], that is, a subset ofmore than one frequencies are used in each hop. In particular,in the multi-Carrier AgilE phaSed ArrayRadar (CAESAR)scheme proposed in [33], the whole array is divided intomultiple non-overlapped subarrays, and each antenna in onesubarray only uses one common frequency from the frequencysubset. CAESAR randomizes both the frequencies and theirallocation among the antenna elements, and induces bothfrequency and spatial agility. It also maintains narrowband transmission from each antenna and introduces the BF ca-pability. These capabilities make CAESAR more attractivethan the original FAR. Let A s denote the index set of theantennas in the s -th subarray, and S be the number of totalsubarrays. Let F k be the set of frequencies selected for hop k , and f k,m ∈ F k denote the centroid frequency of the sub-band selected by antenna m at hop k . The transmitted signalof CAESAR at the m -th antenna can be represented as ψ m ( t ) = ˜ w k,m e j πf k,m t g ( t − kT ) , (10)s.t. (cid:26) f k,m = f k,m (cid:48) , when { m, m (cid:48) } ∈ A s , ∀ s ; f k,m (cid:54) = f k,m (cid:48) , otherwise . where ˜ w k,m is the BF weight.Although FH-MIMO was developed before CAESAR, it canbe treated as a special case of CAESAR where each subarrayhas only one antenna and each frequency is only used byone antenna, that is S = M T and |A s | = 1 . CAESAR canalso be regarded as a generalization of FH-MIMO radar byintroducing the BF capability.Both FH-MIMO radar and CAESAR are based on frequencydivision. They can also be realized on the framework ofMIMO-OFDM, with the frequency hopping concept beingintroduced to subcarriers. D. Major Differences between C&R Systems and Signals
As can be partially observed from the signal models inpreceding subsections, there are some significant differencesbetween C&R systems and signals, despite of their potentialsfor integration. A brief comparison is summarized in Table I,where radar waveforms are mainly referred to traditionalpulsed and continuous waveforms such as chirp. Next, weelaborate two aspects that have considerable impacts on thejoint system design.Firstly, it is a fundamental challenge to address the potentialrequirements for full duplex operation of JCR systems. Onone hand, (mono-static) radar addresses the requirement forfull duplex operation in mainly two approaches, as illustratedin Fig. 1, which may not be replicable in communicationsystems. One approach is typically applied in a pulsed radar,by applying a long silent period to receive echo signals, whichessentially bypasses full-duplex operation and makes the radarwork in a time-division duplex mode; the other is typicallyused in a continuous-wave radar, via using the transmittersignal as the local template signal to the oscillator at thereceiver, and detecting only the “beat” signal, the differencebetween the transmitted and received signals. Such designsenable low-complexity and efficient radar sensing. However,they constrain the options of integrating communications andlimit the achievable communication rates. For example, thereis large uncertainty with the availability and bandwidth of thebeat signal, hence information conveying will be unreliable.On the other hand, full-duplex operation is still immature forcommunications, and there is typically clock asynchronismbetween spatially separated transmitting and receiving nodes.These impose significant limits on integrating radar sensinginto communications.
TABLE IB
RIEF COMPARISON BETWEEN
C&R
SIGNALS AND SYSTEMS . Properties Radar CommunicationsTypicalSignalWaveforms
Signals are unmodulated and have large bandwidth and Low PAPR;Orthogonal if MIMO-radar. Mix of unmodulated (pilots) and modulated symbols; HighPAPR; complicated and diverse signal waveforms.
SignalStructure • A silent period follows each pulse transmission in pulsed radar toallow the reception of echo signals; • In continuous-wave radar, signals can be transmitted continuously,enabled by special hardware designs; • Signal repeats every PRI within CPI to increase received signalpower and enable Doppler frequency estimation. • Typically packet-based. Typically no repetition; • Packet length and interval can be time-varying; • Signal may occupy discontinuous resources in time,frequency and space domains.
TransmissionCapability(Duplex) • In continuous-wave radar, transmitted signal is used as localoscillator input at Rx to realize full duplex. This outputs “beat”signals only, characterizing the variation of the signals; • Pulsed radar operates in half duplex mode with a silent periodfollowing each pulse transmission. Time division duplex or frequency division duplex mode. Fullduplex is immature for communications. Short-term solutionscan be used to enable communication-centric JCR [12].
ClockSynchro-nization
Transmitter and receiver are clock-locked in most radar setups, includingmonostatic, bistatic and multi-static systems. Co-located transmitter and receiver share the same timingclock, but non-colocated nodes typically do not.
ReceiverSignalSampling
A conventional continuous-wave radar samples received signals at a ratemuch smaller than the scanning bandwidth, proportional to the desireddetection capability of the maximal ranging and moving speed. Thismakes information conveying difficult. Sampling rate corresponds to the signal bandwidth. Full-bandwidth information available.
PerformanceMetrics
Detection probability, Cramer-Rao lower bound (CRLB), Mutual infor-mation (MI), Ambiguity function Capacity, Rate, Spectral efficiency, Signal-to-interference-and-noise ratio (SINR), and Bit error rate (BER)
Secondly, C&R signals are originally designed and opti-mized for different applications, and are generally not di-rectly applicable to each other. Radar signals are typicallydesigned to optimize localization and tracking accuracy, andenable simple sensing parameter estimation. The followingproperties of radar signals are desired: low PAPR to en-able high-efficiency power amplifier and long-range operation;and an waveform ambiguity function with steep and narrowmainlobes for high resolution; Comparatively, communicationsignals are designed to maximize the information-carryingcapabilities, and are typically modulated and packet-based. Tosupport diverse devices and meet various quality-of-servicesrequirements, communication signals can have complicatedstructures, with advanced modulations applied across time,frequency, and spatial domains, and being discontinuous andfragmented over these domains.These differences make the integration of C&R an interest-ing and challenging task. As we will see from the followingthree sections, a good JCR design always seek and exploit thecommonalities between C&R, while taking these differencesinto consideration.III. JCR: C
OMMUNICATION -C ENTRIC D ESIGN
In communication-centric JCR systems, radar sensing isintegrated into existing communication systems as a secondaryfunction. Revision and enhancement to communication infras-tructure and systems may be required, but the primary com-munication signals and protocols largely remain unchanged.Considering the topology of communication networks,communication-centric JCR systems can be classified intotwo types, namely, those realizing sensing in point-to-pointcommunication systems and in large networks such as mobile networks. Two good examples are the IEEE 802.11ad JCR sys-tems for vehicular networks [13], [22], [34] and the perceptivemobile networks [12], [24], respectively. They use the singlecarrier and multiuser-MIMO OFDM signals as described inSection II-B, respectively. Both are DFRC systems where asingle transmitted signal is used for both C&R.In this section, we first describe the two types of DFRCsystems, and then review some signal processing techniquesfor general communication-centric JCR systems.
A. 802.11ad DFRC Systems
The 802.11ad standard defines a millimeter-wave packetcommunication system operating in the 60 GHz unlicensedband. There are three types of physical-layer (PHY) pack-ets: single-carrier, OFDM, and control, with OFDM beingoptional. The preamble in each packet is the main signal thathas been exploited for radar sensing [13], [20], [22], [34], [35]in an 802.11ad DFRC system. Although the DFRC system canbe applied in many scenarios, it has been mainly investigatedfor vehicular networks. In a typical setup, the sensing receiveris co-located with the DFRC transmitter, using two separatedanalog arrays. The DFRC device can be located either on theroad side unit (RSU) or on a vehicle.Referring to (1), the noise-free time-domain echo signal atthe sensing receiver can be represented as y ( t ) = L (cid:88) (cid:96) =1 h (cid:96) ( t ) s ( t − τ (cid:96) ) e j πf D,(cid:96) t , (11)where h (cid:96) ( t ) (cid:44) b (cid:96) w R ( t ) T a ( M R , θ (cid:96) ) a T ( M T , θ (cid:96) ) w T ( t ) , w T ( t ) and w R ( t ) are the beamforming vector in the transmitter andreceiver respectively, and the AoA and AoD are assumed to be the same. Note that the clock between the transmitter andsensing receiver is locked, therefore τ o ( t ) = 0 and f o ( t ) = 0 in (1). The primary goal of sensing here is estimating thelocation and velocity of objects via estimating τ (cid:96) , θ (cid:96) , and f D,(cid:96) .The three PHYs in 802.11ad have a similar preamblestructure, consisting of short training field (STF) and channelestimation field (CEF). The STF consists of tens of repeated128-sample Golay sequences, followed by its binary com-plement. The CEF consists of two 512-sample Golay com-plementary pair, which has the property of perfect aperiodicautocorrelation, i.e., s ( t − τ ) (cid:126) s ( t ) (cid:54) = 0 if and only if τ = 0 . Both the STF and CEF can be used for sensing, ineither a hierarchical or joint manner [20]. The hierarchicalstrategy processes the STF and CEF separately, exploiting theirrespective properties. For example, the repetition pattern ofSTF is typically used for packet detection in communications,and hence it is ideal for target detection in sensing; while theperfect aperiodic autocorrelation of CEF can lead to excellentchannel estimation and sensing performance, based on, e.g.,the generalized likelihood ratio test [35]. The joint strategyuses both STF and CEF for common tasks of sensing, basedon, e.g., matched filtering [20]. The sensing performancebounds are also derived in [20], [35]. More advanced sensingalgorithms will be discussed in Section III-C.Both the single-carrier PHY, which has an identical pream-ble with the OFDM PHY, and the control PHY have beenexplored for sensing [20], [35]. There are some differencesbetween their sensing efficiency. On one hand, in the stan-dard, a beamforming training protocol is defined to align thetransmit and receive beams, using beam scanning and thecontrol-PHY signals. Single-carrier or OFDM PHY signals aretypically used after beamforming training. On the other hand,the control PHY has a longer STF. So in terms of sensing,the control PHY enables a wider field-of-view (FoV) andpotentially better accuracy, while the other two are generallylimited to the fixed direction of communications. A multibeamapproach, as will be discussed in Section V-B, can be appliedto relax this limitation. B. Mobile network DFRC Systems
In [24], the framework of perceptive mobile networks(PMNs) is introduced by applying the JCR, more specificallyDFRC, techniques, to cellular networks. Downlink sensing anduplink sensing are defined, corresponding to sensing using thereceived downlink and uplink communication signals, respec-tively, as illustrated in Fig. 2. In the scenario of cloud radioaccess networks (CRANs) where distributed remote radio units(RRUs) cooperatively communicate with user equipment (UE),the received downlink communication signals from one RRUitself and other cooperative RRUs can be used for downlinkactive sensing and downlink passive sensing, respectively.Extend the single user MIMO-OFDM model in Section II-Bto multiuser MIMO-OFDMA. Suppose that one node receivessignals transmitted from a set of nodes q, q ∈ Q T , and uses thesignals for sensing. Let Q T be the cardinality of Q T . Referringto the transmitting signal model in (5) and the channel model Standalone BS
CRAN Central
BBU Pool
Sensing Processing
Unit
RRU 1
RRU 2
Clutter Uplink Comm. & SensingClutter Reflection
Fronthaul
Downlink Comm. Signal
Downlink Active Sensing
Downlink Passive SensingClutter Mobile
Core
Transmitter (Multiuser-MIMO OFDMA Signal) Channel RF ProcessingA/D conversionConvert to frequency domainSynchro- nization
Channel Estimation
MIMO
Equalization
Demodulation and decoding Sensing Parameter Estimation & Pattern Analysis
C&R Cooperation Shared by C&R
C only
R only text
A typical
DFRC transceiver UE UE Fig. 2. Network setup of PMNs (top subfigure) and the brief system blockdiagram of a DFRC transceiver based on MIMO-OFDM (bottom subfigure). in (2), we can represent the received noise-free k -th OFDMsymbol at the n -th subcarrier as ˜ y n,k = (cid:88) q ∈Q T L q (cid:88) (cid:96) =1 b q,(cid:96) e − j πn ( τ q,(cid:96) + τ o,q,k ) f e j πk ( f D,q,(cid:96) + f o,q,k ) T s · a ( M R , φ q,(cid:96) ) a T ( M q , θ q,(cid:96) )˜ x q,n,k (12)Scenarios represented by this model are exemplified below:1) Downlink sensing in a standalone base station (BS) :This is the case where the BS uses its own reflectedtransmitted signals for sensing, similar to a mono-staticradar. In this case, Q T = 1 and τ o,q,k = f o,q,k = 0 ;2) Uplink sensing in a standalone BS : Q T denotes the setof Q T UEs sharing the same subcarriers via SDMA,and τ o,q,k (cid:54) = 0 and f o,q,k (cid:54) = 0 .. Each UE only occupiespartial of the total subcarriers;3) Downlink sensing in an RRU : Q T denotes the set ofRRUs whose downlink communication signals are seenby the sensing RRU, including its own echo signals.The sensing can be based on (12) with the signals ˜ x q,n,k corresponding to both the pilots and data symbols, as willbe detailed next. For more details on the signals usable forsensing, as well as solutions to the full-duplex problems inPMNs, the readers are referred to [12], [24]. C. Sensing Parameter Estimation
Sensing parameter estimation in communication-centricJCR is generally different to that in traditional radar systems,due to the significant differences between the two types ofsignals as described in Section II. Next, referring to the
MIMO-OFDM signal models in Section III-B, we review keytechniques in sensing parameter estimation. Most of themare also applicable to single carrier systems such as theIEEE802.11ad DFRC. We first discuss two important problemsto be resolved, before we review optional sensing algorithms.
1) Direct and Indirect Sensing:
The first problem is how todeal with ˜ x q,n,k in the received signals, which can representeither known pilots or (unknown) data payload in a packet.Both can be used for sensing. For unknown data payload, it canbe demodulated after channel estimation, as in conventionalcommunications. Using data payload can significantly extendthe sensing capability such as the range, as it is much longerthan the pilot. Here, the receiver is assumed to know ˜ x q,n,k or its estimate via demodulating ˜ s q,n,k . For multiuser-MIMOsignals, for example, signals received at an RRU from multipleRRUs in downlink sensing, or signals received at a standaloneBS from multiple UEs, we can use two methods to formulatethe estimation problem.One method, which may be called as direct sensing , directlyfeeds the received signals to sensing algorithms. In some cases,e.g., sensing using the data payload in a MIMO system, thisis the only option as ˜ x q,n,k cannot be readily removed evenwhen they are known. The presence of ˜ x q,n,k often limits theoptional algorithms for sensing parameter estimation.Let us have a look at one example in [24], where directsensing is conducted via the block compressive sensing (CS)techniques [36], and the symbols ˜ x q,n,k are used as part of thesensing matrix. For the clarify of presentation, we consider thecase of Q k = 1 in (12), and ignore the timing offset τ o,q,k .Ignore the noise and rewrite (12) in a more compact matrixform as ˜ y n,k = A ( M R , φ q ) C n D k A T ( M q , θ q )˜ x q,n,k , (13)where A ( M R , φ q ) and A ( M q , θ q ) are matrices with the (cid:96) -thcolumn being a ( M R , φ q,(cid:96) ) and a ( M q , θ q,(cid:96) ) ), respectively, and D k and C n are diagonal matrices with the diagonal elementbeing b q,(cid:96) e j πkf D,q,(cid:96) T s and e − j πnτ q,(cid:96) f , respectively.In order to apply sensing algorithms, we need to re-organizesignals so that we can stack more measurements over the samedomain. Consider the case of collecting samples from all thesubcarriers for the estimation of delay and AoA. Take thetranspose of ˜ y n,k in (13), and rewrite it as ˜ y Tn,k = ˜ x Tq,n,k ( c Tn ⊗ I M q ) V q A T ( M R , φ q ) . (14)where c n is a column vector containing the diagonal elementsof C n , I M q is an M q × M q identity matrix, and V q is a blockdiagonal matrix V q = diag { b (cid:96) e − j πkf D,q,(cid:96) T s a ( M q , θ q,(cid:96) ) } , (cid:96) = 1 , . . . , L q . We have now separated signals ˜ x Tq,n,k ( c Tn ⊗ I M q ) thatdepend on n from those on other variables. We can then stackthe row vectors ˜ y Tn,k from all available subcarriers to a matrix,and obtain ˜ Y k (cid:44) [˜ y ,k , · · · , ˜ y n,k , · · · ] T = WV q A T ( M R , φ q ) , (15)where the n -th row of W is ˜ x Tq,n,k ( c Tn ⊗ I M q ) . The signal model in (15) enables the applications of both1-D multi-measurement vector (MMV) CS and 2-D CS tech-niques. For 1-D MMV CS, c n is expanded to a quantizedon-grid vector, and then W is used as the sensing matrix. Thedelay and V q A T ( M R , φ q ) will then be the outputs of thealgorithm, and the Doppler frequency and AoA can be furtherestimated from the estimates of V q A T ( M R , φ q ) . For 2D CS,both delay and AoD can be estimated together by expandingboth c n and A ( M R , φ q ) to on-grid models. It is easy to seethat if we swap the terms of Doppler frequency and delay in(14), samples across OFDM symbols can be stacked and theDoppler frequencies can be estimated first.The direct sensing method has a high computational com-plexity. Due to the presence of ˜ x q,n,k , the applicable sensingsolutions are also limited. However, it is the only option,when ˜ x q,n,k cannot be removed due to, e.g, insufficientmeasurements.The other method, indirect sensing , first estimate the ele-ments of channel matrix for each node. It decorrelates signalsfrom multiple nodes, removes ˜ x q,n,k or ˜ s q,n,k from the re-ceived signals, and applies sensing parameter estimation tothe estimated channel matrix. In multi-user MIMO systems,referring to (12), this can be achieved by decorrelating signalscollected from K ˜ y n,k s, k = k (cid:48) , k (cid:48) + 1 , · · · , k (cid:48) + K − , K ≥ M T Q T at subcarrier n . Mathematically, this can berepresented as (cid:104) ˜ H ,n,k , · · · , ˜ H Q T ,n,k (cid:105) = [˘ x n, , · · · , ˘ x n,K ] − [˜ y n, , · · · , ˜ y n,K ] , (16)where ˘ x n,k = [˜ x T ,n,k , · · · , ˜ x TQ T ,n,k ] T is a M T Q T × vector.Note that the channel matrix is assumed to be constant overthis interval. Equation (16) indicates that the decorrelation isonly possible when K ≥ M T Q T ˘ x n,k s are available during aCPI and the inversion of [˘ x n, , · · · , ˘ x n,K ] exists.The decorrelation involves high computational complexitydue to matrix inversion and may cause significant noiseenhancement, unless ˜ x q,n,k or ˜ s q,n,k are orthogonal. Henceindirect sensing is particularly suitable for training and pi-lot symbols which are typically orthogonal. After ˜ x q,n,k isremoved, we can equivalently work on the single user chan-nel matrix ˜ H n ( t ) in (2). This can largely simplify sensingparameter estimation, and offer great flexibility in problemformulation. Note that if the precoding matrix P n,k is un-known to the receiver, a T ( M T , θ (cid:96) ) in (2) will be replacedby a T ( M T , θ (cid:96) ) P n,k . This will make the estimation of AoDchallenging.
2) Clutter Removal:
The second problem is how to dealwith clutter signals that are useless for sensing. Commu-nication systems are typically deployed in an environmentwith dense multipath, where many signal propagation pathsinvolve static objects only and are not of the interest ofsensing. Removing clutter before sensing may distort thesignal, however, it can largely reduce the number of parametersto be estimated. In this sense, it is generally a better strategyto remove clutter before the application of sensing algorithms,using, e.g., background subtraction or filtering techniques. For detailed discussions on potential clutter removal techniques,the readers are referred to [24].
3) Sensing Algorithms:
We now discuss options for sensingalgorithms based on the indirect method. Traditional radartypically applies matched filtering for sensing parameter esti-mation, which has also been adopted in some DFRC systems,e.g., 802.11ad DFRC [20], [22], [34]. However, the accuracyand resolution capability of these methods largely depend onthe signal correlation properties (i.e., ambiguity functions).More options that are less affected by the correlation propertycan be explored for communication-centric DFRC signals.From the decorrelated estimates of ˜ H n,k s in (2), we canrepresent the ( m R , m T ) -th element in ˜ H n,k as ˜ h n,k,m R ,m T = L (cid:88) (cid:96) =1 b (cid:96) e − j πnτ (cid:96) f e j πkf D,(cid:96) T s · e j πd R m R sin( φ (cid:96) ) /λ e j πd T m T sin( θ (cid:96) ) /λ , (17)where m R and m T represent the indexes of the receiving andtransmitting antennas, respectively. This is also known as a4-D Harmonic retrieval problem [37], where the observationsignals in each domain can be represented as a Vandermondematrix when the samples are equally spaced. The 4-D har-monic retrieval problem can be reduced to multiple-snapshotlower-dimensional problems by combining one or more of theexponential functions with the unknown variable b (cid:96) . Thus, wecan rewrite them to different matrix and Tensor forms so thatsensing parameters can be estimated in different ways andorders.Since solutions to the classical harmonic retrieval problemsare generally well studied, we ignore the details and onlyprovide a comparison of typical techniques in Table II withreference to our sensing problems. More details of suchtechniques for JCR can be referred to [24], [37]–[40].When selecting sensing algorithms, the following issuesneed to be further considered:1) Modern communication signals are typically very com-plicated in terms of resource usage, and they maybe discontinuous in one and more domains of space,frequency, and time. See [12] for the available sensingsignals and their properties in 5G-based PMNs. Thisrequires sensing algorithms with the capability of pro-cessing discontinuous and varying-interval samples;2) Higher-dimension algorithms can generally identifymore parameters and achieve better estimation perfor-mance at the cost of higher complexity. However, whenthere are insufficient samples in one domain, it could bebetter to use lower-dimension algorithms. D. Resolution of Clock Asynchrony
As described in Section II-A, when the oscillator clocksbetween the transmitter and the sensing receiver are notlocked, the timing offset τ o ( t ) and CFO f o ( t ) in (1) and (2),are typically non-zero and time-varying. They can directlycause ambiguity in range and speed estimation. They alsoprevent from aggregating measurements over a relatively longinterval, e.g., preamble signals from two packets, for joint processing, which is otherwise important for parameter esti-mation, particularly Doppler frequencies. This is a critical andchallenging problem in communication-centric JCR systems.There have been a limited number of works that addressthis problem in passive WiFi sensing [42]–[44], based onthe cross-antenna cross-correlation (CACC) method. The basicassumption is that timing offsets and CFO across multipleantennas in the receiver are the same, as the same clock isused. Therefore these offsets can be removed by computingthe cross-correlation between signals from multiple receivingantennas. Considering a single transmitter with a single an-tenna and referring to (12), the received noise-free signal atthe m -th antenna can be rewritten as ˜ y n,k,m = L (cid:88) (cid:96) =1 b (cid:96) e − j πn ( τ (cid:96) + τ o,k ) f e j πk ( f D,(cid:96) + f o,k ) T s ˙ e jmπ sin( φ (cid:96) ) ˜ x n,k . Let the m -th antenna be the reference. Computing the cross-correlation between ˜ y n,k,m and ˜ y n,k,m yields R ( n, k, m ) = ˜ y n,k,m ˜ y ∗ n,k,m (18) = L (cid:88) (cid:96) m =1 L (cid:88) (cid:96) m =1 b (cid:96) m b ∗ (cid:96) m e − j πn ( τ (cid:96)m − τ (cid:96)m ) f · e j πk ( f D,(cid:96)m − f D,(cid:96)m ) T s e jmπ (sin( φ (cid:96)m ) − sin( φ (cid:96)m )) | ˜ x n,k | . Note that in (18), τ o,k and f o,k are removed. However,cross-correlation causes doubled terms and sensing parametersbecome relative.Two assumptions, which limit the applications, are neces-sary for subsequent processing: (1) The transmitter and sensingreceiver are relatively static and the relative location of thetransmitter is known to the receiver; and (2) there exists aline-of-sight (LOS) path between them and it has much largermagnitude than non-LOS paths. The cross-product betweenLOS paths is invariant over the CPI and can be removed bypassing R ( n, k, m ) through a high pass filter. The cross-termsbetween NLOS and LOS paths thus dominate in the output ofthe filter. The sensing parameters can then be estimated, withrespect to the known parameters of the LOS path.However, the outputs after CACC contain cross-productterms that include signals and their images, and hence thenumber of unknown parameters to be estimated is actuallydoubled. This will not only cause degraded estimation ac-curacy, but also ambiguity between the actual value and itsimage. The authors in [43] proposed an add-minus method tosuppress the image signals by adding a constant to ˜ y n,k,m andsubtracting another one to ˜ y n,k,m . However, this method isfound to be susceptible to the number and power distributionof static and dynamic signal propagation paths. To resolvethese problems, a method is proposed in [41] by introducinga mirrored MUSIC algorithm.Observing from (18), we can see that the relative delays andDoppler frequencies have values symmetric to zero. Exploitingthis symmetric, the mirrored MUSIC algorithm first constructsnew signals from the CACC outputs, or the outputs of a furtherhigh pass filter to remove the dominating static components, TABLE IIC
OMPARISON OF S ENSING P ARAMETER E STIMATION A LGORITHMS
Algorithms Advantages Main limitations
Periodogram such as2D DFT (typicallybased on the outputsof matched filtering) Traditional technique. Simple and easy to implement. May beused as the starting point for other algorithms. • Low resolution; • Generally require a full set of continuous samples ineach domain, which may not always be satisfied.Maximal LikelihoodEstimation [35] Statistically optimal formulation; Particularly suitable for low-dimension signals. Typically require searching to find the solutions and hencecomplexity is high; Complexity also increases with signaldimensions exponentially.Subspace methodssuch as ESPRIT andMUSIC [40], [41] • Separate signal and noise subspaces and hence is re-silient to noise; • ESPRIT can achieve very high resolution and can dooff-grid estimation; • MUSIC can flexibly work with non-continuous samples. • ESPRIT requires a large segment of consecutive sam-ples, which may not always be satisfied; • Resolution of MUSIC depends on searching granularity; • High complexity associated with singular value decom-position.Compressive sensing(On-grid) [24], [38] • Flexible and does not require consecutive samples; • Various recovery algorithms available, allowing goodtradeoff between complexity and performance; • Different dimensions of formulation can be used, adapt-ing to sensing requirements and conditions; • Dense dictionaries can be used to improve resolution. Although it may even work well for estimating a small amountof off-grid parameters, performance can degrade significantlywhen the number of parameters to be estimated is large.Compressive Sensing(Off-grid) suchas atomic normminimization [38] Have all the advantages of on-grid CS algorithms. Capable ofestimating off-grid values. Limitation in real time operation due to very high complexity.Still require sufficient separation between parameter values.Tensor based algo-rithms [37] High-dimension formulation and estimation are made easy.Reduce computational complexity and provide capability inresolving multipath with repeated parameter values. Need to be combined with other algorithms such as ESPRITand CS, thus facing their inherent problems. and then define new basis vectors for MUSIC algorithms. Bothof the new signals and basis vectors are constructed by addingthe original ones with their sample-reversed versions. Themirrored MUSIC algorithm equivalently reduces the numberof unknown parameters by half, and is shown to significantlyimprove the estimation accuracy, and simplify the ambiguityresolution problem associated with image signals.
E. Sensing Assisted Communications
In many location-aware services and applications, e.g., V2Xnetwork, sensing and communication are recognized as a pairof intertwined functions, where communication-centric JCRcan be applied so as to reduce the costs and improve spectral-, energy-, and hardware-efficiency. In addition to those generaladvantages, one may also leverage the sensing results tofacilitate communication, where significant performance gaincan be obtained over that of the conventional communication-only schemes. Examples are sensing assisted secure commu-nications [45] and BF [46]–[49]. Below we briefly review therecent state-of-the-art on sensing-assisted BF.BF for mmWave communications relies on the AoA andAoD parameters of signal propagation paths. With such angu-lar information at hand, the Tx and the Rx can accuratelyalign their beams, such that a high-quality communicationlink can be established. Conventionally, the AoA and AoDare acquired by beam training or beam tracking techniques,i.e., communication-only approaches. The basic idea of theseschemes is to send pilots from the Tx to the Rx before datatransmission, with each pilot being beamformed to a differentdirection. The Rx then estimates the angles from the receivedpilot signal and feeds them back to the Tx. It can be observed from the above procedure that there existsan inherent tradeoff between the estimation accuracy and thesignalling overhead. Indeed, the beam information can be moreprecisely attained by transmitting more pilots, which, however,is at the price of reducing the effective transmission time of theuseful data, as well as of increasing the latency. This problemis particularly pronounced in high-mobility V2X scenarios,where the trained beams can be easily outdated. To cope withthis issue, radar sensing is exploited to enhance the BF per-formance via providing accurate positioning information forvehicles, such that the beam search interval can be narroweddown. Recent results show that with the aid of an extra radarsensor mounted on the road side unit (RSU), the beam trainingoverhead incurred in the vehicle-to-infrastructure (V2I) linkscan be significantly reduced to 6.5% of that of the GlobalNavigation Satellite System assisted approach [46], [47].As a step beyond using stand-alone radar sensors, JCRsignalling is envisioned to play a unique role in V2I com-munications, offering not only considerable reduction in theoverhead, but also the capability to beamform towards pre-dicted directions of the vehicles, in order to adapt the fast-changing vehicular channels. To show this, let us consider ammWave RSU equipped with M T transmit and M R receiveantennas, which acts as a mono-static radar, and is serving asingle-antenna vehicle driving at a nearly constant speed on astraight road. We assume that the RSU communicates with thevehicle over a single LoS path, and that all the antenna arraysare adjusted to be parallel to the road. As a consequence, theAoA equals to the AoD in the V2I LoS channel.At the k th epoch, the RSU transmits a DFRC signal x k ( t ) = f k s k ( t ) from the RSU to the vehicle, with f k being the JCR beamformer, and s k ( t ) being the data stream. Thesignal is partially received by the vehicle’s antenna array, andis partially reflected back to the RSU. The received echo signalcan be expressed in the form of y R ( t ) = b k e j πf D,k t a ( M R , θ k ) a T ( M T , θ k ) · f k s k ( t − τ k ) + z R ( t ) , (19)where the beamformer f k is designed based on a predicted an-gle, which is f k = a ∗ (cid:16) M T , ˆ θ k | k − (cid:17) . Moreover, ˆ θ k | k − is the k th predicted angle based on the ( k − th estimate, and b k , f D,k , θ k , and τ k denote the reflection coefficient, the Dopplerfrequency, the AoA, and the round-trip delay for the vehicleat the k th epoch, respectively. In particular, f D,k and τ k canbe further written as functions of the distance d k , the velocity v k , and the AoA θ k , which are f D,k = v k cos θ k f c c , τ k = d k c .By matched-filtering (19) with a delayed and Doppler shiftedcounterpart of s k ( t ) , one obtains the estimates of the Dopplerand the time-delay, denoted as ˆ f D,k and ˆ τ k . Let us denotethe vehicle’s state as q k = [ θ k , d k , v k , b k ] T . The sensingmeasurement and the vehicle state can be connected by afunction ˜r k = h ( q k ) + z k , which can be expanded as [48] ˜y R = b k E k a ( M R , θ k ) a T ( M T , θ k ) a ∗ (cid:16) M T , ˆ θ k | k − (cid:17) + z θ , ˆ f D,k = 2 v k cos θ k f c c + z f , ˆ τ k = 2 d k c + z τ , (20)where E k is the matched filtering gain, and z k = (cid:2) z Tθ , z f , z τ (cid:3) T denotes the measurement noise.Recalling the assumption that the vehicle is driving on astraight road with a nearly constant speed, the state transitioncan be modeled as q k = g ( q k − ) + ω k , which can beexpressed in the form of [48] θ k = θ k − + d − k − v k − ∆ T sin θ k − + ω θ,k ,d k = d k − − v k − ∆ T cos θ k − + ω d,k ,v k = v k − + ω v,k ,b k = b k − (cid:0) d − k − v k − ∆ T cos θ k − (cid:1) + ω b,k , (21)where ω k = [ ω θ,k , ω d,k , ω v,k , ω b,k ] T represents the state noise,and ∆ T is the duration of one epoch.With both models (20) and (21) above, the RSU can predictand estimate the vehicle’s state at each epoch via variousapproaches, e.g., Kalman filtering and factor graph basedmessage passing algorithms [48]–[50]. The predicted angle isthen employed to design the JCR beamformer for the nextepoch. At the k th epoch, the received signal at the vehicle canbe written as y C ( t ) = β k a T ( M T , θ k ) a ∗ (cid:16) M T , ˆ θ k | k − (cid:17) s k ( t ) + z C ( t ) , where β k is the path-loss of the LoS path, and z C ( t ) is thenoise with variance σ C . Accordingly, the achievable rate isobtained as R k = log (cid:18) (cid:12)(cid:12)(cid:12) β k a T ( M T , θ k ) a ∗ (cid:16) M T , ˆ θ k | k − (cid:17)(cid:12)(cid:12)(cid:12) p k /σ C (cid:19) , where p k is the power of the data stream s k ( t ) . It can beseen that the achievable rate relies critically on the sensingand prediction accuracy of the AoA. Once the next AoA isaccurately predicted, the RSU can keep tracking the vehiclewhile offering high-quality communication service when it iswithin the RSU’s coverage. Remark:
We conclude here the superiorities of the JCRbased predictive BF over conventional communication-onlyapproaches, i.e., beam training and tracking: • First of all, JCR signalling removes the necessity of ded-icated downlink pilots, as the whole JCR downlink blockis exploited both for beam sensing and communication.This reduces the downlink overhead. • Secondly, the uplink feedback is not required, since theRSU estimates the angle from the returned target echosignal instead of from the feedback, which reduces theuplink overhead. • Thirdly, the quantization error generated in the uplinkfeedback is avoided. As such, the estimation of thevehicle’s state can be performed in a continuous manner. • Finally, JCR signalling achieves higher matched-filteringgain than that of beam training and tracking approaches,as the whole downlink frame, rather than a part of it, istailored for both downlink sensing and data transmission.IV. JCR: R
ADAR -C ENTRIC D ESIGN
Radar systems, particularly military radar, have the extraor-dinary capability of long-range operation, up to hundreds ofkilometers. Therefore, a major advantage of implementingcommunication in radar systems is the possibility of achievingvery long range communications, with much lower latencycompared to satellite communications. However, the achiev-able data rates for such systems are typically limited, due tothe inherent limitation in the radar waveform [3], [4], [8], [51].Research on radar-centric JCR has been mainly focusedon the information embedding technologies, and there areonly limited works on other aspects such as communicationprotocol and receiver design based on the radar-centric JCRsignals. In this section, we concentrate on more recent DFRCsystems based on MIMO-OFDM, CAESAR and FH-MIMOradar, because of the remarkable benefits they can offer asdescribed in Section II-C.
A. Embedding Information in Radar Waveform
Realization of communication in radar systems needs tobe based on either pulsed or continuous-wave radar signals.Hence information embedding with little interference on radaroperation is one of the major challenges. This topic has beenwidely investigated, as reviewed in, e.g., [4], [6], [8]. Here,we summarize these techniques in Table III.One of the particular techniques of interest is index modu-lation (IM). IM embeds information to different combinationsof radar signals’ parameters, over one or more domains ofspace, time, frequency and code [8], [10], [26]. Thus IM doesnot change the basic radar waveform and signal structure, TABLE IIIS
UMMARY OF INFORMATION EMBEDDING METHODS IN RADAR - CENTRIC
DFRC
SYSTEMS . Modulations Methods Advantages Disadvantages M od i fi e d W a v e f o r m s Time-frequencyEmbed-ding Apply various combinations ofamplitude, phase and/or fre-quency shift keying to radarchirp signals [4], [6], [52], ormap data to multiple chirp sub-carriers via the use of frac-tional Fourier Transform [53]. • The chirp signal form remains when theinter pulse modulation is used, which isprefered in many radar applications. • The waveform can be implemented inmany existing radar systems with onlymodifications to the software. • The slow time coding is restricted by thePRF of the radar, thereby limiting themaximum rate of communication.Code-domainEmbed-ding Modulate binary/poly-phasedcodes in radar signals us-ing direct spread spectrum se-quences [54]. • Naturally coexist with the CDMA / DSSScommunication signal form. • Enables covert communication by spread-ing the signal over the bandwidth of radar. • Phase modulation will inevitably lead tospectrum alteration of the radar waveform,which may result in energy leakage out-side the assigned bandwidthSpatialembed-ding Modulate information bits tothe sidelobes of the radarbeampattern [4], [6]. • Has little impact on the radar sensingperformance in the mainlobe. • The performance is sentive to the accuracyof array calibration and BF • The multi-path of radar signal may incurinterference to the communication.IndexModulation(Nowaveformmodifica-tion) Represent information by theindexes of antennas, frequen-cies, and/or codes of the sig-nals [8], [10], [55], [56]. • Naturally coexist with the radar function-ality, with negligible impact on radar per-formance; • Generally achieve higher data rates com-pared to modulation with modified wave-form. • Demodulation may be complicated; • Demodulation performance is sensitive tochannel if IM is applied to spatial domain; • Codebook design could be a challenge. and has negligible influence on radar operation. For MIMO-OFDM, CAESAR and FH-MIMO radar, IM can be real-ized via frequency selection/combination and/or antenna se-lection/permutation [56]–[59]. Frequency combination selectsdifferent sets of frequencies, and antenna permutation allocatesthe selected frequencies to different antennas. Information isrepresented by the combinations and permutations. Let thenumber of combinations and permutations be N c and N p ,respectively. Then the number of bits can be represented is log N c and log N p , respectively. Mathematically, frequencycombination and antenna permutation can generally be com-bined. However, decoupling them is consistent with the waythat the information is demodulated, as will be discussed later.For MIMO-OFDM radar with orthogonal frequency alloca-tion, frequency combination allocates the total N subcarriersto M T groups without repetition, with each group havingat least one subcarrier [57], [60]. If without additional con-straint on subcarrier allocation, there are a total of N c = C NM T M N − M T T combinations (i.e., Selecting M T out of N subcarriers first to ensure each group to have at least one, andthen the remained N − M T subcarriers can go to any of the M T groups); if each antenna needs to have the same numberof L s = N/M T subcarriers, the total number of combinationsis N c = C NL s C N − L s L s . . . C L s L s = N ! / ( L s !) M T . The number ofpermutations of allocating M T groups of subcarriers to M T antennas is N p = M T ! .The DFRC system extended from CAESAR is proposed in[58], where each virtual subarray is assumed to have the samenumber of antennas and use one frequency. Hence frequencycombination selects S out of N frequencies, and N c = C NS .The number of total antenna permutations is shown to be N p = M T ! / (( M T /S )!) S .For FH-MIMO DFRC systems [59], [61], the total numberof frequency combinations and antenna permutations are N c = f1 f4 f4 f1 f3 f5 f5 f3 f1 f8 Ant2Ant1 f2 f4 f2 f4 PRI time f1 One hop with freq f1
Fig. 3. A simple example showing the packet structure of FH-MIMO DFRCwith N = 8 and M T = 2 , consisting of a preamble with two identical hopsand 3 hops with embedded information. A total of 4 bits can be conveyed ineach hop with IM. C NM T and N p = M T ! , respectively. This corresponds to S = M T in [58]. Let B k denote the M T × M T antenna permutationmatrix at hop k , which has only a single non-zero element, , in each row and column. The transmitted signal of the FH-MIMO DFRC can be represented as x R ( t ) = B k ψ ( t ) . (22)Note that both B k and the frequency set F k vary with k andare determined by the information bits. One simple exampleof information embedded FH-MIMO DFRC for packet com-munication is shown in Fig. 3.It is noted that the values of N c and N p above definethe maximum achievable bit rates only, without consideringthe communication reception performance. In practice, thenumber of actually used combinations and permutations maybe reduced, due to the overall system design and the con-sideration of the demodulation complexity and performance.In particular, demodulating the bits embedded in antennapermutation is much more difficult and subject to higher de-modulation error, compared to demodulating those embeddedin frequency combination. These issues will be discussed indetail in Section IV-B and IV-C. In addition, the impacts of information embedding on radar performance should also beevaluated, such as the ambiguity functions in the time domain[56] and in the angular domain [60],. B. Signal Reception and Processing for Communications
Since IM in all the three systems involve FH, and theirreceiver processing methods are similar in many aspects, weuse FH-MIMO DFRC as an example to illustrate the signalreception and processing for its relative simplicity. Overall,the research on the receiver design for these systems are stilllimited. Our overview here is mainly based on [56], [61], [62],and also incorporates works on MIMO-OFDM and CAESARDFRCs [58], [60] into the framework of FH-MIMO DFRC.Consider a receiver with M R antennas. The signal receivedfrom each antenna is passed to a mixer with local oscillatorfrequency f c , which is generally the central frequency ofthe N subbands. Assume narrowband communications andthe difference between multipath delays | τ (cid:96) − τ (cid:96) (cid:48) | (cid:28) T .Referring to (1) and (4) and ignoring the variation of Dopplerfrequencies, the noise-free baseband received signal can beapproximated as y ( t ) = M T (cid:88) m =1 L (cid:88) (cid:96) =1 c (cid:96) e j π ( f k,m − f c )( t − τ − τ o ( t )) (23) a ( M R , φ (cid:96) ) a T ( M T , θ (cid:96) ) β k,m g ( t − τ − τ o ( t ) − kT ) , where β k,m is the m -th column of B k , c (cid:96) ∈ C is the equivalentpath coefficient, subsuming multiple terms, and τ (cid:96) ≈ τ is used.The baseband signal is then sampled at T s = 1 /B , generating L p = (cid:98) T /T s (cid:99) samples per hop. Let H (cid:44) L (cid:88) (cid:96) =1 c (cid:96) a ( M R , φ (cid:96) ) a T ( M T , θ (cid:96) ) . (24)For the simplicity of presentation, assume that g ( t ) is arectangular windowing function. Assume that synchronizationis done perfectly. We can stack L p measurements from all M R antennas to a matrix Y k , which is given by Y k = H B k Φ T = M T (cid:88) m =1 H β k,m ψ Tk,m , (25)where Φ = [ ψ k, , . . . , ψ k,M T ] , β k,m is the m -th column of B k , and ψ k,m = { e j π ( f k,m − f c ) (cid:96) p } , (cid:96) p = 0 , . . . , L p − .
1) Demodulation:
The task of demodulation is to retrieveinformation bits from Y k . We assume perfect synchronizationand channel estimation here. It will become clear that channelestimation may not be necessary if only frequency combina-tion needs to be identified.An optimal formulation of the demodulator can be basedon the maximum likelihood principle [58]. But it has veryhigh computational complexity and is infeasible for practi-cal implementation. Alternatively, we can apply sub-optimalmethods such as CS techniques.The patterns of both frequency combination and antennapermutation can be identified by formulating a sparse recoveryproblem. The basic idea is to construct an L p × N dictionarymatrix Φ d by expanding Φ to cover all N subband frequen-cies. Each column of Φ d has the similar expression with ψ k,m for each subband frequency. Then we can get a 1-D MMV-CSformulation as Y Tk = Φ d A MMV , (26)where only M T out of N rows in A MMV are non-zero,corresponding to ( H B k ) T . The M T frequency estimates,which correspond to the frequency combination pattern, canthen be found by using one of the well-known MMV-CSrecovery algorithms. The estimate of the M T non-zero rowsof A MMV , obtained in the recovery process, can be used tofind the antenna permutation pattern, by matching them with ( H B k ) T . This matching process can be realized in either asimpler row-wise way or a more complicated process jointlyacross all rows.Another simpler sub-optimal method is to exploit the or-thogonality of frequencies across antennas and apply a discreteFourier transform (DFT) matrix F : Y k F = H B k Φ Tk F , (27)where each row of Φ Tk F is the windowed DFT output ofa single tone signal and its waveform has the shape of animpulse with a single peak. Thus each row of Y k F representsthe weighted sum of these impulses. Therefore, the frequencycombination pattern may be identified via locating the peaks.This is particularly effective when either the inverse of H exists or when the LOS path is dominating in H . In theformer, we can compute H − Y k and obtain B k Φ Tk F . Thisleads to simple identification of both frequency combinationand antenna permutation patterns, as B k is a permutationmatrix. In the latter, the frequency combination pattern canbe found via the peaks and the antenna permutation pattern isdetermined via exhaustive searching, even in a single antennareceiver [56], [61].
2) Channel Estimation:
An accurate estimate of H iscritical for demodulation. However, it is challenging to designand incorporate long training sequences, which is essential forestimating H , in FH-MIMO DFRC systems. This is becausetraining sequence requires certainty, which will affect therandomness of FH radar operation.There are very limited results on channel estimation forFH-DFRC systems with IM. In [56], both synchronizationand channel estimation are investigated for a single antennareceiver, with the consideration of packet communications.For channels with a dominating LOS-path, which could bea typical operating condition for radar-centric DFRC, a framestructure is proposed with two identical hops serving as pream-ble followed by hops with embedded information. The twoidentical hops are designed to enable effective estimation oftiming offset, carrier frequency offset and channel. To simplifysynchronization and channel estimation, re-ordered hoppingfrequencies are used, which slightly reduces the informationembedding capability in terms of antenna permutation. Timingoffset and channel estimators are proposed by exploiting thesignal differences between two neighbouring antennas. Thework is also extended to NLOS channels by using incompletesampled hops and judiciously designed hopping frequenciesto combat inter-hop and inter-antenna interference. C. Codebook Design
The codebook determines how the patterns of frequencycombination and antenna permutation are selected and mappedto information bits. As was disclosed in [58], the achievablecommunication rates are largely constrained by antenna per-mutation, as its demodulation performance is sensitive to thedifferences between different columns of H .The design criterion can hence be formulated based on thedistance between two codewords of antenna permutation: λ ( m, m (cid:48) ) = (cid:107) H β k,m − H β k,m (cid:48) (cid:107) . (28)Maximizing the minimal distance among all λ ( m, m (cid:48) ) is atypical design criterion. Since directly searching via (28) iscomputational complicated, a method of projection into alower dimensional plane is proposed in [58]. However, giventhat the design needs to be updated once H is changed, thecomplexity is still very high.Such a complicated design may be avoided by using pre-compensation. For example, for LOS-path dominating chan-nels, the channel differences between antenna permutationswill be small when the AoD is small. In [61], an element-wise phase compensation method is proposed to remove theAoD dependence of demodulating antenna permutation. Thusthe distances between different codewords become identical.In addition to its impact on communication performance,codebook may also affect the radar performance, for exam-ple, the ambiguity function as evaluated in [56], [62]. Morespecifically, it is demonstrated in [62] that the probability ofradar waveform degeneration can be reduced by spreadingthe available frequency hops between waveforms as evenlyas possible; and in [56], it is shown that by constraining thecodewords, the receiver processing can be largely simplified,with negligible impact on the radar ambiguity function.V. JCR: J OINT D ESIGN AND O PTIMIZATION
Although no clear boundary exists between the third cate-gory of JCR and the other two, there is more freedom here interms of signal and system design. That is, JCR technologiescan be developed without being constrained to existing C&Rsystems, and they can be designed and optimized to balancethe requirements for C&R, potentially providing a better trade-off between the two functions.Joint waveform optimization is a key research problemhere. It can be conducted in multiple domains, using variousperformance metrics jointly for C&R. In this section, wereview several typical DFRC waveform optimization schemes.For simplicity, we will mainly consider underlying signalsbased on narrowband single carrier communications, and theextension to OFDM signals is generally straightforward.To avoid confusion, we use H C and H R for communicationand radar channels, respectively; and for simplicity, we assume M T = M R = M . Note that H C (cid:54) = H R in downlink sensingand H C = H R in uplink sensing, as detailed for PMNs in[12], [24]. Referring to (4), collect K received signal vectorsover a CPI and stake them to a matrix, generating Y C = H C X + Z C for communications, and Y R = H R X + Z R forsensing. We assume the AWGN matrices Z R and Z C bothhave zero mean and element-wise variance σ z . A. Waveform Optimization via Spatial Precoding
When different beams are needed for C&R, the precodingmatrix P can be optimized. The basic optimization formula-tion is as follows: arg max P λ ( P ) , s.t. Constraints 1, 2 · · · , (29)where λ ( P ) is the objective function. There could be variousmethods and combinations in defining the objective functionsand the constraints. Each can be either for communication orsensing individually, or a weighted joint function. Next, wereview three types of optimizations that consider mutual in-formation (MI), waveform mismatch, and estimation accuracyfor the sensing performance, respectively.
1) Mutual Information (MI) Based:
MI is well knownfor communication systems, and the usage of MI for radarwaveform design can also be traced back to 1990s [63].MI for radar sensing measures how much information aboutthe channel, the propagation environment, is conveyed to thereceiver. The conditional MI is defined as the entropy betweenthe sensing channels and the received signals, conditional onthe transmitted signal. Mathematically, this can be representedas [64] I R ( H R ; Y R | X ) = M log (cid:18) det (cid:18) σ z X H Σ H R X + I K (cid:19)(cid:19) , where I K is an identity matrix of size K × K , and Σ H R = E [ H R H HR ] /M . The conditional MI for communication isgiven by I C ( X ; Y C | H C ) = K log (cid:18) det (cid:18) σ z H HC Σ X H C + I M (cid:19)(cid:19) , where Σ X = E [ XX H ] /K .Based on the two MI expressions, we can formulate variousoptimization problems. In [3], the estimation rate, defined asthe MI within a unit time, is used for analyzing the radarperformance, together with the capacity metric for communi-cations. In [65], a weighted sum of MI for both C&R is for-mulated as the objective function of optimization for a single-antenna OFDM DFRC system. In [64], a more complicatedMI-based joint optimization is conducted for MIMO DFRCsystems, by taking into consideration practical packet structurewith orthogonal training sequences and random data symbols,and the channel estimation error.A general and flexible formulation can be based on aweighted sum of the two MIs [64], [65] F = w R F R I R ( H R ; Y R | X ) + 1 − w R F C I C ( X ; Y C | H C ) , (30)where F C and F R are the maximal MI for C&R individually,and are treated as two known constants in the optimization,and w R ∈ [0 , is a weighting factor. The function in (30)is concave, and can be maximized by using, e.g., the Karush-Kuhn-Tucker (KKT) conditions. The optimal P turns out tobe a water-filling type of solution that jointly considers thedistributions of the eigen-values of Σ X and Σ H R .
2) Waveform/Beampattern Similarity Based:
The DFRCwaveform is typically expected to possess some useful proper-ties that are beneficial for radar sensing, e.g., good auto- andcross-correlations, high peak-to-sidelobe level ratio (PSLR),low peak-to-average power ratio (PAPR), and resilience toclutter and interference. Nevertheless, it could be quite chal-lenging to implement all these features simultaneously in asingle waveform, especially in the case of JCR, where therandomness in the communication data and channels maybreak down the structure of the waveform tailored for sensing.To cope with this issue, one may consider to optimize theDFRC waveform/beampattern while approximating a well-designed benchmark radar signal, which is known to havethe desired characteristics above. This could be achievedby imposing a figure-of-merit for the waveform/beampatternsimilarity, either in the objective function or in the constraints.As an example, the JCR BF design in [16] aims to approximatea baseline radar beampattern while guaranteeing the individualsignal-to-interference-and-noise ratio (SINR) γ k for K single-antenna downlink users. Accordingly, the optimization prob-lem can be formulated as min P ,β (cid:13)(cid:13) PP H − β R (cid:13)(cid:13) F s.t. β ≥ , γ k ≥ Γ k , ∀ k, diag (cid:0) PP H (cid:1) = P T M T M T , (31)where P ∈ C M T × K is the DFRC BF/precoding matrix tobe designed, R ∈ C M T × M T represents the spatial covariancematrix for a benchmark radar waveform, which generates afavorable MIMO radar beampattern P d ( θ ) , given by P d ( θ ) = a H ( M T , θ ) Ra ( M T , θ ) . (32)It can be readily observed that the cost function in (31) isthe Euclidean distance between covaraince matrices for theDFRC waveform and its pure radar benchmark. Moreover, β ≥ is a scaling factor. The remaining constraints aimto ensure the SINR for each user, as well as to restrict theper-antenna transmit power, with P T being the overall powerbudget available. While problem (31) is non-convex, it canbe sub-optimally solved via the semidefinite relaxation (SDR)approach or manifold based algorithms [16].In addition to the above design that approximates theMIMO radar beampattern, a more straightforward method isto directly approximate the MIMO radar waveform itself.Under the same K -user MU-MIMO downlink scenario, letus first rewrite the MIMO communication signal model (4) ina discrete matrix form as Y C = H C X + Z C = S + ( H C X − S ) (cid:124) (cid:123)(cid:122) (cid:125) MUI + Z C , (33)where S ∈ C K × L contains the information symbols intendedfor K communication users. The second term at the right-hand side of the second equality is known to be the multi-user interference (MUI). If the MUI is minimized to zero, then(33) boils down to an AWGN transmission model, where thefading effect incurred by the channel H C vanishes. By noting this fact, [25] formulates the following optimization problemto design a DFRC waveform matrix X min X (cid:107) H C X − S (cid:107) F s.t. (cid:107) vec ( X ) − vec ( X ) (cid:107) ∞ ≤ ε, | x i,j | = P T M T , ∀ i, j, (34)where the first constraint is to explicitly control the distancebetween X and the benchmark X in an L ∞ -norm sense,with a given similarity coefficient ε . The second constraint,on the other hand, requires X to be constant-modulus (CM),i.e., with a 0dB PAPR. X could be any CM radar signalmatrix, e.g., orthogonal chirp waveform. While problem (34)is again non-convex and NP-hard in general, a branch-and-bound (BnB) algorithm is developed in [25], which finds itsglobal optimum within only tens of iterations.
3) Estimation Accuracy Based:
The accuracy of sensingparameter estimation is important for radar sensing. Since thereceived signals are not a linear function of the sensing pa-rameters, it is generally difficult to get closed-form expressionsfor, e.g., the mean square error (MSE) of the estimates, andto apply them in the optimization directly. Alternatively, wecan derive and use the CRLBs of the estimates, which are lowbounds of the MSE. The CRLBs of signal estimates can bederived via the inverse of the Fisher information matrix (FIM).For estimates based on radar signals, they are well known, e.g.,as reported in [66]. For communication signals, the CRLBsfor some sensing parameters based on the beamspace channelmodels have also been derived, e.g., in [67].DFRC waveform optimization based on the CRLBs forsensing performance has also been studied in the literature.However, due to the complicated expressions of the CRLBs,it is generally challenging to obtain closed-form solutionsin such optimizations. In [68], considering a single-antennaOFDM DFRC system, Pareto-optimal waveform design ap-proaches are proposed to simultaneously improve the es-timation accuracy of range and velocity and the channelcapacity for communications. The Pareto-optimal solutions areobtained for a multiobjective optimization problem, and cannotbe improved with respect to any objective function withoutdeteriorating other objective functions, and hence the solutionsare suboptimal. In [69], waveform optimization is studiedwith the application and comparison of multiple sensing per-formance metrics including MI, MMSE and CRLB, togetherwith an approximated SINR metric for communications. It isshown that there are close connections between MI-based andCRLB-based optimizations, and the MI-based method is moreefficient and less complicated compared to the CRLB-basedmethod. Specific to the CRLB-base method, a closed-formsolution is obtained for some special cases, while an iterativealgorithm is proposed as a general solution.
B. Multibeam Optimization for Analog Array
Steerable analog array, which is also the basic componentof a hybrid array, could be widely applied in mmWave JCRsystems. A JCR system may need to support communicationand sensing at different directions, which is challenging to address given the limits on the BF capability of analog array.A good solution is the multibeam technology [23], [70],[71]. The multibeam consists of a fixed subbeam dedicatedto communication and a scanning subbeam with directionsvarying over different communication packets. By optimizingthe beam with multiple subbeams, communication and radarsensing at different directions can be supported simultaneouslywith a single signal. This can largely extend the field of viewof sensing, for example, in the 802.11ad DFRC with the singlecarrier PHY. The multibeam can be applied at both transmitterand receiver, while transmitter is considered here.Two classes of methods have been proposed for the multi-beam optimization: the subbeam-combination method [23],[70], [71] via constructively combining two pre-generated sub-beams according to given criteria, and the global optimization [71] by jointly considering the C&R BF requirements andoptimizing a single BF vector directly. These methods canalso be extended to full digital arrays.
1) Subbeam Combination:
In the subbeam-combinationmethod, two basic beams for C&R are separately generatedaccording to the desired BF waveform, using, e.g., the iterativeleast squares method [23]. The two beams are further shiftedto the desired directions by multiplying a sequence, and thencombined by optimizing a power distribution factor ρ and aphase shifting coefficient ϕ .The BF vector w t in (35) can be represented as w T = √ ρ w T,F + (cid:112) − ρe jϕ w T,S , (35)where w T,F and w T,S are the BF vectors that are predeter-mined, corresponding to the fixed subbeam and scanning sub-beam, respectively. The value of ρ can typically be determinedvia balancing C&R distances [70], and the optimization isconducted mainly with respect to ϕ , which can ensure the pre-generated subbeams are coherently combined when generatingthe multibeam.The multibeam optimization problem can then be formu-lated with desired objective functions and constraints. Con-sider one example of maximizing the received signal powerfor communications with constrained BF gain in scanningdirections. Let the threshold of the BF gain in the i -th sensingdirection φ i be C i (1 − ρ ) M T , where C s i ∈ [0 , is a scalingcoefficient, representing the ratio between the gain of thescanning subbeam in the interested direction and the maximumgain that the array can achieve, i.e., (1 − ρ ) M T . We canformulate the constrained optimization problem as ϕ (1) opt = arg max ϕ w HT H CH H C w T (cid:107) w T (cid:107) , (36)s.t. | a T ( M T , φ i ) w T | || w T || ≥ C i (1 − ρ ) M T , i = 1 , , · · · , N s , where N s is the number of the total constraints, φ i s arethe angles of interest where the BF gain is constrained, anda maximal ratio combiner is assumed to be applied at thecommunication receiver.With w T,F , w T,S and ρ being predetermined, the optimiza-tion problem can be solved by first finding the unconstrainedoptimal solution for the objective function and then looking for its intersection with the intervals determined by the constraints.Closed-form solutions can then be obtained as detailed in [71].The subbeam-combination method enables simple and flex-ible multibeam generation and optimization, and hence ispromising for practical applications that require fast adaptationto changing BF requirements. It is particularly useful formmwave systems where directional BF is used.
2) Global Optimization:
The subbeam-combination methodis an efficient low-complexity solution, but it is suboptimal.A globally optimal solution can be obtained by solving aproblem formulated directly with respect to w T . Consideringa similar example of maximizing the received signal powerfor communication with constraints on BF waveform, theformulation can be represented as w t, opt = argmax w T , w HT w T =1 w HT H CH H C w T , (37a)s.t. (cid:107) A ( M T , φ i ) w T − d v ) (cid:107) ≤ ε w , and/or (37b) | a T ( M T , φ i ) T w T | ≥ ε i , i = 1 , , · · · , N s , , (37c)where (37b) bounds the mismatches between the generatedBF waveform and the desired one d v , (37c) constrains thegain of the scanning subbeam in N s directions, and ε w and ε i are the thresholds for these constraints. These constraints canbe applied individually or jointly.The optimization in (37) is generally a nonconvex NP-hardproblem. In [71], this problem is converted to a homogeneousquadratically constrained quadratic program (QCQP), whichis then solved by the SDR technique.The global optimization method provides a benchmarkfor suboptimal multibeam optimization schemes. Simulationresults in [71] demonstrate that there exist a loss up to 10%in the received signal power for communications and the BFwaveform, when the subbeam combination method is applied. C. Signal Optimization in Other Domains
In addition to spatial optimization, communication signalscan also be optimized across the time and frequency domains,to improve the estimation accuracy of sensing parameters. Forexample, non-uniform preamble is proposed to improve theDoppler estimation performance in [22]; a modified Golaycomplementary sequence is proposed for 802.11ad-based JCRsystems in [34] to reduce the sidelobe and achieve improvedranging and Doppler estimation; and the idea of using andoptimizing nonequidistant subcarriers in MIMO-OFDM radarin [30] can also be extended to a JCR MIMO-OFDM system.Here, we briefly illustrate the idea by referring to the work in[22].In [22], for a single data-stream single-carrier JCR sys-tem based on 802.11ad, non-uniformly placed preambles areproposed to enhance velocity estimation accuracy. The signalhas a packet structure, consisting preamble and data payload.Radar sensing uses the preamble only. A novel metric ofdistortion MMSE (DMMSE) is developed for communicationsin [22]. A log-scale is then applied to the DMMSE and theCRLB for radar, to achieve proportional fairness betweenC&R, such that the two log-scaled metrics can directly be added up in the optimization objective function. The objectivefunction is given by w C K Tr [log DMMSE ] + w R Conv ( 1 L v Tr [log CRLB ]) , where K is the number of symbols, L v is the number ofvelocities to be estimated, Tr [ · ] denotes the trace of a matrix,Conv ( · ) denotes the convex hull operation, and w C and w R are weighting factors for C&R, respectively.Based on the objective function and some constraints, thenumber and position of preambles are optimized in [22].It is found that when preambles are equally spaced, theperformance of radar or communications cannot be effectivelyimproved without affecting the other. Comparatively, non-uniform preambles are found to achieve a better performancetrade-off between C&R, particularly at large radar distances.VI. C ONCLUSION
JCR is a promising technology that can be used to rev-olutionize both traditional communication and radar systems.Although the potentials and prospects for integrating C&R aregreat, there are many challenges and open research problemsto be addressed due to the inherent differences of the signalformats, and system and network structures between them.Signal processing techniques are key enablers to make theintegration happen. For communication-centric JCR, accurateand practical sensing parameter estimation algorithms are thekey, and a viable solution to the clock asynchrony problem canrelax the full-duplex requirement. Sensing assisted communi-cations is a great way of exploiting the benefit of integration.For radar-centric JCR, how to improve the communicationrates without notable impact on radar operation is a bigchallenge. While it is shown that applying index modulationto frequency-hopping DFRC is an attractive solution, moresignal processing techniques are needed for improving thecommunication receiver. For joint design and optimization,the journey is just started, with most work being focused onwaveform optimization in existing systems. A fresh look atthe joint requirements for C&R may lead to more efficientsolutions, particularly those underlying frequency hopping andmillimeter wave signals that have excellent potentials for bothhigh data rates and radar resolution.R
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