A Comprehensive Study of Past, Present, and Future of Spectrum Sharing and Information Embedding Techniques in Joint Wireless Communication and Radar Systems

Wireless spectrum is a limited resource, and the rapid increase in demand for wireless communication-based services is increasing day by day. Hence, maintaining a good quality of service, high data rate, and reliability is the need of the day. Thus, we need to apportion the available spectrum in an e ﬃ cient manner. Dual-Function Radar and Communication (DFRC) is an emerging ﬁ eld and bears vital importance for both civil and military applications for the last few years. Since hybridization of wireless communication and radar designs provoke diverse challenges, e.g., interference mitigation, secure mobile communication, improved bit error rate (BER), and data rate enhancement without compromising the radar performance, this paper reviews the state-of-the-art developments in the spectrum shared between mobile communication and radars in terms of coexistence, collaboration, cognition, and cooperation. Compared to the existing surveys, we explore an open research issue on radar and mobile communication operating with mutual bene ﬁ ts based on collaboration in terms of spectrum sharing. Additionally, this paper provides important perspectives for future research of DFRC technology.


Introduction
To guarantee a high data rate and improved quality of services, increase in the bandwidth is mandatory for wireless communication. Therefore, increased wireless communication applications with aforementioned properties have caused the auction price of available frequency spectrum to a tremendous rise [1][2][3][4][5][6][7][8][9][10]. Since the increased data rate communication requirements have enforced the network providers to ponder upon the reuse of available spectrum, which has been currently allotted to other technologies [11], the radar spectrums are the best candidates to be imparted for different communication systems because huge slabs of the spectrum can become easily accessible at radar frequencies [12]. The conventional radar applications around the world include air traffic control (ATC), geophysical checking, climate perception, and exploration for safeguarding and security [13]. However, the radars used for monitoring purposes are, generally, utilized for the communication by sharing the spectrum [14][15][16] .
Currently, the allotted frequency band can be divided into two broad categories, i.e., radar system and a communication system. However, a significant percentage of frequency bands from 1 to 10 GHz has been mainly distributed among radar operations, yet new cohabitation options of the radar with communication systems, e.g., 5G NR, LTE, and Wi-Fi, lead to new directions [17]. On one hand, sharing the high frequency, e.g., millimeter wave band, benefits both communication and radar platforms for high data rates and improved tracking the targets, respectively, but on the other hand, interference issues have raised the concerns from both military and civilian applications for critical radar operations.
In the recent decades, the radars have evolved with good precision and increased list of capabilities that include multifunctioning such as surveillance, tackling of clutter, and back scanning as well as dealing with false alarm, simultaneously [18]. Therefore, it requires higher frequency bands as compared to traditional radars. Moreover, the growth of civil activities and the emergence of new technologies in social media have raised dramatically, which also put strong pressure on bandwidth allocation board.
Since higher bandwidth for radar as well as communication stand-alone designs is the need of the day, it also warrants the hybridization of both designs (i.e., radar and communication) for getting joint benefits at higher bandwidths. However, all the aforementioned challenges including the identification of frequency bands that could be made available for wireless broadband are to be taken care of for improved overall performance of joint radar and communication designs. International Telecommunication Union (ITU) and World Radio Communication Conference (WRC) review the allocation of the frequency spectrum annually [19], and in United States of America, the National Telecommunications and Information Administration (NTIA) [20] had dedicated its energies to identify frequency bands that could be made available for wireless broadband service provision alongside with radar operations.
In [21][22][23][24][25][26], it has been reported that in L band, GSM system (GPRS and EDGE) can overlap UHF radars that operate between 1 to 2 GHz, whereas in S band, Long-Term Evolution (LTE) and WiMax overlap with Airport Surveillance or Air Traffic Control (ATC) radar with frequency range between 2 and 4 GHz. Other examples of WiMax and radar overlap are mentioned by [27]. Finally, for millimeter waves, which are used for orthogonal frequency division multiplexing (OFDM), single carrier, WLAN, ranges 11 ft to 33 ft, used for indoor communication overlaps with highresolution imaging radar. Similarly, the same OFDM-based Wireless LAN (WLAN) used for outdoor activities ranges from 100 m to 5 km using OFDM overlap with weather radar that operates between 2 and 4 GHz in C band. Thus, to fulfil the need of extra bandwidth for wireless communication, one must work on idea of spectrum sharing. This will help us economically as well as politically and socially, while understanding of this concept is unavoidable in near future [28]. Therefore, innovative way out of the effective and reasonable spectrum sharing is needed [19,29].
In this paper, we review the recent trends in DFRC design with focus on data embedding techniques. We start with reviewing the different spectrum-sharing techniques and then explain the DFRC data model. Then, we discuss the different methods of embedding information in radar waveforms like amplitude and phase shift keying, phase rotation invariance method, and time modulation arrays. After that, we explore the various methods of modifying the communication waveform to facilitate radar functions. Then, we briefly discuss beampattern modulation techniques like subbeam sharing. Additionally, we compare the performance of the diverse DFRC information embedding techniques in terms of interference mitigation, secure communication, improved bit error rate (BER), and data rate enhancement. Finally, we list some of the research challenges in the field and provide directions for future research.
Rest of the paper is organized as follows. Section 2 provides details about the basic spectrum sharing concepts that have evolved with time. In Section 3, data model is presented and methods commonly used for DFRC designs are discussed in detail. Section 4 focuses on information embedding methods via radar waveforms. In Section 5, information embedding by using communication waveform is discussed. Beampattern-based methods are explained in Section 6. Challenges and future work are discussed in Section 7. Conclusion is presented in Section 8.

Spectrum Sharing Approaches for DFRC
It is obvious that crowding of the spectrum cannot be addressed by the traditional communication techniques and beamforming approaches [30][31][32][33]. Thus, coexistence of both the radar and communication design is highly required for the radar emission and communication on the available spectrum [34][35][36][37][38][39][40][41][42][43][44][45][46]. In broader sense, this coexistence can work either by time-based sharing or embedding information into radar emission for a same spectrum. In the following subsections, we provide the details about integrating radar-communication designs and diverse spectrum sharing methods. allowed to communicate, if it lies in sidelobes of the main radar beam. In this case, the performance will be evaluated by keeping the minimum tolerable distance in terms of interference to noise ratio (INR). The main drawback of this technique is that the communication receiver cannot fully utilize the spectrum, and it must keep its power below certain levels. Misdetection due to spectrum sharing between American integrated naval weapon system and with a cellular system including 100 base stations operating at 3.5 GHz in S Band, which raised the interference management and power allocation, respectively, is investigated in [94]. Thus, to improve the abovementioned drawbacks, authors in [95] studied the regulatory policies for 10 GHz band where sharing occurs between radar and communication users in terms of sensing and relocation techniques. In the same line of action, [96] discussed sharing the spectrum with rotating radar in detail and authors in [97,98] studied the spectrum sharing when the distance between radar and communication is fairly large given that performance is not effected. Another study is carried out by [99] to investigate the performance of shared spectrum in L band for rotating radar and fixed communication user. In their study, communication user is supposed to limit its transmit power when it senses the radar main beam.
Precoder-based design is another solution to this problem, which uses interference channel state information (ICSI). In this case, radar transmitter first estimates the information of pilot signal being transmitted by the communication receiver and maintains a given ratio of INR [100]. This technique mitigates the interference efficiently. However, it can only be applied in scenarios where radar has primary privileges. Another drawback to this scheme is its computational complexity cost at the radar transmitter. Likewise, the communication receiver first identifies the mode of the radar (i.e., either probing or scanning) and then starts its communication. The other solution is to build an efficient receiver for improved interference mitigation. The primary task of such receiver is to evaluate the target parameters in existence of the BS interference. This receiver can either be at the radar side or at BS side. In [41], null-space precoder-based approach is used on radar  3 Wireless Communications and Mobile Computing waveform by using singular value decomposition (SVD); this results in zero-forced interference to communication user. The system is further improved by using optimization-based techniques in precoder design in [38] and [101] in the presence of clutter. The overall drawback of aforementioned precoder-based techniques is they relayed on the knowledge of the interfering channel between the radar and the communication user. One way is to have such information is by sending training signal by DFRC transmitter to all communication receivers or by getting through coordination office connected to both radar and communication system [38]; this burdens the system in terms of spectrum and computational complexities. It is concluded by [102] that those communication users who are trying to obtain the spectrum initially allocated to radar must guarantee the target detection rather than obtaining ICSI.

Cognitive Radar and Communication.
In contemplation to provide the dual nature to devices, price may be reduced, and spectrum can be managed efficiently. To balance the requirements of both systems in terms of interference, adaptability shall be provided to communication receiver in order to sense the radar environment and modify radars to sense the communication as well. Cognitive behaviour needs to be implemented for both the transmitter side and the receiver [103][104][105][106][107]. Thus, by upgrading the radars and communication users to do cognition, i.e., ability to take their own decisions according to needs, has been warranted. However, without any central administration, all the networks will face the chaos and congestion.
Note that modified version of JRC having cognition between radars and multiple communication users is discussed in [108] where they used centralised control to assign threshold to power levels to communication users as shown in Figure 4.
In [107], similar ideas have been used for the DFRC network as shown in Figure 5. In this approach, a single hardware is used to transmit dual nature waveform which benefits both radar operations and communication users. Similarly, efficient utilization of the bandwidth by using dynamic frequency allocation has been studied in . In [110,111], applied Lagrangian optimization techniques have been used to obtain solutions for power allocation to the communication user. Moreover, [112] stud-ied the dynamic allocation of power to communication users keeping the satisfactory threshold level for transmission. In [113], authors investigated that the communication user can adaptively adjust its transmit power to maximize the data rate. Optimal power control and adaptive data rate were       Wireless Communications and Mobile Computing proposed in [114,115] to maximize the communication users' capacity keeping average interference power and peak transmission power constraints. Additionally, fast power allocation to communication user has been studied in [116] with low computational complexity constraint to achieve the optimal solution.

Dual-Function Radar and Communication (DFRC).
The other major branch of CRSS is DFRC [117][118][119][120]. In this category, the radar and communication systems work on a single hardware at the transmitter side for both functions as shown in Figure 6. This technique is also called as intentional modulation on a pulse [121] or a coradar [122]. This joint approach provides efficient utilization of power [70], less weight, and reduced system size at one hand and provides compatibility to avoid spectrum congestions on other hand as studied by . The DFRC system performs radar operations and communication task simultaneously by using dual-nature waveform. The overreaching objective of the DFRC is to utilize radar spectrum to capitalize on the resources by using existing infrastructure. These resources may include multisensor beamforming, highpower and high-gain antennas, and large bandwidth.
Keeping in mind the smart nature of the DFRC to sense nearby environment, these are employed in synthetic aperture radar system (SAR) designs, vehicle to vehicle (V2V) communication, vehicle to network, (V2N), vehicle to pedestrian (V2P), and vehicle to cloud (V2C) communication designs as mentioned by [125]. These features enable the DFRC to be the best suitable candidate for the vehicular network applications. The successful communication is mainly aimed at maximizing the data rate by embedding information in the transmitted waveform [126], while radar waveforms focus to maximize detection performance [127][128][129][130][131][132][133]. Thus, a dual-function system that performs radar and communication operations simultaneously involves a performance trade-off between these functions. Three different methods are devised to embed information bits in waveform of a DFRC transmitter side. 1 st is embedding communication bits into radar waveform [134][135][136] while 2 nd is using communication waveform for radar operations as well [137,138], and 3 rd is by using beamforming-based approaches [139,140] as shown in hierarchical structure Figure 7.
The DFRC design has been under study for almost a decade, yet which scheme suits the situation is still a challenging task. Therefore, the DFRC researchers aim to benefit from the bond of knowledge hoarding in the communication literature and trailblazing radar techniques.
To flourish the DFRC systems, researchers needed to devise signaling strategies vigorously and materialize the modulation schemes of the radar that would lead to integrate and improve the use of the existing radio spectrum.
The following section presents an overview of DFRC systems from the information-embedding perspective in terms of data model, data rate, computational complexities, and radar capabilities. Note that it discusses the various techniques and implementation strategies that define the state of the art DFRC designs.

DFRC Data Model
Consider a DFRC system with uniform linear array (ULA), having an interelement spacing to half of the wavelength, which is used for both transmission of radar pulse and communication symbols, simultaneously. The number of antenna elements at DFRC transmitter is M T . We have one radar receiver array which has the same configuration as a transmitter with M R antenna elements. Also, we consider one communication receiver having antenna element N R , which is located at some arbitrary location in far field. The DFRC transmitter and radar receiver are placed close to each other, such that both DFRC transmitter and radar receiver observe the same spatial angle, and size of DFRC transmitter array and radar receiver array needs to be same, while the size of communication receiver antenna array may be different.
The primary task of the dual-function transmitter array is to generate pulses for target tracking in an efficient way, while the secondary objective is to embed the information bits without effecting the radar operation. The vector form of the baseband signals at the input of the transmit antennas is given as where t represents the time within each radar pulse while τ represents pulse number ψ g ðtÞ, t = 1, 2, 3, ⋯ are G orthogonal waveforms, and w g , g = 1, 2, 3, ⋯ weight vector ð:Þ * denotes the complex conjugate.
It is assumed that waveforms must fulfil the conditions of orthogonality with no time delay and can be written mathematically as where T is the pulse width. Let us assume J far-field targets within the radar main beam, and the vector of baseband signals received by the radar is expressed as

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where β m ðτÞ is the reflection coefficient of the m th target, bðθ m Þ is the steering vectors in direction of θ m , aðθ m Þ is the steering vectors in direction of θ m , eðt, τÞ is the interference vector, and nðt, τÞ is the AWG noise with variance σ 2 I.
Let us consider L communication receivers which are located somewhere within the sidelobe region. It is assumed that the dictionary of orthogonal waveform used at the transmitter is known to each of the communication receivers. Assume that the j th communication receiver with arbitrary linear shape antennas receives the following baseband signal.
where α j is the channel coefficient constant from transmitter array towards J th communication receiver, c j ðϕ j Þ is the steering vector from receive array in direction of ϕ j communication receiver, n j ðt, τÞ is the AWG noise with variance σ 2 I, and ðϕ j Þ is the direction of j th communication receiver.

Radar Waveform for Information Embedding
Information bits are embedded into radar waveforms. Radar operation is performed in the main lobe, while the communication receiver operation is performed only in the sidelobe regions [141]. In order to embed information into radar waveform-based DFRC, we review the following techniques.

ASK-Based Method.
Most popular among all methods for information embedding in radar waveform is ASKbased waveform design [123] in which the communication bits are mapped to the sidelobe levels of the received signal at communication receiver. Two sets of weight vectors are used for this purpose. If the received signal has higher power than predefined threshold ε, it will be considered as binary one, and if the received power is below a certain threshold, it is considered as a binary zero as shown in Figure 8.
The overall form of a radar waveform with information embedded to it at the transmitter of the DFRC is Similarly, for the communication receiver, we have the following signals (see Equation (7), next page top) By performing a simple ratio test, we obtain where T is the threshold. ASK is used to modulate the data in sidelobes [142]. Using the same analogy in [143] for multiwaveform, multi-user communication is used by creating multiple sidelobe levels (SLL). This uses an optimization technique to embed binary information. At one hand, this technique is simple to implement but on the other hand, it has limited data rate. For a DFRC system to be more effective, the information embedding is secure against nonlegitimate user located in directions. Another prominent scheme is devised by using sidelobe AM-based communication, having mainlobe dedicated for radar operations, while sidelobe is dedicated for communication purposes. This sidelobe AM-based  Figure 8: Amplitude shift keying-based information embedding [123].
Wireless Communications and Mobile Computing information embedding is achieved by two methods; first is by use of time modulated array (which is explained in subsequent section later), while the second approach is based on the convex optimization. That is, K distinct SLL are achieved by solving a convex beamforming problem to obtain weight vectors. During each radar pulse, one of the k th weight vector is utilized to transmit signal, where each weight vector represents unique binary symbol. Moreover, a generalized sidelobe canceller method is implemented in [144], by using both the active and the listening modes of the radar. In active mode, mainlobe is used for radar operations while sidelobes were dedicated for communication. In listening mode, there is no radar operation and entire duration is dedicated for the communication. Eight SLL are achieved by the author as shown in Figure 9. Two beampatterns with the same power in the mainlobe are used for radar operations while variable sidelobes are used to accommodate four communication receivers. The communication receivers were located at θ c1 = −60°, θ c2 = −40°, θ c3 = 40°, and θ c4 = 60°. Red beampattern represents binary zero, while blue beampattern represents binary one, respectively. The first beampattern having red color has four sidelobe levels starting from SLL 1 = −6dB, SLL 2 = −7dB, SLL 3 = −10dB, and SLL 4 = −5dB, respectively. Similarly, for the 2nd beampattern, blue colors line have the following SLL which are SLL 1 = −11dB, SLL 2 = −9dB, SLL 3 = −8dB, and SLL 4 = −12dB. Thus, to increase the number of communication receivers, the SLL must be increased.

PSK-Based Method.
Another technique is devised in [145], which uses PSK modulation scheme to embed information. The phase shift will let us know whether the embedded bit is 1 or 0. Similarly, authors in [141] proposed phase modulation (PM) for embedding information into radar waveforms. Binary data is mapped with phase of signal, which is decoded by using phase detector at the receiver side. PM-based information embedding provides more accurate results as compared to AM and multiwaveform ASK-based methods. Another advantage of the said scheme is that we can use it for both directional and broadcast mode and for coherent and noncoherent detection. In [146], authors claim that PSK-based method is more secure as compared to ASK method because interference can disintegrate the SLL as compared to the phases of the waveform. If the communication is coherent, only one waveform is used with 1 beamforming weight vector, and if the communication is incoherent, pair of waveforms and beamforming weight vectors are required, as shown in Figure 10. Communication symbols that are embedded into phase of signal equal the total number of waveforms minus one.
To ensure the radar operation, unity power weight vector has to be used.
ψ p ðtÞ and ψ q ðtÞ are two orthogonal radar waveforms with unity power, and in each radar pulse, only one bit of information is embedded in the form of phase symbol.

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The model of the DFRC radar waveform-based signal is as follows: Similarly, the model of the signal received at the communication receiver is given as The embedded phase symbol can be extracted by using It is important to note that both waveforms ψ p ðtÞ and ψ q ðtÞ will be transmitted simultaneously. Hence, at receiver side, difference between both waveform phase will determine the phase symbol. The common terms between both phases will be cancelled out, and this extracted phase value will be compared with original dictionary. Therefore, phase synchronization is not required. Moreover, it is also worth mentioning that if the entire process is noncoherent, and channel coefficient α j is correctly estimated, then two symbols can also be transmitted, and this leads to double the data rate. This technique can hold the benefits of MIMO radar but lacks dual functionality of MIMO radar and MIMO communication. As with the increase in the constellation size, the exact correlation on phase symbol becomes difficult at the receiver end and this affects the communication process. Antenna In [143], phase rotation invariance-based scheme is used. This technique uses two waveforms to embed one bit of information. This technique is easy to implement and gives better data rate, but it needs minimum two matched filters at the communication end. The phase rotation is direction θ j dependent; hence, only the intended communication receiver will receive embedded information that is located at θ j . In this case, communication process is directional. In those situations, where the communication receiver location is not known in advance or communication receiver is moving rapidly, either to iteratively calculate the communication receiver location or broadcast mode will be used. Authors in [143] achieved broadcast mode by using w p as rotated version of w q beamforming weight vectors. where From Equation (14), we conclude that phase difference between two signals is constant. Figure 11 shows comparison of different schemes studied so for in terms of SNR and BER. For θ c = 50°and θ r = 0°, the performance of sidelobe AM-based approach shows worst results as compared to beampattern AM and multiwaveform ASK. Similarly, the beampattern PSK outperforms beampattern ASK, phase modulation, and aforementioned techniques.

Index
Modulation-Based Method. Previous techniques discussed so far were either using amplitudes of waveform or by using phase of transmitter waveform to embed information. Now, we turn to another domain of information embedding which is called index modulation (IM). Index modulation methods use the index or number of antenna elements to convey additional information bits [147]. Multicarrier agile phased array radar (MAPAR) is used to embed information bits for remote user by using the same technique in [147]. Thus, integrating index modulation into a DFRC transmitter side by using radar waveform leads to high spectral and energy efficient system, without degrading radar performance [148]. Sparse array is used by [149] to embed information into orthogonal waveform and permutation of antenna element. However, this reduces transmit power and antenna gain, thus degrading the target detection and overall performance. In [150], the authors propose carrier agile phased array radar (CAESAR), which has the capability to achieve the wideband performance by using narrow band signals. The abovementioned performance is achieved by applying the concept of frequency agile radar (FAR) in which carrier frequency changes from pulse to pulse; thus, combination of unique frequency with different antenna elements provides more degrees of freedom as shown in Figure 12. Index modulation can be achieved by pairing antenna elements with unique waveform. This pairing is known to both of the transmitter and receiver. In case of MIMO radar, there is no fix binding between waveforms and antenna elements. The system model swaps the antenna elements and waveforms randomly. This swapping does not affect the performance of system. Let us consider MIMO with M T antenna elements and G orthogonal waveforms; this pairing provides constellation effect in terms of factorial, i.e.,, G! and the total bit rate becomes signal at the transmitter of DFRC having form in MIMO where P is the permutation matrix of M T × M T , W is the beamforming weight matrix, ψðtÞ is shuffled waveform matrix, and ϕðtÞ is waveform matrix. The received signal at communication receiver with index modulated waveform is where α j is channel coefficient and aðθ j Þ is steering vector in the direction of j th communication receiver ðθ j Þ.
Comparison is provided for symbol decoding in [151] by using maximum likelihood-(ML-) based decoder, noniterative suboptimal decoder, and iterative low complexity decoder as shown in Figure 13; among all, the computationally complex optimal ML decoder achieves the lowest BER values.
As we increase the number of messages, N b grows; however, the overall BER performance degrades as shown in Figure 14.

Code Shift Keying-Based Method.
Changing radar waveform on pulse-to-pulse basis introduced new horizon for researchers [152]. This technique enables us to assign number to waveform and at receiver by decoding the waveform will give extra information. This is itself an information embedding technique because each waveform represents unique symbol. In this technique, binary data is mapped to Gold codes or Kasami codes, initially, and then embedded to the waveform from the dictionary as shown in Figure 15.
By using this technique, the interference between radar and communication user and due to other targets is minimized to remarkable level because they provide low probability of intercept (LPI) [153]. Monte Carlo simulations were used to check the performance of communication receiver by using various code lengths for both Gold and Kasami codes. PSK modulation can be used to increase bit 10 Wireless Communications and Mobile Computing rate. At DFRC, CSK-based waveform is transmitted via omnidirectional antenna, and at radar receiver, narrow beam width is required to achieve scanning by a phased array radar (PAR) antenna. Suppose we have a dictionary of G waveforms, with G assumed to be power of 2, then by assuming each waveform as communication symbol, the bit rate R bit of transmitted waveform can be written as If the code length is N c chips, and duration of each chip is tc, the maximum bit rate to be achieved can be obtained by R = R bit f PRF . Similarly, for binary PSK modulated waveform, the bit rate can be achieved by Furthermore, now the symbol error rate is determined by using Gold codes and Kasami codes in [153] [154][155][156] used frequency hopping waveform for radar purpose only. Keeping the success rate for radar only, they now utilize the same concept in DFRC. In this approach, authors of [157] used PSK symbol into radar waveform to embed information. Subpulse-based architecture is used to cypher the information. The waveform is divided into multiple segments called as hops as shown in Figure 17.

Frequency Hopping-Based Method. Authors of
To decode the PSK symbol, communication receiver needs accurate information about the channel and frequency hopping sequence (FHS). This technique improves the data rate because pulse repetition frequency (PRF) is improved, but on the other hand, the requirements of multiple hops, accurate channel estimation, and multiplicative clutter effect due to timing offsets increase the computational complexity. The MIMO-based DFRC by using FH waveforms is proposed in [159]. This architecture uses radar as primary function, while the communication on secondary basis. During each FH interval, only one bit of information is embedded by using PM. However, due to time variant nature of channel, waveform optimization needs to be done successively to obtain target information and other features as well. These features and target information are later on used to increase the MI between the target response and the target returns. Author of [158] used PSK and DPSK-based symbols for FH waveforms. In this proposed technique, M T antenna elements and K frequencies to generate frequency hopped waveform were used. Greater the number of frequencies, greater will be number of hops ðQÞ, and hence higher the number of symbols ðLÞ per pulse. The number of symbols can be achieved by using This is the simple most method to implement, and it gives higher bit rate ðRÞ as compared to previous approaches.
Numerical results are based on Monte Carlo simulations to validate the effectiveness of this method, i.e., frequency hopping-based waveform design in [107]. A high PRF is used in X band, which in return gives data rate of megabits, respectively. Figure 18 shows the performance in terms of BER vs. SNR for frequency hopping in phase modulated waveform (uncoded) and convolutional encoder of rate 2/3 in waveform (encoded) compared with method 1, i.e., controlling side lobe levels (SLL) for communication users in [160], respectively.

Chirp Slope
Keying-(CSK-) Based Method. In this technique, information is embedded into radar emission by using chirp subcarriers [161]. These chirps are generated by using fractional Fourier transform (FrFFT) [162]. Linear frequency modulated (LFM) pulse is used to preserve the radar performance. This type of information embedding is used to mitigate the interchannel interference (ICI) caused by quasi chirp subcarriers [163]. Authors of  used the slope of chirps to represent the digital modulating data, i.e., 1 and 0. Rising slope or up-chirp means bit equals to 1, while falling slope or down-chirp means bit is zero. Higher constellation can be achieved by using large number of up/down chirp levels [165]. Additionally, Direct Sequence Code Division Multiple Access (DS-CDMA) proposed by [166] avoids mutual interference between communication user and radar. In [167], the authors achieved orthogonality between radar and communication signals by implementing up-chirps and down-chirps. [168] implemented stepped frequency continuous waveforms (SFCW), and [83] [170]. Initially, TMA was limited to the field of radio astronomy only [171] due to slow FR switches, nonavailability of ad hoc design methodologies for on-off sequence of antenna elements, and inefficient implementation of time  Figure 15: Code shift keying-based information embedding [153]. modulation [172]. From the beginning of new century, demand of TMA increased, when low priced array structure, irregular shaped geometry, and low SLL became the demand of industry with unconventional radiation characteristics [173]. Recent developments of TMA in DFRC with each beampattern represent unique binary information. One of the main advantages of using TMA is the use of wide band instead of narrow band signals. Authors in [174] used ULA at DFRC transmitter side; similarly, another study is carried out by [175][176][177][178] to implement TMA for harmonic beamforming, multiprogramming in [179], angle diversity in [180], and [181] conducts a quantitative study on the energy efficiency of the radar and communications integration. The overall efforts were made to reduce the power loses in terms of sideband radiation.
The basic idea of TMA is to use the radar integration time (IT) by dividing it into time slots according to modulation. Specific number of antenna elements was turned off for number of time instant to achieve higher data rate. This switching of antenna element represents 1 bit on or off as shown in Figure 19.  :  Figure 17: Frequency hopping-based information embedding [158]. Wireless Communications and Mobile Computing To keep radar operations uninterrupted, Genetic Algorithm-(GA-) based optimization technique is used [47] and 4 different beampatterns were designed to transmit binary information. In the above methods, the data rate is highly dependent on PRF of the radar and can be achieved only when line-of-sight (LoS) channel is used. Similarly, time modulated linear array (TMLA) is utilized for information embedding by [182]; this obtains low SLL by using single and multiple frequencies in different designs. It is concluded that only by controlling timebased sequence, diverse power levels and different beampatterns can be achieved. [183] used TMA for information embedding by proposing two different architectures which are Sparse TMA (STMA) in which phase angle is set to zero while power is set to unity, and the second is Phase Only Synthesis TMA (POSTMA), in which phase is optimized by using GA.
Heretofore, we have presented an overview of different strategies for radar-embedded communication signals.
Such strategies are key to establishing dual-function systems that permit simultaneous execution of both radar and communication functions from a shared platform. We have provided a balanced and complete account of existing methods and discussed their respective advantages and disadvantages. In the following section, we will overview the methods that use communication signal for radar operations.

Communication Waveform for Radar Operations
As we know, the DFRC shares its resources like spectrum, power, and antenna elements to transmit such a signal which suits both the radar and communication receivers [184][185][186][187][188][189][190][191]. Now we will put a glance over the methods, which utilize the communication-based waveforms that scan the target without any degradation in system efficiency by simply doing small alteration in actual waveform. This approach utilizes digital multiplexing techniques to encode digital data into multiple orthogonal frequency carriers called subcarriers. By using OFDM-based waveform for DFRC, we achieve better characteristics of low side lobes, high Doppler tolerance, and information transmission capacity reported in . Decoding at receiver side is done by using fast Fourier transform (FFT). Because of the diverse nature and wide range of application, the OFDM-based 13 Wireless Communications and Mobile Computing waveform became feasible option to attract the researchers as alternate solution to fulfil the requirements of the industry [198].

Mutual Information-Based Design.
Mutual information between radar and communication plays vital role in terms of channel capacity and radar performance [199][200][201][202]. In this technique, mutual information (MI) between the communication user and radar target is used as optimization objective for radar at transmitter side [203]. Radar MI is used to evaluate the radar performance, while channel capacity calculation is used as performance measure of the communication system. Impact of SNR and number of antenna elements on MI and channel capacity is calculated in [204]. Adaptive OFDM (AOFDM) design-based approach is proposed in [201] in which the conditional MI between the radar and the received signal is used to calculate data information rate (DIR) in frequency selective channel. Similarly, inner bounds on performance of DFRC in terms of DIR and estimation information rate at receiver are also investigated in [205]. Afterwards, the MI maximization is further explored in [206] to minimize the minimum mean square error (MMSE) in terms of target impulse response. Moreover, for communication-based waveform design, a litmus test is to maximize the data rate by adaptively assigning the transmit power according to the CSI [207]. To summarize the discussion, by using OFDM-based waveforms, MI maximization can be solved as convex optimization problem. Therefore, it becomes an attractive measure as compared to other optimization criteria, like probability of detection and Cramer-Rao bound, which are generally nonconvex problems [67].
In OFDM-based systems, the entire bandwidth is divided into K subcarriers and it is important to note that each subcarrier uses unique frequency. Similarly, each communication receiver utilizes one subchannel only, while radar utilizes all subcarriers for estimation purpose as shown in Figure 20.
DFRC transmitter and communication receiver need to be synchronized in terms of frequency [208]. The signal at the output of transmitter of dual-function antenna array is where x contains L symbols and K subcarriers and K ≤ L. F is Inverse Discrete Fourier Transformed matrix, and each row represents OFDM subcarrier. s = ½s 1 , s 2 , s K T , having length K × 1 vector, represents the amplitudes and phases of each subcarrier.
The signal at the radar receiver is given as where H contains all the diagonal values of channel impulse responses and n is AWG noise vector. Similarly, the signal received at communication receiver is given as where G j = diag ðg j Þ and g j = ½gðj, 1Þ, gðj, 2Þ,⋯,gðj, KÞ T denote channel coefficients for the K subcarrier, which are associated with J th communication receiver.
Information is embedded into this OFDM waveform by using QPSK phase as explained in [208]. Each communication receiver is allotted unique subcarrier, which is using unique frequency. Hence, at communication end, the interference is minimum. The main task in OFDMbased waveform design is to manage transmit power of each subcarrier such that radar target identification is improved. The power of each phase can be calculated by p k = js K j 2 . Hence, the overall transmit power of transmitted signal is where trð:Þ represents the trace of matrix. The maximum power allocated to k th subcarrier is represented as p ðk,maxÞ ; hence, the p max = ½p ð1,maxÞ , p ð2,maxÞ T .
The following optimization gives us acceptable radar objectives.
such that ∑ K k=1 w j,k log ð1 + p k σ 2 gj,k /σ 2 m j,k Þ ≤ −γα opt , where σ 2 g j,k is normalized channel gain for communication receiver, σ 2 h k is normalized channel gain for radar target, σ 2 n k is noise components in the K subcarriers at radar receiver, and σ 2 m j,k is noise components in the K subcarriers at J th communication receiver. α opt represents the MI level of the radar and communication users, and γ is the flexibility of radar towards communication user. The value of γ ranges between 0 and 1. For better radar operations, the value of γ is more inclined towards 1.

Wireless Communications and Mobile Computing
Radar function allows the dual-purpose transmitter to vary the power allocation such that the radar mutual information does not fall below γα opt . Figure 21 shows power allocation for communication user by assigning 29 subchannels to user 1 shown by red color while 3 subchannels to user 2 shown by blue color, respectively. Only one radar target is present utilizing all 32 subchannels. The maximum power normalization for each subcarrier is set to 10 units. Maximizing the overall communication mutual information is done by using eq (14) in [208]. It is observed that three subchannels which are assigned to user 2 are low powered; this results in better MI. Similarly, for worst-case scenario, 8 subcarriers are assigned to user 1, while 16 subcarriers are assigned to user 2. The mutual information is degraded with poor channel conditions than the communication receiver 1 in radarfavored subcarriers.

Index
Modulation-Based Design:. Authors in [209] used index modulation for increasing data rate by using OFDM waveform. Information is encoded into waveform by using quadrature amplitude modulation (QAM) as well as by using the indices of antenna elements in DFRC transmitter. These two parameters help us to improve the efficiency as compared to the traditional OFDM [210][211][212][213], and advantages observed are mentioned in [214]. This presented technique gives good results for radar scanning in terms of energy efficiency, reduced PAPR, robustness to ICI, and improved BER, respectively. Similarly, [151] used different antenna elements and frequencies of subcarrier, which act as constellation space. In this technique, authors split the information bits by using bit splitter module, where each bit is mapped to index selector and Golay code sequence inserter module. Afterwards, subblocks or subcarriers are created in the OFDM block creator. All the subcarriers undergo the IFFT and cyclic prefix (CP); then, data is further converted from parallel to serial and transmitted through DFRC transmitter as shown in Figure 22.
The m th OFDM symbol, which is generated by applying IFFT is given below: where matrix X contains frequency domain transmitted symbols and X m,n represents m th symbol transmitted over n th subcarrier. Cyclic prefix of C samples is added to the beginning of the OFDM symbol after applying IFFT as below.
This baseband discrete signal is processed with digital to analog converter and upconverted to desired carrier frequency. The signal to be transmitted through DFRC Tx becomes Here, f c is the carrier frequency, and θ is initial phase of transmitted signal. The channel through which this transmitted signal propagates introduces Doppler shift and delay to each subcarrier in each path. The channel is modeled as where α p represents attenuation factor, τ p is radar time delay, and v p is Doppler frequency shift for p th target. The signal received at the radar in the frequency domain is given as where F s = NΔf is the sampling frequency upon which received signal is sampled and w½n represents the AWG noise vector.
At communication receiver, null subcarrier is used to identify the location of communication receiver and then well-known maximum likelihood (MLL) approximation is used to decode the QAM modulation. The performance of radar is calculated in terms of the MSE, while the performance of communication receiver is calculated in terms of BER.

Beampattern Modulation
Since existing literature mostly focuses the scheme of using a single beam for communication and sensing , we review beamforming-based approaches for radar and communication in this section. Our aim is to study the performance parameters of separate beams for radar operations as well as communication system generated by single aperture by using signal processing algorithms [216]. It is important to note that both radar and communication system have different requirements for beamforming . Working on high frequencies, radio system encounters propagation loss; therefore, communication system at one hand requires stable and LOS beams for large gain, while radar on other hand requires time-varying and directional scanning beams.
6.1. Subbeam Sharing Design. The concept of 3-dimensional multibeam is presented by [219] for radar in terms of a narrow beamwidth in azimuth, circular, or rectangular shape in elevation and low SLL from single aperture. Similarly, authors in [220] used the same concept for 5G communication systems and [221] for two channel selectable down converter for interference mitigation in radar operations, respectively. Recent developments for unified hardwarebased radar and communication multibeam are studied in [220][221][222][223][224][225][226][227][228]. Entire spectrum is divided into portions called subbeam, and one portion is utilized by communication receiver all the time while the remaining portion is used for different radar operations as shown in Figure 23.
Phased array radars can scan in 2 dimensions to fully utilize the available spectrum. This system is capable to transmit and receive simultaneously, and multiple beams are generated using the same transmitter. The general drawback of multiple beams is that total power is divided in multiple beams, and the scan range is reduced. [216] proposed idea to split transmitter antenna array in two parts for joint radar and communication for interference mitigation. The proposed framework implements time division duplex (TDD) for radar operations while OFDM for communication system, respectively. The parameter estimation is done by on-grid compressed sensing-based algorithm.
Finally, for convenience of the reader, Table 1 shows the brief summary of all the algorithms discussed so far in this paper.

Challenges and Future Work
In this section, we will discuss few of the DFRC challenges that need to be explored.

Uplink for Communication in DFRC.
Keeping the current literature review for DFRC in terms of information embedding, there is lot of space to intensify the accomplishment of system by looking at the evolution of uplink channel estimation and multiuser interference mitigation. Error detection and correction should be advised by the sophisticated algorithms.

Limitation in Data Rate.
Another challenge is to improve the data rate by embedding binary information for high data rates, which must be taken in account for wireless channel estimation and equalization. For moving users, fading and multipath effects need to be considered.  Figure 22: OFDM-based index modulation at DFRC Tx [151]. 16 Wireless Communications and Mobile Computing at the radar receiver keeping the signal to interference plus noise (SINR) ratio at a threshold level and minimum utilization of power. Those signals that employ channel coding techniques needs extra bits, which in return reduce the data rate. Thus, there is a trade-off between radar parameter estimation, and high data rate occurs. Estimation of carrier frequency for radar-based waveform design and method for cyclic prefix spectrum density and symbol rate for OFDMbased waveform design need to be revised for DFRC in terms of PARP and SINR for both stationary and moving user as well as communication receiver mounted on ships.

Waveform Diversity and Cognitive Behaviour.
Waveform diversity is required at the DFRC transmitter side in case of nonapproved/malicious user and enemy targets. Cognition is highly recommended between dual-function transmitter and communication receiver. In this case, when waveform is trapped or enemy deciphers the waveform, it should be updated simultaneously by using cognitive techniques.
7.5. Effect of Clutter and Scatters. Dealing with clutter in bistatic DFRC is one of the major challenges due to varying nature of beampattern-based modulation, similarly the same for frequency hopping and index modulation-based approaches. Thus, bit detection performance at communica-tion receiver may be degraded due to interference. Therefore, benefit from the wealth of knowledge developed in communication literature may be utilized to overcome this problem.
7.6. Subbeam Parameter Estimation. There are many challenging problems and possible improvements yet to be done for multibeam beamforming, which includes weight vector generation with quantized magnitude and phase values, communication and sensing subbeam combination methods optimized with respect to certain criterion, and sensing algorithms that work for high-dimension and off-grid models. Moreover, diverse efficient methods are required to resolve angle of arrivals beyond the conventional concept of scanning.
Most of the DFRC literature is restricted to OFDMbased waveform design only. However, there are potential waveforms which need to be explored for DFRC designs. Therefore, we present some of the latest waveform that can also be used in DFRC to accommodate the requirements of 5G and beyond.   [170][171][172][173][174][175][176][177][178][179][180][181][182][183] Communication waveform-based approach OFDM-based mutual information [67,[199][200][201][202][203][204][205][206][207][208] OFDM-based index modulation [151,[209][210][211][212][213][214] Beampattern-based approach Subbeam approach [219][220][221] 17 Wireless Communications and Mobile Computing potential candidate known as orthogonal time frequency space modulation (OTFS). This is a two-dimensional technique, which exploits the full diversity in time and frequency. This generalized form inherits the qualities of both OFDM and CDMA. OFTS utilizes the advantage of equalizer and converts time-varying, high Doppler signals and fading channel in time-independent channel with constant gain for almost all subcarriers. In OFTS, each transmitted symbol is modulated over two-dimensional basis function that spans both in time and frequency. OFTS symbol can be reduced to one dimension, i.e., spreading codes, which is CDMA and to subchannels which is OFDM. 7.8. Space-Division Multiple Access (SDMA). When multiple communication users need to communicate with dualfunction transmitter simultaneously, modulation techniques are needed which split the channel into parallel spatial pipes. Thus, space-division multiple access is needed. This can be achieved by using phased array antenna keeping healthy and safety standards.

Conclusion
This paper presented a review of the recent trends in DFRC design with focus on data embedding techniques. Different spectrum-sharing techniques were discussed, and the DFRC data model was explained. Then, the different methods of embedding information in radar waveforms were discussed. After that, various methods of modifying the communication waveform to facilitate radar functions were reviewed. Then, beampattern modulation techniques like subbeam sharing were explained. Additionally, the paper discussed few major research challenges in the field and provided directions for future research. Finally, for the ease of the reader, a summary of this review paper is provided in a tabular form.

Conflicts of Interest
The authors declare that they have no conflicts of interest.