MIMO waveform design combined with constellation mapping for the integrated system of radar and communication

Signal Processing 170 (2020) 107443

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MIMO waveform design combined with constellation mapping for the integrated system of radar and communication Wen-hua Wu a, Yun-he Cao a,∗, Sheng-hua Wang b, Tat-Soon Yeo a,c, Meng Wang d a

National Laboratory of Radar Signal Processing, Xidian University, Xi’an, 710071, China School of Communications and Information Engineering, Xi’an University of Posts and Telecommunications, Xi’an 710121, China c Department of Electrical and Computer Engineering, National University of Singapore, Kent Ridge 119077, Singapore d Beijing Electro-mechanical Engineering Institute, Beijing, 100074, China b

a r t i c l e

i n f o

Article history: Received 21 August 2019 Revised 5 December 2019 Accepted 20 December 2019

Key words: Multiple input multiple output waveform design Constellation mapping Peak-to-average power ratio Bit error rate Integrated system of radar and communication

a b s t r a c t In this paper, we propose a novel technique to integrate the dual functions of radar and communication in a single platform, sharing the same frequency spectrum. The proposed technique utilizes the constellation mapping method to embed information symbols in the communication direction via transmit beamforming. By minimizing the integrated sidelobe level (ISL) for transmit beamforming, the system can achieve lower sidelobe level (SLL) for radar detection. The transmit level in the communication direction is controlled to ensure dependable communication transmission, taking into account the communication channel between the integrated platform and the communication station (i.e. communication distance and channel fading). We also investigate the communication performance in bit error rate (BER) with respect to angular error in transmit beamforming and resulting pointing error towards communication station. It is shown that our proposed method has better performance in BER and lower probability of interception (LPI) for communication transmission. Simulation results are presented to verify the theoretical derivations. © 2019 Elsevier B.V. All rights reserved.

1. Introduction With developing civil and military radars and communications requirements, spectrum resources have become more and more scarce. Thus, researchers have been propelled to reconsider sharing frequency spectrum between the two systems, an idea first suggested as early as in 1978 [1]. The challenges and issues of spectra sharing are revisited very recently [2–5]. Due to its high transmit power and flexibility in spatial beamforming, a digital array radar platform has much to offer when multi-tasked as a communication system [6–8]. For instance, the functionalities of cognitive radio [9] and cognitive radar [10] are largely similar and could easily be integrated into a single platform to make full use of resources, resulting in enhanced spectrum usage and efficiency. However, the downside in such an integrated system of occupying the same frequency bandwidth would be the inevitable cross-interference between the two system functions. To suppress the cross-interference [11], more degrees of freedom have to be incorporated into the transmit waveform design.

∗

Corresponding author. E-mail address: [email protected] (Y.-h. Cao).

https://doi.org/10.1016/j.sigpro.2019.107443 0165-1684/© 2019 Elsevier B.V. All rights reserved.

An integrated system built upon an airborne radar platform can achieve reliable data transmission and ultra long-distance wireless communication because of its high transmit power and strong beam directivity. However, as its secondary system function, communication should not affect the primary system function of radar detection [12]. The researches of embedding communication signals into radar systems have been addressed in [13–21]. In particular, a novel method using time-modulated arrays to achieve the dual functions of radar and communication in the mainlobe and sidelobe respectively has been introduced in [18]. It varies the sidelobe levels (SLLs) in communication direction from pulse to pulse via adjusting the phases of the antenna array. At the communication receiver, the SLLs are detected and the data information symbols interpreted. An obvious drawback of this method is the high nonlinearity and heavy computational burden of phasemodulated optimization, and it is difficult to design transmit waveforms for information embedding without affecting the mainlobe. To reduce the computational complexity and introduce waveform diversity, a new method to embed information symbols using SLLs is proposed in [20], based on multiple input multiple output (MIMO) radar principle. MIMO radars have high degree of freedom in transmit beam-pattern design because of the distinct advantage of waveform diversity [22–23]. In [20], multiple orthogonal

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waveforms are weighted for transmitting and the beamforming weight vector for each orthogonal waveform is predesigned to form a series of distinct levels in the communication directions. Information symbols can be embedded via controlling SLLs in terms of special information-embedding scheme and interpreted by matched filtering at the communication receiver. However, data rate of this method is somewhat low and cannot meet large data transmission requirements [24–25]. Moreover, the envelope of this transmit scheme is fluctuating in the time domain, and the signal distortion in the transmitter modules becomes a limitation for applications such as far-field target detection and tracking of multiple moving targets [26–28]. To overcome this limitation, the peak-to-average power ratio (PAPR) of transmitted signal should also be taken into account. In [21], the authors propose a phasemodulated method to embed information symbol by designing a bank of beamforming weight vectors. This method can somewhat increase the data rate but cannot achieve lower sidelobe level (SLL) for transmit beam-pattern due to obtaining each beamforming weight vector independently. In communication, vector quantization (VQ) [29] is a common approach to increase the data rate and improve the bit error rate (BER) performance. Different modulation methods for information symbol correspond to the different designs for constellation mapping of symbol vector. Thus, a novel transmit waveform scheme combined with constellation mapping for embedding information symbols is proposed in this paper. Based on the shared MIMO radar platform, a weighted sum of orthogonal waveforms is transmitted at each transmit antenna. Each orthogonal waveform carries the information symbols via mapping its beamforming weight vector onto a certain constellation point towards the communication direction. For the predesigned constellation mapping dictionary of symbol vectors, beamforming weight vectors are obtained via solving the transmit beamforming problem jointly with mapping constraint in the communication direction. Due to the VQ modulation for information symbol, such as PSK and QAM modulations [30], the communication data rate has been increased. Moreover, to obtain a maximum work efficiency of transmitter modules, a low PAPR of a transmitted time-domain signal is desired. To this end, the upper bound on the PAPR of the transmitted waveform is derived, and it is reduced by modifying orthogonal waveform design without impacting on the beamforming weight vectors. Our work on MIMO waveform design for the integrated system of radar and communication has the following attributes:

(1) The spatial-temporal degrees of freedom are applied to design the integrated waveform embedding information symbols via transmit beamforming, so that the crossinterferences between radar system and communication system can be suppressed in the spatial-domain. (2) The transmit beam-pattern has lower SLL for radar target detection with the objective function minimizing the integrated sidelobe level (ISL) for beamforming. (3) The transmit waveform scheme combined with constellation mapping for information embedding can increase communication data rate of the integrated system for larger-scale data transmission. (4) With the derivation of upper bound on PAPR for transmitted time-domain signal, a special structure of orthogonal waveform is designed to constrain the PAPR upper bound to a low level, which makes the integrated waveform suitable for a radar platform shared with a communication system. (5) The influences on BER performance due to angular error in constellation mapping for information embedding and steering error for digital beamforming (DBF) at communication station are investigated.

The remainder of this paper is organized as follows. In the following section the signal model and some background information are given. Section 3 develops the proposed transmit waveform scheme for information embedding, and designs a special structure for orthogonal waveform which lowers the upper bound of PAPR. Section 4 gives the received signal processing method and performance analysis. In the last two sections, simulation results are presented and the paper is concluded.

2. The integrated system model A co-located MIMO radar system which coexists with a MIMO communication system and sharing the same carrier frequency is as shown in Fig. 1. The co-located MIMO radar is used as an integrated platform which has dual functions of target detection and data transmission [31]. In the transmit stage, integrated waveforms are transmitted for target detection and data transmission. In the receive stage, the integrated receiver receives a mixed signal consisting of radar returns from interested targets and communication signals from a communication station located at a distance away. At the integrated platform, the radar measurements would be sampled and transformed into bit data sequence, and then the acquired target information data are embedded into the transmit waveform and subsequently forwarded to the downstream communication station (or information fusion center). On the other hand, the communication station receives the integrated waveform carrying information symbols which are embedded by the predesigned information-embedding scheme. The communication components are then extracted from the integrated waveform and the information symbols decoded. Note that the primary aim of our integrated system is to achieve radar target detection and twoway communications between the integrated platform and communication station. Suppose that the co-located MIMO radar in Fig. 1 has Mt transmit antennas and Mr receive antennas, both collocated in a uniform linear array (ULA) with half-wavelength inter-element spacing. Let sm (t ), m = 1, 2, · · · , Mt denotes the analog baseband waveform transmitted at the mth transmit antenna. The transmitted scheme of MIMO radar is as shown in Fig. 2, where multiple orthogonal waveforms are multiplied with predesigned weights for transmitting at each antenna. As a result, each transmit antenna is transmitting a sum of weighted orthogonal waveforms. Here orthogonal waveforms uq (t ), q = 1, 2, · · · , Q (Q ≤ Mt ) satisfy the

Fig. 1. Co-located MIMO radar shared with a MIMO communication system.

W.-h. Wu, Y.-h. Cao and S.-h. Wang et al. / Signal Processing 170 (2020) 107443

3

respectively. At the integrated platform, the received mixed signals can be written in vector format, given as

yr (t ) =

L 

βl x(θt , t − τl )ar (ϑt ) + h1 sc (t )ar (ϑc ) + zr (t )

(6)

l=1

Fig. 2. The transmit scheme at the transmitter.

orthogonal condition at zero time-delay, i.e.



 Tp

uq (t )u∗q (t )dt =

0, q = q 1, q = q

(1)

where Tp is the pulse width and ( · )∗ denotes the complex conjugate. According to the transmit scheme shown in Fig. 2, the baseband signal vector at the input of the Mt transmit antennas can be written as

s(t ) = [s1 (t ), s2 (t ), · · · , sMt (t )] = T

Q 

cq uq (t )

(2)

q=1

where cq = [cq1 , cq2 , · · · , cqMt ]T denotes the weighted vector for the qth orthogonal waveform and cqm is assigned to the mth transmit antenna. The symbol ( · )T denotes the transpose. Under the non-dispersive propagation condition, the received signal from a far-field target in the broadside direction of θ can be written as

x(θ , t ) = atH (θ )s(t )

(3)

where ( · denotes the conjugate transposition, and at (θ ) is the transmit steering vector, given as )H



at (θ ) = 1, e jπ sin θ , · · · , e jπ (Mt −1) sin θ

T

(4)

In spatial domain, the transmit power at location θ can be written as

P (θ ) = atH (θ )



= atH (θ )



Tp

s(t )sH (t )dt at (θ )

Q 

cq cqH at (θ )

q=1 Q    cqH at (θ )2 =

(5)

q=1

From (5), the transmit beam-pattern (i.e. spatial spectrum) is determined by the weighted vector cq and is independent of the orthogonal waveforms. As discussed in the above section, the information symbols would be embedded in transmit beamforming. Thus it is desirable to form a transmit beam-pattern for strong radar mainlobe, while restraining the term cqH at (θc ), with θ c denoting communication direction, for information embedding. The waveform design for beamforming and information embedding will be discussed in detail in the next section. Under the far-field condition, suppose that there is a target with L scattering points in the radar mainlobe, locating at position (θ t , ϑt ) with θ t denoting the direction of departure (DOD) and ϑt denoting the DOA. Similarly, suppose that the communication station locates at position (θ c , ϑc ) with θ c and ϑc denoting DOD and DOA

where β l is the radar cross section (RCS) from the lth scattering point, τ l is the delay of the lth scattering point, ar (ϑt ) and ar (ϑc ) are the receive steering vectors for target and station directions respectively, h1 is the channel coefficient of the propagation from communication station to integrated platform, sc (t) is the communication signal transmitted at communication station, and zr (t) is the Gaussian noise vector with zero mean and covariance σr2 IMr where IMr is the Mr order identity matrix. To further perform the radar and communication signal processing at the integrated platform, the radar return and communication signal should first be separated to obtain two channels of signals without crossinterference. At the communication station with Nc receive antennas, the baseband signal vector received from the integrated platform can be written as

yc (t ) = h2 x(θc , t )b(φc ) + zc (t )

(7)

where h2 is the channel coefficient of the propagation from integrated platform to communication station, b(φ c ) is the Nc × 1 receive steering vector with φ c denoting the DOA with respect to the integrated platform, and zc (t) denotes the Gaussian noise vector with zero mean and covariance σc2 INc . With the predesigned transmit power towards communication direction, there is line of sight (LoS) power and thus (7) is typically governed by Rician fading [32–33]. Typically, the LoS power can be effectively employed to lower the BERs. Therefore, for the integrated platform implementing wireless communication, the transmit power towards communication direction should be carefully predetermined to ensure the dependable communication transmission. Note that the multiple receive antennas are coherent for the received DBF to improve SNR. Due to the movement of the integrated platform, there also exists outdated channel state information (CSI) issue for data transmission resulting in the inaccurate channel estimation. We here assume there is feedback channel to combat the outdated CSI so that the receivers can have accurate channel estimation. 3. Waveform design for transmit beamforming with information-embedding In order to achieve the dual functions of the integrated system and reduce their cross-interference as much as possible, embedding information symbols towards the communication direction via transmit beamforming without distortion on radar signal is highly desired. With this idea in mind, the design of beamforming weight vectors is a key problem with information-embedding constraint. 3.1. Transmit beamforming design From Eq. (5), it can be seen that transmit beam-pattern can be synthesized by the Q weight vectors cq , q = 1, 2, · · · , Q. In [20], the authors exploit the Chebyshev criterion to minimize the peak SLL within the sidelobe region for beamforming. Therein, Q times of optimizations are performed independently to obtain the Q weight vectors. However, there is no guarantee a lower SLL for the transmit beam-pattern synthesized by (5) can be achieved by the said procedure. To focus radar transmit power towards the desired directions and obtain a lower SLL, the criterion of minimizing the ISL is adopted in this paper. Note that ISL is also a figure of merit (FOM) to assess how much energy of a spectrum leaks to its sidelobe region [34]. To develop our waveform design for transmit

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beamforming, we first divide the spatial angles into three parts, i.e. the mainlobe angle region ml , the sidelobe angle region sl , and communication angle θ c . The integrated power in the mainlobe and sidelobe can be respectively given by

 Pml =

ml



P (θ )dθ =

Q    cqH at (θ )2 dθ

ml q=1

(8)

and

 Psl =

sl

P (θ )dθ =



Q  

sl q=1

 cqH at (θ )2 dθ

(9)

To maximize Pml and meanwhile minimize Psl corresponds to minimizing the cost function J(C), given by

J (C ) =

C Asl m2 Psl = Pml C Aml m2

(10)

where C = [c1 , c2 , · · · , cQ ]H is the weight matrix, Aml and Asl are the mainlobe and sidelobe steering matrices respectively, and  · m2 denotes the m2 -norm of matrix defined as

Bm2 =

m  n    bi j 2 ,

where B = (bi j )m×n ∈ Cm×n

(11)

i=1 j=1

To minimize the ISL with information embedding in the communication direction, the transmit beamforming design can be written as

min

J (C )

s.t.

C at (θc ) = 

C

(12)

where  = [ρ1 eϕ1 , ρ2 eϕ2 , · · · , ρQ eϕQ ]T , and ρ q and ϕ q are respectively the amplitude and phase modulated for embedding information symbols onto the qth orthogonal waveform. Note that ρ q determines the transmit power towards the communication direction and ϕ q provides more degree of freedom to embed information symbols. Since the cost function is the ratio of two functions in terms of C, for compact formulation, the transmit beamforming design can be transformed into

min C

s.t.

C Asl m2 C Aml m2 = 1 C at (θc ) = 

(13)

As (13) involves a nonconvex equality constraint for the normalized power of the mainlobe, we use the relaxation constraint for optimization, given as

min C

s.t.

C Asl m2 F (C Aml ) = 1 C at (θc ) = 

where F (B ) =

m n i=1 j=1

(14)

bi j is the summation of elements. The problem

(14) is convex and can be solved efficiently by the interior point methods [35] or CVX tool box [36]. Obviously, the above model is also suitable for more than two communication stations but the number of communication receivers should be typically less than that of transmit antennas of integrated system in practical applications. That is because it could then guarantee a feasible solution for (14) with enough degrees of freedom. 3.2. The proposed transmit waveform scheme for information embedding Analysing the method of information embedding in [20], we found two aspects that need to be improved on: 1) the transmitted data rate is not adequate for the communication task, especially

when the amount of data is large, 2) while [20] has predesigned some special SLLs in the communication direction with embedded information symbols, it cannot guarantee that spans among these SLLs are optimal within a small neighborhood of the communication angle. This would lead to a decrease in BER performance for communication transmission. From this viewpoint, we propose the following transmit waveform scheme for the integrated system of radar and communication, using constellation mapping for information embedding. In this way, the data rate is increased for communication transmission at the same time. At the integrated platform, the bit data sequence of radar measurement is transformed into information symbols by regarding K bits of information as a symbol, and each symbol is assigned to an orthogonal waveform. Thus K × Q bits of information are delivered through the transmitter during each radar pulse. Note that only Q/2 bits are achieved during a single pulse for the method in [20] and K bits for the method in [21]. According to (12),  has the degree of freedom of amplitude and phase for constellation mapping. Considering the LoS power for data transmission and the SLL for target detection, the radiation intensity in communication direction should be determined by taking a tradeoff. Therefore, the amplitudes of  are predetermined and fixed during a single pulse so that information symbols will be embedded into their phases. Now, we predesign the constellation mapping dictionary of PSK modulation as below:



 = v(m) , m = 0, 1, · · · , M − 1M = 2K

(15)

where v(m ) = e j2π m/M is the mth symbol constellation point. After K × Q bits of information have been mapped onto symbol vectors vq ∈ , q = 1, 2, · · · , Q sequentially, the beamforming design with information-embedding constraint can be rewritten as

min C

s.t.

C Asl m2 F (C Aml ) = 1 ˜ C at (θc ) = ρ 

(16)

˜ = [v1 , v2 , · · · , vQ ]H , and ρ is a communication channel where  dependent constant (i.e., ρ is proportional to the minimum detectable SNR of the communication receiver). It is necessary to point out that information symbols are directly mapped onto the beamforming weight vectors together, which joins to the ISL optimization for transmit beamforming. This is distinct from the phase-modulated method in [21]. As for the random information transmission, problem (16) needs to be solved repeatedly form pulse to pulse. In summary, our transmit waveform scheme can be described as in Fig. 3. To achieve the dual functions for the integrated platform using the same transmit waveforms, radar detection is implemented in the mainlobe while the data of target returns is further forwarded to a communication station using the above information embedding scheme. As shown in Fig. 3, the transmitted waveforms are obtained by the following steps during each pulse: 1) Consolidating each K information bits as an information symbol for the ˜ is obbit data sequence, and thus the mapping symbol vector  tained by matching constellation dictionary ; 2) Solving problem ˜ to obtain the optimal weight matrix C˜; 3) Generating (16) with  transmitted waveforms by multiplying the obtained weight matrix C˜ and preselected orthogonal waveforms uq (t ), q = 1, 2, · · · , Q according to the transmitted scheme shown in Fig. 2. It is worthy to note that a same weight vector may be assigned to any two orthogonal waveforms depending on their mapping

Fig. 3. The diagram of proposed information embedding scheme.

W.-h. Wu, Y.-h. Cao and S.-h. Wang et al. / Signal Processing 170 (2020) 107443

information symbols. In the extreme case, there may be Q information symbols mapping onto the same constellation point consecutively so that only one weight vector is applied for beamforming, i.e. the rank of C˜ is one. In this case, MIMO radar is reduced to a phased-array radar since each transmit antenna is transmitting the same weighted waveform, namely, the sum of all orthogonal waveforms multiplied with the same weight vector. In spite of this, the information symbols can be recovered at communication station due to the orthogonality for matched filtering operation. On the other hand, it is necessary to point out that the information embedding method of controlling SLLs [20] becomes ineffective when the communication station is located in the radar mainlobe. In this case, our proposed method still works though the value of ρ needs to be selected carefully to not impacting on the mainlobe. Note that the information symbols shall be detectable due to the high transmit power in the mainlobe. 3.3. PAPR analysis Due to the weighted sum of multiple orthogonal waveforms, the envelope of transmitted waveform at each antenna is fluctuating in time domain. To obtain the maximum work efficiency for the transmitters, a low PAPR of time-domain waveform is desired. For simplicity, the PAPR would be derived by the discrete-time waveform. The discrete transmitted waveform at the mth antenna can be written as

sm ( n ) =

Q 

cq,m uq (n ),

n = 1, 2, · · · , Ns

where Ns is the number of samples required to approximate the analog waveform. Let c¯m = [c1,m , c2,m , · · · , cQ,m ]T denotes the weight vector of the Q orthogonal waveforms for the mth transmit antenna, and u¯ (n ) = [u1 (n ), u2 (n ), · · · , uQ (n )]T denotes the Q × 1 vector collecting the nth sample of the Q orthogonal waveforms. The PAPR of the mth transmit antenna can be defined as m max{Pinst ( n )} m Pmax n = Pamv Pamv

(18)

m where Pmax denotes the peak instantaneous power, and Pamv denotes the average transmitted power at the mth transmit antenna, given as

⎧ 2 ⎫ ⎬ ⎨ Q   Pamv = E  cq,m uq (n ) n ⎩ ⎭ q=1

H  = E c¯m u¯ (n )u¯ H (n )c¯m n

H = c¯m c¯m

(19)

m (n ) is the instantaneous power of the nth sampling, given and Pinst as m Pinst

 2   Q   (n ) =  cq,m uq (n )  q=1 

(20)

where E{ · } denotes the expectation. Eq. (19) indicates that the mth average transmitted power equals to the norm of the weight vector of the mth antenna. Eq. (20) shows that the upper bound on the instantaneous power is also related to the norm of the weight vector. Combining (19) and (20), we have n

Pamv

≤

(22)

Then the Q orthogonal waveforms can be generated by the following relationship expression, given as:



ukP+ p (k + (n − 1 ) p0 + 1 ) =

g p (n ), n = 1, 2, · · · , Ns 0,

others

k = 0, 1, · · · , p0 − 1; p = 1, 2, · · · , P (23) To maintain the unit power of orthogonal waveforms, the new orthogonal waveforms should be multiplied with a constant √ coefficient of p0 . For instance, the case of generating Q = 4 orthogonal waveforms with P = 2 orthogonal basic waveforms is shown as follows:

⎡

g1 ( 1 ) , 0 , g1 ( 2 ) , 0 , · · · √ ⎢g2 (1 ), 0, g2 (2 ), 0, · · · G = 2⎣ 0 , g1 ( 1 ) , 0 , g1 ( 2 ) , · · · 0 , g2 ( 1 ) , 0 , g2 ( 2 ) , · · ·

⎤

, g1 (Ns − 1 ), 0, g1 (Ns ), 0 , g2 (Ns − 1 ), 0, g2 (Ns ), 0⎥ , 0, g1 (Ns − 1 ), 0, g1 (Ns )⎦ , 0, g2 (Ns − 1 ), 0, g2 (Ns )

(24)

where the qth row of G denotes the qth orthogonal waveform vector, q = 1,2,3,4. It can be seen from (24) that each column of G has the same number (i.e. P) of nonzero elements. According to (21), √ the new upper bound of PAPR becomes P p0 correspondingly. Thus, the PAPR is reduced by carefully selecting the P orthogonal basic waveforms and thus the designed transmit waveform is suitable for radar integrated platform application. 4. Signal processing and performance analysis 4.1. Signal processing at the communication station

yc (t ) = h2 x(θc , t )b(φc ) + zc (t )

 H 2 2 = c¯m u¯ (n ) ≤ |c¯m |2 |u¯ (n )|

m max{Pinst ( n )}

{g p (1 ), g p (2 ), · · · , g p (Ns )| p = 1, 2, · · · , P }

Since the weight matrix C˜ = [c˜1 , c˜2 , · · · , c˜Q ]H is obtained at a certain pulse, according to (7), the received signal vector at communication station can be rewritten as

H = c¯m u¯ (n )u¯ H (n )c¯m

PAPRm =

For an unit of BPSK or QPSK orthogonal waveforms |u¯ (n )|2 = Q, the PAPR is less than Q. In other words, the upper bound of PAPR is dependent on the non-zero elements of u¯ (n ). To a certain extent, lowering the upper bound of PAPR can reduce the fluctuation of time-domain envelope. For the transmit waveform scheme shown in Fig. 2, one method to reduce the upper bound of PAPR is to design the weight vector with special format [23]. In doing so, the weight vector for each antenna has the predesigned number of nonzero elements so that the upper bound of PAPR can be reduced. However, this idea is not suitable for our waveform design because our weight vectors have already been designed for beamforming with information embedding. Thus, we directly design orthogonal waveforms with constraint on nonzero-element number, to achieve lower upper bound of PAPR. Suppose there are P (1 < P < Q and p0 = Q/P is an integer) groups of perfect orthogonal waveforms with unit power (e.g. generated by exploiting Hadamard codes), used as the orthogonal basic waveforms, given as:

(17)

q=1

PAPRm =

5

|c¯m |2 max |u¯ (n )|2 n Hc c¯m m

= max |u¯ (n )|

2

n

(21)

= h2

Q 

atH (θc )c˜q uq (t )b(φc ) + zc (t )

(25)

q=1

Applying the DBF on the above received signal vector yields

yc (t ) = α h2

Q 

atH (θc )c˜q uq (t ) + bH (φc )zc (t )

(26)

q=1

where α is a constant gain by the DBF operation. To separate each orthogonal waveform for information symbols extraction, we perform matched filtering for the qth orthogonal waveform and

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W.-h. Wu, Y.-h. Cao and S.-h. Wang et al. / Signal Processing 170 (2020) 107443

then have



yˆq =

Tp

yc (t )u∗q (t )dt = α h2 atH (θc )c˜q + zˆq

(27)

where zˆq is the Gaussian noise term after matched filtering. According to the information embedding scheme, there is atH (θc )c˜q = vq . Thus we have

yˆq = α h2 vq + zˆq

(28)

By exploiting maximum likelihood (ML) criterion, the information symbol decision expression can be given as

ˆ = arg m

min

m=0,1,··· ,M−1

D(yˆq , v(m ) )

(29)

where D(yˆq , v(m ) ) = yˆq − v(m ) 2 is a decision function of Euclidean distance. Generally, the mapping dictionary of information symbol is also known accurately at the communication station. Therefore, the transmitted bit data sequence from integrated platform can be decoded via the corresponding demodulation on v(mˆ ) .

and communication signals from the communication station. Due to their different spatial location, they can be separated in the spatial-domain for the mitigation of cross-interference. To obtain respectively the communication signal and radar echo without interference, radar weight vector is designed to form a null in communication direction and a peak in target direction, while communication weight vector is designed to form a null in target direction and a peak in communication direction. The procedures of obtaining these two DBF weight vectors are described as follows. At the phase of digital signal processing, the discrete format of (6) can be written as

yr (n ) = yt (n ) + ys (n ) + zr (n ) where

yt (n ) =



sian noise with zero-mean and variance σˆ c2 = ασc2 . Let ηq = |yˆq | be the magnitude of the communication output. Obviously, ηq follows Rician distribution and its probability density function can be given as:

  2 ¯2 ηq ξ¯ ηq − (ηq2σ+ˆc2ξ ) pdf(ηq ) = 2 e I0 σˆ c σˆ c2

4.2. Signal processing at the integrated platform As shown in Fig. 1, a mixed signal is received at the integrated platform receiver, including radar echoes from the targets

βl x(θt , n − τl )ar (ϑt )

(31)

and ys (n ) = h1 sc (n )ar (ϑc ). To separate the communication signal ys (n) and radar echo yt (n), two DBF weight vectors would be applied for (30) to yield two channels of received signals. The radar DBF weight vector can be obtained by solving the following problem:

⎧ ⎨min wr s.t.

where ξ¯ = |ξ | and I0 ( · ) is the modified Bessel function of the first kind with order zero. Define the Rice factor as KR = ξ¯ 2 /2σˆ c2 , and note that KR denotes the ratio of LoS power to non-LoS (NLoS) power. Obviously, ηq reduces to Rayleigh distribution when KR = 0 i.e. under the NLoS fading environment. Moreover, if the received channels are incoherent, the channel coefficients of different receivers would be different and the DBF operation is thus invalid. In this case, a more comprehensive statistical distribution for the data transmission should be considered, which is out of the scope of this paper. For detailed discussions on the generalized-Rician fading under LoS condition, see [32–33].

L  l=1



For a certain information symbol vq , the term of ξ = α h2 vq is a complex variable which is assumed to be constant and zˆq is Gaus-

(30)

⎩

wrH Rs wr wrH ar (ϑt ) = 1, wrH ar

(32)

( ϑc ) = 0

where Rs = E {yr (n )yrH (n )} is the covariance matrix. Note that the direction of communication station is accurately known by the integrated radar platform. However, the direction of target is an estimated value approximately. Thus, the communication DBF weight vector should be obtained by solving the following problem similarly:

⎧ ⎨min wc s.t.

⎩

wcH Rs wc wcH ar (ϑc ) = 1, wcH ar

(33)

( t ) = 0, t ∈ (ϑt − δ /2, ϑt + δ /2)

where δ is potentially the estimated error of target angle. The example of DBFs for separating the mixed return signal with ϑc = −40◦ , ϑt = 0◦ , and δ = 2◦ is shown in Fig. 4.

Fig. 4. The example of DBF for signal separation.

W.-h. Wu, Y.-h. Cao and S.-h. Wang et al. / Signal Processing 170 (2020) 107443

Applying the obtained DBF weight vectors of wr and wc on (30), the radar echo and communication signal can be extracted respectively:

r1 (n ) = wrH yr (n )



= wrH

L 

βl x(θt , n − τl )ar (ϑt ) + g(n )ar (ϑc ) + zr (n )

l=1

=

L 

βl x(θt , n − τl ) + z1 (n )

where z1 (n ) = wrH zr (n ) and z2 (n ) = wcH zr (n ). Note that (34) consists of the target information related to τ l (time delay) and β l (RCS) which can be estimated by the conventional radar signal processing [22]. From (35), the communication signal from station has been captured so that the carried communication information can be decoded. By now, the integrated system has achieved the functions of target detection and two-way communications between integrated radar platform and communication station.

(34)

5. Numerical simulations

(35)

In this section, we present simulation results to illustrate the performance of our proposed method. We first show the performance of transmit beamforming with constellation mapping in communication direction. Then we show the performance of the

l=1

and

r2 (n ) = wcH yr (n ) = h1 sc (n ) + z2 (n )

7

Fig. 5. Comparison of the performance in transmit beamforming: (a) the SLLs control method, (b) the proposed method, (c) the transmit beam-patterns synthesized by (5).

8

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proposed information embedding scheme in terms of BER and compare it with the existing methods. We also investigate the influence of angular errors in mapping design and of steering error at communication station on BER performance, respectively. 5.1. Beamforming performance with constellation mapping In this subsection, we present the performance of beamforming weight vector design for transmit beamforming via solving the optimization problem (14). Suppose that the number of radar transmit antennas is Mt = 10. The target direction is set to be 0◦ , and the communication directions are set to be −50◦ , −30◦ and 40◦ respectively. The number of orthogonal waveforms is Q = 4, and thus the constellation mapping dictionary is modulated by QPSK, i.e. [1, j, −1, − j]. First, to compare the beamforming performance of the method in [20] (here called SLLs control method) and our proposed method, the phases are set to be ϕq = 0, q = 1, 2, 3, 4 and the amplitudes are set to be ρ1 = −20dB, ρ2 = −21.76dB, ρ3 = −24.77dB, and ρ4 = −40dB with respect to the radar mainlobe, respectively. As a result, the respective beam-patterns formed by each beamforming weight vector are shown in Fig. 5. (a) and (b). Finally, the overall transmit beam-pattern synthesized by (5) is shown in Fig. 5. (c). Fig. 5. (a) and (b) show that all beamforming weight vectors have almost the same pattern within the mainlobe. This indicates that the radar operation will not be impaired no matter which weight vector is used for transmitting waveform. On the other hand, Fig. 5. (c) shows that the peak SLL of the proposed method is lower than that of SLLs control method by about 2 dB. This implies that the proposed method using ISL criterion for beamforming can achieve lower peak SLL, which means that the radar system would have better performance in energy saving and clutter interference cancelation. Moreover, the SLLs towards communication directions are clearly separated from each other for the proposed method, which facilitate embedding of information symbols as described in [20]. However, as shown in Fig. 5(a) or (b), an inevitable drawback of the SLLs controlling method is that the radiation intensity in the communication directions is too low resulting from the distinct spacing design (e.g., it is −40 dB for the 4th beampattern), and thus not beneficial to communication, and may even lead to information symbol loss. In practice, it is more reasonable to design the radiation intensity in communication direction via the channel condition between integrated platform and communication station, such as communication distance and channel fading. Suppose that the center of radar mainlobe is 0◦ and a communication station is located at −50◦ . Fig. 6. shows the case that the SLL at −50◦ is fixed at −18 dB which is just a little higher than the peak SLL. Here, four beam-patterns are formed with constellation mapping dictionary of [1, j, −1, − j], respectively. It can be seen from Fig. 6(a) that all beam-patterns are nearly the same within the mainlobe. This indicates that the randomness of bit data for constellation mapping has no impact on the radar operation. Furthermore, it demonstrates that the rank of weight matrix C˜ also has no influence on transmit beamforming with information embedding for the integrated system. To guarantee dependable communication and not impact on target detection as much as possible, the amplitude in communication direction should be carefully selected according to the channel fading from pulse to pulse. 5.2. Bit error rate performance In this subsection, we compare our proposed method, the SLLs control method [20], and the phase-modulation method [21] in

Fig. 6. The proposed method for integrated system transmit beamforming.

BER performance. Suppose there is a communication station located in the broadside direction of −40◦ with respect to the integrated radar platform. Two orthogonal waveforms are weighted for transmitting, and BPSK is used for constellation mapping to embed communication bit data. For the SLLs control method, here we adopt the signaling strategy 2 in [20] to embed information, because it avoids selecting the threshold. The BER curves of SLLs control method, phase-modulation method, and our proposed method are shown in Fig. 7. As a reference, the BER curves of theoretical BPSK with Gaussian channel and of Rician-fading BPSK with Rice factor KR = 8 are also plotted. Note that 2 × 104 Monte-Carlo simulations are performed for the BER count. From Fig. 7, the BER of our proposed method reduces to 10−4 at the SNR of only 15 dB, which has the SNR improvement about 3.1 dB and 1.2 dB respectively as compared to SLLs control method and phase-modulation method. It indicates that our proposed method has better BER performance than the SLLs control method and phase-modulation method. Although we also use BPSK for constellation mapping to embed information symbols, it has 4 dB loss of SNR compared to theoretical BPSK. However, the curve of proposed method is close to that of Rician-fading BPSK. This demonstrates our derivation of data transmission undergoing Rician fading due to the LoS.

W.-h. Wu, Y.-h. Cao and S.-h. Wang et al. / Signal Processing 170 (2020) 107443

Fig. 7. BER versus SNR for comparison.

9

Fig. 9. BER versus angle error in steering vector.

Fig. 10. PAPR versus antenna index. Fig. 8. BER versus angle.

Due to the movement of integrated radar platform, there are angle measurement errors in the transmit beam-pattern for constellation mapping and in the DOA estimation at communication station for DBF operation. To compare the performance in secured communication transmission, BER versus transmit spatial angle are displayed in Fig. 8. The communication direction is −40◦ and the SNR at the receiver is fixed at 14 dB. It can be seen from Fig. 8 that the proposed method has narrower notch than that of SLLs control method. In other words, the proposed method has more inherent security against information interception in spatial domain. As a result, transmit waveforms for the integrated system has advantage in low probability of interception (LPI). To assess the influence of steering error on information interpretation at communication station, the BER curve versus angular error in steering vector is displayed in Fig. 9. Here, the number of receive antennas at communication station is Nc = 4 and the receive SNR is 14 dB. From Fig. 9, the BER keeps below 10−3 within 7◦ error of the steering vector. It is worthy to note that the angular error of steering vector for DBF only leads to the loss of SNR but does not destroy the information symbols carried by the received signal. Therefore, it has less impact on the BER performance. Fur-

thermore, the angular error of DOA at communication station is typically smaller than 7◦ . 5.3. PAPR of the proposed transmit waveform scheme For the transmit waveform scheme in Fig. 2, the PAPR of our proposed transmitted waveform scheme is investigated using the same set up as per subSection 5.1. Original orthogonal waveforms are generated by Hadamard codes, and the number of samples is Ns = 1024. According to the PAPR definition of (21), the PAPR distributions of the original orthogonal waveform design and the modified orthogonal waveform design are shown in Fig. 10. Note that the modified waveform design exploits the scheme of (23) with √ P = 2. Thus the upper bound on PAPR is reduced from 4 to 2 2. Fig. 10 shows that the PAPR of the original waveform design is nearly 4, approximating the upper bound, while that of the modified waveform design is about 2.1, lower than the new upper bound. It is thus confirmed that the modified scheme for orthogonal waveform design has achieved PAPR reduction of approximately 2, compared to the original PAPR. To investigate the variation of PAPR with respect to different schemes for orthogonal waveform design, we show the comparison

10

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pervision, Validation, Visualization. Tat-Soon Yeo: Writing - review & editing. Meng Wang: Resources, Funding acquisition. Acknowledgement This work was supported by the National Natural Science Foundation of China (61771367), and partially supported by the Science and Technology on Communication Networks Laboratory (HHS19641×003). References

Fig. 11. PAPR comparison versus orthogonal waveform number.

between the true PAPR and the theoretical upper bound in Fig. 11. Here, the number of group dividing is p0 = 2 and the number of orthogonal waveform varies from 2 to√10. In this way, the new upper bound on PAPR becomes (Q/2 ) 2, while the original upper bound on PAPR is Q as discussed in Section 3. Fig. 11 shows that the new PAPR exploiting modified scheme of (23) for orthogonal waveform design is much lower than the original, and is also lower than the new upper bound. It indicates that the modified scheme can efficiently achieve PAPR reduction, which makes the transmit waveforms suitable for practical applications on the integrated radar platform. 6. Conclusion In this paper, a novel transmit waveform scheme to embed information symbols was proposed for the integrated system of radar and communication. Without impacting on the mainlobe for target detection, the proposed scheme combined with constellation mapping method to increase the communication data rate via mapping information symbols onto beamforming weight vectors in the procedure of transmit beamforming design. Moreover, exploiting ISL criterion for transmit beamforming, a lower SLL was achieved. By modifying the orthogonal waveform design, a lower PAPR of transmitted waveform was obtained. The BER performance was also investigated when there are angular error in constellation mapping for transmit beamforming and steering error for DBF at communication station. Simulation results indicated that our proposed information-embedding method has better performance in BER and LPI for communication transmission as compared to the existing methods. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Wen-hua Wu: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Software, Writing - original draft. Yun-he Cao: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Software, Writing - original draft. Sheng-hua Wang: Su-

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