Novel radar and communication integration waveform based on shaped octal phase-shift keying modulation

Physical Communication 38 (2020) 100985

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Novel radar and communication integration waveform based on shaped octal phase-shift keying modulation ∗

Yue Liu a , Ning Cao a , , Minghe Mao a , Gang Li b a b

School of Computer and Information, Hohai University, Nanjing 210098, China Information Center, Ministry of Water Resources of the People’s Republic of China, Beijing 100032, China

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Article history: Received 29 December 2018 Received in revised form 5 December 2019 Accepted 17 December 2019 Available online 20 December 2019 Keywords: Radar and communication integration Waveform design Continuous phase modulation Signal processing

a b s t r a c t In light of increasing requirement for electromagnetic spectrum, spectrum efficiency improvement of radar and communication integration waveform is gaining interest. In this paper, to improve conventional linear frequency modulation (LFM)–continuous phase modulation (CPM) spectrum efficiency, a modified radar and communication integration waveform is proposed. Considering high spectral efficiency of shaped-offset quadrature phase-shift keying (SOQPSK), we generate a new modulation: shaped octal phase-shift keying (S8PSK) by combining the precoding method and CPM with octal phase-shift keying (8PSK). S8PSK is then used to encode communication data into LFM radar signal to form a novel radar and communication integration waveform: LFM-S8PSK. Numerical results demonstrate that compared with LFM–CPM, LFM-S8PSK can provide better spectrum efficiency in exchange for slightly worse bit error rate (BER). Also, it is shown that LFM-S8PSK almost maintains comparable radar performance with respect to LFM. © 2019 Elsevier B.V. All rights reserved.

1. Introduction The expansion in the number of consumers and wireless devices has placed increasing demand on signal bandwidth. Crowding and unavailability of the spectrum has greatly motivated many radar researchers to improve the efficiency of radar system. Besides, many applications and platforms place a dual function requirement on radar: completing radar detection and sending communication information to the collaborative system. One way to address the above challenges is to design a radar and communication integration system, which can simultaneously share hardware, power and bandwidth while performing radar and communication tasks [1–3]. The features of this integration system are beneficial for multiple applications. For instance, in the intelligent transportation system, vehicles need to locate each other and transmit information [4]. The airborne warning and control system (AWACS) radar is required to transmit information to the combat platform and the intelligence center during detecting, target positioning and guidance. Unmanned Aerial Vehicle (UAV) is operating the detection and imaging task on the ground moving targets and the integration signal enables the mutual information exchange between the UAVs, which is mainly designed for space-efficient intention in warfare environment [5]. ∗ Corresponding author. E-mail addresses: [email protected] (Y. Liu), [email protected] (N. Cao), [email protected] (M. Mao), [email protected] (G. Li). https://doi.org/10.1016/j.phycom.2019.100985 1874-4907/© 2019 Elsevier B.V. All rights reserved.

Though many works have been carried out on systems with dual functions of radar and communication [6,7], there are still some shortcomings. For one thing, sharing resources in these schemes requires devising effective approaches to limit crossinterference between radar and communication. For another, considering the multiplexing form, many integration systems use frequency division multiplexing or time division multiplexing. The former increases the system bandwidth without sharing energy, and may cause intermodulation problems, while the latter would reduce resource utilization since the radar cannot detect when communicating. Overall, interference of radar and communication signals can hardly be avoided in these schemes and still double resources for radar and communication respectively is needed. In this context, a more favorable approach for radar and communication integration would be to design an integration waveform. This solution can support target detection while carrying information at the same time. The communication receiver demodulates data from the waveform, while the radar receives the echoes of the waveform and extracts information about objects. Hence, the integration waveform not only can avoid the interference between radar and communication but also decrease the needed resources, then both the energy efficiency and the spectrum efficiency can be increased. [8–10]. In the following, we provide a brief overview of the previous work on integration waveform and highlight the motivations and contributions of this paper.

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Y. Liu, N. Cao, M. Mao et al. / Physical Communication 38 (2020) 100985

1.1. Related work and existing problems

1.2. Motivations and contributions

Integration waveform design has seen a lot of new development in recent years. In these designs, many researchers choose to deploy orthogonal frequency division multiplexing (OFDM) as integration waveform. In [11], the authors extend the OFDM waveform by embedding communication codes to communication-embedded OFDM chirp waveforms for delayDoppler radar applications. In [12], the authors propose OFDM chirp waveform for target detection in low grazing angle region. A MIMO OFDM approach based on random frequency- and timedivision multiplexing is presented in [13]. However, the peak average power ratio (PAPR) of OFDM is so high that serious distortion is inevitable with the nonlinear region of the high-power amplifier for radar’s detection and tracking. Under this consideration, a waveform with constant envelop which can avoid the distortion caused by the nonlinearity of the amplifier is preferred. Besides, as for radar’s detection and tracking, the linear frequency modulation (LFM) is widely used and many sophisticated signal processing schemes are proposed and realized [14,15]. This paper constrains the radar signal to LFM. To both make use of the radars signal processing schemes and avoid the distortion caused by the nonlinearity of the amplifier, LFM-MFSK and LFM-MPSK has been studied by some researchers. An LFM-FSK waveform generator is proposed for the transceiver design to avoid ghost target detection in a multitarget environment in [16]. To further improve the coding efficiency, researchers tend to choose LFM-MPSK signal. [17] uses reduced phase-angle binary phase shift keying (BPSK) along with overlapped (channelized) spread-spectrum phase discretes based on pseudorandom noise sequences to encode multiple messages in a single pulse. [18] refers to technologies including 2PSK and CDMA. Nevertheless, LFM-MPSK discontinuous phase tends to be subject to spectral regrowth when passing through nonlinear amplifiers, which inevitably results in the reduction of spectral efficiency. Since the nonlinear components of the amplifier in the radar transmitter can make signal with non-constant envelope or discontinuous phase generate extra bandwidth, the integration waveform with constant envelope and continuous phase is a favorable choice. To the best of our knowledge, only a few researchers combined CPM which has achieved wide attention in communication literature due to its constant envelope and continuous phase with LFM to form an integration waveform LFM– CPM. LFM–CPM was firstly proposed in 2017 [19]. Till now, a few researchers have modified it to get better spectral performance. In 2017, [19] proposed a three-section LFM–CPM waveform. And in 2019, LFM–CPM with an adjustment of communication symbols and low-density parity-check (LDPC) codes is carried out in [20]. They all made contributions to reducing LFM–CPM occupied bandwidth through decreasing data transmission rate. However, this paper proposes a different method to narrow the LFM–CPM bandwidth. We generate a new symbol alphabet {0, ±1, ±2, ±3, ±4} through using the devised S8PSK precoder. Compared to conventional symbol alphabet of LFM–CPM {±1, ±3, . . . , ±(M −1)}, M denotes the modulation order, symbol distance is smaller in our proposed alphabet. Hence, we narrow the bandwidth at the sacrifice of deteriorating BER. Overall, comparing the most recent LFM–CPM modification method [20] and our proposed method, although the final bandwidth obtained in [20] is narrower than ours, this work guarantees the transmission rate. Since our focus is to reduce the LFM–CPM occupied bandwidth in a different performance trade-off, we mainly compare performance with LFM–CPM.

The goal of this research is to design a new integration waveform that improves the spectrum efficiency of LFM–CPM while preserving the radar performance. Shaped offset quadrature phase-shift keying (SOQPSK) was introduced in [21] as a means of limiting QPSK signal bandwidth through combining a narrower precoder and CPM with QPSK. This paper adopts similar method to enable higher-order modulation method 8PSK to achieve high spectrum efficiency. Then, we combine this novel modulation with LFM to form a new integration waveform, aiming to increase spectrum efficiency while maintain radar performance of LFM. In summary, our main contributions can be listed as follows: (a) Inspired by SOQPSK’s efficient modulation and wide application [22,23], this paper presents a new modulation technology: shaped octal phase-shift keying (S8PSK). It is based on a constrained differential coding scheme and continuous phase modulation ensuring smooth phase changes. The coding efficiency is also improved owing to its higherorder characteristic. In one word, S8PSK combines all the advantages of SOQPSK and enhances coding efficiency. (b) We use S8PSK mapping to embed communication information into LFM radar and propose a novel radar and communication integration waveform: LFM-S8PSK. This method not only obtains higher spectrum efficiency but also almost maintains LFM radar performance. A potential application of this proposed integration waveform is that when navy sends messages to other naval ships, they can tract their targets and transmit communication information to them simultaneously via the proposed waveform without occupying a specific communication link. Beamforming technique ensures the separation of the transmitting signals from other interfering signals [24]. (c) Communication and radar performance of LFM-S8PSK are derived, compared to that of conventional LFM–CPM with even-length nonbinary data alphabets. Both the theoretical and simulation results show that benefitting from the narrower alphabet, LFM-S8PSK can guarantee that its spectrum produces smaller extension when transmitting the same amount of information. Therefore, an overall spectrum efficiency improvement can be achieved. Apart from this, the transmission of communication information almost does not impair radar detection performance, namely, LFM-S8PSK basically obtains comparable radar performance in relative to LFM signal. 1.3. Organization The remainder of this paper is organized as follows. In Section 2, the precoding method and CPM is combined with 8PSK to produce a new modulation method, S8PSK, and a new integration waveform LFM-S8PSK is proposed. In Section 3, spectrum, BER and radar performance of LFM-S8PSK are investigated. The simulation results on communication and radar performance of LFM-S8PSK and LFM–CPM are shown and analyzed in Section 4. Finally, the paper is concluded in Section 5. For ease of exposition, the major symbols and notations used throughout this paper are listed in Table 1. 2. Signal model 2.1. Generation of S8PSK 8PSK symbol constellation diagram is given in Fig. 1(a). The modulation has eight phases and each phase contains three bits binary information. Its phase change is abrupt and non-linear.

Y. Liu, N. Cao, M. Mao et al. / Physical Communication 38 (2020) 100985

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Table 1 List of major symbols and notations. fc ai bi B B0 Tp Ts h L

Carrier frequency Original binary symbol Final transmitted symbol LFM radar signal bandwidth Integration signal bandwidth Pulse duration Symbol duration Modulation index Memory length

This feature makes MPSK notorious for being spectrally inefficient and easily generating regrowth frequency spectrum after passing through the amplifier. Thus, this kind of modulation method is not suitable for the design of integration waveforms. To satisfy the need for efficient use of frequency spectrum, we propose a new modulation method, shaped 8PSK (S8PSK), by combining the precoding method and continuous phase modulation with 8PSK. Mathematical expression of S8PSK is:

√ ss8psk (t) =

Es Ts

ejφ (t) ,

(1)

where Es and Ts are symbol energy and symbol duration, respectively. The phase φ (t) is:

φ (t) = 2π h

∑

bi q(t − iTs ),

(2)

i

where h is the modulation index, bi is transmitted symbol, Ts is the symbol duration. The modulation index is h = 1/4. The transmitted symbol is bi with odd-length data alphabets {0, ±1, ±2, ±3, ±4}, where time index is i ∈ Z . The symbol duration is Ts = Tb logM = 3Tb , where Tb , M are the bit duration and modulation order, respectively. Shaping pulse of CPM q(t) is defined as: q(t) =

⎧ ⎨∫0 ⎩

t 0 1 2

t≤0 d(τ )dτ

0 < t < LTs

(3)

t ≥ LTs ,

where d(t) is a frequency pulse with low-pass characteristics and duration LTs ,

{ d(t) =

1 2LTs

0

0 ≤ t ≤ LTs

(4)

else,

Fig. 1. Constellation of modulation (a) 8PSK, phase state indicated by the arrow varies discretely at each point and (b) S8PSK, phase state indicated by the arrow changes continuously from one state to another along the constellation.

Note that this study considers the case of a full response, namely, L = 1. Motivated by SOQPSK, a precoding is used in S8PSK to convert the original binary input ai into the transmitted symbols bi . Table 2 lists the corresponding precoding rules. The first row denotes the eight possible binary sets in the previous phase, and the first column represents the eight possible binary sets in the current phase. The data bi in the rest of Table 2 indicates the changes between the previous and current phases, i.e., bi is the final transmitted symbol. We provide the relationship between bi and ai : Step 1. Let Ai = {a1i , a2i , a3i } denotes the set of bits transmitted by the ith phase. Step 2. The initial Gray code for each phase is shown in Fig. 1. We adopt the mapping of −1 → 0, +1 → 1 and then decode the Gray code into a common binary code. Within each Gray set, the leftmost data remains unchanged. An exclusive OR (XOR) operation is performed from the second bit in sequence. Decoded value of the bit is the XOR of its original value and its left decoded bit. We obtain ′ ′ ′ the decoded set A′i = {ai 1 , ai 2 , ai 3 }, i = 1, 2, 3, . . ., where ′ ′ ′ ′ ′1 ai = a1i , ai 2 = a2i ⊕ ai 1 , ai 3 = a3i ⊕ ai 2 . Step 3. After being converted the decoded binary code to decimal form, the first row of Table 2 is easily drawn as {0, 1, 2, 3, 4, 5, 6, 7} and the first column is {0, 1, 2, 3, 4,

Table 2 S8PSK precoder.

†

CBS, PBS and TS denote current binary set, previous binary set (vertical arranged) and the final transmitted symbols, respectively.

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Y. Liu, N. Cao, M. Mao et al. / Physical Communication 38 (2020) 100985

Fig. 2. Integration process. ai ∈ {0, 1} denotes the original binary bit information, bi ∈ {0, ±1, ±2, ±3, ±4} denotes the final transmitted symbol.

5, 6, 7}. The final transmitted symbol bi is expressed by:

{ bi =

dei

i=1

dei − dei−1

i = 2, 3, 4, . . . ,

(5)

where dei represents the decimal data in the current ′ ′ ′ phase and dei = 22 ∗ ai 1 + 21 ∗ ai 2 + 20 ∗ ai 3 . To limit the phase change within π for each symbol duration:

⎧ ⎨ bi + 8 bi < − 4 bi = bi − 4 ≤ bi ≤ 4 ⎩ bi − 8 bi > 4.

Since LFM with large time-bandwidth product is widely used in radar [14], this paper considers it as the baseline radar waveform. The radar pulse linearly sweeps the bandwidth B over a pulse duration Tp and the resulting expression is: 2

t)t).

s(t) =

N −1 ∑

rect(

t − kTs Ts

· exp(jπ h(

) · exp(j2π (fc t + k ∑

i=k−L+1

2.2. LFM modulation

µ

The integration signal can be built by using S8PSK mapping to embed communication data into LFM. Expression of resulting integration waveform LFM-S8PSK is:

k=0

(6)

The effect of bi on the phase states is as follows: bi valuing 0, ±1, ±2, ±3, and ±4 respectively indicates that 0, ±π/4, ±2π/4, ±3π /4, and ±4π/4 changes between previous and current phase. Furthermore, as given in (3) and (4), phase of S8PSK is generated by convolution of smooth shaping pulse q(t) lasting duration Ts with bi . The frequency pulse d(t) represents phase conversion speed; i.e., on data transitions, the phase of the waveform changes smoothly and linearly at a constant rate of 1/(2Ts ) for the duration of Ts and remains at 1/2 when t ≥ Ts . The phase obtained in this way changes (bi π )/4 for each duration Ts . Moreover, the phase change is ensured to be within π for each symbol duration, which disperses the spectral energy in a more uniform manner. The constellation of S8PSK is shown in Fig. 1(b). Unlike the abrupt phase alteration of 8PSK, the phase vector of S8PSK rotates from one state to another along the unit circle. In this process, the phase vector maintains a constant rotation speed of bi /(2Ts ). The S8PSK waveform thus guarantees the phase continuity and maintains envelope constant. Compared to widely used mapping methods in radar such as MPSK, MSK and SOQPSK, S8PSK not only implements a constant envelop but also can be applicable to polyphase-coded rather than only to binary-coded waveforms. On top of this, data alphabets of bi with narrower symbol distance and addition of zero differentiates S8PSK from traditional CPM. This characteristic ensures that a sequence of negative and positive phase state transition, or vice versa, is always interrupted by bi = 0 is the most essential for the good spectral containment.

slfm (t) = Alfm · exp(j2π (fc +

2.3. Integration waveform

(7)

To simplify the discussion, we set amplitude Alfm = 1. The linear frequency modulation rate is µ = B/Tp and fc is the initial frequency. Without loss of generality, we assume the phase to be zero. Its spectrum is concentrated in [fc , fc + B].

bi

t − kTs LTs

µ

+

2

t 2 ))

k−L ∑

(8) bi )),

i=0

where N indicates the number of communication symbols contained in one pulse and Ts is the duration of one transmitted symbol bi according to Table 2. Hence, the pulse width is Tp = NTs . The flow chart of the integration process is shown in Fig. 2. The designed S8PSK precoder converts the original binary sequence {ai } into the final transmitted symbol sequence {bi } according to Table 2. Combine {bi } with frequency pulse d(t) (4) and then integrate to form phase function φ (t) containing communication information. Divide φ (t) into in-phase (I) and quadrature-phase (Q) cos(φ (t)) and sin(φ (t)) and then load them on LFM’s I, Q signals cos(2π fc t +πµt 2 ) and sin(2π fc t +πµt 2 ), respectively. The final integration waveform LFM-S8PSK can be achieved through combining signals from I, Q channels. Several papers [10,19] have investigated processing schemes for similar integration waveforms such as LFM-MSK and LFM– CPM. They are also applicable to LFM-S8PSK. In the transmitter, communication data is directly loaded on LFM to form a single waveform, so there is no interference between communication and radar. As to the receiver, it can only receive signal from our target without other interference depending on the spatial directivity of beamforming [24]. 3. Performance analysis In this section, we discuss the performance analysis of the dual-function radar-communication waveform. We derive the spectrum and ambiguity function expression of LFM-S8PSK and provide theoretical comparison with LFM–CPM. 3.1. Communication performance 3.1.1. Spectrum performance STFT is widely used in time–frequency analysis of nonstationary signals [25]. The definition of STFT for a given signal x(t) is: STFTx (t , f ) =

∫

x(u) · g ∗ (u − t) · exp(−j2π fu) du,

(9)

where g(t) is a real symmetric window function, that is, g ∗ (t) = g(t). The spectrum of x(t) is defined as Sx (t , f ) = |STFTx (t , f )|2 .

Y. Liu, N. Cao, M. Mao et al. / Physical Communication 38 (2020) 100985

Therefore, the STFT of the integration signal s(t) (8) is: STFTx (t , f ) =

∫ ∑ N

rect(

u − (k − 1)Ts′ Ts′

k=1

· exp(jπ (2fc u + µu2 +

) k−1 ∑ + h′ ( bi − kbk )))

h′ b k u Ts′

i=0

· g ∗ (u − t) · exp(−j2π fu) du. (10) Based on the additive property of STFT, the equation can be rewritten as: STFTx (t , f ) =exp(−jπ µt 2 ) ·

N ∑

rect(

t − (k − 1)Ts′ Ts′

k=1

∫ ·

) (11)

exp(jZ ) · exp(jπµ(u − t)2 ) · g(u − t)

· exp(−j2π f (u − t)) · exp(−j2π ft) du, where Z

hbk )u 2Ts

= 2π (fc + µt +

+ πh

∑k−1 i=0

bi . Let T (f ) =

exp(jπ µu ) · g(u) · exp(−j2π fu)du. It is easy to conclude that this is a Fourier transform of the windowed LFM signal exp(jπµu2 ) · g(u). According to Fourier time-varying and frequency-changing properties, the spectral expression of an integration signal can be expressed as:

∫

2

STFTx (t , f ) =exp(jπ (µt 2 − 2ft + 2fc t + 2

·

N ∑

rect(

t − (k − 1)Ts Ts

k=1

· exp(jπ h(

k−1 ∑

hbk 2Ts

t))

)

bi − kbk )) · T (f − (fc + µt +

hbk 2Ts

)). (12)

When the window function is Gaussian function, g(t) = exp (−t 2 /(2 · σ 2 )), the expression of T (f ) is given: T (f ) =

exp(jπ µu2 ) · exp(−

u2 2σ 2

) · exp(−j2π fu) du,

(13)

the phase integral is:

φ = jπ µu2 −

communication symbols, the real bandwidth B0 of the integration signal will be widened and exceed the LFM bandwidth B. To restrict the spectrum of integration waveform, we set bi data alphabets as {0, ±1, ±2, ±3, ±4}, as discussed in Section 2.1. The fact that the narrower distance between symbols in the proposed alphabet and a sequence of negative and positive phase state transition, or vice versa, is always interrupted by bi = 0 enables LFM-S8PSK outperform conventional LFM–CPM on the spectrum efficiency.

3.1.2. BER performance In terms of S8PSK BER performance, Fig. 1 presents that the distribution of phase in its constellation diagram is the same as that of 8PSK. The precoding method just makes its phase change smoothly to avoid mutations. This means that precoding method does not have influence on BER performance. Besides, due to the symbol transmitted by S8PSK denotes the change between the previous and current symbols, S8PSK can achieve the same BER performance as 8DPSK. Considering the integration waveform (8), it is obvious that loading S8PSK on LFM signal directly has no impact on Euclidean distance between different symbols. Therefore, under the condition of matched filtering and no energy leakage, LFM-S8PSK owns the same BER performance of S8PSK. Utilization of MPSK and high order modulation is bound to bring higher BER than CPM [26], so searching solutions to degrade BER is the focus of our future work.

3.2. Radar performance

i=0

∫

u2

− j2π fu. (14) 2σ 2 To gain a smooth phase, we derive (14) and set the result as zero. We have: j2π f u= . (15) jπ µ − 2σ1 2

The pulse compression of LFM-S8PSK integration signal is essentially a matched filter. The ambiguity function of LFM-S8PSK can be expressed as:

χ (τ , f d ) =

∫

∞

xT S(t)SH (t − τ )x · exp(j2π fd t) dt ,

T (f ) = √

(2π σ 2 µ)2 + 1

· exp(−j

where x = [1, 1, . . . , 1]T is an N-dimensional column vector and τ , fd are delay resolution and Doppler resolution, respectively. S[t ] = [s1 (t), s2 (t), . . . , sN (t)]T , where sn (t) represents the integration signal in the nth symbol, 1 ≤ n ≤ N. The detailed expression could be divided as two cases: when (k − l)Ts ≤ τ ≤ (k − l + 1)Ts ,

χ (τ , f d ) =

N N ∑ ∑

((k − l + 1)Ts − τ )Dkl

k=1 l=1

Substituting (16) into (12) and applying the definition of Sx (t , f ), the integration waveform spectrum is: Sx (t , f ) = A2 · exp(−

· sinc {[µτ + fd +

πµ · (2π f )2 2 · (σ π f ) 2 + ). 2 2 (2πσ µ) + 1 (2πσ 2 µ)2 + 1 (16)

2πσ · (f − (fc + B0 ))2 (2πσ 2 µ)2 + 1

where real bandwidth B0 = µt +

∑N

),

t −(k−1)·Ts h·bk ) 2T , k=1 rect( Ts s

(17) and

A denotes amplitude. It is easy to conclude when loaded with

(18)

−∞

We then substitute (15) into (13):

√ 2σ 2 π

5

h 2LTs

k ∑

(

bm −

m=k−L+1

l ∑

(19) bn )]

n=l−L+1

· ((k − l + 1)Ts − τ )}, when (k − l − 1)Ts ≤ τ ≤ (k − l)Ts ,

χ (τ , f d ) =

N N ∑ ∑

((l − k + 1)Ts − τ )Dkl

k=1 l=1

· sinc {[µτ + fd +

h 2LTs

· ((l − k + 1)Ts − τ )},

(

k ∑ m=k−L+1

bm −

l ∑ n=l−L+1

(20) bn )]

6

Y. Liu, N. Cao, M. Mao et al. / Physical Communication 38 (2020) 100985

Fig. 3. Waveform diagrams of (a) LFM-8PSK and (b) LFM-S8PSK.

where Dkl = exp{jπ[−µτ 2 + h

k−L ∑

ba − h

l−L ∑

a=0

+

h L

(

k ∑

l ∑

bm (k − m) −

m=k−L+1

+ (µτ + fd +

ba

a=0

bn (l − n)) − (fd + µτ )Tp

n=l−L+1

h 2LTs

(

k ∑

bm −

m=k−L+1

l ∑

bn ))

4. Simulation and discussion

n=l−L+1

× ((k + l + 1)Ts + τ − Tp )]}. (21) Compared to the ambiguity function peak value of ∑k of LFM, the ∑ l f hN ( m=k−L+1 bm − LFM-S8PSK is τ = −{ µd + 2LB n=l−L+1 bn )}. Because of the influence from the random symbol bi , the peak f appears randomly near τ = − µd . Doppler resolution and delay resolution of LFM-S8PSK is analyzed in the following. 3.2.1. Doppler resolution Consider no delay difference between two targets echo symbol sequences (k = l), namely, τ = 0 in the ambiguity function (19) (20). Then, the resulting Doppler resolution is:

|χ (0, fd )| = |NTs · sinc(NTs fd )| .

(22)

It can be seen that the Doppler resolution of integration waveform is 1/Tp , namely, it only depends on the signal pulse duration and is independent from the transmitted data. 3.3. Delay resolution Consider no Doppler shift difference between two targets, i.e., fd = 0 in the ambiguity function (19) (20). In real applications, the delay resolution τ is much smaller than symbol duration Ts , namely, 0 ≤ τ ≪ Ts . Under this consideration, we conclude two cases: when (k − l)Ts ≤ τ ≤ kTs ,

|χ (τ , 0)| =

N N ∑ ∑

|(Ts − τ )sinc(µτ (Ts − τ ))| ,

(23)

k=1 l=1

when (k − l − 1)Ts ≤ τ ≤ (k − l)Ts ,

⏐ N N ⏐ ∑ ∑ ⏐ ⏐ h ⏐ ⏐ |χ (τ , 0)| = ⏐τ sinc((µτ + 2LTs (bk − bl−L+1 ))τ )⏐ .

(24)

k=1 l=1

Under the condition of τ ≪ Ts , we can ignore the effect of (24) and the delay resolution is:

|χ (τ , 0)| = Tp sinc(Bτ ).

Here, the delay resolution is inversely proportional to designed bandwidth B. If τ ≪ Ts is not satisfied, we cannot ignore the impact from communication data. It is difficult to achieve an accurate expression of delay resolution, but simulations will confirm that the addition of communication signals in LFM-S8PSK would generate extra bandwidth and the improved delay resolution [27]. Besides, it is noticed that the communication data may cause higher side lobes in delay resolution.

(25)

In this section, we provide numerical simulation results based on MATLAB (version 9.4) to quantify the performance of the proposed integration waveform LFM-S8PSK. All the results can be achieved within 60s in this simulation. Without loss of generality, we set carrier frequency fc = 5 MHz, the designed bandwidth B = 20 MHz and pulse duration Tp = 20 µs and the duty ratio of pulses 10% in the examination. A similar analysis is performed for LFM–CPM for comparison purposes. The results are computed over a Monte Carlo simulations with 10 000 iterations, since for both of them the performance is affected by the transmitted sequence of random communication data. 4.1. Communication performance In Fig. 3, the phase diagram of LFM-8PSK and LFM-S8PSK are plotted. It is clear that LFM-8PSK generates phase discontinuity, LFM-S8PSK maintains its phase continuous, as discussed in Section 2.1. Communication performance is expressed in terms of spectrum and BER. The used Rician and Rayleigh channels are defined as follows. We set three paths to experience Rayleigh fading. The path loss is [−2, −1, 0] dB; delay is [0, 0.1, 0.2] µs and phase shift is [0, π, 2π]. The Rician channel adds a line-of-sight (LOS) path to the Rayleigh channel with Rician factor K = 5. Since we use the MATLAB built-in rician/rayleighchan functions to simulate the Rician and Rayleigh channels and test performances of the proposed LFM-S8PSK without any additional specification, the parameters in this paper are selected only based on the relevant guidance from MATLAB help documentation [28]. We make sure that the parameter settings in this paper are within the allowable range of MATLAB simulation and without loss of generality. Here, we give some references which also provide corresponding parameter setting examples or MATLAB codes to help readers in the utilization of the MATLAB built-in fading channel model functions [29–31]. Partial enlargement of four radar waveforms spectrum on varying symbol number and for three different channel models are displayed in Fig. 4. It can be seen that for all the analyzed conditions, the LFM-S8PSK’s spectrum expansion is significantly smaller than LFM-8PSK’s and LFM–CPM’s relative

Y. Liu, N. Cao, M. Mao et al. / Physical Communication 38 (2020) 100985

7

Fig. 4. Partial enlargement of LFM, LFM-8PSK, LFM–CPM and LFM-S8PSK spectrum. (a) symbol number N = 60 in AWGN channel, (b) N = 500 in AWGN channel, (c) N = 60 in Rician channel, (d) N = 500 in Rician channel, (e) N = 60 in Rayleigh channel, and (f) N = 500 in Rayleigh channel.

to LFM’s spectrum. Under condition of small number of communication data (Fig. 4(a), (c) and (e)), the frequency spectrum of LFM-S8PSK and LFM–CPM signal approximates that of LFM, whereas spectrum of LFM-8PSK expands about 20 dB compared with LFM. In Fig. 4(b), (d), (f), the gap in spectrum between LFM and the two integration waveform increases when N = 500. We observe that the spectrum of LFM-S8PSK and LFM–CPM differs from that of LFM by less than 20 dB. The spectrum of LFM-8PSK differs from that of LFM by nearly 40 dB. In all the conditions considered, LFM-S8PSK outperforms LFM–CPM about 1 ∼ 5 dB. Assuming t = NTs , according to (7), the bandwidth range of LFM is [fc , fc +B]. We can get the integration waveform bandwidth ∑N t −(k−1)Ts hbk B0 = fc + B + k=1 rect( ) 2T from (17). Since bk is drawn T s

s

from {0, ±1, ±2, ±3, ±4} for LFM-S8PSK and bk is drawn from {±1, ±3, . . . , ±(M − 1)}, M = 8, for conventional LFM–CPM, we can conclude that the bandwidth range for LFM-S8PSK and LFM– 4h 7h CPM is [fc , fc + B + 2T ] and [fc , fc + B + 2T ], respectively. When the s

Fig. 5. BER of LFM–CPM and LFM-S8PSK.

s

∑N t −(k−1)Ts hbk rect( ) 2T ) Ts s [ ]k=1 [ 4h 4h 7h < 0, the range is fc + B − 2Ts , fc + B + 2Ts and fc + B − 2T , s ] 7h fc + B + 2T . Therefore, the bandwidth of both integration waves number of symbols N is so large that (B +

forms expands than that of LFM. In Fig. 4, the relationship between the spectrum amplitude difference and the bandwidth

difference is ∆A = 20lg |∆B|, where ∆A is the amplitude difference and ∆B denotes ratio of occupied bandwidth, namely, ∆B = B0 /B. When N = 60, Ts = Tp /N, the spectrum amplitude of LFM4h S8PSK differs that of LFM by 20lg |(B + 2T )/B| = 2.28 dB. Using s

8

Y. Liu, N. Cao, M. Mao et al. / Physical Communication 38 (2020) 100985

Fig. 6. Radar resolution of LFM, LFM–CPM and LFM-S8PSK. (a) Doppler resolution and (b) delay resolution with symbol number N = 60, (c) delay resolution with N = 500, (d) delay resolution with N = 60 and Doppler shift.

the same method, we can derive that compared with bandwidth amplitude of LFM, the amplitude of LFM–CPM increases up to 3.67 dB. When N = 500, spectrum amplitude of LFM-S8PSK expands that of LFM up to 10.88 dB and LFM–CPM expands about 14.61 dB. Hence, the spectrum expansion in Fig. 4(a) (b) are both smaller than 20 dB. Rayleigh and Rician channels may have influence on the signal spectrum. Since the detailed numerical influence is out of the scope of this paper, we only provide the simulation results from Fig. 4(c) to (f). Overall, due to continuous phase modulation, both LFM-S8PSK and LFM–CPM can obtain narrower bandwidth than LFM-8PSK. Besides, with the narrower alphabet, LFM-S8PSK can decrease the spectrum expansion. In general, for fixed amount of transmitting communication data, in order to achieve higher spectrum efficiency, LFM-S8PSK is preferred than LFM–CPM. BER of the two integration waveforms subject to AWGN, Rician and Rayleigh channels is evaluated and shown in Fig. 5. For all the analyzed channel models, LFM-S8PSK is outperformed by LFM–CPM. This is due to the poor BER performance that high order MDPSK presents, as discussed in Section 3.1.2. In our simulation, we set Rician factor K = 5. Since the only difference between Rician channel and Rayleigh channel is the LOS path, which is affected by K , there exists difference of the signal performance between two channels. We can see that the performance difference of LFM–CPM between these two channels is more pronounced than that of LFM-S8PSK. We speculate that the proposed precoding method could make LFM-S8PSK more sensitive to the LOS path. We will consider this problem in the future research. In a word, our main consideration is the BER performance comparison between LFM-S8PSK and LFM–CPM rather than the channel difference. We plot the results in three channels just for universality. 4.2. Radar performance Doppler resolution and delay resolution diagrams estimated from ambiguity function of LFM–CPM, LFM-S8PSK are presented in Fig. 6.

4.2.1. Doppler resolution Zero-delay cuts in Fig. 6(a) show a same trend between LFMS8PSK, LFM–CPM and LFM waveform. This is due to Doppler resolution is inversely proportional to the pulse width Tp . Communication in integration signal rarely generates influence on Doppler resolution, which is consistent with the discussion above. 4.2.2. Delay resolution In order to evaluate the delay resolution of the proposed LFMS8PSK, two cases are carried out: N = 60 and N = 500. Firstly, the results obtained in Fig. 6(b) when N = 60, confirm that LFMS8PSK and LFM–CPM present a general similar trend in terms of delay resolution and side lobes. As to radar waveform, delay resolution is proportional to the inverse of the bandwidth. In Fig. 6(b), we set the number of transmitted symbol N = 60. As shown in Fig. 4(a), when N = 60, the spectral difference between LFM–CPM and LFM-S8PSK is small, so these two waveforms exhibit similar range resolution. The randomness of the communication information in both the integrated waveforms results in the large side lobes. The second case regarding the comparison with LFM-S8PSK and LFM–CPM in the presence of 500 communication symbols is shown in Fig. 6(c). It is interesting that with N increasing, side lobes near to the main lobe is compressed, making for enhancing detection of adjacent weak signals. Note that real bandwidth B0 used by the two integration waveforms is much larger than LFM bandwidth B because of the random communication symbols, so the improved delay resolution is achieved [27]. An engineering trade-off between the waveform bandwidth and delay resolution is presented. While adopting LFM-S8PSK will ensure smaller spectrum, it will also reduce the radar delay resolution. Next, in Fig. 6(d), we plot zero-Doppler cuts for three waveforms with Doppler shift in the presence of N = 60. Similar to Fig. 6(b), delay resolution of LFM-S8PSK is comparable with that of LFM–CPM. In general, the Doppler resolution and delay resolution of LFMS8PSK have similar characteristics to those of LFM. Therefore, the proposed integration waveform can well perform radar tracking and detection.

Y. Liu, N. Cao, M. Mao et al. / Physical Communication 38 (2020) 100985

5. Conclusion In this manuscript, to improve spectrum efficiency of LFM– CPM, a modified radar and communication integration waveform: LFM-S8PSK has been proposed. Communication and radar performance of the proposed waveform have been assessed and compared with conventional LFM–CPM. Simulation results have shown that LFM-S8PSK presents better spectrum efficiency, slightly trading BER performance. Moreover, the results have also confirmed that the proposed waveform provides comparable radar resolution with LFM and LFM–CPM. This waveform is suitable for a wide range of civil and military applications, but it needs to be further investigated. The shortages of poor BER performance and high side lobes in delay resolution need to be addressed in our future work. 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 Yue Liu: Methodology, Software, Investigation, Writing - original draft. Ning Cao: Conceptualization, Supervision. Minghe Mao: Validation, Writing - review & editing. Gang Li: Writing - review & editing. Acknowledgments This work was supported by the National Natural Science Foundation of China for Young Scholars under grant No. 61701167 and the Fundamental Research Funds for the Central Universities, China, No. 2019B00814 and National Natural Science Foundation of China under grant No. 41830110. References [1] A. Hassanien, M.G. Amin, Y.D. Zhang, F. Ahmad, Signaling strategies for dual-function radar communications: an overview, IEEE Aerosp. Electron. Syst. Mag. 31 (10) (2016) 36–45, http://dx.doi.org/10.1109/MAES.2016. 150225. [2] Q. He, Z. Wang, J. Hu, R.S. Blum, Performance gains from cooperative mimo radar and mimo communication systems, IEEE Signal Process. Lett. 26 (1) (2019) 194–198, http://dx.doi.org/10.1109/LSP.2018.2880836. [3] M. Arik, O.B. Akan, Realizing joint radar-communications in coherent mimo radars, Phys. Commun. 32 (2019) 145–159, http://dx.doi.org/10.1016/j. phycom.2018.11.011. [4] S. Wei, Y. Zou, X. Zhang, T. Zhang, X. Li, An integrated longitudinal and lateral vehicle following control system with radar and vehicle-tovehicle communication, IEEE Trans. Veh. Technol. 68 (2) (2019) 1116–1127, http://dx.doi.org/10.1109/TVT.2018.2890418. [5] B. Xiao, Y. Liu, K. Huo, J. Zhao, Z. Zhang, Ofdm integration waveform design for radar and communication application, in: International Conference on Radar Systems (Radar 2017), 2017, pp. 1–5, http://dx.doi.org/10.1049/cp. 2017.0524. [6] J.A. Zhang, X. Huang, Y.J. Guo, J. Yuan, R.W. Heath, Multibeam for joint communication and radar sensing using steerable analog antenna arrays, IEEE Trans. Veh. Technol. 68 (1) (2019) 671–685, http://dx.doi.org/10.1109/ TVT.2018.2883796. [7] L. Zheng, M. Lops, X. Wang, Adaptive interference removal for uncoordinated radar/communication coexistence, IEEE J. Sel. Top. Sign. Proces. 12 (1) (2018) 45–60, http://dx.doi.org/10.1109/JSTSP.2017.2785783. [8] Q. Zhang, Y. Zhou, L. Zhang, Y. Gu, J. Zhang, Waveform design for a dualfunction radar-communication system based on ce-ofdm-pm signal, IET Radar Sonar Navig. 13 (4) (2019) 566–572, http://dx.doi.org/10.1049/ietrsn.2018.5260.

9

[9] F. Liu, L. Zhou, C. Masouros, A. Li, W. Luo, A. Petropulu, Toward dualfunctional radar-communication systems: Optimal waveform design, IEEE Trans. Signal Process. 66 (16) (2018) 4264–4279, http://dx.doi.org/10.1109/ TSP.2018.2847648. [10] X. Chen, Z. Liu, Y. Liu, Z. Wang, Energy leakage analysis of the radar and communication integrated waveform, IET Signal Process. 12 (3) (2018) 375–382, http://dx.doi.org/10.1049/iet-spr.2017.0248. [11] M. Li, W. Wang, Z. Zheng, Communication-embedded ofdm chirp waveform for delay-doppler radar, IET Radar Sonar Navig. 12 (3) (2018) 353–360, http://dx.doi.org/10.1049/iet-rsn.2017.0369. [12] S.Y. Nusenu, H. Chen, W. Wang, Ofdm chirp radar for adaptive target detection in low grazing angle, IET Signal Process. 12 (5) (2018) 613–619, http://dx.doi.org/10.1049/iet-spr.2017.0329. [13] C. Knill, F. Roos, B. Schweizer, D. Schindler, C. Waldschmidt, Random multiplexing for an mimo-ofdm radar with compressed sensing-based reconstruction, IEEE Microw. Wirel. Compon. Lett. 29 (4) (2019) 300–302, http://dx.doi.org/10.1109/LMWC.2019.2901405. [14] N. Levanon, E. Mozeson, Radar signals, Electromagn. News Rep. (2) (2004) 18. [15] S. Baher Safa Hanbali, R. Kastantin, Automatic modulation classification of lfm and polyphase-coded radar signals, Radioengineering 26 (4) (2017) 1118–1125, http://dx.doi.org/10.13164/re.2017.1118. [16] T. Grabowski, J. Dziupiński, E. Szpakowska-Peas, Selected problems of processing a radar signal with a lfm-fsk modulation, Aviation 19 (1) (2015) 25–30, http://dx.doi.org/10.3846/16487788.2015.1015289. [17] M. Nowak, M. Wicks, Z. Zhang, Z. Wu, Co-designed radar-communication using linear frequency modulation waveform, IEEE Aerosp. Electron. Syst. Mag. 31 (10) (2016) 28–35, http://dx.doi.org/10.1109/MAES.2016.150236. [18] Z. Zhao, D. Jiang, A novel integrated radar and communication waveform based on lfm signal, in: 2015 IEEE 5th International Conference on Electronics Information and Emergency Communication, 2015, pp. 219–223, http://dx.doi.org/10.1109/ICEIEC.2015.7284525. [19] Y. Zhang, Q. Li, L. Huang, C. Pan, J. Song, A modified waveform design for radar-communication integration based on lfm-cpm, in: 2017 IEEE 85th Vehicular Technology Conference (VTC Spring), 2017, pp. 1–5, http: //dx.doi.org/10.1109/VTCSpring.2017.8108563. [20] Q. Li, K. Dai, Y. Zhang, H. Zhang, Integrated waveform for a joint radar-communication system with high-speed transmission, IEEE Wirel. Commun. Lett. (2019) 1, http://dx.doi.org/10.1109/LWC.2019.2911948. [21] J. B. Anderson, T. Aulin, C.-E. Sundberg, Digital phase modulation, 1986, http://dx.doi.org/10.1007/978-1-4899-2031-7. [22] R. Othman, Y. Louët, A. Skrzypczak, Joint channel estimation and detection of soqpsk using the pam decomposition, in: 2018 25th International Conference on Telecommunications (ICT), 2018, pp. 154–158, http://dx.doi. org/10.1109/ICT.2018.8464828. [23] H. Yao, L. Yang, Q. Yiming, A new schemes of joint clock and phase estimation for soqpsk-tg, in: 2018 International Conference on Smart Grid and Electrical Automation (ICSGEA), 2018, pp. 76–79, http://dx.doi.org/10. 1109/ICSGEA.2018.00026. [24] B.D.V. Veen, K.M. Buckley, Beamforming: A versatile approach to spatial filtering, IEEE ASSP Mag. 5 (2) (2002) 4–24, http://dx.doi.org/10.1109/53. 665. [25] H.J. Zepernick, A. Finger, Pseudo random signal processing, 2005, http: //dx.doi.org/10.1002/9780470866597. [26] T. Schonhoff, Symbol error probabilities for m-ary cpfsk: Coherent and noncoherent detection, IEEE Trans. Commun. 24 (6) (1976) 644–652, http://dx.doi.org/10.1109/TCOM.1976.1093344. [27] K. Suwa, M. Iwamoto, T. Kirimoto, A bandwidth extrapolation technique for improved range resolution of polarimetric radar data, in: Proceedings of the 41st SICE Annual Conference, in: SICE 2002, vol. 5, 2002, pp. 2944–2948, http://dx.doi.org/10.1109/SICE.2002.1195572. [28] MathWorks, Fading channels, https://ww2.mathworks.cn/help/comm/ug/ fading-channels.html. [29] L. Polak, T. Kratochvil, Simulation and measurement of the transmission distortions of the digital television dvb-t/h part 3: Transmission in fading channels, Radioengineering 19 (2010). [30] E.T. Ahmed, M.M. Ali, M.Z.I. Sarkar, Ber performance analysis of rayleigh fading channel in an outdoor environment with mlse, in: 2012 7th International Conference on Electrical and Computer Engineering, 2012, pp. 157–160, http://dx.doi.org/10.1109/ICECE.2012.6471509. [31] A.R. Shankar, P. Rani, S. Kumar, An analytical approach to qualitative aspects of wimax physical layer, in: 2010 Second Vaagdevi International Conference on Information Technology for Real World Problems, 2010, pp. 36–41, http://dx.doi.org/10.1109/VCON.2010.14.

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Y. Liu, N. Cao, M. Mao et al. / Physical Communication 38 (2020) 100985 Yue Liu received her B.S. from School of Computer and Information, Hohai University, Nanjing, China, in 2017. She is currently pursing the Ph.D. degree in Computer and Information, Hohai University, Nanjing, China. Her research interests include wireless communications, as well as the design of radar and communication integrated waveform.

Ning Cao received the B.S. and M.S. degrees in electrical engineering from Southeast University, Nanjing, China, in 1984 and 1990, respectively. He is now a professor with the College of Computer and Information, Hohai University, Nanjing, China. His current research interests include statistical signal processing, sensor array processing, and wireless communications.

Minghe Mao received his B.S. and Ph.D. degrees from School of Computer and Information, Hohai University, Nanjing, China, in 2009 and 2016, respectively. He is now a postdoctoral fellow at the Department of Electronic Information Engineering in School of Computer and Information, Hohai University, Nanjing, China. His research interests include Cognitive Radios, Multi-Hop Relaying, Heterogeneous Networks for wireless communications, as well as Biomimetic Robotics Control and Communication. He has won a National Natural Science Foundation of China in 2017. Gang Li received his B.S. degrees from School of Electrical and Information Engineering, Hohai University, Nanjing, China, in 2004. He received his M.S. degrees from School of Software Engineering, Nanjing University, Nanjing, China, in 2011. He is now a associate professor, Ministry of Water Resources, Beijing, China. His research interests include water resources information construction, satellite Communication and wireless communications.