Design of an Underwater Acoustic Waveform and Integrated System for Communication and Detection

Abstract

Combining underwater communication and detection can reduce system size and power consumption as well as improve secrecy. This paper presents a waveform that integrates continuous phase modulation (CPM) for data communication with linear frequency modulation (LFM) for detection. It is shown that the velocity ambiguity and range performance with this waveform are similar to those with only LFM. An integrated underwater acoustic system is also proposed to achieve simultaneous communication and detection. A symbol suffix (SS) is introduced into the signal frame at the transmitter and a two-step algorithm is employed at the receiver for frequency and phase offset estimation. Results are presented, showing that this decreases the sensitivity to CPM and reduces the range ambiguity side lobes. Further, the proposed system can effectively recover the data from the received signal. The bit error rate (BER) is shown to be better than that of traditional systems without a symbol suffix. With changes in the signal-to-noise ratio (SNR), the bit error rate (BER) in underwater acoustic environments is comparable to that in an additive white Gaussian noise (AWGN) channel, indicating a significant improvement in communication performance within the underwater acoustic channel.

1. Introduction

Autonomous unmanned vehicles (AUVs) have been widely used in the fields of geological surveying, geophysical exploration, emergency rescue, and military operations [1,2,3,4]. To carry out diverse tasks, AUVs typically need to be equipped with various devices, including underwater acoustic detection and communication systems, posing challenges in terms of platform miniaturization, power consumption, and signal processing complexity. Communication is used for data exchange, while radar and sonar are typically used for target detection and identification. Typically, communication and detection are performed separately, with separate resources. Despite their differing objectives, they have commonalities in terms of operation, system structure, and signal processing, which make their integration feasible [5,6,7]. Communication and detection integration is now an important research direction [8,9]. Typically, communication and detection systems are designed separately, which can lead to issues such as redundant hardware, low power efficiency, and internal system interference [10,11]. Integration enables resource sharing, such as with the use of transducers, software, and hardware, which can reduce system size and power consumption and improve secrecy.

Integrated communication and detection technology is mainly divided into four operational systems: time division, frequency division, beam division, and full sharing systems. The time division system executes communication and detection functions separately in different time slots. Its design is relatively simple and easy to implement. Early examples included the Ku-band radar-communication integration system [12], which adopted time division switching to achieve dual functionalities. However, due to the inability to perform communication and detection simultaneously, there is an issue of low resource utilization. The frequency division system processes communication and detection signals separately by dividing different frequency bands, thereby reducing mutual interference between the two. The automotive radar system designed by Winkler is a typical example, which allocates frequency bands for communication by utilizing the side lobes of the radar spectrum [13]. However, such systems still face the problem of inadequate spectrum resource utilization. The beam division system integrates communication and detection by partitioning the beam of the array antenna. An integrated communication and detection system proposed by Hassanien utilizes the main beam for detection and the side lobes of the beam for communication [14]. However, the division of total energy leads to a limited detection range, and there is an issue of interference from the side lobes to the main lobe. The full sharing system simultaneously realizes communication and detection by using a shared waveform, avoiding the division of time, frequency and power resources. Ellinger employs OFDM to modulate multi-carrier phase coded (MCPC) sequences to realize radar detection and communication simultaneously, and a novel radar detection scheme is proposed to overcome the large autocorrelation side lobes of the received signal introduced by MCPC. Additionally, it introduces a new method that leverages the orthogonality of MCPC sequences to overcome the effects of multipath fading and inter-carrier interference, enabling the system to balance both radar detection and communication performance [15]. Despite the need for careful design of shared waveforms in the full sharing system and the relatively complex signal processing at the receiving end, this method boasts the highest resource utilization efficiency and has gradually become a focal point of research in integrated communication and detection technology.

Waveform design is crucial for the full-sharing system [16,17,18]. Research on this began with radar. The design of integrated waveforms can be divided into three categories. The first is the superposition of two orthogonal waveforms to perform detection and communication. A multi-function RF architecture based on linear frequency modulation (LFM) was proposed by Roberton [19]. In this system, up-LFM is used for communication while down-LFM is used for radar detection. These waveforms are superimposed and occupy the same frequency band, but separate receivers are used for communication and detection. The second category is based on communication waveforms. With this approach, a communication waveform is modified or directly used for detection. An integrated radar–communication waveform based on minimum shift keying (MSK) direct sequence spread spectrum was proposed by Liu [20]. The spread spectrum is used to improve the autocorrelation of the digital baseband signal. It also has excellent ambiguity to meet detection requirements. The third category is based on radar waveforms. In this case, the data are modulated onto the radar waveform. A multi-input multi-output (MIMO) design was proposed by Hassanien that embeds data onto an MIMO radar waveform using frequency hopping [21]. Phase shift keying (PSK) is used to modulate the data in each frequency hopping interval. The data rate is a function of the number of transmit antennas and the pulse repetition frequency. The superposed shared waveform features simple modulation, but the straightforward superposition of communication and detection signals leads to significant interference between the two types of signals, making signal separation and information processing difficult. The shared waveform based on the communication waveform ensures the system’s data transmission rate, yet its non-constant modulus and high peak-to-average power ratio (PAPR) characteristics constrain the system’s detection performance [22]. Additionally, the non-constant modulus characteristic poses challenges for the design of power amplifiers, potentially causing waveform distortion and low power efficiency. On the other hand, the shared waveform based on the detection waveform guarantees the system’s detection performance but limits the data rate.

Compared to radar, sonar has a much smaller frequency band, smaller aperture arrays, and slower propagation rate, due to the underwater acoustic environment. Therefore, time division, frequency division, and beam division multiplexing for underwater acoustics are not practical. Time division results in large detection blind zones, frequency division imposes high bandwidth requirements, and beam division reduces the energy available for communication and detection. Consequently, the full sharing system is more appropriate for underwater acoustics. The application of underwater autonomous underwater vehicles (AUVs) primarily focuses on detection, where the capability to detect targets is critical. Therefore, integrated systems based on detection waveforms represent a significant developmental direction. The mainstream shared waveform is based on the linear frequency modulation (LFM) signal. Zhang proposes a minimum shift keying-linear frequency modulation (MSK-LFM) approach, which exhibits robust multi-target detection capabilities [23]. Chen introduces an integrated signal based on fractional Fourier transform (FRFT) and OFDM-LFM, demonstrating enhanced range resolution and reduced bit error rates under frequency-selective fading conditions [24]. Ma designed an integrated waveform of high order radar communication combining an 64QAM signal and LFM pulse [25]. This shows that the waveform has a higher frequency band utilization rate than the integrated signal of BPSK-LFM and MSK-LFM. Bao et al. proposed a sector-modulated linear frequency modulation (SM-LFM) signal for an integrated system of underwater detection and communication (ISUDC). They divided the Fresnel domain into sectors of equal length and improved the maximum unambiguous velocity by calculating the relative radial velocity in the Fresnel domain instead of the frequency domain [26].

Due to CPM’s constant envelope and superior spectral efficiency, as well as LFM’s large time–bandwidth product, LFM-CPM has also attracted the attention of many researchers. Zhang proposed a modified three-section integrated waveform based on linear frequency modulation and continuous phase modulation (LFM-CPM) [27]. The modified waveform shows significant improvement in bit error rate (BER) performance under strong interference conditions. In the dual-functional radar communication system proposed by Cao, the CPM-LFM signal is adopted to enhance both the radar’s range resolution and the bit error rate [28].

However, due to the characteristics of underwater acoustic signals, such as slow transmission speed, narrow bandwidths, and significant signal attenuation, the integration of underwater acoustic communication and detection presents even greater challenges. Whether the aforementioned waveforms and systems for radar–communication integration are applicable to underwater acoustics still requires extensive exploration.

In this paper, the CPM-LFM waveform is studied for underwater acoustic sonar–communication integration. The minimum Euclidean distance, bit error rate (BER), and ambiguity function [29] of the shared waveform are derived and analyzed to test the waveform’s communication and detection performance. Underwater acoustic channels exhibit characteristics such as multi-path effects and significant propagation delays. Due to variations in seabed topography and sound velocity, precise estimation of propagation delays is challenging. These factors will impact the timing synchronization and frequency offset in underwater acoustic communication, resulting in a decline in its performance. Additionally, the underwater movement of AUVs can cause significant Doppler effects, further affecting the reliability of underwater acoustic communication. To address these challenges, an integrated underwater communication and detection system has been proposed. An information frame structure with symbol suffixes (SSs) is introduced to reduces the side lobe amplitude of the range ambiguity function and improve communication performance with two-step frequency and phase estimation and correction.

The main contributions of this paper are summarized as follows:

• 1.. A shared waveform that integrates continuous phase modulation (CPM) with linear frequency modulation (LFM) is proposed for underwater acoustic communication and detection application, and its performance in communication and detection under an additive white Gaussian noise (AWGN) channel is derived.

• 2.. A system model for integrated underwater communication and detection is proposed. The system’s transmission module and the communication information processing flow in the reception module are well designed. Specifically, this paper presents an information frame structure that features symbol suffixes (SSs). The introduction of SSs effectively reduces the side lobe amplitude of the range ambiguity function, improving ranging performance, and employs repeated symbols for enhanced two-step frequency and phase estimation and correction, thereby boosting communication performance.

• 3.. Simulation analysis is conducted to verify the feasibility of the proposed communication and detection waveform, as well as the system.

The subsequent arrangement of the article is as follows. In Section 2, the mathematical model of the shared waveform and its characteristics in the time–frequency domain are presented. Under an AWGN channel, the bit error rate performance of the shared waveform in communication applications and the ambiguity function performance in detection applications are derived. Section 3 presents the models for the transmitter and receiver of the integrated acoustic communication and detection system. The focus is on the information processing of the communication system at the receiver. A symbol suffix (SS) frame structure is proposed, which utilizes preamble codes and repeated data blocks for precise frequency and phase offset estimation. Finally, Section 4 presents the simulation results, and conclusions are presented in Section 5.

2. Waveform Design

2.1. Signal Model

A constant envelope waveform is considered with CPM data combined with LFM. This is given by

(1)$S_{\mathit{CPM}-\mathit{LFM}}\left(t\right)=S_{\mathit{CPM}}\left(t\right)S_{\mathit{LFM}}\left(t\right)$

which can be expressed as

(2)$S_{\mathit{CPM}-\mathit{LFM}}\left(t\right)=A\mathrm{rect}(t/T_p\left)\mathit{exp}[j\right(\pi \mu t^2+\varphi (t,I)+{\varphi }_0\left)\right]$

with

(3)$\varphi (t,I)={\sum }_{n=0}^{N-1}\mathrm{rect}\left(\right(t-n{T}_s)/T_s)\left(\pi h{\sum }_{i=0}^{n-L}{I}_i+2\pi h{\sum }_{i=n-L+1}^n{I}_{i}q(t-i{T}_s)\right)$

Here, S_CPM(t) represents the expression of a CPM modulated signal, S_LFM(t) represents a linear frequency modulation (LFM) signal, and S_CPM-LFM (t) denotes a composite waveform signal that carries the constant envelope phase information of CPM using the linear frequency modulation signal. S_CPM-LFM (t) is obtained by multiplying S_CPM(t) and S_LFM(t). We employ the equivalent lowpass representation, A is the amplitude of the LFM signal, T_p is the pulse width, μ is the modulation rate, μ = B/T_p, B is the bandwidth of the LFM signal. ϕ(t,I) is the information-carrying phase, {I_i} is the sequence of M-ary information symbols selected, and I_i$\in \{$±1, ±3, ⋯, ±(M − 1)}. N is the number of data symbols within an LFM pulse, and T_s is the symbol duration, $T_s=T_p/N$, h is the modulation indices. ϕ₀ is the initial phase of CPM. The waveform q(t) is represented in general as the integral of pulse g(t). Three popular pulse shapes are given in Table 1, and LREC denotes a rectangular pulse with duration LT, where L is a positive integer, T is sampling duration. LRC denotes a raised cosine pulse with duration LT. The third pulse is a GMSK pulse with bandwidth parameter B’, which represents the −3 dB bandwidth of the Gaussian pulse.

Equation (2) shows that the CPM-LFM waveform differs from CPM only by the term πμt² in the phase. Thus, it has continuous phase and constant envelope. Figure 1 illustrates the signal generation.

Simulation was conducted to obtain the time domain and frequency domain characteristics of the proposed waveform. The parameters considered are A = 1, B = 4 KHz, T_p = 0.5 s, h = 0.5, ϕ₀ = 0.5, L = 2, and LREC pulse. Figure 2 presents the time domain characteristics of the LFM and CPM-LFM waveforms. This shows that the superposition of CPM does not alter the constant envelope characteristic of the LFM waveform. Thus, it will be robust to amplifier nonlinearity, so the distortion will be minimal. This makes the waveform compatible with existing sonar systems.

Figure 3 illustrates the frequency domain characteristics of LFM, the proposed waveform, and GMSK-LFM. Note that GMSK is a special case of CPM. This shows that the CPM is within the LFM frequency range. Using LFM as the carrier allows data to be transmitted via phase modulation. At the receiver, a matched filter can be used to remove the LFM and recover the data signal. Compared to LFM, the proposed waveform does not require additional bandwidth and has similar spectral characteristics, so the rapid out-of-band roll-off is retained.

2.2. Performance Analysis

In an AWGN channel, the received signal can be expressed as

(4)$$\begin{gathered} S_r\left(t\right)=S_{CPM}\left(t\right)S_{LFM}\left(t\right)+n\left(t\right) \\ =Arect(t/T_p)exp\left[j\right(p{mt}^2+j(t,I)+j_o\left)\right]+n\left(t\right) \end{gathered}$$

where n(t) of zero means white Gaussian noise. As the phase is used for data transmission, it is necessary to first process the received signal to extract the phase information. For simplicity, in this section, the frequency and phase offsets due to the relative motion between the transmitter and receiver are ignored. Multiplying by the conjugate of the LFM signal gives

(5)$\begin{array}{c}{S}_{ra}\left(t\right)=S_r\left(t\right)S_{LFM}^{*}\left(t\right)\hfill \\ =A\mathrm{rect}(t/T_p\left)\mathit{exp}[j\right(\varphi (t;I)+{\phi }_0\left)\right]+S_{LFM}^{*}\left(t\right)n\left(t\right)\hfill \\ =S_{CPM}\left(t\right)+S_{LFM}^{*}\left(t\right)n\left(t\right)\hfill \end{array}$

According to reference [30], the Euclidean distance between S_ra(t) and S_CPM(t) for an observation duration of NT_s can be expressed as

(6)$d_{i,j}={\left[{\int }_0^{N{T}_s}\left[s_i\right(t)-s_j(t){]}^{2}dt\right]}^{1/2}$

where s_i(t) = S_i−ra(t) and s_j(t) = S_j-CPM(t). For simplicity, consider the squared Euclidean distance

(7)$\begin{array}{cc}{d}_{i,j}^2& ={{\displaystyle {\int }_0^{N{T}_s}\left[s_i(t)-s_j(t)\right]}}^{2}dt\hfill \\ & ={{\displaystyle {\int }_0^{N{T}_s}\left[S_{i-CPM}(t)+S_{LFM}^{*}(t)n(t)-S_{j-CPM}(t)\right]}}^{2}dt\hfill \\ & ={{\displaystyle {\int }_0^{N{T}_s}\left[\left(S_{i-CPM}(t)-S_{j-CPM}(t)\right)+S_{LFM}^{*}(t)n(t)\right]}}^{2}dt\hfill \\ & ={{\displaystyle {\int }_0^{N{T}_s}\left[S_{i-CPM}(t)-S_{j-CPM}(t)\right]}}^{2}dt+{{\displaystyle {\int }_0^{N{T}_s}\left[S_{LFM}^{*}(t)n(t)\right]}}^{2}dt\hfill \\ & +2{\displaystyle {\int }_0^{N{T}_s}\left[\left(S_{i-CPM}(t)-S_{j-CPM}(t)\right)S_{LFM}^{*}(t)n(t)\right]}dt\hfill \end{array}$

The second term is the integral of the product of the energy of the LFM signal and the energy of the noise, and it is not a function of the modulation parameters. The third term is the integral of the product of a deterministic signal and the noise and so is considered to be zero. Thus, the second and third terms have a negligible effect on the performance due to changes in the parameters, so the focus here is on the first term. The shared waveform is affected by the modulation parameters in the same way as continuous phase modulation. Next, we will analyze the first term,

(8)$d^2={\int }_0^{NT}\left[s_{i-CPM}\right(t)-s_{j-CPM}(t){]}^{2}dt$

where S_i-CPM(t) and S_j-CPM(t) are two different signals with distinct phase trajectories, which are ϕ(t,I_i) and ϕ(t,I_j), respectively. The first symbols of the sequences I_i and I_j are different. Let the symbol for energy be ε, and the bit energy be ε_b = ε/log₂M, then,

(9)$\begin{array}{cc}{d}^2\hfill & ={\int }_0^{N{T}_s}{\left[S_{i-CPM}\right(t)-S_{j-CPM}(t\left)\right]}^{2}dt\hfill \\ & =2E_b{\displaystyle \frac{{\log }_{2}M}{T_s}}{\int }_0^{M{T}_i}\{1-\mathrm{c}\mathrm{o}\mathrm{s}[\varphi (t,I_i)-\varphi (t,I_j)\left]\right\}dt\hfill \end{array}$

where δ_ij² is defined as the bit energy normalized Euclidean distance, its expression is:

(10)${\delta }_{ij}^2={\displaystyle \frac{{\log }_{2}M}{T}}{\int }_0^{N{T}_i}\{1-\mathrm{c}\mathrm{o}\mathrm{s}[\varphi (t,I_i)-\varphi (t,I_j)\left]\right\}dt$

When utilizing the maximum likelihood estimation (MLE), the bit error rate (BER) of CPM signals is

(11)$P_M=K_{{\delta }_{min}}Q({\displaystyle \frac{{\sqrt{\mathcal{E}}}_b}{N_0}}{d^2}_{min})$

where $K_{{\delta }_{min}}$ represents the number of paths with the minimum Euclidean distance, and d²_min is the minimum Euclidean distance for bits.

(12)$\begin{array}{c}{d}_{min}^2=\underset{N\to \mathrm{\infty }}{lim}{\mathrm{m}\mathrm{i}\mathrm{n}}_{i,j}{\delta }_{ij}^2\hfill \\ =\underset{N\to \mathrm{\infty }}{lim}{\mathrm{m}\mathrm{i}\mathrm{n}}_{i,j}\{{\displaystyle \frac{{\log }_{2}M}{T_s}}{\int }_0^{N{T}_i}[1-\mathrm{c}\mathrm{o}\mathrm{s}\varphi (t,I_i-I_j\left)\right]dt\}\hfill \end{array}$

Taking the 2-ary modulated fully responsive signal as an example, I_i = +1, −1, I₂, I₃, I_j = −1, +1, I₂, I₃. The first two symbol sequences are different, but the symbol sequences after the second symbol are the same, and the phase trajectories of the sequences coincide afterwards. Considering the difference sequence is I_i − I_j = {2, −2, 0, 0……}, we can derive the upper bound of the binary fully responsive signal as

(13)$d_B^2(h)=2\left(1-{\displaystyle \frac{\mathit{sin}2\pi h}{2\pi h}}\right),\hspace{1em}M=2$

By extending this concept, we can obtain the upper bound for M-ary fully responsive signals as

(14)$d_B^2(h)={\mathrm{m}\mathrm{i}\mathrm{n}}_{1\ll k\ll M-i}\{(2{\mathrm{l}\mathrm{o}\mathrm{g}}_{2}M)(1-{\displaystyle \frac{\sin 2\mathrm{k}\mathsf{\pi }\mathrm{h}}{2\mathrm{k}\mathsf{\pi }\mathrm{h}}})\}$

Then, simulation analysis on the observed Euclidean distance and upper bound of the signal under the influence of M, modulation index h, and the correlation length L is conducted.

Figure 4 presents upper bounds on the Euclidean distance obtained via simulation for modulation order M = 2, 4, 8 and response functions LREC and LRC versus the modulation index h. These results show that the bounds increase with h until a given value and then they fluctuate. Further, the bounds generally increase with the radix. For M = 2, the upper bounds with LREC and LRC are similar when h is small, but for large values, the bounds with LREC are greater.

2.3. Ambiguity Function Analysis

Ambiguity function analysis is widely used in the design of detection waveforms. It is employed to analyze the distance resolution and velocity resolution of signal detection under ideal conditions. In this section, the ambiguity function of the proposed CPM-LFM waveform is obtained and used to analyze the detection performance. The ambiguity function of this waveform is given as [29],

(15)$$\begin{gathered} \chi (\tau ,f_d)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{S}_{CPM-LFM}(t)S_{CPM-LFM}^{*}(t-\tau )exp(j2\pi f_{d}t)dt \\ ={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}exp(j2\pi f_{d}t){\sum }_{k=1}^{N}rect({\displaystyle \frac{t-(k-1)T_s}{T_s}})exp(j\pi u^2+j\varphi (t,I_i))\times {\sum }_{i=1}^{N}rect({\displaystyle \frac{t-(l-1)T_s}{T_s}})exp(j\pi u(t-\tau {)}^2+j\varphi (t-\tau ,I_i))dt \end{gathered}$$

where f_d is the Doppler frequency and τ is the delay. This is illustrated in Figure 5. This can be further expressed as

(16)$\chi \left(\tau ,f_d\right)=\begin{array}{cc}{X}_{kl}{T}_{\tau }\mathit{sinc}\left\{\left[\mu \tau +f_d+{\displaystyle \frac{h\overline{I}}{2L{T}_s}}\right]T_{\tau }\right\}& \begin{array}{c}\begin{array}{c}{T}_{\tau }=(k-l+1)T_s-\tau \hfill \\ (k-l)T_s\le \tau \le (k-l+1)T\hfill \end{array}\\ or\\ \begin{array}{c}{T}_{\tau }=(l-k+1)T_s-\tau \hfill \\ (k-l-1)T_s\le \tau \le (k-l)T\hfill \end{array}\end{array}\end{array}$

(17)$\overline{I}={\sum }_{m=k-L+1}^k{I}_m-{\sum }_{n=l-L+1}^l{I}_n$

(18)$X_{kl}=\mathit{exp}\left\{j\pi \left[\begin{array}{c}-\mu {\tau }^2+h{\sum }_{a=0}^{k-L}{I}_a-h{\sum }_{a=0}^{l-L}{I}_a+{\displaystyle \frac{h}{L}}\left({\sum }_{m=k-L+1}^k{I}_m(k-m)-{\sum }_{n=l-L+1}^l{I}_n(l-n)\right)\hfill \\ -\left(f_d+\mu \tau \right)T_p+\left(\mu \tau +f_d+{\displaystyle \frac{h}{2L{T}_s}}\overline{I}\right)\left((k+l+1)T_s+\tau -T_p\right)\hfill \end{array}\right]\right\}$

Within a single repetition period, setting the delay in (9) to zero and taking the absolute value yields the velocity ambiguity

(19)$\left|\chi \left(0,f_d\right)\right|=N{T}_s\left|\mathit{sinc}\left(f_{d}N{T}_s\right)\right|$

(20)$\left|{\chi }_{\mathit{LFM}}\left(0,f_d\right)\right|=T_p\left|\mathit{sinc}\left(f_d{T}_p\right)\right|$

where T_s = T_p/N is the symbol duration and the frame length is equal to the LFM pulse width T_p. Therefore, the velocity ambiguity of the proposed waveform is the same as for LFM and the velocity resolution is 1/T_p.

Now the Doppler frequency f_d is set to 0 to obtain the range ambiguity

(21)$$\begin{gathered} |\chi (z,0)|=|(T_z-\tau )\mathrm{s}\mathrm{i}\mathrm{n}c(\mu \tau (T_z-\tau ))|+|\tau \mathrm{s}\mathrm{i}\mathrm{n}c\{[\mu \tau +{\displaystyle \frac{h}{2L{T}_z}}(b_k-b_{l-L+1})]\tau \}| \\ k=l,T_s\le \tau \le (k-l+1)T_s \end{gathered}$$

When the number of data symbols is small, |τ|≪T_s, so the second term in (14) can be ignored. Then the range ambiguity can be expressed as

(22)$\left|\chi \left(\tau ,0\right)\right|=T_p\left|\sin \mathrm{c}\left(B\tau \right)\right|$

so the time resolution is 1/B. As the number of data symbols increases, T_s decreases. Thus, when there are a large number of data symbols, the condition 0 ≤ τ ≪ T_s may not be satisfied, leading to more distance side lobes.

3. Hydroacoustic Integrated System Architecture

The underwater integrated system is illustrated in Figure 6. During operation, the transmitter sends communication signals to the other users. This signal can also be used to detect targets via the signal echoes. In the waveform design, it is better to accommodate existing sonar systems, so a detection waveform is selected. This facilitates the use of CPM.

A block diagram of the integrated hydroacoustic system is shown in Figure 7. The transceiver comprises two processing modules, a communication module and a detection module. The communication module’s first channel encodes the transmit data, then applies CPM modulation and combines it with an LFM waveform, and sends it out with transducer array after amplification. At the receiving end, the signal is received by the transducer array, filtered and amplified, and then split for separate processing. Specifically, the communication receiving end demodulates the data using Viterbi decoding, and then channel decodes it to the destination.

3.1. Communication Transceiver and Symbol Suffix

The generation of the shared waveform is illustrated in Figure 8. The communication symbols are channel encoded, then combined into signal frames, and subsequently CPM modulated. The CPM modulated signal is then multiplied with an LFM signal to obtain a shared waveform signal. After DA conversion and power amplification, the signal is sent out.

At the receiver, communication and detection processing are conducted. For detection, matched filtering can be employed. The focus here is on recovering the data. The received signal is first filtered, amplified, converted from analog to digital, and down-converted to obtain the baseband signal. The baseband signal is then framed and multiplied by the conjugate of the LFM template signal to obtain the CPM signal. After matching filtering, frequency estimation and compensation are performed. Finally, Viterbi decoding and channel decoding are applied to obtain the received information sequence. The signal processing flowchart is shown in Figure 9. Here, we introduce a frame format with a symbol suffix for two-step frequency and phase estimation, enhancing the system’s communication performance. The frame format is shown in Figure 10. The shaded part in the figure is elaborated in Figure 11.

To address the Doppler effect and multipath effect, a frame structure employing symbol suffix (SS) has been designed for intra-frame compensation. The shared waveform signal of the designed symbol suffix frame structure can be simplified as SS-CPM-LFM. The frame structure is shown in Figure 10. The Head is a preamble sequence from a fixed codebook {1, −1, 1, −1 …}, where the corresponding signal of the preamble sequence is an LFM signal with a fixed phase offset. Leveraging the excellent autocorrelation properties of LFM allows for signal synchronization and initial frequency compensation. The preamble is used for frame detection via correlation to obtain the peak. To reduce the computational complexity, downsampling can be applied.

To demonstrate the improvement of the SS frame structure on the communication and detection performance of the integrated system, the traditional frame structure without a sign suffix is considered. In this case, a preamble is inserted before the data.

In the two frame structures, the preamble satisfies I_n = −I_n+1. Then the preamble consists of LFM with a fixed phase offset, which has favorable autocorrelation characteristics. This is used for synchronization and frequency and phase estimation and compensation.

3.2. Frequency and Phase Bias Estimation

The two-step frequency and phase estimation and compensation method is employed, based on SS. It utilizes the preamble and the initial Data1 segment for frequency estimation and compensation, and then uses the frequency-compensated preamble and the Data1 SS for phase compensation and intra-frame compensation. The flowchart of this process is shown in Figure 11.

Figure 11

The proposed two-step frequency and phase estimation and compensation method.

[Figure omitted. See PDF]

The frequency and phase bias estimation and compensation method based on the proposed frame structure are described as follows. After frame detection, a coarse frequency offset estimate using the preamble is obtained using the maximum likelihood parallel carrier recovery algorithm. By performing autocorrelation on two adjacent and identical synchronization pilot (SP) sequences within the preamble sequence, we can obtain the phase difference between these two adjacent SP sequences. Since carrier frequency offset is the accumulation of phase difference of all SP sequences over time, a coarse estimate of the carrier frequency offset can be derived through the following calculations:

(23)$f_{d1}={\displaystyle \frac{f_s}{2\pi N_{\mathit{pre}}}}tan{\left({\displaystyle \frac{\mathit{Im}\left[\sum S_{pre}\left(n\right)S_{pre}^{*}(n-N_{pre})\right]}{\mathit{Re}\left[\sum S_{pre}\left(n\right)S_{pre}^{*}(n-N_{pre})\right]}}\right)}^{-1}$

where f_s is the carrier frequency, N_pre is the period of the SP sequence, and S_pre(n) is the nth code in one SP period. Using the Data1 symbol segment in the communication frame to complete the second step of frequency estimation, the multiplication estimation algorithm is utilized to calculate the second step frequency estimation value f_d2. The baseband Data1 signal after the first step of frequency offset correction is

(24)$X\left(k{T}_s\right)=S_{Data1}\left(k{T}_s\right)+n\left(k{T}_s\right)$

where n(kT_s) is zero-mean Gaussian white noise and

(25)$S_{Data1}\left(k{T}_s\right)=\mathit{exp}\left[j\left(2\pi f_{d2}k{T}_s+\mathsf{\Delta }\theta +\overline{\theta }\right)\right]A\mathit{exp}\left[j\varphi \left(k{T}_s,I\right)\right]$

where f_d2 is the residual frequency offset after coarse frequency offset correction, Δθ is the frequency offset corresponding to the data symbol, and $\widehat{\theta }$ is the time-varying phase variation introduced by the channel. For the time-delay multiplication algorithm

(26)$Z\left(k{T}_s\right)=X\left(k{T}_s\right)X^{*}\left[(k-D)T_s\right]$

where D is the delay, which is typically set to 1. Substituting (26) into (25) gives

(27)$S_{Data1}\left(k{T}_s\right)={A_r}^2\mathit{exp}\left[j\left(2\pi f_{d2}k{T}_s\right)\right]\mathit{exp}\left[j\left(\varphi \left(k{T}_s,I\right)-\varphi \left((k-D)T_s,I\right)\right)\right]+N\left(k{T}_s\right)$

where N(kT_s) is the zero-mean noise term. Taking the expected value gives

(28)$E\left\{Z\left(k{T}_s\right)\right\}={A_r}^{2}A\left(k{T}_s\right)\mathit{exp}\left[j\left(2\pi f_{d2}k{T}_s\right)\right]$

where

(29)$A\left(t\right)=E\left\{\mathit{exp}\left[j\left(\varphi \left(k{T}_s,I\right)-\varphi \left((k-D)T_s,I\right)\right)\right]\right\}$

A(t) can be considered a constant independent of the frequency offset. The expected value over L₀ symbols with N samples per symbol is

(30)$E\left\{{\sum }_{k=0}^{N{L}_0-1}Z\left(k{T}_s\right)\right\}={A_r}^{2}N{L}_0\overline{A}\mathit{exp}\left(j2\pi f_{d2}D{T}_s\right)$

where $\overline{A}$ is the average of A(t). Then f_d2 can be obtained from the phase as

(31)$f_{d2}={\displaystyle \frac{1}{2\pi D{T}_s}}\mathit{arg}\left\{E\left\{{\sum }_{k=0}^{N{L}_0-1}Z\left(k{T}_s\right)\right\}\right\}$

In practice, this is estimated by taking the average

(32)${\widehat{f}}_{d2}={\displaystyle \frac{1}{2\pi D{T}_s}}\mathit{arg}\left\{{\sum }_{k=0}^{N{L}_0-1}Z\left(k{T}_s\right)\right\}$

The next step is to perform frequency correction. Then, the preamble is extracted, and the phase shift Δθ is obtained as

(33)$\mathsf{\Delta }\theta =\mathit{arg}\left\{{\sum }_{k=0}^{N_{pre}-1}{S}_{pre}\left(k{T}_s\right)\right\}-{\theta }_0$

The Data1 block before and after phase correction is then used to obtain the phase difference θ₂ − θ₁. The phase variation is given by

(34)$\widehat{\theta }={\displaystyle \frac{{\theta }_2-{\theta }_1}{N_{num}{T}_s}}n{T}_s$

After frame phase compensation, the estimation and compensation of the frequency and phase offsets are complete. The resulting communication signal is input to the Viterbi decoder to obtain the data.

4. Simulations

The ambiguity function and communication performance of the CPM-LFM waveform in an AWGN (additive white Gaussian noise) channel is simulated. Its differences in range and velocity ambiguity functions with those of the LFM waveform are analyzed. Additionally, we analyzed the impact of the modulation index h, the modulation order M, and the correlation length L of the CPM-LFM waveform on its communication performance. Furthermore, simulations on the ambiguity function and communication performance of the proposed shared waveform and the hydroacoustic integrated system under the BELLHOP underwater acoustic channel are conducted. The range and velocity ambiguity functions of the LFM, CPM-LFM, SS-CPM-LFM signals are compared, as well as the bit error rate (BER) performance of the CPM, CPM-LFM, SS-CPM- LFM signals. The simulation block diagram is shown in Figure 12 and Figure 13.

4.1. Simulations on Ambiguity Function and BER of CPM-LFM Signals in AWGN Channels

A comparison of the ambiguity functions of LFM and CPM-LFM signals in AWGN channels is presented. The detection performance of the shared waveform is analyzed based on the velocity ambiguity function given in formulas (19) and (20), as well as the range ambiguity function given in formulas (21) and (22). The following parameters are used: B = 1 kHz, T_p = 0.5 s, h = 0.5, L = 2, binary CPM, LREC, and N = 50.

The normalized ambiguity functions of the proposed and LFM waveforms are shown in Figure 14a,b, respectively. This shows that the proposed waveform has a spike ambiguity function, while the LFM signal has a much broader ambiguity function. Both waveforms demonstrate good detection capabilities, indicating the feasibility of using the proposed waveform for detection. The velocity resolution for the proposed and LFM waveform are shown in Figure 14c,d respectively. This shows that the resolution is similar, which is consistent with the theory. The corresponding distance resolution results are shown in Figure 14e,f. This shows that the waveforms have the same main lobe width, with a single peak, so the distance resolution is similar. However, the proposed waveform has larger and more irregular side lobes compared to LFM. This can be attributed to the CPM waveform as indicated by (15).

Figure 15 shows the distance resolution of the LFM waveform and proposed waveform for different numbers of data symbols. This shows that the side lobes increase with the number of symbols, which is consistent with (15). This is because increasing the number of symbols leads to the condition 0 ≤ τ ≪ T_s being violated. Consequently, the effect of the second term in (15) increases, resulting in more side lobes. However, the proposed waveform still maintains the single-peak characteristic of LFM, and the main lobe width is the same, indicating similar distance resolution capabilities.

In summary, the proposed waveform inherits the good detection performance of the LFM signal. They have the same velocity ambiguity function and velocity resolution, as well as similar distance ambiguity functions and distance resolution.

Next, based on the bit error rate for CPM-LFM signals given in (11) in an AWGN channel derived in Subsection B of Section 2, the communication performance of the shared waveform signal is analyzed under ideal conditions. The impact of the modulation index h, the number of modulation orders

M, and the correlation length L on the communication performance are considered.

Figure 16 gives the simulation results of the impact of the modulation index h on the system’s BER under the conditions of M = 2, L = 2, and LREC. Figure 17 simulates the impact of the number of modulation orders M on the system’s BER under the conditions of L = 2, h = 1/2, and LREC. Figure 18 shows the impact of the correlation length L on the system’s BER. In previous theoretical analyses, a larger correlation length L needs to be used in conjunction with a larger modulation index h to achieve better communication performance. Therefore, combinations of correlation lengths L = 1, 2, 3 and modulation indices h = 0.5, 0.8 were tested under the conditions of M = 2 and LREC.

The following conclusions can be drawn from the results shown in Figure 16, Figure 17 and Figure 18.

According to the upper bound of the minimum Euclidean distance shown in Figure 4, an increase in the modulation index h results in an increase in the upper bound on the Euclidean distance up to a given index, after which it fluctuates. In addition, the bit error rate decreases as h increases.

The upper bound on the Euclidean distance increases with the modulation order M. Thus, the BER decreases with increasing M. However, an increase in M increases the number of CPM phases, leading to a greater demodulation complexity. Thus, there is a tradeoff between communication performance and system complexity.

An increase in the correlation length L results in an improvement in the BER if h is also increased. This is because increasing h will increase d_B². Otherwise, if h is small, the BER may increase with an increase in L.

The above results indicate that, in a practical system design, the parameters should be chosen to achieve a balance between BER and complexity.

4.2. Simulations on the Ambiguity Function and BER of CPM-LFM Signals in BELLHOP Underwater Acoustic Channels

Underwater acoustic channels are more complex than terrestrial wireless channels, with characteristics such as large delays and significant Doppler and time variations. The speed of sound varies at different depths, and multipaths occur for sound waves underwater, due to factors such as reflection, refraction, and scattering. The underwater acoustic channel is modeled to evaluate the communication performance of the proposed system. This research utilizes the BELLHOP ray model. The specific simulation parameters are presented in Table 2.

Next, simulations on the ambiguity function and BER of the proposed shared waveform and the hydroacoustic integrated system under the BELLHOP underwater acoustic channel are conducted. The parameters of the designed waveform and integrated system are given in Table 3.

Figure 19 presents the ambiguity with the proposed SS-CPM-LFM. This shows that the signal ambiguity has a very pronounced peak, indicating good velocity and range resolution.

Figure 20 shows that signals with and without SS have the same speed ambiguity, as it is inherited from the good speed resolution of LFM signals. However, Figure 21 indicates that the distance ambiguity with SS has significantly lower side lobes. This reduces the sensitivity to the data and improves ranging performance. To further evaluate the ranging performance, Hamming window compression was applied to the proposed signal with zero Doppler frequency. The results in Figure 22 show that the SS-CPM-LFM with windowing has a single peak with a main lobe to side lobe ratio of 17.72 dB. This is sufficient for effective ranging.

Next, the BER of three signals, CPM, CPM-LFM, and SS-CPM-LFM, under underwater acoustic channels are simulated. The SS frame structure allows the receiver to employ a two-step frequency and phase estimation and compensation method. To verify the effectiveness of the proposed two-step frequency and phase offset estimation method, we compare the BER of SS-CPM-LFM under both AWGN and BELLHOP underwater acoustic channels.

As shown in Figure 23, without frequency and phase offset compensation, the BERs of CPM-LFM and CPM are close to each other. In this case, the BER is around 0.5, making normal communication impossible. When the traditional preamble frame structure is employed in the CPM-LFM system, and the preamble is used for frequency and phase compensation, the system performance improves significantly, achieving a BER of 10^−2.8 at an SNR of 8 dB. However, the SS-CPM-LFM combined with the two-step frequency and phase offset estimation method reduces the system BER to 10^−3.6 at an SNR of 8 dB. This result is close to the BER of SS-CPM-LFM in an AWGN channel. It demonstrates that the SS frame structure, along with the two-step frequency and phase compensation method, can effectively mitigate the multipath and Doppler effects inherent in the underwater acoustic channel, thereby improving the system’s communication performance.

5. Conclusions

This paper considered the design of a waveform for integrated communication and detection in underwater acoustic environments. Data are transmitted via CPM on an LFM waveform. An underwater acoustic system was also developed. The detection and communication performances were evaluated to verify the effectiveness of the proposed design. It was shown that the proposed waveform provides good velocity ambiguity, and the range ambiguity degradation is acceptable, considering the communication capability.

The frame structure employs a symbol suffix frame structure with a SS-CPM-LFM signal. This suffix is used for frequency estimation and signal frame compensation to adapt to complex underwater acoustic channels. Simulation results were obtained which show that the corresponding velocity ambiguity is consistent with the LFM signal and the sensitivity of the range ambiguity to the data signal is reduced, which improves the ranging performance. The proposed frequency offset and phase offset estimation methods provide BER performance approaching that of an AWGN channel. This verifies the effectiveness of the proposed integrated underwater system.

Author Contributions

Conceptualization, T.L. and Y.W.; methodology, Q.T. and Y.W.; software, Y.W. and J.W.; validation, T.L., Q.T. and Y.W.; formal analysis, T.L., Q.T. and Y.W.; investigation, Y.W.; resources, T.L.; data curation, T.L., Q.T. and Y.W.; writing—original draft preparation, T.L., Q.T., Y.W. and J.W.; writing—review and editing, J.C., Y.Z., Y.Y. and T.A.G.; visualization, Y.W. and J.W.; supervision, T.L.; project administration, T.L.; funding acquisition, T.L. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Constant envelope CPM-LFM signal generation.

Figure 2. Amplitude of LFM and CPM-LFM waveforms.

Figure 3. Frequency domain characteristics of three waveforms.

Figure 4. The upper bound of the minimum Euclidean distance.

Figure 5. Schematic diagram for calculating the ambiguity function of a shared waveform.

Figure 6. The hydroacoustic integrated system.

Figure 7. The integrated hydroacoustic system based on constant envelope waveforms.

Figure 8. Signal generation at the transmitter.

Figure 9. Signal processing flowchart at the receiver.

Figure 10. The data frame structure.

Figure 12. The block diagram of the simulations in AWGN channels.

Figure 13. The block diagram of the simulations in BELLHOP underwater acoustic channel.

Figure 14. Ambiguity functions of the CPM-LFM and LFM waveforms.

Figure 15. Distance resolution of the LFM and proposed waveforms.

Figure 16. BER with different modulation indices h.

Figure 17. BER with different modulation orders M.

Figure 18. BER with different correlation lengths L.

Figure 19. Ambiguity function for the SS-CPM-LFM signal.

Figure 20. Velocity ambiguity comparison.

Figure 21. Range ambiguity comparison.

Figure 22. Output with a Hamming window and zero Doppler frequency.

Figure 23. BER comparison of the proposed waveform and integrated system.

Table 1

Three commonly used CPM pulse shapes.

	$\mathit{g}(\mathit{t})$	$\mathit{q}(\mathit{t})$
LREC	$g(t)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{2LT}}& (0\le t\le LT)\\ 0& \mathrm{else} \end{array}\right.$	$q(t)=\left\{\begin{array}{cc}1/2,& LT<t\\ {\displaystyle \frac{t}{2LT}},& 0\le t\le LT\\ 0,& 0<t\end{array}\right.$
LRC	$g(t)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{2LT}}\left(1-\mathit{cos}{\displaystyle \frac{2\pi t}{LT}}\right)& (0\le t\le LT)\\ 0& \mathrm{else}\end{array}\right.$	$q(t)=\left\{\begin{array}{cc}1/2& LT<t\\ {\displaystyle \frac{t}{2LT}}-{\displaystyle \frac{1}{4\pi }}\mathit{sin}\left({\displaystyle \frac{2\pi t}{LT}}\right),& 0\le t\le LT\\ 0& 0<t\end{array}\right.$
GMSK	$g(t)=\left\{\begin{array}{c}Q\left[2\pi B^{‘}\left(t-{\displaystyle \frac{T}{2}}\right)/(\mathit{ln}2{)}^{1/2}\right]\\ -Q\left[2\pi B^{‘}\left(t+{\displaystyle \frac{T}{2}}\right)/(\mathit{ln}2{)}^{1/2}\right]\end{array}\right\}$where $Q(t)={\int }_0^{\infty }{\displaystyle \frac{1}{\sqrt{2\pi }}}{e}^{-x^2/2}dt$	$q(t)={\displaystyle \frac{1}{\sqrt{2\pi }}}{\int }_t^{\infty \int \left({\displaystyle \frac{-{\tau }^2}{2}}\right)}exp$

Table 2

Simulation parameters of BELLHOP.

Parameter	Value
Sea water depth	200 m
Longitudinal wave velocity	1500 m/s
Interpolation method	C-type linear
Sound source depth	10 m
Receiver depth	10 m 50 m 100 m 150 m
Distance between sound source and receiver	1000 m

Table 3

Simulation parameters of the designed waveform and integrated system.

Parameter	Value
Signal bandwidth B	1000 Hz
pulse width Tp	0.5 s
Modulation index h	0.5
Correlation length L	2
Symbol pulse function g(t)	$g(t)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{2LT}}& (0\le t\le LT)\\ 0& \mathrm{else} \end{array}\right.$
Modulation order M	2
carrier frequency fc	1500 Hz
Total number of symbols in a frame	598
Data1	35
Data2	400
Preamble	128
Doppler deviation of frequency fd Phase deviation φd	0.20.1π

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