# Orthogonal Frequency Division Multiplexing Underwater Acoustic Communication System with Environmental Cognition Ability

Authors: Jinqiu Wu; Xiaofei Qi; Kang Guo; Jiaqiong Zhou; Yi Zhang
Journal: Security and Communication Networks
 (2021)

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## Abstract

In UWAC (underwater acoustic communication), UWA (underwater acoustic) channels change rapidly due to varying environment conditions. AMC (adaptive modulation and coding) is an efficient technique to improve system efficiency by changing transmission parameters according to channel conditions in UWA channels. In this paper, we propose an environmental cognition orthogonal frequency division multiplexing (OFDM) UWAC system and compare it with AMC algorithm with six transmission modes together with three threshold detection algorithms. Simulation and experimental results show the effectiveness of the proposed system. The system will play an important role in future communication networks which can significantly improve the efficiency of the system.


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## Body

## 1. Introduction

Several studies have focused on UWAC in recent years, with both multicarrier transmissions [1–11] and single carrier transmissions. [12–15] In an UWAC system, the rapidly varying multipath channel and the limitation of the bandwidth are major constraints [16–18].The UWA channel is one of the most complex wireless channels whose characteristics are affected by various parameters, such as the propagation distance of the acoustic signal, the interference signal caused by multipath propagation, the environmental noise, and the Doppler shift caused by movement or the roughness of the sea surface. [19, 20] Adaptive modulation and coding (AMC) technology can change transmission parameters, according to the changes in underwater acoustic channels to improve the efficiency of the communication system. This algorithm will further promote the development of the networking technology. In recent years, several studies have examined frequency band utilization improvement of the UWA channel [21–26].Radosevic et al. [22] design a criterion to maximize the system throughput under a target averaged bit error rate (BER) and present adaptive modulation results for UWAC communication links with real-time at-sea experiments. In [23], the relationship between modulation modes and threshold algorithms is analyzed through underwater experiment. Wan et al. [24] discuss adaptive modulation and coding for underwater orthogonal frequency division multiplexing based on a finite number of transmission modes whose objective is to maximize the data rate via mode switching. For the same source data, Lee et al. [25] adopt four different transmission methods at the transmitting terminal of the communication system. At the receiving terminal, the AMC system uses a threshold detection algorithm to choose a transmission mode as the best performance mode for the system. Jaradat et al. and Huang and Roee [26, 27] focus on the support vector machine training model, which is used to classify the underwater channels, after which the appropriate modulation mode is chosen.The typical procedure of AMC is as follows: a transmitter (TX) node initiates a request-to-send (RTS) message and then the receiver (RX) node replies with a clear-to-send (CTS) message, including the channel conditions, upon which the TX node can choose a suitable transmission mode and transmit a data burst to the RX node. [24] The transmission of RTS and CTS signals not only will waste the limited energy, but will also be unable to adjust the transmission mode during transmission. In addition, these kinds of procedures estimate channel condition only once and do not permit sensing of the channel in real time. Unless the RTS and CTS signals transmit before each communication, the system can adopt its transmitting mode according to the channel condition involved in the CTS signal. However, this will waste a lot of time and affect the transmission efficiency. Moreover, when the channel changes rapidly, the system will be unable to match its transmitting mode with the changing channel.To overcome these obstacles, an environmental cognition (EC) OFDM UWAC system is proposed in this paper. The accuracy of the UWA channel estimation affects the overall performance of the AMC system. A modified compressed-sensing (CS) channel estimation algorithm is proposed, which can evaluate the UWA channel through each communication. Therefore, the system can achieve robust channel estimation results to improve system performance. In the field of UWAC, the physical layer algorithm is the basis of building the network layer. Due to the particularity of underwater acoustic network [27–30], the physical layer technology is particularly important. This paper starts from the physical layer technology, which can effectively connect the physical layer technology with the network and is an important research direction in the future.The paper is organized as follows. The EC OFDM UWAC system model is introduced in Section2. The simulation and experimental results are discussed in Section 3. The conclusion is presented in Section 4.


## 2. Proposed System

### 2.1. Environmental Cognition System Structure

In the EC OFDM UWAC system, at the transmitting end, the input data is first mapped; then, the OFDM modulation is performed, which matches the demodulation procedure at the receiving end. The cyclic prefix (CP) and preamble sequence (PS) are added after OFDM modulation. After the modulated signal passes through the UWA channel, at the receiving terminal, a coarse synchronization is first performed by the PS. At the same time, the number of the UWA channel multipaths is roughly estimated by the PS and is fed back to the channel estimation module for the CS channel estimation algorithm to achieve a faster convergence speed and higher estimation accuracy. Then, OFDM demodulation is performed before CS channel estimation, after which, the signal is divided into two parts: one is the demapping procedure, after which the demodulated signal can be obtained, and the other is the channel quality assessment process, according to which the optimum mapping mode can be selected. Then, parameters that represent the optimum mode are fed back to the transmitting end for mapping the data to be transmitted. The framework of the EC OFDM UWAC system is shown in Figure1.Figure 1
Framework of the EC OFDM UWAC system.


#### 2.1.1. EC Transceiver Model

In the EC OFDM UWAC system, we adopt convolutional coding to design the size of information bits. Six multiplexed modes together with the set of transmission modes are shown in Table1. Different transmission rates are produced by varying the modulation scheme and the convolutional code rate. The modulation schemes are BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying), and 16PSK (16 Phase Shift Keying) in this paper, and the convolutional code rate adopted are 1/2 and 2/3.Table 1
Modulation parameters.
ModeCoding rateModulation11/2BPSK22/3BPSK31/2QPSK42/3QPSK51/216PSK62/316PSKThe switching criterion between different modes of AMC technology is based on channel conditions, so the accuracy of the channel evaluation criterion has a crucial effect on the performance of the entire system. The channel evaluation criteria are discussed in the following section.


#### 2.1.2. Channel Quality Assessment Criteria

The accuracy and reliability of the channel state information obtained by the receiving end will directly affect communication quality. The establishment of a physical quantity that successfully reflects and evaluates the channel state is important. This paper mainly discusses three assessment criteria of the UWA channel: the input signal-to-noise ratio (ISNR), pilot signal-to-noise ratio (PSNR), and effective signal-to-noise ratio (ESNR).(i)
ISNR: the ISNR is the ratio of received signal power to noise power. After the received signal is synchronized, the signal and noise can be separated. The calculation formula for the ISNR is defined as follows:(1)ISNR=Eyn2−Ewn2Ewn2,wherey represents the sampling signal at the receiving end and w is the sampling noise.(ii)
PSNR: the PSNR is calculated after the received signal undergoes a fast Fourier transform (FFT), which has taken the inter-subcarrier interference into consideration. The energy in the pilot subcarrier represents the energy of the effective signal, while the energy in the empty subcarrier is treated as noise. The PSNR ratio is defined as follows:(2)PSNR=Ek∈SPzk2−Ek∈SNzk2Ek∈SNzk2,wherezk is the observation of the kth subcarrier, SP is the set of pilot subcarriers, SN is the set of empty subcarriers, and SD is the set of data subcarriers.(iii)
ESNR: the definition of ESNR is as follows:(3)ESNR=Ek∈SDH^ksk2Ek∈SDzk−H^ksk2,wherezk is the frequency-domain received signal on the kth subcarrier, H^k is defined as the frequency-domain channel estimation result on the kth subcarrier, and sk is the transmitted signal carried on the kth carrier.The ISNR is calculated after synchronization and is proportional to the power of the received signal; this means that it cannot capture the intercarrier interference caused by the Doppler shift. Although the PSNR captures the inter-subcarrier interference, the calculation is performed before channel estimation, meaning the interference caused by channel estimation is, therefore, not reflected in the PSNR. The ESNR is a physical quantity that can characterize the influencing factors mentioned and is calculated at the receiving end of the decoded signal. In [24], the ESNR is calculated using the Acknowledge Character (ACK), which does adequately reflect channel characters because of the limited length of the ACK. Therefore, we propose an improved ESNR (IESNR) criterion which is shown as follows:(4)IESNR=Ek∈SH^csksk2Ek∈Szk−H^csksk2.Note that, in this paper, we use formula (4) to estimate the SNR. The set of S used in IESNR is different from that in ESNR. S is made of the entire transmitting signal which is received from the transmitter to evaluate the channel quality. The signal, used for channel evaluation in the IESNR, has a longer duration time and a wider frequency bandwidth than the signal used in the traditional AMC system (ESNR). Therefore, gains can be obtained in the time and frequency domain, which overcomes the problem of estimation errors in the traditional AMC system and the inability to track the channel in time. The advantage of IESNR is proved as follows.We setH^csksk=Rk and zk−H^csksk=Nk, for each k∈S. By the choice of the set S, we can assume that Rk and Nk for each k∈S are both IID (Independent and Identically Distributed) Gaussian distributions with means 0 and variances σr2 and σn2, respectively, where σr2 and σn2 are the variances of Rk and Nk. Note that both the numerator and denominator are summations of square of IID, and hence, they both satisfy chi-square distributions. As a result, the quotient is shown as follows:(5)IESNR∼FN,Nσr2σn2.It satisfies theF-Distribution, where N=S denotes the number of elements in the set S. It can be deduced that the mean and variance of this estimator are(6)meanIESNR=σr2σn2NN−2,varIESNR=σr4σn44NN−1N−2N−4.Therefore, our estimator IESNR is an asymptotic unbiased estimator. Moreover, the accuracy increases asN goes to infinity. As examples, we compare our estimator IESNR with ESNR. The probability density functions of IESNR and ESNR are shown in Figure 2. From this figure, we conclude that our estimator IESNR is better than ESNR.Figure 2
Probability density functions of IESNR and ESNR.As the accuracy of channel estimation directly determines the performance, an improved CS channel estimation algorithm is proposed and discussed in Section3, which is used in the proposed IESNR criterion.


#### 2.1.3. Switching Criterion

This paper discusses the switching criteria of three modulation coding methods, which are switching algorithms based on the lowest signal-to-noise ratio (L-SNR), the average SNR (A-SNR), and the corrected average SNR (CA-SNR).(i)
L-SNR criterion:the main objective of this criterion is to establish the minimum SNR in the subband and to compare this value with the threshold of each modulation mode, according to which the next transmission scheme is selected. The carriers in the entire subband are modulated by this scheme. The expression for this is as follows:(7)γq=mink=1,…,Nsγk,q,in which,γk,q is the kth subcarrier in the qth subband, q = 1, 2, …, Q and k = 1, 2, …, Ns.This criterion sacrifices system throughput in exchange for increased BER performance.(ii)
SNR criterion: to improve system throughput, the A-SNR, which calculates the average SNR in the subband, is proposed by researchers. The expression is as follows:(8)γq=1Ns∑k=1Nsγk,q.Because of the different channel fluctuations in each subband, the BER performance of the AMC system based on this criterion is relatively poor, especially for a deep fading channel.(iii)
CA-SNR criterion: the main purpose for the modified mean method is to calculate the fluctuation degree of the SNR in the subband and to sacrifice part of the throughput in exchange for a better BER performance, which uses the variance or standard deviation to indicate the regression of SNR. The associated mathematical expression is as follows:(9)σq=1Ns−1∑k=1Nsγk,q−γq¯2,γq=γq¯−σq,in whichγ¯k represents the average SNR in each subband.In this paper, we adopt the CA criterion, whose performance is between the first two criterions.


### 2.2. Channel Estimation

#### 2.2.1. CS Channel Estimation Algorithm

According to the expression for ESNR, the accuracy of channel estimation affects the performance of the whole system. To deal with Doppler shift, an improved algorithm based on CS channel estimation is proposed to obtain important channel estimation results.The OFDM discrete Fourier transform (DFT) technology is associated with CS to simplify the calculation. The DFT procedure is equivalent to the base matrixQ, and the frequency domain observational data of the channel are equivalent to a small part of observation Y. Since Y is sparse in the time domain and satisfies the conditions of CS for signal reconstruction, the UWA channel can be accurately recovered using CS technology:(10)Y=XH+W=XFh+W.Equation (10) represents signals in the frequency domain; Y is the receiving signal, X is the transmitting signal, H the channel, W the noise, and F the Fourier matrix. Extracting the pilot information using equation (10) gives(11)YP=XPHP=XPFPh=Θh+WP,where Θ=XPFP is the perception matrix and h is the sparse signal to be reconstructed, that is, the channel impulse response. At the receiving end, where Xp,Yp, and Fp are known, the CS reconstruction algorithm can be used to recover the sparse UWA channel impulse response h, and then, a Fourier transform is performed to obtain the channel transfer function H.


#### 2.2.2. Proposed CS Channel Estimation Algorithm

In other AMC OFDM UWA communication systems, the process of channel estimation is completed by ACK andXpandYp are the received and transmitted ACKs. Even if the CS channel estimation algorithm is used, the estimated channel is not accurate enough. In addition, in other research studies that adopt the CS channel estimation algorithms, there are no prior information regarding the channel multipaths’ number, which will not only waste computing time but also cause inaccurate estimation. The algorithm flow proposed in this paper is shown in Figure 3; it is suitable for real-time duplex communication systems. The channel tap coefficients obtained by PS are fed back to the CS algorithm so that the system can complete more accurate channel estimation in a shorter time. Then, during the CS channel estimation procedure, XpandYp are signals obtained from the whole transmitting OFDM signal, which will mainly be pilot signals. This CS algorithm is adopted in the ESNR channel quality assessment criterion known as the IESNR criterion.Figure 3
Framework of the proposed CS channel estimation algorithm.


## 2.1. Environmental Cognition System Structure

In the EC OFDM UWAC system, at the transmitting end, the input data is first mapped; then, the OFDM modulation is performed, which matches the demodulation procedure at the receiving end. The cyclic prefix (CP) and preamble sequence (PS) are added after OFDM modulation. After the modulated signal passes through the UWA channel, at the receiving terminal, a coarse synchronization is first performed by the PS. At the same time, the number of the UWA channel multipaths is roughly estimated by the PS and is fed back to the channel estimation module for the CS channel estimation algorithm to achieve a faster convergence speed and higher estimation accuracy. Then, OFDM demodulation is performed before CS channel estimation, after which, the signal is divided into two parts: one is the demapping procedure, after which the demodulated signal can be obtained, and the other is the channel quality assessment process, according to which the optimum mapping mode can be selected. Then, parameters that represent the optimum mode are fed back to the transmitting end for mapping the data to be transmitted. The framework of the EC OFDM UWAC system is shown in Figure1.Figure 1
Framework of the EC OFDM UWAC system.


### 2.1.1. EC Transceiver Model

In the EC OFDM UWAC system, we adopt convolutional coding to design the size of information bits. Six multiplexed modes together with the set of transmission modes are shown in Table1. Different transmission rates are produced by varying the modulation scheme and the convolutional code rate. The modulation schemes are BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying), and 16PSK (16 Phase Shift Keying) in this paper, and the convolutional code rate adopted are 1/2 and 2/3.Table 1
Modulation parameters.
ModeCoding rateModulation11/2BPSK22/3BPSK31/2QPSK42/3QPSK51/216PSK62/316PSKThe switching criterion between different modes of AMC technology is based on channel conditions, so the accuracy of the channel evaluation criterion has a crucial effect on the performance of the entire system. The channel evaluation criteria are discussed in the following section.


### 2.1.2. Channel Quality Assessment Criteria

The accuracy and reliability of the channel state information obtained by the receiving end will directly affect communication quality. The establishment of a physical quantity that successfully reflects and evaluates the channel state is important. This paper mainly discusses three assessment criteria of the UWA channel: the input signal-to-noise ratio (ISNR), pilot signal-to-noise ratio (PSNR), and effective signal-to-noise ratio (ESNR).(i)
ISNR: the ISNR is the ratio of received signal power to noise power. After the received signal is synchronized, the signal and noise can be separated. The calculation formula for the ISNR is defined as follows:(1)ISNR=Eyn2−Ewn2Ewn2,wherey represents the sampling signal at the receiving end and w is the sampling noise.(ii)
PSNR: the PSNR is calculated after the received signal undergoes a fast Fourier transform (FFT), which has taken the inter-subcarrier interference into consideration. The energy in the pilot subcarrier represents the energy of the effective signal, while the energy in the empty subcarrier is treated as noise. The PSNR ratio is defined as follows:(2)PSNR=Ek∈SPzk2−Ek∈SNzk2Ek∈SNzk2,wherezk is the observation of the kth subcarrier, SP is the set of pilot subcarriers, SN is the set of empty subcarriers, and SD is the set of data subcarriers.(iii)
ESNR: the definition of ESNR is as follows:(3)ESNR=Ek∈SDH^ksk2Ek∈SDzk−H^ksk2,wherezk is the frequency-domain received signal on the kth subcarrier, H^k is defined as the frequency-domain channel estimation result on the kth subcarrier, and sk is the transmitted signal carried on the kth carrier.The ISNR is calculated after synchronization and is proportional to the power of the received signal; this means that it cannot capture the intercarrier interference caused by the Doppler shift. Although the PSNR captures the inter-subcarrier interference, the calculation is performed before channel estimation, meaning the interference caused by channel estimation is, therefore, not reflected in the PSNR. The ESNR is a physical quantity that can characterize the influencing factors mentioned and is calculated at the receiving end of the decoded signal. In [24], the ESNR is calculated using the Acknowledge Character (ACK), which does adequately reflect channel characters because of the limited length of the ACK. Therefore, we propose an improved ESNR (IESNR) criterion which is shown as follows:(4)IESNR=Ek∈SH^csksk2Ek∈Szk−H^csksk2.Note that, in this paper, we use formula (4) to estimate the SNR. The set of S used in IESNR is different from that in ESNR. S is made of the entire transmitting signal which is received from the transmitter to evaluate the channel quality. The signal, used for channel evaluation in the IESNR, has a longer duration time and a wider frequency bandwidth than the signal used in the traditional AMC system (ESNR). Therefore, gains can be obtained in the time and frequency domain, which overcomes the problem of estimation errors in the traditional AMC system and the inability to track the channel in time. The advantage of IESNR is proved as follows.We setH^csksk=Rk and zk−H^csksk=Nk, for each k∈S. By the choice of the set S, we can assume that Rk and Nk for each k∈S are both IID (Independent and Identically Distributed) Gaussian distributions with means 0 and variances σr2 and σn2, respectively, where σr2 and σn2 are the variances of Rk and Nk. Note that both the numerator and denominator are summations of square of IID, and hence, they both satisfy chi-square distributions. As a result, the quotient is shown as follows:(5)IESNR∼FN,Nσr2σn2.It satisfies theF-Distribution, where N=S denotes the number of elements in the set S. It can be deduced that the mean and variance of this estimator are(6)meanIESNR=σr2σn2NN−2,varIESNR=σr4σn44NN−1N−2N−4.Therefore, our estimator IESNR is an asymptotic unbiased estimator. Moreover, the accuracy increases asN goes to infinity. As examples, we compare our estimator IESNR with ESNR. The probability density functions of IESNR and ESNR are shown in Figure 2. From this figure, we conclude that our estimator IESNR is better than ESNR.Figure 2
Probability density functions of IESNR and ESNR.As the accuracy of channel estimation directly determines the performance, an improved CS channel estimation algorithm is proposed and discussed in Section3, which is used in the proposed IESNR criterion.


### 2.1.3. Switching Criterion

This paper discusses the switching criteria of three modulation coding methods, which are switching algorithms based on the lowest signal-to-noise ratio (L-SNR), the average SNR (A-SNR), and the corrected average SNR (CA-SNR).(i)
L-SNR criterion:the main objective of this criterion is to establish the minimum SNR in the subband and to compare this value with the threshold of each modulation mode, according to which the next transmission scheme is selected. The carriers in the entire subband are modulated by this scheme. The expression for this is as follows:(7)γq=mink=1,…,Nsγk,q,in which,γk,q is the kth subcarrier in the qth subband, q = 1, 2, …, Q and k = 1, 2, …, Ns.This criterion sacrifices system throughput in exchange for increased BER performance.(ii)
SNR criterion: to improve system throughput, the A-SNR, which calculates the average SNR in the subband, is proposed by researchers. The expression is as follows:(8)γq=1Ns∑k=1Nsγk,q.Because of the different channel fluctuations in each subband, the BER performance of the AMC system based on this criterion is relatively poor, especially for a deep fading channel.(iii)
CA-SNR criterion: the main purpose for the modified mean method is to calculate the fluctuation degree of the SNR in the subband and to sacrifice part of the throughput in exchange for a better BER performance, which uses the variance or standard deviation to indicate the regression of SNR. The associated mathematical expression is as follows:(9)σq=1Ns−1∑k=1Nsγk,q−γq¯2,γq=γq¯−σq,in whichγ¯k represents the average SNR in each subband.In this paper, we adopt the CA criterion, whose performance is between the first two criterions.


## 2.1.1. EC Transceiver Model

In the EC OFDM UWAC system, we adopt convolutional coding to design the size of information bits. Six multiplexed modes together with the set of transmission modes are shown in Table1. Different transmission rates are produced by varying the modulation scheme and the convolutional code rate. The modulation schemes are BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying), and 16PSK (16 Phase Shift Keying) in this paper, and the convolutional code rate adopted are 1/2 and 2/3.Table 1
Modulation parameters.
ModeCoding rateModulation11/2BPSK22/3BPSK31/2QPSK42/3QPSK51/216PSK62/316PSKThe switching criterion between different modes of AMC technology is based on channel conditions, so the accuracy of the channel evaluation criterion has a crucial effect on the performance of the entire system. The channel evaluation criteria are discussed in the following section.


## 2.1.2. Channel Quality Assessment Criteria

The accuracy and reliability of the channel state information obtained by the receiving end will directly affect communication quality. The establishment of a physical quantity that successfully reflects and evaluates the channel state is important. This paper mainly discusses three assessment criteria of the UWA channel: the input signal-to-noise ratio (ISNR), pilot signal-to-noise ratio (PSNR), and effective signal-to-noise ratio (ESNR).(i)
ISNR: the ISNR is the ratio of received signal power to noise power. After the received signal is synchronized, the signal and noise can be separated. The calculation formula for the ISNR is defined as follows:(1)ISNR=Eyn2−Ewn2Ewn2,wherey represents the sampling signal at the receiving end and w is the sampling noise.(ii)
PSNR: the PSNR is calculated after the received signal undergoes a fast Fourier transform (FFT), which has taken the inter-subcarrier interference into consideration. The energy in the pilot subcarrier represents the energy of the effective signal, while the energy in the empty subcarrier is treated as noise. The PSNR ratio is defined as follows:(2)PSNR=Ek∈SPzk2−Ek∈SNzk2Ek∈SNzk2,wherezk is the observation of the kth subcarrier, SP is the set of pilot subcarriers, SN is the set of empty subcarriers, and SD is the set of data subcarriers.(iii)
ESNR: the definition of ESNR is as follows:(3)ESNR=Ek∈SDH^ksk2Ek∈SDzk−H^ksk2,wherezk is the frequency-domain received signal on the kth subcarrier, H^k is defined as the frequency-domain channel estimation result on the kth subcarrier, and sk is the transmitted signal carried on the kth carrier.The ISNR is calculated after synchronization and is proportional to the power of the received signal; this means that it cannot capture the intercarrier interference caused by the Doppler shift. Although the PSNR captures the inter-subcarrier interference, the calculation is performed before channel estimation, meaning the interference caused by channel estimation is, therefore, not reflected in the PSNR. The ESNR is a physical quantity that can characterize the influencing factors mentioned and is calculated at the receiving end of the decoded signal. In [24], the ESNR is calculated using the Acknowledge Character (ACK), which does adequately reflect channel characters because of the limited length of the ACK. Therefore, we propose an improved ESNR (IESNR) criterion which is shown as follows:(4)IESNR=Ek∈SH^csksk2Ek∈Szk−H^csksk2.Note that, in this paper, we use formula (4) to estimate the SNR. The set of S used in IESNR is different from that in ESNR. S is made of the entire transmitting signal which is received from the transmitter to evaluate the channel quality. The signal, used for channel evaluation in the IESNR, has a longer duration time and a wider frequency bandwidth than the signal used in the traditional AMC system (ESNR). Therefore, gains can be obtained in the time and frequency domain, which overcomes the problem of estimation errors in the traditional AMC system and the inability to track the channel in time. The advantage of IESNR is proved as follows.We setH^csksk=Rk and zk−H^csksk=Nk, for each k∈S. By the choice of the set S, we can assume that Rk and Nk for each k∈S are both IID (Independent and Identically Distributed) Gaussian distributions with means 0 and variances σr2 and σn2, respectively, where σr2 and σn2 are the variances of Rk and Nk. Note that both the numerator and denominator are summations of square of IID, and hence, they both satisfy chi-square distributions. As a result, the quotient is shown as follows:(5)IESNR∼FN,Nσr2σn2.It satisfies theF-Distribution, where N=S denotes the number of elements in the set S. It can be deduced that the mean and variance of this estimator are(6)meanIESNR=σr2σn2NN−2,varIESNR=σr4σn44NN−1N−2N−4.Therefore, our estimator IESNR is an asymptotic unbiased estimator. Moreover, the accuracy increases asN goes to infinity. As examples, we compare our estimator IESNR with ESNR. The probability density functions of IESNR and ESNR are shown in Figure 2. From this figure, we conclude that our estimator IESNR is better than ESNR.Figure 2
Probability density functions of IESNR and ESNR.As the accuracy of channel estimation directly determines the performance, an improved CS channel estimation algorithm is proposed and discussed in Section3, which is used in the proposed IESNR criterion.


## 2.1.3. Switching Criterion

This paper discusses the switching criteria of three modulation coding methods, which are switching algorithms based on the lowest signal-to-noise ratio (L-SNR), the average SNR (A-SNR), and the corrected average SNR (CA-SNR).(i)
L-SNR criterion:the main objective of this criterion is to establish the minimum SNR in the subband and to compare this value with the threshold of each modulation mode, according to which the next transmission scheme is selected. The carriers in the entire subband are modulated by this scheme. The expression for this is as follows:(7)γq=mink=1,…,Nsγk,q,in which,γk,q is the kth subcarrier in the qth subband, q = 1, 2, …, Q and k = 1, 2, …, Ns.This criterion sacrifices system throughput in exchange for increased BER performance.(ii)
SNR criterion: to improve system throughput, the A-SNR, which calculates the average SNR in the subband, is proposed by researchers. The expression is as follows:(8)γq=1Ns∑k=1Nsγk,q.Because of the different channel fluctuations in each subband, the BER performance of the AMC system based on this criterion is relatively poor, especially for a deep fading channel.(iii)
CA-SNR criterion: the main purpose for the modified mean method is to calculate the fluctuation degree of the SNR in the subband and to sacrifice part of the throughput in exchange for a better BER performance, which uses the variance or standard deviation to indicate the regression of SNR. The associated mathematical expression is as follows:(9)σq=1Ns−1∑k=1Nsγk,q−γq¯2,γq=γq¯−σq,in whichγ¯k represents the average SNR in each subband.In this paper, we adopt the CA criterion, whose performance is between the first two criterions.


## 2.2. Channel Estimation

### 2.2.1. CS Channel Estimation Algorithm

According to the expression for ESNR, the accuracy of channel estimation affects the performance of the whole system. To deal with Doppler shift, an improved algorithm based on CS channel estimation is proposed to obtain important channel estimation results.The OFDM discrete Fourier transform (DFT) technology is associated with CS to simplify the calculation. The DFT procedure is equivalent to the base matrixQ, and the frequency domain observational data of the channel are equivalent to a small part of observation Y. Since Y is sparse in the time domain and satisfies the conditions of CS for signal reconstruction, the UWA channel can be accurately recovered using CS technology:(10)Y=XH+W=XFh+W.Equation (10) represents signals in the frequency domain; Y is the receiving signal, X is the transmitting signal, H the channel, W the noise, and F the Fourier matrix. Extracting the pilot information using equation (10) gives(11)YP=XPHP=XPFPh=Θh+WP,where Θ=XPFP is the perception matrix and h is the sparse signal to be reconstructed, that is, the channel impulse response. At the receiving end, where Xp,Yp, and Fp are known, the CS reconstruction algorithm can be used to recover the sparse UWA channel impulse response h, and then, a Fourier transform is performed to obtain the channel transfer function H.


### 2.2.2. Proposed CS Channel Estimation Algorithm

In other AMC OFDM UWA communication systems, the process of channel estimation is completed by ACK andXpandYp are the received and transmitted ACKs. Even if the CS channel estimation algorithm is used, the estimated channel is not accurate enough. In addition, in other research studies that adopt the CS channel estimation algorithms, there are no prior information regarding the channel multipaths’ number, which will not only waste computing time but also cause inaccurate estimation. The algorithm flow proposed in this paper is shown in Figure 3; it is suitable for real-time duplex communication systems. The channel tap coefficients obtained by PS are fed back to the CS algorithm so that the system can complete more accurate channel estimation in a shorter time. Then, during the CS channel estimation procedure, XpandYp are signals obtained from the whole transmitting OFDM signal, which will mainly be pilot signals. This CS algorithm is adopted in the ESNR channel quality assessment criterion known as the IESNR criterion.Figure 3
Framework of the proposed CS channel estimation algorithm.


## 2.2.1. CS Channel Estimation Algorithm

According to the expression for ESNR, the accuracy of channel estimation affects the performance of the whole system. To deal with Doppler shift, an improved algorithm based on CS channel estimation is proposed to obtain important channel estimation results.The OFDM discrete Fourier transform (DFT) technology is associated with CS to simplify the calculation. The DFT procedure is equivalent to the base matrixQ, and the frequency domain observational data of the channel are equivalent to a small part of observation Y. Since Y is sparse in the time domain and satisfies the conditions of CS for signal reconstruction, the UWA channel can be accurately recovered using CS technology:(10)Y=XH+W=XFh+W.Equation (10) represents signals in the frequency domain; Y is the receiving signal, X is the transmitting signal, H the channel, W the noise, and F the Fourier matrix. Extracting the pilot information using equation (10) gives(11)YP=XPHP=XPFPh=Θh+WP,where Θ=XPFP is the perception matrix and h is the sparse signal to be reconstructed, that is, the channel impulse response. At the receiving end, where Xp,Yp, and Fp are known, the CS reconstruction algorithm can be used to recover the sparse UWA channel impulse response h, and then, a Fourier transform is performed to obtain the channel transfer function H.


## 2.2.2. Proposed CS Channel Estimation Algorithm

In other AMC OFDM UWA communication systems, the process of channel estimation is completed by ACK andXpandYp are the received and transmitted ACKs. Even if the CS channel estimation algorithm is used, the estimated channel is not accurate enough. In addition, in other research studies that adopt the CS channel estimation algorithms, there are no prior information regarding the channel multipaths’ number, which will not only waste computing time but also cause inaccurate estimation. The algorithm flow proposed in this paper is shown in Figure 3; it is suitable for real-time duplex communication systems. The channel tap coefficients obtained by PS are fed back to the CS algorithm so that the system can complete more accurate channel estimation in a shorter time. Then, during the CS channel estimation procedure, XpandYp are signals obtained from the whole transmitting OFDM signal, which will mainly be pilot signals. This CS algorithm is adopted in the ESNR channel quality assessment criterion known as the IESNR criterion.Figure 3
Framework of the proposed CS channel estimation algorithm.


## 3. Simulation and Experimental Results

### 3.1. Simulation Results

Channels 1 and 2 in Figure4 are measured time-varying channels obtained from the experiment at Lianhua Lake in Heilongjiang Province. The two channels are used as the simulation channels. The maximum multipath delays of channel 1 and channel 2 are about 10 ms and 16 ms, respectively. To verify the effectiveness of the proposed CS channel estimation algorithm, a series of related simulations is carried out.Figure 4
Simulation channels. (a) Channel 1. (b) Channel 2.
(a)(b)Firstly, we compare the proposed CS channel estimation algorithm with the LS channel estimation algorithm, and the simulation result is shown in Figure5.Figure 5
Comparison of the proposed CS channel estimation algorithm with LS.Figure5 shows that the proposed algorithm delivers a 2 dB better BER performance than LS.The proposed CS and traditional CS are shown in Figures6(a) and 6(b).Figure 6
CS channel estimation results. (a) Proposed CS. (b) Proposed CS.
(a)(b)Figure6(a) shows a comparison between the real channel impulse and the channel impulse estimated by the proposed CS algorithm; Figure 6(b) shows the traditional CS algorithm. In traditional CS algorithm, there are many interference impulses near each real channel impulse in the traditional CS algorithm, which not only prolongs the running time but also causes interference in the entire system. However, the proposed algorithm can provide a better estimation result.The BER performance of the proposed algorithm and the ACK-based CS algorithm in channels 1 and 2, subject to ESNR criteria, are compared in Figure7. Figure 7 shows that the proposed algorithm delivers a better BER performance than the ACK-based CS algorithm, which is widely used in AMC OFDM communication systems. The comparison is performed subject to the ESNR criterion to further verify the stability of the proposed CS algorithm. The curves of the proposed CS algorithm are closer together than those of the widely used ACK-based CS algorithm, among different channels, which confirms the effectiveness of the IESNR criterion.Figure 7
BER performance of different CS algorithms.Figures8(a)–8(c) compare the BER performances of systems with different modulation and coding modes which subject to ISNR, PSNR, and IESNR channel quality assessment criteria. Clearly, the performance curves are close to each other for different channel conditions which subject to the IESNR criteria, which means the IESNR reflects channel conditions accurately. This paper adopts the IESNR as the criterion for mode switching in the proposed EC OFDM UWAC system.Figure 8
BER performance of OFDM systems with different modulation and coding modes which subject to different channel quality assessment criteria.
(a)(b)(c)The designed EC OFDM UWAC system is illustrated in Figure9, the switching BER of which is 10–3, which subjects to the IESNR criterion. The switching threshold can be modified by neural networks’ algorithms to enhance the adaptability of the system in the future [31, 32]. The switching thresholds are −0.5, 1.2, 3.8, 7.8, and 13.8. The EC OFDM UWAC transmission mode is shown in Table 2.Figure 9
Switching BER of the proposed EC OFDM UWAC system.Table 2
EC OFDM UWAC transmission mode which subjects to the IESNR criterion.
Mode12456IESNR range[−0.5, 1.2)[1.2, 3.8)[3.8, 7.8)[7.8, 13.8)[13.8, ∞)Figures10(a) and 10(b) compare the frequency utilization rate of the proposed system with that of the traditional AMC system [24], which subjects to different switching criteria. Whenever in channel 1 or channel 2, the proposed system is better than the traditional AMC system. However, the frequency utilization rate decreases with deterioration of the channel. This is because the construction of the handover criterion in this paper is based on the premise of a given BER, and the bandwidth utilization rate is sacrificed in exchange for BER performance.Figure 10
Frequency utilization rate of the different systems. (a) Frequency utilization rate in channel 1. (b)Frequency utilization rate in channel 2.
(a)(b)Figure11 compares the BER performance of the proposed EC OFDM UWAC system based on the CA-SNR switching criterion with single transmission modes 2, 4, and 6 under channel 1. Clearly, the proposed system delivers a good BER performance.Figure 11
BER performance of proposed system and single models.


### 3.2. Experimental Results

To verify the effect of the EC OFDM UWAC system, different channel conditions are obtained through experiments in small pool and big pool, respectively. The size of the small pool is 1 m × 0.5 m × 0.5 m, and the size of the big pool is 25 m × 15 m × 10 m. Figure12 shows the small pool used in the experiment, whose channel impulse is shown in Figure 13, and there are sound-absorbing wedges (shown in Figure 14) around the pool. The laying depth of the transducers in Figure 15 is 0.25 m. The horizontal distance between the transducers is 1 m.Figure 12
Small pool in experiment.Figure 13
Channel impulse of the small pool.Figure 14
Sound-absorbing wedge.Figure 15
Transducers.Figure15 shows transducers for sending and receiving signals whose bandwidths are 8–16 kHz.The highest measured IESNR of the experimental channel in the small pool is 6.98 dB, and the proposed system adopted transmitting models for signal transmission according to the criterion in Table2. The BER of the proposed EC OFDM UWAC system is 0 and the frequency utilization is 0.6658. Experiments using different models are conducted. The BERs of models 1 to 4 are all 0, while that of model 5 is 0.0026 and that of model 6 is 0.0465.The big pool is an anechoic pool and is shown in Figure16, and the channel impulse is shown in Figure 17. The laying depth of the transducers in Figure 16 is 3 m. The horizontal distance between the transmitter and the hydrophone is 11.5 m. The highest measured IESNR of the experimental channel in the small pool is 14.2 dB, and the proposed system adopted transmitting models for signal transmission according to the criterion in Table 2. Under this experimental environment, all transmitting modes BER is 0, including the proposed EC OFDM UWAC system whose frequency utilization reached to 1.3316.Figure 16
Experimental anechoic pool.Figure 17
Channel impulse of the big pool.


## 3.1. Simulation Results

Channels 1 and 2 in Figure4 are measured time-varying channels obtained from the experiment at Lianhua Lake in Heilongjiang Province. The two channels are used as the simulation channels. The maximum multipath delays of channel 1 and channel 2 are about 10 ms and 16 ms, respectively. To verify the effectiveness of the proposed CS channel estimation algorithm, a series of related simulations is carried out.Figure 4
Simulation channels. (a) Channel 1. (b) Channel 2.
(a)(b)Firstly, we compare the proposed CS channel estimation algorithm with the LS channel estimation algorithm, and the simulation result is shown in Figure5.Figure 5
Comparison of the proposed CS channel estimation algorithm with LS.Figure5 shows that the proposed algorithm delivers a 2 dB better BER performance than LS.The proposed CS and traditional CS are shown in Figures6(a) and 6(b).Figure 6
CS channel estimation results. (a) Proposed CS. (b) Proposed CS.
(a)(b)Figure6(a) shows a comparison between the real channel impulse and the channel impulse estimated by the proposed CS algorithm; Figure 6(b) shows the traditional CS algorithm. In traditional CS algorithm, there are many interference impulses near each real channel impulse in the traditional CS algorithm, which not only prolongs the running time but also causes interference in the entire system. However, the proposed algorithm can provide a better estimation result.The BER performance of the proposed algorithm and the ACK-based CS algorithm in channels 1 and 2, subject to ESNR criteria, are compared in Figure7. Figure 7 shows that the proposed algorithm delivers a better BER performance than the ACK-based CS algorithm, which is widely used in AMC OFDM communication systems. The comparison is performed subject to the ESNR criterion to further verify the stability of the proposed CS algorithm. The curves of the proposed CS algorithm are closer together than those of the widely used ACK-based CS algorithm, among different channels, which confirms the effectiveness of the IESNR criterion.Figure 7
BER performance of different CS algorithms.Figures8(a)–8(c) compare the BER performances of systems with different modulation and coding modes which subject to ISNR, PSNR, and IESNR channel quality assessment criteria. Clearly, the performance curves are close to each other for different channel conditions which subject to the IESNR criteria, which means the IESNR reflects channel conditions accurately. This paper adopts the IESNR as the criterion for mode switching in the proposed EC OFDM UWAC system.Figure 8
BER performance of OFDM systems with different modulation and coding modes which subject to different channel quality assessment criteria.
(a)(b)(c)The designed EC OFDM UWAC system is illustrated in Figure9, the switching BER of which is 10–3, which subjects to the IESNR criterion. The switching threshold can be modified by neural networks’ algorithms to enhance the adaptability of the system in the future [31, 32]. The switching thresholds are −0.5, 1.2, 3.8, 7.8, and 13.8. The EC OFDM UWAC transmission mode is shown in Table 2.Figure 9
Switching BER of the proposed EC OFDM UWAC system.Table 2
EC OFDM UWAC transmission mode which subjects to the IESNR criterion.
Mode12456IESNR range[−0.5, 1.2)[1.2, 3.8)[3.8, 7.8)[7.8, 13.8)[13.8, ∞)Figures10(a) and 10(b) compare the frequency utilization rate of the proposed system with that of the traditional AMC system [24], which subjects to different switching criteria. Whenever in channel 1 or channel 2, the proposed system is better than the traditional AMC system. However, the frequency utilization rate decreases with deterioration of the channel. This is because the construction of the handover criterion in this paper is based on the premise of a given BER, and the bandwidth utilization rate is sacrificed in exchange for BER performance.Figure 10
Frequency utilization rate of the different systems. (a) Frequency utilization rate in channel 1. (b)Frequency utilization rate in channel 2.
(a)(b)Figure11 compares the BER performance of the proposed EC OFDM UWAC system based on the CA-SNR switching criterion with single transmission modes 2, 4, and 6 under channel 1. Clearly, the proposed system delivers a good BER performance.Figure 11
BER performance of proposed system and single models.


## 3.2. Experimental Results

To verify the effect of the EC OFDM UWAC system, different channel conditions are obtained through experiments in small pool and big pool, respectively. The size of the small pool is 1 m × 0.5 m × 0.5 m, and the size of the big pool is 25 m × 15 m × 10 m. Figure12 shows the small pool used in the experiment, whose channel impulse is shown in Figure 13, and there are sound-absorbing wedges (shown in Figure 14) around the pool. The laying depth of the transducers in Figure 15 is 0.25 m. The horizontal distance between the transducers is 1 m.Figure 12
Small pool in experiment.Figure 13
Channel impulse of the small pool.Figure 14
Sound-absorbing wedge.Figure 15
Transducers.Figure15 shows transducers for sending and receiving signals whose bandwidths are 8–16 kHz.The highest measured IESNR of the experimental channel in the small pool is 6.98 dB, and the proposed system adopted transmitting models for signal transmission according to the criterion in Table2. The BER of the proposed EC OFDM UWAC system is 0 and the frequency utilization is 0.6658. Experiments using different models are conducted. The BERs of models 1 to 4 are all 0, while that of model 5 is 0.0026 and that of model 6 is 0.0465.The big pool is an anechoic pool and is shown in Figure16, and the channel impulse is shown in Figure 17. The laying depth of the transducers in Figure 16 is 3 m. The horizontal distance between the transmitter and the hydrophone is 11.5 m. The highest measured IESNR of the experimental channel in the small pool is 14.2 dB, and the proposed system adopted transmitting models for signal transmission according to the criterion in Table 2. Under this experimental environment, all transmitting modes BER is 0, including the proposed EC OFDM UWAC system whose frequency utilization reached to 1.3316.Figure 16
Experimental anechoic pool.Figure 17
Channel impulse of the big pool.


## 4. Conclusions

This paper proposes an EC OFDM UWAC system that can used in the transceiver and the full duplex system. Firstly, an OFDM UWAC system that perceives the UWAC environment is proposed, which can change the transmission model according to channel quality. Secondly, the proposed system utilizes the whole received signal for environmental perception, delivering an accurate channel quality assessment for the performance of the system. Thirdly, the proposed system can be applied to duplex, networking scenarios, which will greatly improve the spectrum utilization of the UWA system and achieve efficient information transmission. The EC OFDM UWAC system will play an important role and will have broad application prospects in future intelligent UWAC networking. However, the switching threshold is customized by the researchers according to the environment, which will cause waste of personnel and energy, and the system is not intelligent enough. In future research, artificial intelligence algorithm will be added to the parameter selection of the system, which will further improve the system performance.



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*Source: 1640072-2021-08-10.xml*