# Time Reversal Aided Bidirectional OFDM Underwater Cooperative Communication Algorithm with the Same Frequency Transmission

Authors: Lingling Zhang; Jianguo Huang; Chengkai Tang; Houbing Song
Journal: Journal of Sensors
 (2017)

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## Abstract

In underwater acoustic channel, signal transmission may experience significant latency and attenuation that would degrade the performance of underwater communication. The cooperative communication technique can solve it but the spectrum efficiency is lower than traditional underwater communication. So we proposed a time reversal aided bidirectional OFDM underwater cooperative communication algorithm. The algorithm allows all underwater sensor nodes to share the same uplink and downlink frequency simultaneously to improve the spectrum efficiency. Since the same frequency transmission would produce larger intersymbol interference, we adopted the time reversal method to degrade the multipath interference at first; then we utilized the self-information cancelation module to remove the self-signal of OFDM block because it is known for sensor nodes. In the simulation part, we compare our proposed algorithm with the existing underwater cooperative transmission algorithms in respect of bit error ratio, transmission rate, and computation. The results show that our proposed algorithm has double spectrum efficiency under the same bit error ratio and has the higher transmission rate than the other underwater communication methods.


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## Body

## 1. Introduction

Underwater communication, as one of the most challenging wireless communications, is of great difference compared to terrestrial wireless communication in system design. In underwater acoustic environment, the serious signal attenuation and severe reflection and diffusion result in short communication distance [1] and slow data rate [2]. Early underwater communications rely mainly on the increase of transmit power at underwater node to achieve long range signal transmission, but the requirement of large-scale power amplification equipment in this case limited the application in underwater mobile node [3]. With the increasing exploitation of marine resources, underwater communication is becoming more and more important. The underwater communication rate and the underwater communication distance seriously restrain the development of marine resources [4]. How to improve the underwater communication rate and increase underwater communication distance is the key problems that need to be solved in underwater communication nowadays.An underwater communication system based on time domain channel equalization is presented in [5], which migrate the multipath induced intersymbol interference through adaptive equalization of time domain samples. To decrease the complexity for equalization in large latency underwater acoustic channel, frequency domain channel equalization is presented in [6], but both of these are insufficient to avoid the short range issue owing to the serious attenuation. To this end, underwater cooperative communication method is proliferated to extend the communication distance, in which data hops from the source to destination through several relays. However, it leads to more serious multipath effect, which results in high bit error rate. An underwater acoustic cooperative communication based on LDPC coding proposed in [7] can decrease the bit error rate, but with high complexity. An underwater acoustic cooperative communication based on frequency domain multiple access is supposed to increase the data rate by allowing several sensors to transmit signals simultaneously, but since the underwater acoustic channel is bandwidth limited, the performance is unsatisfactory [8]. Most underwater acoustic cooperative communications adopt time domain multiple access, which allows only one task in each time slot; therefore it leads to poor spectrum efficiency [9]. To this end, this paper presents a new underwater acoustic cooperative communication method based on time reversal and self-interference suppression in the same frequency. In this network, cooperative nodes share the common uplink and downlink frequency and transmit to the central base station simultaneously, to realize spectrum resource multiplexing. Moreover, the time reversal technology is adopted at the base station to migrate multipath interference. Furthermore, using the acknowledged information of self-signal, self-interference is suppressed in the forwarded signal from the base station. In this network, the spatial processing requirement of the cooperative nodes is quite low; therefore, the size can be compact. In addition, OFDM modulation is adopted to decrease the complexity of channel equalization and frequency converter. This structure is available to current underwater detection and communication network.


## 2. Bidirectional Underwater Communication System Model

The complex underwater environment causes kinds of interferences in the communication channels, most of which attributes to multipath interference and signal attenuation. The structure of the self-interference suppressed time reversal cooperative transmission system is shown in Figure1.Figure 1
Underwater cooperative transmission system structure.Assume the distance between these two sensor nodes is quite far; then because of the severe attenuation over long range underwater acoustic channel, the base station is required for relaying to enable the bidirectional transmission [10]. In Figure 1, taking into account the fact that the size of the sensor nodes is often limited, it supposes only one transmitter and receiver elements are available at each node. As the core of this cooperative network, there are NR pairs of transmitter and receiver elements at the Underwater Base Station, with each pair locating at the same position. Group the transmitted information of each sensor node to blocks of length Na, and denote the nbth information block of the ntth sensor node which is(1)antnb=antnb,0,antnb,1,…,antnb,Na-1T,where antnb,0∈0,1 and j=0,1,…,Na-1. Encode the information block with coding rate Rc; then we could get the encoded bits with block length N=Na/Rc as(2)bntnb=bntnb,0,bntnb,1,…,bntnb,N-1T.In order to avoid the burst error and decrease the correlation between adjacent bits, interleave the encoded bits as(3)cntnb=cntnb,0,cntnb,1,…,cntnb,N-1T.Conversing these bits from serial to parallel with lengthQ=log2⁡M, we can obtain Kd vectors, and (3) could be represented as(4)cntnb=cnt,0Tnb,cnt,1Tnb,…,cnt,Kd-1TnbT,where Kd=N/Q, and kdkd=0,1,…,Kd-1th vector is(5)cnt,kdnb=cntnb,kdQ,cntnb,kdQ+1,…,cntnb,kdQ+Q-1T.Map this vector according to Mary order PSK asmntnb,kd=αm∈S, with the alphabet(6)S=α0,α1,…,αM-1,and the corresponding vector pattern is cm=cm,0,cm,1,…,cm,Q-1T. Therefore, the transmitted symbol within the nbth block of the ntth sensor node is(7)mntnb=mntnb,0,mntnb,1,…,mntnb,Kd-1T.Multiplexing these symbols to orthogonal frequency bins, the obtained OFDM signal is represented as(8)xntt=R∑nb∑kdntnb,kej2πkΔftgntt-nbTbej2πf0t=R∑nb∑k∈Θantdntnb,kej2πkΔftgntt-nbTbej2πf0t,where k denotes the index of the subcarrier, with the range k∈0,K-1, K denotes the total number of subcarriers, Δf denotes the subcarrier spacing, f0 denotes the starting frequency of the uplink transmission, and gt denotes the pulse shaping. Aiming at measuring the noise level or preventing frequency leakage, null subcarriers of the ntth user node in the nbth block are assigned as dntnb,k=0 for k∈Θnullnt. Denote Θant as the active subcarrier set of the ntth user node; we have Θant∪Θnullnt=0,K-1 and Θant∩Θnullnt=∅. The active subcarriers are categorized into Kp pilot subcarriers and Kd data subcarriers, with dntnb,k=mntnb,kd if k∈Θdatant, while dntnb,k=pntnb,kd if k∈Θpilotnt. To avoid interference, set Θpilotnt∪Θdatant=Θant and Θpilotnt∩Θdatant=∅.At thenrth receiver element of the base station, it collects signals from all user nodes as(9)ynrt=∑nt∑phpnr,ntxntt-τp+ξnrt,where p denotes the path index, with hp and τp denoting the amplitude and time delay of the corresponding path, respectively. For description brevity, all time delay has been mapped to grid, inserting some zeros in hpnr,nt artificially to ensure the delay of the pth path of any arbitrary transceiver pair to be τp. The received ocean noise at the nrth element of the base station denoted as ξnrt is assumed to be additive.


## 3. Time-Reverse-and-Forward Module

Assume the amplitude and time delay of the underwater acoustic channel are constant and reciprocal in a certain interval [11–13]; that is to say, the downlink from the nrth element of the base station to the ntth user node is assumed to be the same as the uplink from the ntth user node to the nrth element of the base station. On this basis, to reduce the processing complexity at the base station and improve transmission efficiency, rather than demodulating the received signal at the base station, it convolutes the received signal with time reversed channel response and forwards the mixture signal to all user nodes. In this case, the signal arrived at the ntth user node is(10)qntt=∑nt∑phpnr,ntznrt-τp+wntt.Since the frequency is shared by all user nodes, the mixture signalznrt includes the information from all user nodes. Therefore, the received signal at each user node includes not only information from other user nodes, but also self-information backpropagation, in addition to the serious multipath effect, which rises great challenge to bidirectional cooperative communication. Limited by the size of the user nodes, only single transmitter element and receiver element are deployed; thus it is hard to eliminate the multipath interference and self-information interference with single channel.In a two-user nodes scenario as shown in Figure1, we aim to solve the multipath interference and self-information interference, adopt the time reversal processing at the base station, and shift the frequency to downlink frequency as(11)znrt=ynrt⊗hnr,1-t⊗hnr,2-tej2πf2-f1t,where f2 denotes the central downlink frequency and f1=f0+K/2∗Δf denotes the central uplink frequency. Uplink and downlink transmit simultaneously with this frequency division scheme, rather than partitioning different frequency to each user node, since it is easy to expand this cooperative transmission to more user nodes, even though the bandwidth of underwater acoustic channels is quite limited.In the bidirectional cooperative transmission, the equivalent channel filter experienced by the signal transmitted by user 1 through thenrth element of the base station to itself is described as(12)v11nr=hnr,1t⊗hnr,1-t⊗hnr,2-t⊗hnr,1t.The equivalent channel filter experienced by the signal transmitted by user 1 through thenrth element of the base station to user 2 is described as(13)v12nr=hnr,1t⊗hnr,1-t⊗hnr,2-t⊗hnr,2t.The equivalent channel filter experienced by the signal transmitted by user 2 through thenrth element of the base station to user 1 is described as(14)v21nr=hnr,2t⊗hnr,1-t⊗hnr,2-t⊗hnr,1t.The equivalent channel filter experienced by the signal transmitted by user 2 through thenrth element of the base station to itself is described as(15)v22nr=hnr,2t⊗hnr,1-t⊗hnr,2-t⊗hnr,2t.Therefore, the received signal at user node 1 is written as(16)q1t=∑nrx2tej2πf2-f1t⊗v21nrt+∑nrx1tej2πf2-f1t⊗v11nrt+w1′t=x2tej2πf2-f1t⊗v21t︸q1st+x1tej2πf2-f1t⊗v11t︸q1it+w1′t︸q1nt.Likewise, the received signal at user node 2 is written as(17)q2t=x1tej2πf2-f1t⊗v12t︸q2st+x2tej2πf2-f1t⊗v22t︸q2it+w2′t︸q2nt,where qnts denotes the desirable signal from the other user node to the ntth user node, while qnti denotes the unwanted interference from itself. According to the spatial reciprocity of the channel, qnts is temporal and spatial focusing of the desirable signal, and the equivalent channel is represented as(18)v11t=∑nrv11nrt,v12t=∑nrv12nrt,v21t=∑nrv21nrt,v22t=∑nrv22nrt.According to the underwater physics, the equivalent channel is aq-function, and it approaches a Dirac delta function in ideal case.


## 4. Self-Interference Cancelation Method

At the receiver end of thentth user node, downshift the frequency to baseband firstly, and then isolate the received signal from its self-information interference, since self-signal is the main contribution in the interference. The self-information interference cancelation method is shown in Figure 2.Figure 2
Underwater cooperative transmission system structure.In ideal case, after self-information cancelation, the residue signalrntt is proportion to the transmitted signal from the other user node. Therefore, the estimation of self-information interference is represented as(19)q^ntnt=∑icixntt-τ-i,where τ denotes the delay of the channel filter, and the coefficients of the cancelation are updated by(20)cin+1=cin+ηe∗nxntt-τ-i,where η denotes the update step, and the residue signal is represented as(21)rntt=qntt-q^ntnt.Transform the residue signal into frequency domain; then we have(22)Rnt=Vnt,nt′dnt′+Wnt.According to the linear minimum mean square error criterion, the desired transmitted symbol estimated at the user node nt is denoted as(23)d^nt′=d¯nt′+CRntdnt′CRntRnt-1Rnt-Vnt,nt′dnt′,where d¯nt′ denotes the expectation of the transmitted symbols, R¯nt denotes the expectation of the received symbols, CRntdnt′ denotes the covariance matrix of the transmitted symbols and received symbols as(24)CRntdnt′=Ednt′-d¯nt′Rnt-R¯ntH=Φnt′Vnt,nt′H,and CRntRnt denotes the autocovariance of the received symbols as(25)CRntRnt=Vnt,nt′Φnt′Vnt,nt′H+ση2,where Φnt′ denotes the autocovariance of the transmitted symbols(26)Φnt′=Ednt′-d¯nt′dnt′-d¯nt′H.Suppose the transmitted symbols on different frequency bins are dependent on each other; thus(27)Φnt′=diagσnt′20,σnt′21,…,σnt′2K-1.At the beginning, since no prior information is available, the estimation symbols are represented as(28)d^nt′=Vnt,nt′HVnt,nt′Vnt,nt′H+ση2I-1Rnt.


## 5. Simulation and Analysis

According to the statistical analysis of lake channel, a sparse and spatial reciprocal channel is adopted to simulate the underwater acoustic channel [14]. The cooperative network includes two user nodes and one base station. Each user node deploys single transmitter and receiver. The base station consists of 16 transmitters and receivers. The channel between each user node to any element of the base station is independent of other and considers each as a six paths’ random walk process with mean delay interval of 3 ms. The amplitude is constant with each OFDM block and follows Gaussian distribution with initial exponent power delay profile. At the transmitter of each user node, the data is encoded by (3,[57]) convolution encoder and randomly interleaved; then QPSK constellation is mapped to form blocks of OFDM symbols.


### 5.1. Channel Interference Analysis

To evaluate the channel interference suppression performance, the time evolution of the equivalent channel filter from the source user node to the end user node in time-reverse-and-forward underwater acoustic cooperative communication is shown in Figure3. For comparison, under the same channel condition, the time evolution of the equivalent channel filter from the source user node to the end user node in amplify-and-forward underwater acoustic cooperative communication is shown in Figure 4. From Figures 3 and 4, we can see that the channel is compressed in time-reverse-and-forward underwater acoustic cooperative communication but dispersed in amplify-and-forward underwater acoustic cooperative communication. Therefore, spatial diversity gain is easier to collect in time-reverse-and-forward underwater acoustic cooperative communication.Figure 3
The equivalent channel filter in time-reverse-and-forward underwater acoustic cooperative communication.
(a)
v 11 (b)
v 12 (c)
v 21 (d)
v 22Figure 4
The equivalent channel filter in amplify-and-forward underwater acoustic cooperative communication.
(a)
v 11 (b)
v 12 (c)
v 21 (d)
v 22


### 5.2. Bit Error Ratio Performance

In the bidirectional cooperative communication, spatial focusing is achieved by time-reverse-and-forward for the desired signal transmission direction. However, since the equivalent channel is aq-function, rather than an ideal Dirac delta function, the communication performance degrades due to the self-information interference [16]. Therefore, the bit error ratio performance of time-reverse-and-forward underwater acoustic cooperative communication with respect to different numbers of taps of additional self-interference cancelation is shown in Figure 5. From Figure 5, it can be seen that, with small numbers of taps, the bit error ratio is still large, since the residue self-information interference cannot be well eliminated. With the increasing of the number of taps, the bit error ratio is decreasing and reaches 10-3 with 11 taps of self-interference cancelation while SNR is at 19 dB. When the number of taps is over 13, the performance reaches saturation.Figure 5
Bit error ratio with respect to different numbers of taps.Comparison of the proposed time-reverse-and-forward underwater acoustic cooperative communication method to the existing underwater acoustic cooperative communication method is shown in Figure6. From Figure 6, it can be seen that the same frequency bidirectional amplify-and-forward underwater cooperative method applied in [10] has poor performance. It requires 25 dB to keep the bit error ratio below 10-3. That is attribute to the cochannel interference and severe multipath as shown in Figure 4. The frequency division cooperative transmission method applied in [8] requires 18 dB to keep the bit error ratio below 10-3. Because of the complexity of underwater acoustic channel and the mutual interference to adjacent frequency bands, the performance is still unsatisfactory. Both the time division cooperative transmission method applied in [9] and MIMO signal processing applied in [6] show superiority in the bit error ratio performance that the bit error ratio reaches 10-3 at about 17 dB. The performance of the proposed time-reverse-and-forward underwater acoustic cooperative communication method shows a little more progress, since multipath interference is compressed through time-reverse processing, while residue self-information interference is eliminated by additional cancelation. Moreover, the other virtue reflects in the simultaneous exchange of information between those two user nodes.Figure 6
Bit error ratio over sparse channel with respect to different signal to noise ratio.Sparsity of underwater acoustic channel is often large in deep sea and calm sea state, while it may be weaker in coastal waters or rough sea state. To this end, a more complex channel is adopted to validate the performance of the proposed time-reverse-and-forward underwater acoustic cooperative communication method. The maximum time delay is 60 ms, with random numbers of paths within 30 to 60, and the amplitude follows Rayleigh distribution. The resulting bit error ratio is shown in Figure7. From Figure 7, it can be seen that all the existing cooperative communication methods show 2-3 dB degradation compared to that in Figure 6, since the multipath effect is more severe in complex channel. The proposed time-reverse-and-forward underwater acoustic cooperative communication method shows about 0.5 dB degradation compared to that in Figure 6, because of the adaption of time-reverse processing to different channel condition.Figure 7
Bit error ratio over complex channel with respect to different signal to noise ratio.


### 5.3. Transmission Rate Analysis

Signal transmission over underwater acoustic channel suffers from the frequency dependant attenuation. Thus, the bandwidth of underwater acoustic channel is severely limited. Therefore, how to utilize the limited bandwidth of the underwater acoustic channel efficiently to provide high transmission rate plays a key role in design of the cooperative communication. Comparison of the transmission rate of the proposed time-reverse-and-forward underwater acoustic cooperative communication method to that of the existing cooperative method is shown in Table1.Table 1
Comparison of transmission rate.
SNR (dB) The proposed method TDMA FDMA MIMO 5 1.7 0.85 0.85 0.87 10 1.94 0.968 0.965 0.968 15 1.992 0.997 0.996 0.997 20 1.9996 0.9998 0.9995 0.9998In Table1, it can be seen that when the signal to noise ratio is over 15 dB, the transmission rate of the proposed time-reverse-and-forward bidirectional underwater acoustic cooperative communication method is about two times of that of the existing underwater acoustic cooperative communication methods. That is credited to the simultaneous bidirectional transmission and the efficient self-information interference cancelation.


## 5.1. Channel Interference Analysis

To evaluate the channel interference suppression performance, the time evolution of the equivalent channel filter from the source user node to the end user node in time-reverse-and-forward underwater acoustic cooperative communication is shown in Figure3. For comparison, under the same channel condition, the time evolution of the equivalent channel filter from the source user node to the end user node in amplify-and-forward underwater acoustic cooperative communication is shown in Figure 4. From Figures 3 and 4, we can see that the channel is compressed in time-reverse-and-forward underwater acoustic cooperative communication but dispersed in amplify-and-forward underwater acoustic cooperative communication. Therefore, spatial diversity gain is easier to collect in time-reverse-and-forward underwater acoustic cooperative communication.Figure 3
The equivalent channel filter in time-reverse-and-forward underwater acoustic cooperative communication.
(a)
v 11 (b)
v 12 (c)
v 21 (d)
v 22Figure 4
The equivalent channel filter in amplify-and-forward underwater acoustic cooperative communication.
(a)
v 11 (b)
v 12 (c)
v 21 (d)
v 22


## 5.2. Bit Error Ratio Performance

In the bidirectional cooperative communication, spatial focusing is achieved by time-reverse-and-forward for the desired signal transmission direction. However, since the equivalent channel is aq-function, rather than an ideal Dirac delta function, the communication performance degrades due to the self-information interference [16]. Therefore, the bit error ratio performance of time-reverse-and-forward underwater acoustic cooperative communication with respect to different numbers of taps of additional self-interference cancelation is shown in Figure 5. From Figure 5, it can be seen that, with small numbers of taps, the bit error ratio is still large, since the residue self-information interference cannot be well eliminated. With the increasing of the number of taps, the bit error ratio is decreasing and reaches 10-3 with 11 taps of self-interference cancelation while SNR is at 19 dB. When the number of taps is over 13, the performance reaches saturation.Figure 5
Bit error ratio with respect to different numbers of taps.Comparison of the proposed time-reverse-and-forward underwater acoustic cooperative communication method to the existing underwater acoustic cooperative communication method is shown in Figure6. From Figure 6, it can be seen that the same frequency bidirectional amplify-and-forward underwater cooperative method applied in [10] has poor performance. It requires 25 dB to keep the bit error ratio below 10-3. That is attribute to the cochannel interference and severe multipath as shown in Figure 4. The frequency division cooperative transmission method applied in [8] requires 18 dB to keep the bit error ratio below 10-3. Because of the complexity of underwater acoustic channel and the mutual interference to adjacent frequency bands, the performance is still unsatisfactory. Both the time division cooperative transmission method applied in [9] and MIMO signal processing applied in [6] show superiority in the bit error ratio performance that the bit error ratio reaches 10-3 at about 17 dB. The performance of the proposed time-reverse-and-forward underwater acoustic cooperative communication method shows a little more progress, since multipath interference is compressed through time-reverse processing, while residue self-information interference is eliminated by additional cancelation. Moreover, the other virtue reflects in the simultaneous exchange of information between those two user nodes.Figure 6
Bit error ratio over sparse channel with respect to different signal to noise ratio.Sparsity of underwater acoustic channel is often large in deep sea and calm sea state, while it may be weaker in coastal waters or rough sea state. To this end, a more complex channel is adopted to validate the performance of the proposed time-reverse-and-forward underwater acoustic cooperative communication method. The maximum time delay is 60 ms, with random numbers of paths within 30 to 60, and the amplitude follows Rayleigh distribution. The resulting bit error ratio is shown in Figure7. From Figure 7, it can be seen that all the existing cooperative communication methods show 2-3 dB degradation compared to that in Figure 6, since the multipath effect is more severe in complex channel. The proposed time-reverse-and-forward underwater acoustic cooperative communication method shows about 0.5 dB degradation compared to that in Figure 6, because of the adaption of time-reverse processing to different channel condition.Figure 7
Bit error ratio over complex channel with respect to different signal to noise ratio.


## 5.3. Transmission Rate Analysis

Signal transmission over underwater acoustic channel suffers from the frequency dependant attenuation. Thus, the bandwidth of underwater acoustic channel is severely limited. Therefore, how to utilize the limited bandwidth of the underwater acoustic channel efficiently to provide high transmission rate plays a key role in design of the cooperative communication. Comparison of the transmission rate of the proposed time-reverse-and-forward underwater acoustic cooperative communication method to that of the existing cooperative method is shown in Table1.Table 1
Comparison of transmission rate.
SNR (dB) The proposed method TDMA FDMA MIMO 5 1.7 0.85 0.85 0.87 10 1.94 0.968 0.965 0.968 15 1.992 0.997 0.996 0.997 20 1.9996 0.9998 0.9995 0.9998In Table1, it can be seen that when the signal to noise ratio is over 15 dB, the transmission rate of the proposed time-reverse-and-forward bidirectional underwater acoustic cooperative communication method is about two times of that of the existing underwater acoustic cooperative communication methods. That is credited to the simultaneous bidirectional transmission and the efficient self-information interference cancelation.


## 6. Conclusion

Communications over underwater acoustic channel suffer from the strong multipath interference and great attenuation; thus it is hard to realize long range transmission. Underwater cooperative transmission has been regarded as the optimal solution. However, only single transmission is allowed in existing underwater acoustic cooperative transmission that limited the transmission rate. To solve this problem, a time-reverse-and-forward bidirectional underwater acoustic cooperative communication based on OFDM is investigated. Common uplink and downlink frequency bands are shared by all user nodes, and the received signal at the base station is time-reverse-and-forward to all user nodes without separation. Moreover, self-signal backpropagation is isolated at the received end to eliminate the self-information interference. Comparison from the respect of channel interference, bit error ratio, and transmission rate reveal that the proposed method is superior to the existing underwater cooperative transmission method. Specifically, the transmission rate of the proposed method is near double of the existing method when the required bit error ratio is no more than10-3 and the signal to noise ratio is over 16.5 dB.



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