Precoding based channel prediction for underwater acoustic OFDM

The life duration of underwater cooperative network has been the hot topic in recent years. And the problem of node energy consuming is the key technology to maintain the energy balance among all nodes. To ensure energy efficiency of some special nodes and obtain a longer lifetime of the underwater cooperative network, this paper focuses on adopting precoding strategy to preprocess the signal at the transmitter and simplify the receiver structure. Meanwhile, it takes into account the presence of Doppler shifts and long feedback transmission delay in an underwater acoustic communication system. Precoding technique is applied based on channel prediction to realize energy saving and improve system performance. Different precoding methods are compared. Simulated results and experimental results show that the proposed scheme has a better performance, and it can provide a simple receiver and realize energy saving for some special nodes in a cooperative communication.


Introduction
Recently, cooperative communication has become a hot topic due to the ability of improving communication performance. In sensor networks, the devices rely on batteries for their operations, so energy efficiency is an important factor to be considered. In Cui et al. (2004), single-antenna node was cooperated with each other in a group and transmitted to another group of single-antenna nodes by using distributed multiple-input multiple-output (MIMO) techniques. Jayaweera (2006) extended the work of Cui et al. (2004) by taking extra training consumption and the impact of the channel path loss exponent on the energy efficiency into account. In Sadek et al. (2009), a source node was transmitted to a destination node with the assistance of relay nodes. In Lai et al. (2014), coalition formation game was proposed in dynamic settings. The common shortage was that they did not take computational complexity into account. For some special nodes, such as cluster-head, due to the additional processing in receiving and retransmitting information, the power consumed in receiving and processing circuitry constitutes a significant portion of the total consumed power. To simplify the receiving unit, ensure energy efficiency of these special nodes and achieve the longer lifetime of communication networks, this paper proposes precoding technique, which preprocesses the signal at transmitter and enhances the system performance.
In this paper, an underwater acoustic orthogonal frequency division multiplexing (OFDM) system with a simple receiver is proposed to realize energy efficiency by using precoding technology at transmitter. Channel prediction based on sparse structure of underwater acoustic channel is used to provide reliable channel state information (CSI) to transmitter. Based on null subcarriers, Doppler shifts are compensated. Different precoding methods are compared. Simulated results and experimental results demonstrate that the proposed system is capable of providing a simple receiver and realizing energy saving for some special nodes in cooperative communications.

Receiver design for reliable CSI
To achieve the reliable CSI, Doppler shifts compensation and a time domain predictor are applied in this paper, and these steps can be done in handshake phase in cooperative communication systems.

Doppler effect estimation
According to Li et al. (2008), the residual Doppler shift can be modeled as carrier frequency offset (CFO) by resampling and can be estimated based on null subcarriers for underwater acoustic OFDM.
A CFO estimate is defined for each OFDM block by finding a selection matrix Θ that picks the frequency domain measurements out of all the K subcarriers. The energy of the null subcarriers is used as the cost function to find the CFO estimate as: where denotes the 2-norm, F is the K × K Fourier translation matrix with the (p, q) entry , (·) H stands for complex conjugate, y is the received signal, and D . CFO estimation can be solved via a one-dimensional search on ε.

A time channel predictor
According to Lin et al. (2015), by exploiting the sparse features of underwater acoustic channel, the channel prediction method only uses a small number of predictors, which brings a lower complexity. Compressed sensing (CS) is used to estimate the channel. In the process of channel estimation by CS, tap selection is done. It means that additive steps for tap selection are not needed. Recursive leastsquares (RLS) are adopted for channel prediction.
The time domain channel estimation of the l-th subcarrier on the m-th frame can be obtained as: is the noise in the time domain.

Precoding design
According to Section 2, the transmitter obtains the reliable CSI in handshake phase, which is the key factor for precoding design. Based on the achieved reliable CSI, the precoding design is provided.

Precoding design based on the linear technologỹ s
An OFDM system with the linear precoding is shown in Fig. 1. The transmitted signal x which is processed by precoding technique can be expressed as x=Fs. The received signal can be expressed as: where F is the precoding matrix, p is the power factor in receiver, H represents the effect of underwater acoustic chan-nel, and v is noise. In order to compensate the influence of the channel and make pHF=I, two criterions are adopted. One is zero-forcing (ZF) criterion (Spencer et al., 2004) and the other is minimize mean square error (MMSE) criterion (Lee and Oh, 2007).

Precoding design based on ZF criterion
According to Horn and Johnson (1990), it achieves that where the power factor p needs to be where R s is the covariance matrix of the signal s.
Precoding design based on the ZF criterion is useful to achieve the complete original signal and simplify the receiver, but the noise which has an effect on the received signal is amplified.

Precoding design based on the MMSE criterion
According to the MMSE criterion, the following equations are achieved.
Based on Lagrange multipliers (Bandemer et al., 2006), the precoding matrix F can be expressed as: where presents the power of the original signal s, presents the power of noise v, eye(N) is the N×N identity matrix, and N is the length of the signal. The power factor p can be expressed as: Compared with the ZF criterion, the MMSE criterion takes into account the effect of noise, which produces a better performance and it is shown clearly in Section 4.

Precoding design based on the nonlinear technology
Precoding design based on nonlinear technology is discussed in this section. It has a better performance than linear technology at the cost of complexity.

Precoding design based on ZF-TH criterion
Precoding based on ZF-TH criterion means that an OF-DM system with Tomlinson-Harashima Precoding (Tomlinson, 1971) mitigates noise by using the ZF criterion at the where Q is an unitary matrix with N×N. R=[r ij ] is an upper triangular matrix in which the main diagonal elements are real. H is the effect of underwater acoustic channel. So The recovered signal at the receiver is expressed as:

Precoding design based on the MMSE-TH criterioñ s
The error between the transmitted signal s and the recovered signal is that The covariance matrix can be expressed as: P, B, and F can be expressed as:

Simulated results
The multipath channel consists of 15 discrete paths, where the inter-arrival time follows an exponential distribution with the mean of 1 ms. Amplitudes are Rayleigh distributed with the average power decreasing exponentially with the delay. The cycle prefix-OFDM signal parameters are as follows. Out of 1024 subcarriers, 96 are null subcarriers with 24 on each edge for band protection and 48 distributed evenly in the middle. The CFO term is randomly generated ε[-∆f/2, ∆f/2].
The data symbols are drawn from a quadrature phase shift keying (QPSK) constellation, and 256 pilot subcarriers are used for channel estimation. A 64-state rate-1/2 convolutional code is used for channel coding. The bit-error-rate (BER) after the Viterbi decoding is used as the performance metric.
In this paper, precoding method is adopted in the transmitter and simple zero forcing equalizer is used in the receiver. The performance of the linear precoding schemes is compared in Fig. 3. It shows that both the ZF precoding method and MMSE precoding method are feasible. They can improve the system performance in an underwater acoustic system with a simple receiver. It also implies that the MMSE precoding method has a better performance than the ZF precoding method, which verifies the discussion.
By varying SNR level, the performance comparison of the nonlinear precoding schemes is shown in Fig. 4. It presents that the ZF-THP method and the MMSE-THP method are useful to have a good performance in an underwater acoustic system with a simple receiver. Meanwhile, it shows that an OFDM system with the MMSE-THP method outperforms the OFDM system with the ZF-THP method.

Experimental pool experiments
This experiment was conducted at the experimental pool in Xiamen University. There were one transmitter and one receiving hydrophone located in an area in the size of 18   m×5 m. They were both located at the depth of 0.8 m below the surface and the distance between them was 6 m. The parameters of OFDM were the same as in the simulations. The estimated channel for one OFDM block is shown in Fig. 5. It can be seen that the channel for the case of 6 m has larger energy.
In the receiver, it can obtain the performance of OFDM signal in the pool. Then the SNR can be estimated. White Gaussian noise is added to the received signal to generate several semi-experimental data sets with different SNRs. Fig. 6 shows the demodulation performance of the semiexperimental data sets with different precoding methods. Table 1 shows the demodulation performance of different pool experimental data sets. They both show that the OF-DM system with a simple receiver has a good performance by adopting precoding at the transmitter. The performance of THP methods is better than that of linear methods.

Shallow water experiments
This experiment was carried out in the shallow water near Xiamen University. System specifications are shown in Table 2. The relative distance of the transmitter and the receiver was about 105 m. The transmitter and the receiver were located at the depth of 3.5 m below the surface. Table 3 shows the results of shallow water experiments. It is obviously shown that the proposed system can produce a good performance and ensure reliable communication by adopting precoding at the transmitter. The performance of THP methods outperforms that of linear methods.

Conclusion
In this paper, an OFDM system with a simple receiver is proposed to realize energy saving for the receiver. The proposed scheme can be used in cooperative communications to ensure energy saving for some special nodes. Precoding method is adopted to improve the performance of the proposed OFDM system and ensure the longer lifetime of an underwater cooperative network. Simulated and experimental results show that the proposed scheme has a good performance, especially with precoding at the transmitter. By adopting this scheme, it can realize energy saving for some special nodes in an underwater cooperative communication.