Research on underwater acoustic channel estimation and temperature factors based on FBMC

GUO Yin-jing， LIU Zhen， YANG Wen-jian， NIU Chen-xi， LIU Hui

(1. College of Electronic Information Engineering, Shandong University of Science and Technology, Qingdao 266590， China；2. Qingdao Zhihai Muyang Technology Co., Ltd., Qingdao 266590, China)

Abstract： The complexity of underwater environment poses a challenge to underwater acoustic communication. In marine environment, different temperatures, depths and salinities would affect the performance of acoustic communication. The analysis of the underwater acoustic channel under the influence of temperature factors provides a reference for further study of the underwater acoustic channel estimation problem based on filter bank multi-carrier(FBMC). The FBMC based offset quadrature amplitude modulation(OQAM) technology(FBMC/OQAM) was introduced into the underwater acoustic communication. Based on FBMC, the underwater acoustic channel estimation technology was studied. By changing the pilot structure to adapt to the complex and variable underwater acoustic channel, the iterative method was used to obtain the channel information with higher accuracy and further improve the performance of channel estimation. Theoretical analysis and simulation results show that iterative channel estimation algorithm based on the new interference approximation method (IAM) pilot proposed in this paper has better performance in underwater acoustic channel．

Key words： filter bank multi-carrier (FBMC); underwater acoustic channel estimation; temperature; pilot; interference approximation method (IAM)

0 Introduction

Ocean area accounts for 71% of the Earth’s total area, and marine resources are of great significance to human development. At present, because orthogonal frequency division multiplexing(OFDM) based on cyclic prefix (CP-OFDM) has features such as robustness to multipath effects and high spectral efficiency, it is adopted in underwater acoustic communication. Inter-symbol interference (ISI) and inter-carrier interference (ICI) caused by cyclic prefix in OFDM will affect the communication system. The fifth generation cellular radio (5G) proposes to apply filter bank multi-carrier (FBMC) technology to wireless communication system[1-2]. The prototype filters of the FBMC/offset quadrature amplitude modulation (OQAM) system include a raised cosine filter, a PHYDYAS filter[3], an isotropic orthogonal transform algorithm (IOTA) filter[4]and so on. Because such prototype filters could reduce side lobes, FBMC/OQAM can alleviate ISI and ICI issues to provide higher transmission rates without guard intervals or cyclic prefixes unlike OFDM. Studies have shown that the application of FBMC/OQAM modulation scheme can outperform CP-OFDM in terms of bit error rate (BER) and spectral efficiency[5]. The influence of underwater acoustic communication technology on underwater positioning and navigation is also irreplaceable. It is a hot research topic to optimize the channel estimation technology to achieve high speed and reliability of underwater communication.

Like other communication systems, channel estimation is critical for the FBMC/OQAM system to recover transmitted data at the receiver. Since the FBMC system only satisfies the real number field orthogonality, many channel estimation methods available for OFDM systems cannot be directly applied to the FBMC/OQAM system. This means that in FBMC/OQAM transmission, real-valued data will be subject to inherent interference from imaginary-valued data[6]. Aiming at the interference of imaginary part, researches have proposed some channel estimation methods based on FBMC system. According to different interference mechanisms, these pilot-assisted channel estimation methods can be divided into three categories: the first method is based on interference cancellation. The pilot structure is designed at the transmitter, so that the inherent interference does not affect the pilot position, and the conventional channel estimation method can be directly used at the receiver, such as auxiliary pilot (AP)[7], code auxiliary pilot method (CAP)[8]and discrete fourier transformation (DFT)-based FBMC system channel estimation method[9]. The interference cancellation method achieves better channel tracking performance while reducing spectral efficiency or increasing computational complexity[6]. The second method is based on the interference approximation method (IAM), for example, IAM-real (IAM-R)[10]whose pilot value is a real value of ±1, so that the interference of the pilot symbols from the first-order neighbors contributes to channel estimation. IAM-imaginary (IAM-I) is similar to IAM-R, with an intermediate pilot element of ±j. IAM-complex (IAM-C) is an improved method of IAM-R with an intermediate pilot element of ±1 or ±j[11]. To further improve performance, an extended version of IAM-C (called as EIAM-C) is proposed, with two pilot values around the pilot sequence being ±1 or ±j[12]. The IAM can maximize the effect of intrinsic interference on the channel and realize channel estimation of the FBMC/OQAM system. The third method is the channel estimation method based on interference avoidance. The channel frequency domain response is derived mainly by computational techniques or filtering, such as paired pilot method (POP). The advantage is that the whole system is not inherently designed. The interference calculation cancels out the inherent interference of the system in terms of operation. The disadvantage is that the POP scheme needs to be determined by the inverse equalizer, which leads to further errors, such as noise enhancement[13].

In a complex marine environment, the speed of sound in water depends on the depth, temperature and salinity of the seawater[14]. Based on the FBMC/OQAM system, this paper conducts a comprehensive study on underwater temperature factors and underwater acoustic channel estimation techniques. On the basis of IAM, the IAM pilot is improved. The channel estimation accuracy is improved by multiple iterations, and its performance is verified by simulation.

1 FBMC system model

1.1 Bastic theory of FBMC/OQAM system

The modulation and demodulation block diagram of the FBMC/OQAM system is shown in Fig.1, whereMindicates the number of subcarriers,am,nrepresents then-th OQAM symbol of them-th carrier, andm∈{1,2,…,M-1}. The steps of obtaining OQAM data are as follows: firstly, the transmission bit stream pass through the quadrature amplitude modulation (QAM) to obtain a complex symbol; secondly, the real number symbols are obtained by the real part and the imaginary part of the complex symbol; lastly, these data are transmitted by the virtual real part misalignment half symbol period.g(k) is a real symmetric prototype filter with length ofL. The data symbolam,nis firstly multiplied the phase factor ejπ(m+n)/2to keep the real field orthogonal between the subcarrier and the FBMC symbol. Then, all data is modulated by inverse fast fourier transform (IFFT) onto the subcarriers, and added together after passing the prototype filter outputs. Lastly, transmit over the channel. Similarly, in order to recover the transmitted data, the received data is demodulated by a filter combined Fourier transform, and the signal on the subcarrier is converted into a complex signal by OQAM post processing.

Fig.1 FBMC/OQAM system block diagram

According to the system model, the baseband transmission signals(k) of the FBMC/OQAM system can be expressed as

(1)

where the position ofam,nis represented by a time frequency point (TFP) (m,n);gm,n(k) repressents the subcarrier basis function at (m,n), and the expression is

(2)

(3)

According to the definition of the ambiguity function, the orthogonality condition of the FBMC/OQAM system can be expressed as

(4)

(5)

It can be seen from Eq.(5) that if you want to recover the original signal, you need to perform the real part operation to eliminate the imaginary part interference.

1.2 Temperature and underwater acoustic communication

Changes in the marine environment will affect the performance of underwater acoustic communications. This section examines the impact of changes in water temperature on communications. The transmission of sound in the ocean will be affected by the physical and chemical properties of seawater and the sound will travel the sea through many paths. The specific path of propagation depends on the sound velocity structure in the water and the location of the transmitter and receiver[14]. Sound speedcis a function of temperatureT, depthz(or pressure) and seawater salinityS[16]. The speed of sound (units of m/s) in a shallow water channel can be expressed as

c=1 412+3.21T+1.19S+0.016 7z.

(6)

Transmission loss (Ltr) is defined as the cumulative decrease in sound intensity when sound waves propagate outward from the source. The acoustic signal in shallow water propagates within a cylinder bounded by a surface of water and seabed, forming a cylindrical diffusion. The transmission loss caused by cylindrical diffusion and absorption can be expressed as

Ltr=10logr+αr×10-3,

(7)

whereαis the absorption coefficient (dB/km) andris transmission distance (m). Due to the presence of trace amounts of boric acid (B/(OH)3) and magnesium sulfate (MgSO4) in the ocean, the transmission of sound waves in the ocean is mainly attenuated by viscous absorption (viscosity can be considered as the flow resistance of the fluid) and ion relaxation effects[17]. The expression of the absorption coefficientαis[1,18-19]

(8)

wheref1represents the relaxation frequency of B/(OH)3, kHz, and the expression is

(9)

whereSis salinity, 1/1 000;Tis temperature, ℃;f2represents the relaxation frequency of MgSO4, kHz, and the expression is

(10)

A1represents the B/(OH)3component in seawater and it can be expressed as

(11)

wherePHrepresents the PH of water andcis the speed of sound;P1represents the depth pressure to which the B/(OH)3component in seawater is subjected, and it can be expressed as

P1=1;

(12)

A2represents the MgSO4component in seawater and it can be expressed as

(13)

P2represents the depth pressure of MgSO4component in seawater and it can be expressed as

P2=1-1.37×10-4z+6.2×10-9z2;

(14)

A3represents the pure water (viscosity) component in seawater, and its expression is

(15)

andP3indicates the pressure to which the pure water (viscosity) component is subjected,

P3=1-3.83×10-5z+4.9×10-10z2.

(16)

The traditional absorption coefficient model is only a function of frequency, such as the Thorp model. The absorption coefficient model used in this paper includes environmental factors such as temperature, salinity, pH value and water depth. Due to this paper studies the relationship between temperature factor and underwater acoustic communication, other underwater environmental factors are limited: salinity is set to the global observation average of 35 ppt, depth is 20 m,PH=8, and the absorption coefficient can be expressed asα(T,f). Then the transmission loss in the shallow water area is expressed as

Ltr(r,T,f)=10logr+α(T,f)r×10-3.

(17)

The sound velocity curve and absorption coefficient will be affected by temperature changes, which will actually change transmission loss and BER. In the research of underwater acoustic channel estimation technology, the emphasis is on reducing the BER and improving the performance of underwater acoustic communication.

2 Pilot-based underwater acoustic channel estimation technique for FBMC/OQAM systems

2.1 Traditional interference approximate channel estimation algorithm

Suppose the channel of each subcarrier is a flat channel,η(k) is an additive white Gaussian noise with a mean of zero, so the received signal can be expressed as

(18)

ηm0,n0, (m=m0+p,n=n0+q).

(19)

(20)

(21)

wherecm0,n0is the equivalent pilot data transmitted at the time-frequency grid point (m0,n0). When the transmitted pilot symbolam0,n0and the neighbor rangeΩm0,n0are known, the channel frequency domain response is estimated at (m0,n0),

(22)

It can be seen from Eq.(22) that if the accuracy of the channel estimation value is improved, the second term of the interference term on the right side of Eq.(22) is operated to minimize the interference of the channel estimation.

2.2 Improved IAM pilot channel estimation

From the above analysis, the interference term is the product of the symbols around the pilot and the internal product of the subcarrier basis function corresponding to the TFP. And the inner product of the prototype filter function called as the time-frequency offset is the interference coefficient[13]. The interference weight coefficient matrix is generally expressed as

(23)

The expression of interference weight coefficient is shown in Eq.(24). This paper takesβ=0.323 9,γ=0.566 4,δ=0.205 8.

(24)

The transmission lossLtrin underwater acoustic communication has been obtained in the previous section. When the distance and frequency of the receiving end are fixed, the power of the received signalPris

(25)

wherePtrepresents the power of the transmitted signal.The core principle of IAM channel estimation is to increase the equivalent pilot power and reduce the impact of noise on channel estimation. Guided by the idea of maximizing the equivalent pilot power, leta1be the amplitude of the pilot in an ideal environment, then the amplitude of the pilot in underwater acoustic communication can be expressed as

(26)

Assuming that the transmission signal power is constant, the smaller the transmission loss caused by temperature, the better the effect of IAM channel estimation. Therefore, this paper proposes a new pilot structure to improve the impact of transmission loss on channel estimation.

2.2.1 New IAM pilot structure design

In the past channel estimation studies based on the FBMC system, the channels used were all maritime wireless channels. In this paper, the FBMC/OQAM channel estimation method with different pilot structure is simulated in the underwater acoustic channel. It is found that the channel estimation performance by introducing complex structure pilot sequences is better than the traditional IAM-C and EIAM-C schemes. The pilot structure is designed according to Eqs.(23)-(24).

In the pilot structure shown in Fig.2, when the subcarrierm≤3, the pilot data is 0. When the subcarrierm∈{4,5,…,M-1} is in the middle position, take the pilot sequence [1-j j -1+j -j] as a cyclic sequence, and according to the value of the intermediate pilot sequence, discuss the power of the equivalent pilot data in the structure. When the intermediate pilot data is ±1∓j, the number of subcarriers is odd, and the pilot sequence values on both sides are 0. At this time, the pilots of the left and right columns have an equivalent pilot power, that isP1=a2|-1+j+2β|2=3.186 3a2. It is worth noting that atm=5, the equivalent pilot power is 3.088 3a2, which is approximately equal toP1. When the subcarrier is in the even position, the intermediate pilot sequence is ±j, the pilot sequences on both sides are placed at ∓j, the equivalent pilot power isP2=a2|1+2β-2jβ|2=2.415 3a2. Different from the EIAM-C pilot structure, the proposed pilot data of the left and right sides of the new IAM pilot structure are the same, so the interference weight coefficientγdoes not contribute to the equivalent pilot power. The new IAM pilot structure has an equivalent pilot power ofP=(P1+P2)/2=2.800 7a2. By comparison analysis, the equivalent pilot power fluctuates between IAM-C and EIAM-C.

Fig.2 New IAM pilot structure

2.2.2 Iterative based IAM pilot channel estimation

In order to further improve the estimation accuracy, the IAM pilot structure proposed in this paper is iteratively operated, and the estimation error is reduced by reconstructing the equivalent pilot. The steps are as follows:

Step 1：Demodulate the pilot symbols received at the receiver to obtain an equivalent pilot;

Step 5： Set the number of iterations in advance and repeat Step 3 and Step 4 to get a more accurate channel estimate.

3 Simulation experiment

This section selects the underwater acoustic channel environment and verifies the performance of the algorithm through Matlab simulation. The parameter settings are shown in Table 1. The characteristics of underwater acoustic channel include bandwidth limitation, multipath effect, Doppler effect, ocean environment noise and time variation of channel. Fig.3 is the shallow seawater acoustic channel impulse response diagram selected in this paper.

Table 1 Simulation parameters

Fig.3 Shallow seawater acoustic channel impulse response diagrame

The iterative channel estimation method(It-IAM) based on the new pilot structure proposed in this paper and the channel estimation method based on the traditional IAM-C and EIAM-C pilot structure are simulated. Fig.4 is a comparison diagram of BER of different pilot channel estimation methods in the above-described underwater acoustic channel environment. In Fig.4, the channel estimation of It-IAM with the iteration of 0, 1 time and 2 times are compared. It can be seen that the performance of estimation is average when there is no iteration, the performance is significantly improved after 1 time iteration, and when the iteration is 2 times, the performance is not significantly improved compared to the 1 time iteration. Since the equivalent pilot power of the It-IAM pilot structure fluctuates between the equivalent pilot power values of IAM-C and EIAM-C, when the It-IAM channel estimation is iterated 0 time, the BER curve is also located in the middle. It can be seen from Fig.4 that the channel estimation after 1-2 iterations has an improvement of about 3-4 dB over EIAM-C at a BER of 10-2.

Fig.4 Performance comparison of algorithms in underwater acoustic channel (1)

In order to verify the effect of the algorithm proposed in this paper on underwater acoustic communication channels, there is a comparison and verification of pilot channel estimation methods based on IAM. Fig.5 shows the simulation of IAM-R, IAM-I, IAM-C, EIAM-C and It-IAM with iterating 1 time. From this similation, it can be seen that in the same underwater environment, It-IAM algorithm proposed in this paper has the best performance.

In the second section, the influence of temperature on the underwater acoustic communication process is analyzed. According to Eqs.(8)-(16), the relationship between seawater absorption coefficient and underwater temperature can be obtained, as shown in Fig.6. From Eq.(7), it can be found that the transmission loss is positively correlated, so the relationship between transmission loss and temperature in the underwater acoustic communication process can also be represented by the curve shown in Fig.6. The It-IAM channel estimation performance introduced in this paper gradually increases with temperature increase when it is lower than 8 ℃, and the performance is negatively correlated when the underwater temperature exceeds 8 ℃.

Fig.5 Performance comparison of algorithms in underwater acoustic channel (2)

4 Conclusion

The paper applied the FBMC/OQAM system to the underwater, the influence relationship between temperature factors and underwater acoustic communication was analyzed comprehensively. By studying the FBMC/OQAM channel estimation technique, an iterative channel estimation method for new pilot structure was proposed. It-IAM increased the equivalent pilot power by introducing complex numbers in the pilot structure design, and also reduced the interference of noise on channel estimation, and inserted zero value at the front end of the pilot structure in response to the frequency shift and delay characteristics of the underwater acoustic channel. The algorithm performance is verified by simulation experiments, and the influence of underwater acoustic channel with different temperature on channel estimation performance is summarized. In the future, the underwater acoustic channel estimation technology will be studied in combination with the underwater salinity and depth factors to improve the underwater performance of the FBMC/OQAM communication system.