**CI/OFDM Underwater Acoustic Communication System**

Fang Xu and Ru Xu *Xiamen University China* 

## **1. Introduction**

94 Underwater Acoustics

[20] C. Muschallik, "Influence of RF Oscillators on an OFDM Signal", IEEE Transactions on

[21] C. Muschallik, V. Armbruster., "Verfahren und Schaltungsanordnung zur Verbesserung

des Empfangsverhaltens bei der Ubertragung von digitalen Signalen", German Pat.

Consumer Electronics, Vol. 41, No. 3, August 1995, pp. 592-603.

appl., AZ P195 20 353.4, June 1995.

The underwater acoustic channel (UAC) is one of the most challenging environments to be encountered for the communication. Because of the absorption of the signal, the path loss depends on the signal frequency (Berkhovskikh & Lysanov, 2003; Jensen et al., 2011). Multipath transmission causes intersymbol interference (ISI), and it extends over tens to hundreds of milliseconds according to the communication distance (Stojanovic & Preisig, 2009). Since the velocity of sound in water is about 1500m/s, any relative motion includes the transmitter or receiver and even surface waves will cause non-negligible Doppler effects, including shifting and spreading. All these phenomena dramatically limit the data rate achievable and the performance of the communications. The bandwidth is very limited, and the system is actually a broadband communication system because the center frequency of the signal is always at the same order of the bandwidth (Stojanovic, 1996; Stojanovic, 2007; Stojanovic & Preisig, 2009).

In order to achieve high data rate, it is important to use bandwidth-efficient modulation methods in UAC. Multi-carrier modulation is one of the candidates that can be used. Orthogonal Frequency Division Multiplexing (OFDM) (Lam & Ormondroyd, 1997; Kim & Lu, 2000; Stojanovic, 2006; Stojanovic, 2008; Li et al., 2008), direct-sequence spread-spectrum (DSSS) (Freitag et al. 2001; Frassati et al. 2005), frequency-hopped spread-spectrum (FHSS) (Stojanovic, 1998; Freitag et al., 2001) and code-division multiple access (CDMA) (Charalampos et al. 2001; Stojanovic & Freitag, 2006; Tsimenidis, 2001)were used in UAC channels in recent years and much literature focus on the conceptual system analysis and computer simulations.

In this chapter, we introduce a new multi-carrier modulation into the UAC channels which is called Carrier Interferometry OFDM (CI/OFDM) (Nassar et al., 1999; Wiegandt & Nassar, 2001; Nassar et al., 2002a, 2002b). Compared with OFDM, the CI/OFDM has a low PAPR characteristic and inherent frequency selective combining, which makes it a very attractive signaling scheme in frequency selective fading channels (Wiegandt & Nassar, 2001; Wiegandt et al., 2001; Wiegandt & Nassar, 2003; Wiegandt et al., 2004 ).

The chapter is organized as follows. In Section II, the characteristics of CI signal are analyzed. Two algorithms are proposed in Section III. Details are focused on the PAPR performance, and new algorithms to complete the modulation and demodulation of the

CI/OFDM Underwater Acoustic Communication System 97

0

1

N-1

*j***0** *e*

*j kN***( 1)** *<sup>N</sup> <sup>e</sup>* 

cos( )

(6)

 *w*

, interferences are close to zero. While in frequency selective channel,

*ir* is defined as

*a***<sup>0</sup>** On all carriers

**<sup>1</sup>** *a* On all carriers

*s t***( )**

**( )** *<sup>k</sup> s t*

*i* ,

*<sup>N</sup>* **<sup>1</sup>** On all carriers *a*

**0** *a*

**1** *a*

*<sup>N</sup>* **<sup>1</sup>** *a*

*j***0** *e*

*<sup>j</sup>***2 ( 1)** *N f e* 

**<sup>2</sup>**

Fig.2 depicts the modulation theory of CI/OFDM in transmitter and the detection of the kth symbol signal at the receiver side (Nassar et al. 2002). Assume perfect synchronization, the received signal is first projected onto the N orthogonal carriers, multi-carrier demodulation and phase offsets remove are carried out after that. This leads to the decision vector

1

 

and the second part is the interferences of the other N-1 information symbols which

Different combining strategies are employed to help restore orthogonality between subcarriers. In AWGN channel, the optimal combining is equal gain combining (EGC). After

different combining strategies are used to get combining gains, for example, the maximum ratio combining (MRC), the minimum mean square error combining (MMSEC) (Itagkai &

0,

The first part of (6) is the desired information symbol which is randomly faded by factor

*N k i i i ik i j k j i j jk*

*r Aa A a*

Serial to Parallel

**01 1 , ,...,** *<sup>N</sup> aa a*

k

=

Fig. 1. The conceptual CI/OFDM Transmitter

modulated on the same carrier.

1

*i i C r* 

*N*

0

performing

01 1 ( , ,..., ) *k kk k r rr r <sup>N</sup>* for the information symbol *<sup>k</sup> <sup>a</sup>* , where *<sup>k</sup>*

Adachi, 2004). After combining, the signals are sent to the detector.

*k a*

CI/OFDM. The configuration of the CI/OFDM underwater acoustic communication system is presented in Section IV. Furthermore, the key algorithms including synchronization, channel estimation and equalization are described. In Section V, Performance results for different field tests are summarized. Conclusions are drawn in Section VI.

## **2. CI/OFDM signals**

#### **2.1 The theory of the CI/OFDM**

In CI/OFDM transmitter, after serial to parallel transform, information symbols are modulated onto all the N parallel subcarriers and then added linearly together to get the output signal (Nassar et al. 2002). As shown in Fig.1 , the output of the signal is

$$s(t) = \sum\_{k=0}^{N-1} s\_k(t) = \text{Re}\left\{\sum\_{k=0}^{N-1} a\_k c\_k(t)\right\} \quad 0 \le t \le T \tag{1}$$

where ( ) *<sup>k</sup> s t* is the modulated signal for the kth information symbol *<sup>k</sup> a* . Re( ) is the real part of the signal and ( ) *<sup>k</sup> c t* is the kth CI signal, which can be express by

$$\mathbf{c}\_{k}(t) = \sum\_{i=0}^{N-1} e^{j2\pi i\Delta ft} \cdot e^{j\theta\_k^i} \tag{2}$$

It is easy to see that ( ) *<sup>k</sup> c t* is a multi-carrier signal with different phase offsets (2 ) *<sup>i</sup> <sup>k</sup> N ki* . Submit (2) into (1), we get the continuous baseband transmitted signal

$$\mathbf{s}(t) = \text{Re}\left\{ \sum\_{k=0}^{N-1} a\_k \sum\_{i=0}^{N-1} e^{j2\pi i \Delta \theta\_i} \cdot e^{\frac{j2\pi}{N}ki} \right\} \quad 0 \le t \le T \tag{3}$$

We rewrite the discrete form of (3) with the Nyquist sampling rate of *sf N f*

$$\mathbf{s}(n) = \text{Re}\left\{ \sum\_{k=0}^{N-1} a\_k \sum\_{i=0}^{N-1} e^{j\frac{2\pi}{N}in} \cdot e^{j\frac{2\pi}{N}ik} \right\} \quad n = 0, 1, \ldots, N - 1 \tag{4}$$

where 1 *<sup>s</sup> f T* ( *Ts* is one CI/OFDM symbol duration) to ensure orthogonality among subcarriers, and (2 ) *Nki* is the phase offset used for *<sup>k</sup> a* which ensures the orthogonality among the N information symbols.

After transmitted over a frequency selective fading channel, the received signal at receiver side is

$$r(n) = \sum\_{k=0}^{N-1} \sum\_{i=0}^{N-1} \alpha\_i a\_k e^{j\frac{2\pi}{N}in} \cdot e^{j\frac{2\pi}{N}ik} \cdot e^{j\phi\_i} + w(n) \quad n = 0, 1, \ldots, N-1 \tag{5}$$

where*<sup>i</sup>* and *<sup>i</sup>* are the amplitude fade and phase offset on the ith carrier, respectively. *w n*( ) is the addictive white Gaussian noise (AWGN).

96 Underwater Acoustics

CI/OFDM. The configuration of the CI/OFDM underwater acoustic communication system is presented in Section IV. Furthermore, the key algorithms including synchronization, channel estimation and equalization are described. In Section V, Performance results for

In CI/OFDM transmitter, after serial to parallel transform, information symbols are modulated onto all the N parallel subcarriers and then added linearly together to get the

different field tests are summarized. Conclusions are drawn in Section VI.

output signal (Nassar et al. 2002). As shown in Fig.1 , the output of the signal is

1 1

*k k k*

*st s t ac t t T*

where ( ) *<sup>k</sup> s t* is the modulated signal for the kth information symbol *<sup>k</sup> a* . Re( ) is the real part

1 2

*N*

*i ct e e* 

0 ( ) *<sup>i</sup>*

*<sup>k</sup> N ki* . Submit (2) into (1), we get the continuous baseband transmitted signal

2 1 1 2

 

*st a e e t T*

( ) Re 0,1,..., 1

where 1 *<sup>s</sup> f T* ( *Ts* is one CI/OFDM symbol duration) to ensure orthogonality among

After transmitted over a frequency selective fading channel, the received signal at receiver

( ) ( ) 0,1,..., 1 *<sup>i</sup>*

*<sup>i</sup>* are the amplitude fade and phase offset on the ith carrier, respectively. *w n*( )

*N N j*

*rn ae e e wn n N*

 

*sn a e e n N* 

*N N*

 

It is easy to see that ( ) *<sup>k</sup> c t* is a multi-carrier signal with different phase offsets

(1)

(2)

(3)

(4)

*k*

*Nki* is the phase offset used for *<sup>k</sup> a* which ensures the orthogonality

(5)

*j i ft j*

0 0 ( ) ( ) Re ( ) 0 *N N*

*k k*

*k*

0 0 ( ) Re 0 *N N j ki j i ft <sup>N</sup>*

We rewrite the discrete form of (3) with the Nyquist sampling rate of *sf N f*

0 0

2 2 1 1

*N N j in j ik*

*i k*

0 0

*k i*

is the addictive white Gaussian noise (AWGN).

*k k i*

2 2 1 1

*N N j in j ik*

*k k i*

of the signal and ( ) *<sup>k</sup> c t* is the kth CI signal, which can be express by

**2. CI/OFDM signals** 

(2 ) *<sup>i</sup>*

 

subcarriers, and (2 )

side is

where*<sup>i</sup>* and  among the N information symbols.

**2.1 The theory of the CI/OFDM** 

Fig. 1. The conceptual CI/OFDM Transmitter

Fig.2 depicts the modulation theory of CI/OFDM in transmitter and the detection of the kth symbol signal at the receiver side (Nassar et al. 2002). Assume perfect synchronization, the received signal is first projected onto the N orthogonal carriers, multi-carrier demodulation and phase offsets remove are carried out after that. This leads to the decision vector 01 1 ( , ,..., ) *k kk k r rr r <sup>N</sup>* for the information symbol *<sup>k</sup> <sup>a</sup>* , where *<sup>k</sup> ir* is defined as

$$r\_i^k = A a\_i a\_k + A \cdot \sum\_{j=0, j \neq k}^{N-1} a\_i a\_j \cos(\theta\_k^i - \theta\_j^i) + w\_i \tag{6}$$

The first part of (6) is the desired information symbol which is randomly faded by factor*i* , and the second part is the interferences of the other N-1 information symbols which modulated on the same carrier.

Different combining strategies are employed to help restore orthogonality between subcarriers. In AWGN channel, the optimal combining is equal gain combining (EGC). After performing 1 0 *N i i C r* , interferences are close to zero. While in frequency selective channel, different combining strategies are used to get combining gains, for example, the maximum ratio combining (MRC), the minimum mean square error combining (MMSEC) (Itagkai & Adachi, 2004). After combining, the signals are sent to the detector.

CI/OFDM Underwater Acoustic Communication System 99

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

The real part of the CI signal

Time

The imaginary part of the CI signal

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time

The Envelope of the CI signal

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time

2 2 1

*N j ik j in N N*

( ) ( ) 0,1,..., 1

It is obviously that (9) is an inverse discrete Fourier transform (IDFT) with weighting

22 2 2 0 0 1 0 <sup>0</sup> ( 1) 0 <sup>2</sup> <sup>0</sup> 00 0 0

*a e a e a e a e*

*a e a e a e a e*

11 1 1

*NN N N*

*ae ae ae ae*

<sup>0</sup> 22 2 2 0 1 1 1 <sup>1</sup> ( 1) 1 <sup>2</sup> <sup>1</sup> 11 1 1

*j i NN N N*

*j i NN N N*

which change with the index *k* and *i* . The IDFT weighting coefficient

*j j j i j N*

22 2 2 0 ( 1) 1 ( 1) ( 1) ( 1) ( 1)

*e a e a e*

*j N j N j iN jNN NN N N*

*jj j i j N*

0 subcarrier 1 subcarrier i subcarrier subcarrier ## # #

 

(9)

 

 

 

2 22 <sup>1</sup> ( 1)

*j k j ik j Nk N NN k k*

 

 

(10)

(N-1)

 

*sn a e e n N* 

0

*i*

*k*



0 0.5 1

0 1

Amplitude

Magnitude

Fig. 3. Baseband CI signals

**3. Proposed algorithms 3.1 Multi-carrier algorithm** 

> 2 *j ik N <sup>k</sup> a e*

can be written as a matrix

*N*

 

*N*

<sup>2</sup> ( 1)

*j iN N*

<sup>2</sup> <sup>0</sup> <sup>2</sup>

*j ik N*

*j k*

*a e a*

*N k k*

efficients

1

*a e*

*a e*

*k*

*a e*

1

*a e*

*N*

As in (4), the discrete *kth* transmitted symbol is

0 1

Amplitude

As presented to date, the implementation of original CI/OFDM is complicated, and it is important to note that the receiver is designed for detecting only one information symbol. Although CI/OFDM had been proved that it could improve BER performance by exploiting frequency diversity and depress the PAPR simultaneously, its implementation was complicated and only conceptual transmitter and receiver models had been given in the literature.

Fig. 2. The CI/OFDM receiver for the kth symbol

## **2.2 The characteristics of the CI signal**

The baseband CI signal (Nassar et al. 2002) is given bellow

$$\mathbf{c}(t) = \sum\_{i=0}^{N-1} \mathbf{c}^{j2\pi i \mathbf{A} \mathbf{\hat{r}}} \tag{7}$$

where N is the number of the subcarriers and *f* is the interval of the subcarriers. It is obviously that CI signal is a periodic signal. Simulation results are shown in Fig. 3. In simulations, 8 *N* , *f* 1*Hz* , the width of the main lobe and the side lobe are 2 ( ) 0.125 *Nf s* and 1 ( ) 0.0625 *Nf s* , respectively. By selecting optimal phase offsets, CI signals are orthogonal to each other.

We rewrite the discrete CI signal as bellow

$$c(n) = \sum\_{i=0}^{N-1} e^{j\frac{2\pi}{N}in} \tag{8}$$

It is clearly that the discrete CI signal is the result of sampling a rectangle pulse with the sampling rate *f* in the frequency domain. It has constant amplitude (CA).

Based on the analysis of the CI signal, two novel algorithms for CI/OFDM modulation and demodulation are presented in this chapter.

98 Underwater Acoustics

As presented to date, the implementation of original CI/OFDM is complicated, and it is important to note that the receiver is designed for detecting only one information symbol. Although CI/OFDM had been proved that it could improve BER performance by exploiting frequency diversity and depress the PAPR simultaneously, its implementation was complicated and only conceptual transmitter and receiver models had been given in the

> 0 *<sup>k</sup> <sup>j</sup> e*

> > 0 *k r*

> > 1 *k r*

k R

(7)

(8)

ˆ

k

a

1 *k Nr*

1 *<sup>k</sup> <sup>j</sup> e* 

*<sup>k</sup> r*

*<sup>N</sup>* <sup>1</sup> *<sup>k</sup> <sup>j</sup> e* 

> 1 2

*j i ft*

0

where N is the number of the subcarriers and *f* is the interval of the subcarriers. It is obviously that CI signal is a periodic signal. Simulation results are shown in Fig. 3. In simulations, 8 *N* , *f* 1*Hz* , the width of the main lobe and the side lobe are 2 ( ) 0.125 *Nf s* and 1 ( ) 0.0625 *Nf s* , respectively. By selecting optimal phase offsets, CI

2 1

*N j in N*

0

*i cn e*

It is clearly that the discrete CI signal is the result of sampling a rectangle pulse with the

Based on the analysis of the CI signal, two novel algorithms for CI/OFDM modulation and

( )

sampling rate *f* in the frequency domain. It has constant amplitude (CA).

*i ct e*

( ) *N*

<sup>0</sup> *<sup>j</sup>*(0 ) *e* 

<sup>1</sup> *j ft* (2 ) *e* 

<sup>1</sup> (2 ( 1) ) *<sup>N</sup> j N ft e* 

The baseband CI signal (Nassar et al. 2002) is given bellow

Fig. 2. The CI/OFDM receiver for the kth symbol

**2.2 The characteristics of the CI signal** 

signals are orthogonal to each other.

We rewrite the discrete CI signal as bellow

demodulation are presented in this chapter.

 

literature.

Fig. 3. Baseband CI signals

## **3. Proposed algorithms**

#### **3.1 Multi-carrier algorithm**

As in (4), the discrete *kth* transmitted symbol is

$$\mathbf{s}(n) = \sum\_{i=0}^{N-1} (a\_k \cdot e^{j\frac{2\pi}{N}ik}) e^{j\frac{2\pi}{N}in} \quad n = 0, 1, \ldots, N-1 \tag{9}$$

It is obviously that (9) is an inverse discrete Fourier transform (IDFT) with weighting efficients 2 *j ik N <sup>k</sup> a e* which change with the index *k* and *i* . The IDFT weighting coefficient can be written as a matrix

CI/OFDM Underwater Acoustic Communication System 101

used to implement orthogonal multi-carrier modulation. Parallel data is first transformed to serial data, then the complex base-band signal is then up-converted to the transmission frequency, and the real part of the signal is sent out to the channel. In the receiver, the signal is first down-converted to the base-band. Serial to parallel transformation followed by orthogonal multi-carrier demodulated which completed by the first discrete Fourier transform (DFT). Then CI code de-spreading is implemented by the second DFT and finally,

The CI spread code in (10) is similar to the polyphase codes (Heimiller, 1961). Polyphase

123 1 1 2 1 1 2 1 12 1 1,1,...,1,1, , , ,...., ,1, , ,..., ,1, , ,..., ,1, , ,..., *pp p*

Polyphase code were proven to be a constant amplitude , zero autocorrelation (CAZAC) sequence (Heimiller, 1961). According to the characteristics of the CAZAC sequence, if *ui* is a CAZAC sequence, then *ui* , where *u* denotes complex conjugation, is also a CAZAC sequence (Milewski, 1983). Note that the orthogonality, periodicity, constant amplitude and zero autocorrelation are not changed, it suggests a new way of thinking about constructing

In this chapter, the new CI signals are complex conjugations of primary CI signals (Nassar et

22 2 2 0 0 1 0 <sup>0</sup> ( 1) 0 <sup>2</sup> <sup>0</sup> 00 0 0

*j j j i j N*

 

 

 

 

*j j j i j N*

0 subcarrier 1 subcarrier i subcarrier ## # #

*e a e a e a e*

11 1 1

*ae ae a e a e*

Fig.5 shows the proposed system using the single-carrier algorithm. In the transmitter, the input data is mapping into a baseband constellation. Then the data sequence is converted to parallel and enters the first DFT to perform CI spreading. After that, the IDFT is used to implement orthogonal multi-carrier modulation. The complex baseband signal is then up-

Then, the CI/OFDM signal is mathematically characterized by the following equation

22 2 2 <sup>0</sup> <sup>1</sup> ( 1)

*jk jk j ik j Nk NN N N kk k k*

*jN jN j iN jNN NN N N NN N N*

22 2 2 0 ( 1) 1 ( 1) ( 1) ( 1) ( 1)

<sup>0</sup> 22 2 2 0 1 1 1 <sup>1</sup> ( 1) 1 <sup>2</sup> <sup>1</sup> 11 1 1

*j i NN N N*

*a e a e a e a e a e*

*a e a e a e a e a e*

*j i NN N N*

 

22 2 33 3 11 1

 

(13)

 

 

> 

> 

> 

(14)

 

subcarrier

(N-1)

*ppp p*

 

, 0 1 *k p* is a primitive Pth root of unity, the sequence has zero

codes were proven to have good periodic correlation properties, the sequence is

 

the phase constellation of the data is extracted ( Xu et al. 2007).

 

periodic correlation except for the peaks at 2 2 *i pp* 0, ,2 ,... .

**3.2 Single-carrier algorithm** 

al. 2002), which can be written as

where *<sup>j</sup>*(2 ) *<sup>k</sup> <sup>p</sup> <sup>k</sup> e*

new CI signals.

1

1

*a e*

2

 

*j ik <sup>N</sup> <sup>k</sup>*

*N*

*N*

<sup>2</sup> ( 1)

converted to the transmission frequency.

*<sup>a</sup> a e*

*j iN <sup>N</sup> <sup>N</sup>*

Since *i* is the index of subcarrier, the columns of the matrix are corresponding to different subcarriers, that is

$$\underbrace{\sum\_{k=0}^{N-1} a\_k e^{j\frac{2\pi}{N}0 \cdot k}}\_{\text{0\textquotedblleft subcarrier}} \quad \underbrace{\sum\_{k=0}^{N-1} a\_k e^{j\frac{2\pi}{N}1 \cdot k}}\_{\text{1\textquotedblleft subcarrier}} \quad \cdots \underbrace{\sum\_{k=0}^{N-1} a\_k e^{j\frac{2\pi}{N}i \cdot k}}\_{i^{\text{\textquotedblleft subcarrier}}} \quad \cdots \underbrace{\sum\_{k=0}^{N-1} a\_k e^{j\frac{2\pi}{N}(N-1) \cdot k}}\_{\text{(N-1)\textquotedblright subcarrier}} \tag{11}$$

(11) implies that the coefficient of the IDFT can also be corresponding to another IDFT (Xu et al., 2007a, 2007b). Hence, the CI/OFDM modulation model employed in this chapter corresponds to

$$\begin{split} s(n) &= \sum\_{k=0}^{N-1} a\_k c\_k \binom{nTs}{N} \\ &= \sum\_{k=0}^{N-1} a\_k \sum\_{i=0}^{N-1} e^{j\frac{2\pi}{N}ki} \frac{j\pi\_{ni}}{e^N} \\ &= \sum\_{i=0}^{N-1} \left(\sum\_{k=0}^{N-1} a\_k e^{j\frac{2\pi}{N}ki} \right) e^{j\frac{2\pi}{N}ni} \\ &= N \cdot IDFT \left[ N \cdot IDFT(a\_k) \right] \\ &= N^2 \cdot IDFT \left[ IDFT(a\_k) \right] \qquad n = 0, 1, \ldots, N-1 \end{split} \tag{12}$$

Fig.4 shows a block diagram of the proposed system. At the transmitter side, the input data is first mapped into a baseband constellation. Then the data sequence is converted to parallel and enters the first IDFT to perform CI spreading. After that, the second IDFT is

Fig. 4. The block diagram of the multi-carrier algorithm

used to implement orthogonal multi-carrier modulation. Parallel data is first transformed to serial data, then the complex base-band signal is then up-converted to the transmission frequency, and the real part of the signal is sent out to the channel. In the receiver, the signal is first down-converted to the base-band. Serial to parallel transformation followed by orthogonal multi-carrier demodulated which completed by the first discrete Fourier transform (DFT). Then CI code de-spreading is implemented by the second DFT and finally, the phase constellation of the data is extracted ( Xu et al. 2007).

#### **3.2 Single-carrier algorithm**

100 Underwater Acoustics

Since *i* is the index of subcarrier, the columns of the matrix are corresponding to different

subcarrier subcarrier subcarrier subcarrier ## # #

(11) implies that the coefficient of the IDFT can also be corresponding to another IDFT (Xu et al., 2007a, 2007b). Hence, the CI/OFDM modulation model employed in this chapter

( )

*N IDFT IDFT a n N*

Fig.4 shows a block diagram of the proposed system. At the transmitter side, the input data is first mapped into a baseband constellation. Then the data sequence is converted to parallel and enters the first IDFT to perform CI spreading. After that, the second IDFT is

( ) 0,1,..., 1

(12)

*i N*

 

(11)

 

00 0 0 0 1 ( 1)

1

*N*

*sn ac*

*k*

() ( )

*k k*

*N N j ki j ni*

*aee*

*N N*

 

> 

*nTs*

*N*

*N N*

*<sup>k</sup> n i*

*<sup>k</sup> n i*

0 2 2 1 1

 

0 0

 

*k k i*

0 0

*i k*

2

Fig. 4. The block diagram of the multi-carrier algorithm

2 2 1 1

*N N j ki j ni*

*ae e*

( )

*N IDFT N IDFT a*

*k*

*ae ae a e a e*

22 2 2 11 1 1 <sup>0</sup> <sup>1</sup> ( 1)

*NN N N j k j k j i k j N k NN N N kk k k kk k k*

 

subcarriers, that is

corresponds to

The CI spread code in (10) is similar to the polyphase codes (Heimiller, 1961). Polyphase codes were proven to have good periodic correlation properties, the sequence is

$$1, 1, \ldots, 1, 1, \xi\_1, \xi\_2, \xi\_3, \ldots, \xi\_{p-1}, 1, \xi\_1^2, \xi\_2^2, \ldots, \xi\_{p-1}^2, 1, \xi\_1^3, \xi\_2^3, \ldots, \xi\_{p-1}^3, 1, \xi\_1^{p-1}, \xi\_2^{p-1}, \ldots, \xi\_{p-1}^{p-1} \tag{13}$$

where *<sup>j</sup>*(2 ) *<sup>k</sup> <sup>p</sup> <sup>k</sup> e* , 0 1 *k p* is a primitive Pth root of unity, the sequence has zero periodic correlation except for the peaks at 2 2 *i pp* 0, ,2 ,... .

Polyphase code were proven to be a constant amplitude , zero autocorrelation (CAZAC) sequence (Heimiller, 1961). According to the characteristics of the CAZAC sequence, if *ui* is a CAZAC sequence, then *ui* , where *u* denotes complex conjugation, is also a CAZAC sequence (Milewski, 1983). Note that the orthogonality, periodicity, constant amplitude and zero autocorrelation are not changed, it suggests a new way of thinking about constructing new CI signals.

In this chapter, the new CI signals are complex conjugations of primary CI signals (Nassar et al. 2002), which can be written as

Then, the CI/OFDM signal is mathematically characterized by the following equation

Fig.5 shows the proposed system using the single-carrier algorithm. In the transmitter, the input data is mapping into a baseband constellation. Then the data sequence is converted to parallel and enters the first DFT to perform CI spreading. After that, the IDFT is used to implement orthogonal multi-carrier modulation. The complex baseband signal is then upconverted to the transmission frequency.

CI/OFDM Underwater Acoustic Communication System 103

Since lower PAPR is the most important characteristic of CI/OFDM, and the algorithms presented here are somewhat different from the theoretical realization of the CI/OFDM, it is reasonable for us to verify the PAPR performance based on these two algorithms. Fig. 7 shows the simulation result. A conclusion can be drawn that the two algorithms presented in this chapter have the same PAPR and BER performance as the conceptual CI/OFDM, and

> Theory IFFT/IFFT FFT/IFFT

Theory algorithm IFFT-IFFT algorithm FFT-IFFT algorithm

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> 10-5

Fig. 6. Performance comparisons of three algorithms under AWGN channels

Eb/N0

CCDF of the Signal

<sup>4</sup> 4.5 <sup>5</sup> 5.5 <sup>6</sup> 6.5 <sup>7</sup> 7.5 <sup>8</sup> 10-3

**4. Configuration of the CI/OFDM underwater acoustic communication system**  Based on the aforementioned algorithms, two CI/OFDM underwater acoustic communication systems are proposed. Simplified block diagrams of the proposed systems are shown in Fig.8

and Fig.9. We also replace the IDFT by the IFFT due to the efficiency of the algorithm.

PAPR(dB)

lower complexity which make it applicable to engineering.

10-4

10-2

Fig. 7. PAPR Performance comparisons of three algorithms

Pr(PAPR>x)

10-1

100

10-3

BER

10-2

10-1

$$\begin{split} s(n) &= \sum\_{k=0}^{N-1} a\_k c\_k(\frac{nT\mathbf{s}}{N}) = \sum\_{k=0}^{N-1} \sum\_{i=0}^{N-1} a\_k e^{-j\frac{2\pi}{N}ki} e^{j\frac{2\pi}{N}ni} \\ &= \sum\_{i=0}^{N-1} \left(\sum\_{k=0}^{N-1} a\_k e^{-j\frac{2\pi}{N}ki} \right) e^{j\frac{2\pi}{N}ni} \\ &= N \cdot IDFT \left[ DFT(a\_k) \right] \qquad n = 0, 1, \ldots, N-1 \end{split} \tag{15}$$

In the receiver, the signal is down-converted to the baseband. After serial to parallel transformation, the signal is first demodulated by DFT, Then CI de-spreading is implemented by the IDFT and the phase constellation of the data is extracted.

Fig. 5. The block diagram of the single-carrier algorithm

#### **3.3 The comparisons between the conceptual CI/OFDM and the proposed algorithms**

In the conceptual model of CI/OFDM, the computational complexity increases with the number of parallel information symbols dramatically, which make it unpractical to the engineering. In the conceptual model of CI/OFDM, the CI spreading needs *N N* complex multiplications *N N* ( 1) complex additions. While in multi-carrier algorithm or singlecarrier algorithm, only 2 *N N* 2log complex multiplications and 2 *N N* log complex additions are needed. For example, when 1024 *N* , we need 1048576 complex multiplications and 1046529 complex additions in conceptual CI/OFDM, while only 5120 complex multiplications and 10240 complex additions are needed in our algorithms.

Of course, the two algorithms have their own problems. As in the multi-carrier method, the physical concept is not very clear, since there are two cascaded IDFT in the transmitter which may cause confusion about the transformation between the frequency domain and time domain. On the other hand, in the single-carrier method, filter should be well designed to compress the bandwidth of the output signal.

As shown in fig.6, the performance of CI/OFDM system is verified under AWGN channel. We replace the IDFT by the inverse fast Fourier transform (IFFT) due to the efficiency of the algorithm. It is obviously that there is no difference between the conceptual CI/OFDM and the two algorithms proposed in this chapter.

102 Underwater Acoustics

0 0 0

*nTs sn ac ae e N*

*N N*

*N IDFT DFT a n N*

*k k k k k i N N j ki j ni*

 

In the receiver, the signal is down-converted to the baseband. After serial to parallel transformation, the signal is first demodulated by DFT, Then CI de-spreading is

**3.3 The comparisons between the conceptual CI/OFDM and the proposed algorithms**  In the conceptual model of CI/OFDM, the computational complexity increases with the number of parallel information symbols dramatically, which make it unpractical to the engineering. In the conceptual model of CI/OFDM, the CI spreading needs *N N* complex multiplications *N N* ( 1) complex additions. While in multi-carrier algorithm or singlecarrier algorithm, only 2 *N N* 2log complex multiplications and 2 *N N* log complex additions are needed. For example, when 1024 *N* , we need 1048576 complex multiplications and 1046529 complex additions in conceptual CI/OFDM, while only 5120 complex

Of course, the two algorithms have their own problems. As in the multi-carrier method, the physical concept is not very clear, since there are two cascaded IDFT in the transmitter which may cause confusion about the transformation between the frequency domain and time domain. On the other hand, in the single-carrier method, filter should be well designed

As shown in fig.6, the performance of CI/OFDM system is verified under AWGN channel. We replace the IDFT by the inverse fast Fourier transform (IFFT) due to the efficiency of the algorithm. It is obviously that there is no difference between the conceptual CI/OFDM and

multiplications and 10240 complex additions are needed in our algorithms.

2 2 1 1

*ae e*

*<sup>k</sup> n i*

implemented by the IDFT and the phase constellation of the data is extracted.

( )

*k*

() ( )

0 0

*i k*

Fig. 5. The block diagram of the single-carrier algorithm

to compress the bandwidth of the output signal.

the two algorithms proposed in this chapter.

2 2 1 1 1

*N N N j ki j ni*

( ) 0,1,..., 1

*N N*

(15)

 

Since lower PAPR is the most important characteristic of CI/OFDM, and the algorithms presented here are somewhat different from the theoretical realization of the CI/OFDM, it is reasonable for us to verify the PAPR performance based on these two algorithms. Fig. 7 shows the simulation result. A conclusion can be drawn that the two algorithms presented in this chapter have the same PAPR and BER performance as the conceptual CI/OFDM, and lower complexity which make it applicable to engineering.

Fig. 6. Performance comparisons of three algorithms under AWGN channels

Fig. 7. PAPR Performance comparisons of three algorithms

## **4. Configuration of the CI/OFDM underwater acoustic communication system**

Based on the aforementioned algorithms, two CI/OFDM underwater acoustic communication systems are proposed. Simplified block diagrams of the proposed systems are shown in Fig.8 and Fig.9. We also replace the IDFT by the IFFT due to the efficiency of the algorithm.

CI/OFDM Underwater Acoustic Communication System 105

We use Linear Frequency Modulation (LFM) (Rihaczek, 1969; Shaw & Srivastava, 2007) signal to get coarse synchronization and CI complex spreading sequence to get accurate

synchronization and fractional frequency offset estimation.

Fig. 9. The block diagram of the system based on single-carrier algorithm

*rect*

**4.1.2 Fine synchronization and fractional frequency shift estimation** 

2

(16)

(17)

0 <sup>1</sup> <sup>2</sup>

*t*

*T*

<sup>2</sup> () ( ) *j f t ut <sup>t</sup> s t A rect e T*

where A is the amplitude of the signal, T is the width of the signal, 0*f* is the carrier frequency, *u* is the gradient of the instantaneous frequency which is called chirp rate,

<sup>1</sup> 1, <sup>2</sup> ( ) <sup>1</sup> 0, <sup>2</sup>

*t T*

*T t*

Since the ambiguity function of LFM signals is wide in Doppler axis (Rihaczek, 1969), it is highly tolerant of the Doppler shift which makes it useful in mobile wireless communication

Two identical CI complex sequences are used as fine synchronization signals and sliding correlator is applied at the receiver side to obtain the correlation peak. CI complex

**4.1 Synchronization** 

**4.1.1 Coarse synchronization** 

*u BT* 2

systems.

sequences is given by

The expression for LFM signal is given as

. *rect*( ) is a rectangle function, defined as

As shown in Fig.8, based on the multi-carrier algorithm, the input data is first coded by Low Density Parity Check Codes (LDPC). After baseband mapping, the data sequence is converted to parallel and enters the first IFFT to perform CI spreading. Pilot signals are inserted before the second IFFT. The second IFFT is used to implement orthogonal multicarrier modulation. A cyclic prefix and postfix are also appended to the data sequence as guard intervals in order to combat the ISI induced by the multi-path delay spread in the UWA channel. The complex base-band signal is then up-converted to the transmission frequency and the real part of the signal is sent out to the UWA channel by the transducer.

In the receiver, the signal is first down-converted to the base-band. Then the signal is demodulated by the first FFT. Channel estimation is performed to track the channel response and compensations of the signal are performed. Then CI code de-spreading is implemented by the second FFT, and finally, the phase constellation of the data is extracted.

Fig. 8. The block diagram of the system based on multi-carrier algorithm

Fig.9 shows a simplified block diagram of the proposed system based on single-carrier algorithm. In the transmitter, the input data is first encoded by LDPC and then mapping into a baseband constellation. The data sequence is converted to parallel and enters the first FFT to perform CI spreading. After that, the IFFT is used to implement orthogonal multicarrier modulation. A cyclic prefix is also appended as a guard interval to the data sequence in order to combat the inter ISI induced by multipath delay spread in the selective fading channel. In addition, a pilot signal is appended for the purposes of channel estimation in the receiver. The complex baseband signal is then up-converted to the transmission frequency. In the receiver, the signal is down-converted to baseband. The signal is first demodulated by FFT, and diversity combining scheme is employed as frequency-domain equalization where the combining weights are estimated by the pilot signal. Then de-spreading is implemented by the IFFT and the phase constellation of the data is extracted. Finally, the data is mapped back to the binary form, and a soft LDPC decoding is performed.

We here focus on the multi-carrier algorithm and explain the key technologies used in the underwater acoustic communication system.

## **4.1 Synchronization**

104 Underwater Acoustics

As shown in Fig.8, based on the multi-carrier algorithm, the input data is first coded by Low Density Parity Check Codes (LDPC). After baseband mapping, the data sequence is converted to parallel and enters the first IFFT to perform CI spreading. Pilot signals are inserted before the second IFFT. The second IFFT is used to implement orthogonal multicarrier modulation. A cyclic prefix and postfix are also appended to the data sequence as guard intervals in order to combat the ISI induced by the multi-path delay spread in the UWA channel. The complex base-band signal is then up-converted to the transmission frequency and the real part of the signal is sent out to the UWA channel by the transducer. In the receiver, the signal is first down-converted to the base-band. Then the signal is demodulated by the first FFT. Channel estimation is performed to track the channel response and compensations of the signal are performed. Then CI code de-spreading is implemented by the second FFT, and finally, the phase constellation of the data is extracted.

Fig. 8. The block diagram of the system based on multi-carrier algorithm

back to the binary form, and a soft LDPC decoding is performed.

underwater acoustic communication system.

Fig.9 shows a simplified block diagram of the proposed system based on single-carrier algorithm. In the transmitter, the input data is first encoded by LDPC and then mapping into a baseband constellation. The data sequence is converted to parallel and enters the first FFT to perform CI spreading. After that, the IFFT is used to implement orthogonal multicarrier modulation. A cyclic prefix is also appended as a guard interval to the data sequence in order to combat the inter ISI induced by multipath delay spread in the selective fading channel. In addition, a pilot signal is appended for the purposes of channel estimation in the receiver. The complex baseband signal is then up-converted to the transmission frequency. In the receiver, the signal is down-converted to baseband. The signal is first demodulated by FFT, and diversity combining scheme is employed as frequency-domain equalization where the combining weights are estimated by the pilot signal. Then de-spreading is implemented by the IFFT and the phase constellation of the data is extracted. Finally, the data is mapped

We here focus on the multi-carrier algorithm and explain the key technologies used in the

We use Linear Frequency Modulation (LFM) (Rihaczek, 1969; Shaw & Srivastava, 2007) signal to get coarse synchronization and CI complex spreading sequence to get accurate synchronization and fractional frequency offset estimation.

Fig. 9. The block diagram of the system based on single-carrier algorithm

## **4.1.1 Coarse synchronization**

The expression for LFM signal is given as

$$s(t) = A \cdot \operatorname{rect}(\frac{t}{T}) e^{j2\pi \left(f\_0 t + \frac{1}{2}\mu t^2\right)}\tag{16}$$

where A is the amplitude of the signal, T is the width of the signal, 0*f* is the carrier frequency, *u* is the gradient of the instantaneous frequency which is called chirp rate, *u BT* 2. *rect*( ) is a rectangle function, defined as

$$rect(\frac{t}{T}) = \begin{cases} 1, & \left|\frac{t}{T}\right| \le \frac{1}{2} \\ 0, & \left|\frac{t}{T}\right| > \frac{1}{2} \end{cases} \tag{17}$$

Since the ambiguity function of LFM signals is wide in Doppler axis (Rihaczek, 1969), it is highly tolerant of the Doppler shift which makes it useful in mobile wireless communication systems.

## **4.1.2 Fine synchronization and fractional frequency shift estimation**

Two identical CI complex sequences are used as fine synchronization signals and sliding correlator is applied at the receiver side to obtain the correlation peak. CI complex sequences is given by

CI/OFDM Underwater Acoustic Communication System 107

Two kinds of pilot sequences which are both CAZAC sequences are chosen to estimate the

x 104

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(a) (b) Fig. 10. Sliding correlation peak under AWGN channel. (a) Peak of LFM signal (b) Peak of

CI complex sequence was given in equation (18). It is easy to prove the CAZAC feature of the CI complex sequence. Fig. 11 gives simulation results of the CI complex sequence.

(a) (b)

Fig. 11. The CAZAC feature of the CI complex sequence. (a) constant amplitude (b) zero

Amplitude

<sup>0</sup> <sup>500</sup> <sup>1000</sup> <sup>1500</sup> <sup>2000</sup> <sup>2500</sup> <sup>3000</sup> <sup>3500</sup> <sup>0</sup>

<sup>0</sup> <sup>200</sup> <sup>400</sup> <sup>600</sup> <sup>800</sup> <sup>1000</sup> <sup>1200</sup> <sup>1400</sup> <sup>1600</sup> -200

Sample

The autocorrelation characteristic

underwater acoustic channel response.

0 0.5 1 1.5 2 2.5 3


Frequency


CI spreading sequence

1. CI complex sequence

3.5 x 10-3 The frequency-amplitude characteristic

**4.2.1 Pilot** 

0.5 1 1.5 2 2.5 3

autocorrelation

Amplitude

2.5 x 105

$$1, 1, \ldots, 1, 1, \xi\_1, \xi\_2, \xi\_3, \ldots, \xi\_{N-1}, 1, \xi\_1^2, \xi\_2^2, \ldots, \xi\_{N-1}^2, 1, \xi\_1^3, \xi\_2^3, \ldots, \xi\_{N-1}^3, 1, \xi\_1^{N-1}, \xi\_2^{N-1}, \ldots, \xi\_{N-1}^{N-1} \tag{18}$$

where *<sup>j</sup>*(2 ) *k N <sup>k</sup> e* ,0 1 *k N* . Suppose the two received sequences are 1*r m*( ) and 2*r m*( ) (Hlaing et al. 2003; Ren, 2005), the cross-correlation function of the two sequences is

$$R(n) = \sum\_{m=0}^{L-1} \left( r\_1^\*(m) r\_2(m+n) \right) \tag{19}$$

where the L is the length of the sequence. Since the sequences are identical at the transmitter, the impact of the channel is assumed to be same to the two sequences, (18) can be written as

$$R(n) = \sum\_{m=0}^{L-1} \left( r\_1^\*(m) r\_2(m+n) \right) = \sum\_{m=0}^{L-1} \left( r\_1^\*(m) r\_1(m+L+n) \right) \tag{20}$$

The cross-correlation of two sequences can be changed into auto-correlation of one sequence, that is

$$R\{0\} = \sum\_{m=0}^{L-1} \left( r\_1^\*(m) r\_2(m) \right) = \sum\_{m=0}^{L-1} \left( r\_1^\*(m) r\_1(m+L) \right) \tag{21}$$

The time offset can be estimated from

$$
\hat{m} = \arg\max\_{n} \left( \left| R(n) \right|^2 \right) \tag{22}
$$

Assuming that the frame synchronization is accurate, the difference between two CI complex sequences can be approximately regarded as the result of the frequency shift

$$\theta = \operatorname{angle}(R(\hat{n})) \tag{23}$$

$$
\Delta f = \theta / (2\pi \,\mathrm{T}/2) = \theta / (\pi \,\mathrm{T}) \tag{24}
$$

where *f* is the fractional frequency shift, is the phase offset caused by frequency shift, *T* is the period of the synchronization signal which is equals to the CI/OFDM signal.

Fig. 10 shows the sliding correlation peaks of LFM signal and CI complex sequence at the receiver side in AWGN channel.

#### **4.2 Channel estimation and equalization**

When the pilot is a CAZAC sequence, it was proven that in the presence of noise, the mean square error of the channel response estimation is minus (Milewski, 1983). The mean square error equals to the variance of the noise in the channel, that is

$$L(\sum\_{i} \left| \hat{r}\_i - r\_i \right|^2) = L\sigma^2 \sum\_{i} \left| \upsilon\_i \right|^2 = \sigma^2 \tag{25}$$

where *<sup>i</sup> v V* , *V U* 1 , *U* is the Fourier transform of the pilot sequence.

Two kinds of pilot sequences which are both CAZAC sequences are chosen to estimate the underwater acoustic channel response.

Fig. 10. Sliding correlation peak under AWGN channel. (a) Peak of LFM signal (b) Peak of CI spreading sequence

## **4.2.1 Pilot**

106 Underwater Acoustics

123 1 1 2 1 1 2 1 1 2 1 1,1,...,1,1, , , ,...., ,1, , ,..., ,1, , ,..., ,1, , ,..., *NN N*

 

,0 1 *k N* . Suppose the two received sequences are 1*r m*( ) and 2*r m*( )

 

<sup>1</sup> \* 1 2

( ) ( ( ) ( ))

where the L is the length of the sequence. Since the sequences are identical at the transmitter, the impact of the channel is assumed to be same to the two sequences, (18) can

() ( ) ( ) ( )( )

The cross-correlation of two sequences can be changed into auto-correlation of one

1 1 \* \* 12 11

*R r mr m r mr m L* 

<sup>2</sup> <sup>ˆ</sup> arg max ( ) *<sup>n</sup>*

Assuming that the frame synchronization is accurate, the difference between two CI complex sequences can be approximately regarded as the result of the frequency shift

*fT T*

Fig. 10 shows the sliding correlation peaks of LFM signal and CI complex sequence at the

When the pilot is a CAZAC sequence, it was proven that in the presence of noise, the mean square error of the channel response estimation is minus (Milewski, 1983). The mean square

> 2 2 2 2 ( ) ˆ *i i i i i E rr L v*

*T* is the period of the synchronization signal which is equals to the CI/OFDM signal.

 (2 2) ( ) 

 

0 0 (0) ( ) ( ) ( ) ( )

*Rn r mr m n r mr m L n*

 1 1 \* \* 1 2 1 1

*Rn r mr m n* 

0

(Hlaing et al. 2003; Ren, 2005), the cross-correlation function of the two sequences is

*L*

*m*

0 0

*L L*

*m m*

*L L*

*m m*

The time offset can be estimated from

where *f* is the fractional frequency shift,

**4.2 Channel estimation and equalization** 

error equals to the variance of the noise in the channel, that is

where *<sup>i</sup> v V* , *V U* 1 , *U* is the Fourier transform of the pilot sequence.

receiver side in AWGN channel.

where *<sup>j</sup>*(2 ) *k N <sup>k</sup> e*

be written as

sequence, that is

   

22 2 33 3 1 1 1

(18)

 

(19)

 

 

 

(20)

(21)

*n Rn* (22)

*angle R n* ( ( )) ˆ (23)

is the phase offset caused by frequency shift,

(24)

(25)

*NNN N*

1. CI complex sequence

CI complex sequence was given in equation (18). It is easy to prove the CAZAC feature of the CI complex sequence. Fig. 11 gives simulation results of the CI complex sequence.

Fig. 11. The CAZAC feature of the CI complex sequence. (a) constant amplitude (b) zero autocorrelation

CI/OFDM Underwater Acoustic Communication System 109

In the conceptual model of CI/OFDM, the information symbols are simultaneously modulated on multi-subcarrier which makes CI/OFDM inherently having the frequency diversity. At the receiver side, frequency combining may be used to improve the

We still focus on the multi-carrier algorithm which makes use of the properties of IDFT/DFT, such as the linearity and the circular shift. Since every parallel input signal of the second IDFT is the summation of information signals, which are spread by CI signal, the frequency diversity combining should be at the end of the first DFT module at the receiver side.At the receiver, after orthogonal multi-carrier demodulation, the output of the first

2 1

*N j ik N ii k i k r H ae n*

2 1

( ) *N j ik N*

0

3.5 x 104

0.5 1 1.5 2 2.5 3

(a) (b) Fig. 14. Channel impulse respond estimated by CHU sequence (a) AWGN channel (b) 4-path

*i ii i i k i k R wr w H a e n*

where *wi* is the gain of the ith subcarrier determined by different combining strategies. Since *Ri* includes all information about transmitted symbols, the second FFT not only is applied for decomposing the CI spreading into the subcarrier components, but also is used

(26)

(27)

<sup>0</sup> <sup>200</sup> <sup>400</sup> <sup>600</sup> <sup>800</sup> <sup>1000</sup> <sup>1200</sup> <sup>0</sup>

0

where *i N* [1, ] is the number of the subcarrier, *Hi* is the transition function of the sub-

According to Fig. 15, the input signals at the second FFT module which can be expressed as

**4.2.2 Frequency domain equalization** 

channel and *<sup>k</sup> a* is the information symbol, *k N* [1, ] .

to complete the frequency combining.

<sup>0</sup> <sup>200</sup> <sup>400</sup> <sup>600</sup> <sup>800</sup> <sup>1000</sup> <sup>1200</sup> <sup>0</sup>

performance of the system.

FFT is

0.5

Rayleigh channel

1

1.5

2

2.5

3

3.5 x 104

#### 2. CHU sequence

CHU sequence is a polyphase code with a periodic autocorrelation function (CHU, 1972). It was proven that the CHU sequence can be constructed for any code length. When N is even,

CHU sequence is defined as 2 exp( ) *<sup>k</sup> <sup>M</sup> <sup>k</sup> a i N* . When N is odd, it is ( 1) exp( ) *<sup>k</sup> M kk a i N* ,

where M is an integer relatively prime to N. Fig. 12 shows the amplitude-frequency and autocorrelation results of CHU sequence. Fig. 13 and Fig.14 show the channel impulse respond estimated by CI complex sequence and CHU sequence under AWGN and 4-path Rayleigh channel.

Fig. 12. The CAZAC feature of the CHU sequence (a) constant amplitude (b) zero autocorrelation

Fig. 13. Channel impulse respond estimated by CI complex sequence (a) AWGN channel (b) 4-path Rayleigh channel

#### **4.2.2 Frequency domain equalization**

108 Underwater Acoustics

CHU sequence is a polyphase code with a periodic autocorrelation function (CHU, 1972). It was proven that the CHU sequence can be constructed for any code length. When N is even,

where M is an integer relatively prime to N. Fig. 12 shows the amplitude-frequency and autocorrelation results of CHU sequence. Fig. 13 and Fig.14 show the channel impulse respond estimated by CI complex sequence and CHU sequence under AWGN and 4-path

0

500

1000

Amplitude

(a) (b)

100

(a) (b) Fig. 13. Channel impulse respond estimated by CI complex sequence (a) AWGN channel (b)

200

300

400

500

600

700

Fig. 12. The CAZAC feature of the CHU sequence (a) constant amplitude (b) zero

1500

2000

. When N is odd, it is ( 1) exp( ) *<sup>k</sup>*

<sup>2500</sup> The zero autocorrelation characteristics

*M kk a i*

<sup>0</sup> <sup>200</sup> <sup>400</sup> <sup>600</sup> <sup>800</sup> <sup>1000</sup> <sup>1200</sup> -500

<sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> <sup>900</sup> <sup>0</sup>

N(sample)

*N* ,

2

*N* 

exp( ) *<sup>k</sup> <sup>M</sup> <sup>k</sup> a i*

2. CHU sequence

Rayleigh channel.

autocorrelation

Amplitude

CHU sequence is defined as


f(Hz)

<sup>0</sup> <sup>200</sup> <sup>400</sup> <sup>600</sup> <sup>800</sup> <sup>1000</sup> <sup>1200</sup> <sup>0</sup>

4-path Rayleigh channel

The frequency-amplitude characteristics

In the conceptual model of CI/OFDM, the information symbols are simultaneously modulated on multi-subcarrier which makes CI/OFDM inherently having the frequency diversity. At the receiver side, frequency combining may be used to improve the performance of the system.

We still focus on the multi-carrier algorithm which makes use of the properties of IDFT/DFT, such as the linearity and the circular shift. Since every parallel input signal of the second IDFT is the summation of information signals, which are spread by CI signal, the frequency diversity combining should be at the end of the first DFT module at the receiver side.At the receiver, after orthogonal multi-carrier demodulation, the output of the first FFT is

$$r\_i = H\_i \cdot \sum\_{k=0}^{N-1} a\_k e^{j\frac{2\pi}{N}i\cdot k} + n\_i \tag{26}$$

where *i N* [1, ] is the number of the subcarrier, *Hi* is the transition function of the subchannel and *<sup>k</sup> a* is the information symbol, *k N* [1, ] .

According to Fig. 15, the input signals at the second FFT module which can be expressed as

$$R\_i = w\_i r\_i = w\_i (H\_i \sum\_{k=0}^{N-1} a\_k e^{\frac{j\Delta \pi}{N} \cdot k} + n\_i) \tag{27}$$

where *wi* is the gain of the ith subcarrier determined by different combining strategies. Since *Ri* includes all information about transmitted symbols, the second FFT not only is applied for decomposing the CI spreading into the subcarrier components, but also is used to complete the frequency combining.

Fig. 14. Channel impulse respond estimated by CHU sequence (a) AWGN channel (b) 4-path Rayleigh channel

CI/OFDM Underwater Acoustic Communication System 111

The experimental pool in Xiamen University is an un-censored pool which size is

Channel estimation was carried out, 13kHz single carrier signal is sent at the 30ms intervals. The sample rate of A/D is 160kHz. The transmitted and received signals are shown in Fig. 17. We can see that key features of the channel are multi-path transmission with low noise because of the stationary water in the pool. The maximum delay is about 19 ms which


In this experiment, LFM signal was used to get coarse synchronization of the frame and CI complex sequence was applied to achieve accurate synchronization and fractional frequency shift estimation (Xu et al., 2008). SNR estimation algorithm is borrowed from the work (Ren, 2005) with synthesis of CI complex sequence. CI complex sequence is used as pilot to estimate the impulse response of the channel. Frequency-domain equalization ORC is used at the receiver to improve the performance of the system. Table 1 shows the parameters of

The results are shown in Table 2. Since the water in pool is stationary, the SNR is high and the average SNR is about 12dB. BER performance is good and the average fractional frequency shift is about 0.07Hz, which is very small compared with the subcarrier interval



0

Amplitude

0.2

0.4

X: 8.569e+004 Y: 0.521

8.5 8.6 8.7 8.8 8.9 9 9.1 9.2 9.3 9.4

Sample

Received signal

X: 8.764e+004 Y: 0.1035X: 8.875e+004 Y: 0.02456

x 104

**5. Field test results** 

**5.1.1 Experimental pool** 

430(L)x320(W)x200(H)cm.

magnitude is under 3% of the maximum one.

Transmitted signal

0 1000 2000 3000 4000 5000

Sample

**5.1.2 Results of experimental pool** 

the CI/OFDM system.

*f* 6000 /1024 5.86*Hz* .

Fig. 17. The transmitted and received signal (13kHz)

**5.1 Experiment I** 


Amplitude

Several frequency combining strategies such as EGC, the MRC, orthogonal restoration combining (ORC) and MMSEC are considered in frequency selective channel (Itagkai & Adachi, 2004). Computer simulation results are shown in Fig. 16. In CI/OFDM system, though both combing strategies are sensitive to the inter-carrier interference (ICI), the MRC performance is worse than EGC. It is because that in MRC, the phase changes of the signals are lost, which is very important to CI/OFDM. Since ORC equalization perfectly restores frequency non-selective channel but produces the noise enhancement, its performance is better than MRC and EGC but worse than MMSEC. As SNR increases, the BER performance of ORC gets better, but MMSEC equalization provides the best performance. AS we know, the MMSEC not only restores frequency non-selective channel but also minimizes the noise.

Fig. 15. Frequency combining in multi-carrier algorithm

Fig. 16. Performance comparisons of ORC, MMSEC, EGC and MRC

## **5. Field test results**

## **5.1 Experiment I**

110 Underwater Acoustics

Several frequency combining strategies such as EGC, the MRC, orthogonal restoration combining (ORC) and MMSEC are considered in frequency selective channel (Itagkai & Adachi, 2004). Computer simulation results are shown in Fig. 16. In CI/OFDM system, though both combing strategies are sensitive to the inter-carrier interference (ICI), the MRC performance is worse than EGC. It is because that in MRC, the phase changes of the signals are lost, which is very important to CI/OFDM. Since ORC equalization perfectly restores frequency non-selective channel but produces the noise enhancement, its performance is better than MRC and EGC but worse than MMSEC. As SNR increases, the BER performance of ORC gets better, but MMSEC equalization provides the best performance. AS we know, the MMSEC not only restores frequency non-selective channel but also minimizes the noise.

0*r*

*i r*

*<sup>N</sup>* <sup>1</sup> *r*

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>14</sup> <sup>16</sup> <sup>18</sup> <sup>20</sup> 10-4

SNR (dB)

CI/OFDM

Fig. 15. Frequency combining in multi-carrier algorithm

no combining ORC MMSEC EGC MRC

Fig. 16. Performance comparisons of ORC, MMSEC, EGC and MRC

10-3

10-2

BER

10-1

100

*r n*( )

*w*0

*R*0

*Ri*

*RN*<sup>1</sup>

0 *a*ˆ

ˆ*i a*

<sup>1</sup> ˆ*<sup>N</sup> a*

*wi*

*wN*<sup>1</sup>

## **5.1.1 Experimental pool**

The experimental pool in Xiamen University is an un-censored pool which size is 430(L)x320(W)x200(H)cm.

Channel estimation was carried out, 13kHz single carrier signal is sent at the 30ms intervals. The sample rate of A/D is 160kHz. The transmitted and received signals are shown in Fig. 17. We can see that key features of the channel are multi-path transmission with low noise because of the stationary water in the pool. The maximum delay is about 19 ms which magnitude is under 3% of the maximum one.

Fig. 17. The transmitted and received signal (13kHz)

## **5.1.2 Results of experimental pool**

In this experiment, LFM signal was used to get coarse synchronization of the frame and CI complex sequence was applied to achieve accurate synchronization and fractional frequency shift estimation (Xu et al., 2008). SNR estimation algorithm is borrowed from the work (Ren, 2005) with synthesis of CI complex sequence. CI complex sequence is used as pilot to estimate the impulse response of the channel. Frequency-domain equalization ORC is used at the receiver to improve the performance of the system. Table 1 shows the parameters of the CI/OFDM system.

The results are shown in Table 2. Since the water in pool is stationary, the SNR is high and the average SNR is about 12dB. BER performance is good and the average fractional frequency shift is about 0.07Hz, which is very small compared with the subcarrier interval *f* 6000 /1024 5.86*Hz* .

CI/OFDM Underwater Acoustic Communication System 113

As shown in Fig. 18, multi-path signals is visible during the 100ms intervals though the amplitude of the multi-path signal is about 2% of the maximum one. The amplitude of the 14KHz signal was changed after 100ms. Fig. 19 denotes the different amplitudes of the sweeping signals which reveal the time-varying and frequency-varying features of the

x 105

Table 3 is the parameters of CI/OFDM underwater acoustic communication system. Table 4 is the BER performance of the system without and with frequency selective combining. The BER performance was significantly improved due to the frequency diversity combining by

Data rate 4.97kbps/1.24kbps in 4-fold frequency diversity

BER (without frequency diversity) BER (with 4-fold frequency diversity)


Amplitude

0 0.5 1 1.5 2 2.5

Sample

Received signal

x 105

acoustic underwater channel.


Amplitude

0 0.5 1 1.5 2

**5.2.2 Results of experiment II** 

the cost of decrease of the data rate.

Table 3. System parameters

Table 4. BER performance

Sample

Baseband mapping QPSK Subcarrier mapping Localized Synchronization signal LFM

Pilot pattern Block Equalization MMSEC Bandwidth 5kHz Carrier frequency 15kHz Sampling rate 60kHz Number of the parallel signal 1024

Pilot CI/OFDM signal

0.014257 0.0058714

Fig. 19. Transmitted and received sweeping signal (9kHz to 21kHz)

Transmitted signal


Table 1. System parameters


Table 2. BER performance

## **5.2 Experiment II**

## **5.2.1 Shallow water in Wuyuan Bay of Xiamen**

A CI/OFDM underwater acoustic communication experiment was conducted on Dec. 12, 2008 in Wuyuan Bay of Xiamen, China. The distance between the transmitter and the receiver was 1000m, and they were deployed at 3 m and 2 m below the sea-surface, respectively. The average depth of the water is 4. 5m which was changed with the tide. The channel probing signals include two kinds. One is a single carrier signal which was transmitted at the 100ms intervals repeatedly. The other is a sweeping signal which frequency is from 9kHz to 21kHz. It was also be transmitted once every 100ms.

Fig. 18. Transmitted and received signal (14kHz)

112 Underwater Acoustics

Synchronization signal LFM/CI complex spreading sequence

Pilot CI complex sequence

SNR (dB) Fractional frequency shift (Hz) BER

12.33659 0.068643 3.48771e-06

frequency is from 9kHz to 21kHz. It was also be transmitted once every 100ms.

A CI/OFDM underwater acoustic communication experiment was conducted on Dec. 12, 2008 in Wuyuan Bay of Xiamen, China. The distance between the transmitter and the receiver was 1000m, and they were deployed at 3 m and 2 m below the sea-surface, respectively. The average depth of the water is 4. 5m which was changed with the tide. The channel probing signals include two kinds. One is a single carrier signal which was transmitted at the 100ms intervals repeatedly. The other is a sweeping signal which

> -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Amplitude

X: 8.149e+004 Y: 2.315

> X: 8.211e+004 Y: 0.7444

8.2 8.3 8.4 8.5 8.6 8.7

Sample

Received signal

X: 8.644e+004 Y: 2.028

X: 8.609e+004 Y: 0.2453

x 104

Baseband mapping QPSK Subcarrier mapping Localized

Pilot pattern Block Equalization ORC Bandwidth 6kHz Carrier frequency 13kHz Sampling rate 156kHz Number of the parallel signal 1024 System rate 4.97kbps

**5.2.1 Shallow water in Wuyuan Bay of Xiamen** 

Transmitted signal

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Sample

Fig. 18. Transmitted and received signal (14kHz)

Table 1. System parameters

Table 2. BER performance

**5.2 Experiment II** 


Amplitude

As shown in Fig. 18, multi-path signals is visible during the 100ms intervals though the amplitude of the multi-path signal is about 2% of the maximum one. The amplitude of the 14KHz signal was changed after 100ms. Fig. 19 denotes the different amplitudes of the sweeping signals which reveal the time-varying and frequency-varying features of the acoustic underwater channel.

Fig. 19. Transmitted and received sweeping signal (9kHz to 21kHz)

## **5.2.2 Results of experiment II**

Table 3 is the parameters of CI/OFDM underwater acoustic communication system. Table 4 is the BER performance of the system without and with frequency selective combining. The BER performance was significantly improved due to the frequency diversity combining by the cost of decrease of the data rate.


Table 3. System parameters


Table 4. BER performance

CI/OFDM Underwater Acoustic Communication System 115

The Frequency-varying feature is different from the feature in short range at the same water domain. In this experiment, the ambient noise was much higher than that in the

x 105


(a) (b)

Fig. 21. Received signals. (a) received sweeping signals ( 8kHz to 16kHz) (b) received single

Based on the channel probing results, we concluded that the channel in Baicheng water was worse than that in Wuyuan Bay. In experiments, 4-fold frequency diversity and (2,1) LDPC were applied in CI/OFDM systems (Bai et al., 2009) in order to guarantee the BER

System parameters are same in Table 3 except that the comb pilot pattern is used instead of the block pilot. The results of using (2,1) LDPC is the performance improvement and the

Date BER (before LDPC decoding ) BER (after LDPC decoding )

Fig. 22 is the received CI/OFDM signals in short range (2000m) experiment. The amplitude of the received signal changed dramatically, and the level of ambient noise was high. There

Dec. 17, 2009 0.0393 0 Dec. 31, 2009 0.06598 0

Amplitude

4.5 4.6 4.7 4.8 4.9 5 5.1

Sample

Received signal

x 104

short range.


Amplitude

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Sample

carrier signal (14kHz and 14.5kHz)

**5.3.2 Results of experiment III** 

performance of the system.

decrease of the data rate.

Table 5. BER performance

Received signal

## **5.3 Experiment III**

## **5.3.1 Shallow water in Baicheng water**

Two CI/OFDM underwater acoustic communication experiments were conducted on Dec. 17, 2009 and Dec. 31, 2009 in Baicheng water of Xiamen, China, respectively. The transmitter was deployed at 2.5m above the sea-floor in 5.5m deep water and the receiver was deployed at 9m below the sea-surface in 16m deep water. The horizontal distance between the transmitter and receiver were 2000m and 5000m, respectively.

The channel probing signals used in these two experiments were same sweeping signals, with frequency from 8KHz to 16KHz. The time interval between different frequencies was 30 ms.

Fig.20 is the received probing signal at the short range (2000m). The sea condition was calm but vessels passed through the water frequently. The Frequency-varying feature is different from the feature in Wuyuan Bay. In this experiment, the amplitudes of the lower and higher frequency were faded significantly. The ambient noise was much higher in this underwater channel. From the enlarged map of received signal of 14KHz and 14. 5KHz, it is easy to see that the amplitudes of the strongest arrival changed with time and frequencies. The high level of noise made it difficult to distinguish multi-path signals from the ambient noise. Note that there is no apparent impulse interference and the amplitudes of multi-path signals are much smaller than that of the main path.

Fig. 20. Received signals. (a) received sweeping signals ( 8kHz to 16kHz) (b) received single carrier signal (14kHz and 14.5kHz)

Fig. 21. is the transmitted and received probing signal at the long range (5000m). It was a windy day, and the sea condition was not calm. Many vessels passed through the water. 114 Underwater Acoustics

Two CI/OFDM underwater acoustic communication experiments were conducted on Dec. 17, 2009 and Dec. 31, 2009 in Baicheng water of Xiamen, China, respectively. The transmitter was deployed at 2.5m above the sea-floor in 5.5m deep water and the receiver was deployed at 9m below the sea-surface in 16m deep water. The horizontal distance between the

The channel probing signals used in these two experiments were same sweeping signals, with frequency from 8KHz to 16KHz. The time interval between different frequencies was

Fig.20 is the received probing signal at the short range (2000m). The sea condition was calm but vessels passed through the water frequently. The Frequency-varying feature is different from the feature in Wuyuan Bay. In this experiment, the amplitudes of the lower and higher frequency were faded significantly. The ambient noise was much higher in this underwater channel. From the enlarged map of received signal of 14KHz and 14. 5KHz, it is easy to see that the amplitudes of the strongest arrival changed with time and frequencies. The high level of noise made it difficult to distinguish multi-path signals from the ambient noise. Note that there is no apparent impulse interference and the amplitudes of multi-path signals

(a) (b)


Amplitude

Received signal Received signal

8.7 8.8 8.9 9 9.1 9.2 9.3

Sample

x 104

Fig. 20. Received signals. (a) received sweeping signals ( 8kHz to 16kHz) (b) received single

x 104

Fig. 21. is the transmitted and received probing signal at the long range (5000m). It was a windy day, and the sea condition was not calm. Many vessels passed through the water.

**5.3 Experiment III** 

30 ms.


Amplitude

**5.3.1 Shallow water in Baicheng water** 

are much smaller than that of the main path.

carrier signal (14kHz and 14.5kHz)

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>1</sup>

Sample

transmitter and receiver were 2000m and 5000m, respectively.

The Frequency-varying feature is different from the feature in short range at the same water domain. In this experiment, the ambient noise was much higher than that in the short range.

Fig. 21. Received signals. (a) received sweeping signals ( 8kHz to 16kHz) (b) received single carrier signal (14kHz and 14.5kHz)

## **5.3.2 Results of experiment III**

Based on the channel probing results, we concluded that the channel in Baicheng water was worse than that in Wuyuan Bay. In experiments, 4-fold frequency diversity and (2,1) LDPC were applied in CI/OFDM systems (Bai et al., 2009) in order to guarantee the BER performance of the system.

System parameters are same in Table 3 except that the comb pilot pattern is used instead of the block pilot. The results of using (2,1) LDPC is the performance improvement and the decrease of the data rate.


Table 5. BER performance

Fig. 22 is the received CI/OFDM signals in short range (2000m) experiment. The amplitude of the received signal changed dramatically, and the level of ambient noise was high. There

CI/OFDM Underwater Acoustic Communication System 117

A few problems exist in the system. The most important one is that the inherent frequency diversity of CI/OFDM did not play its due role in the system. According to our analysis, the orthogonality between the different symbols modulated on the same subcarrier will be destroyed if the phases were changed when signals transmitted in the channel. It means that the intersymbol interference cancels out the diversity combining gain. Future researches should focus on the optimization of the algorithms in order to take advantage of the inherent frequency diversity and other realizations based on the conceptual

This work was supported by the Fundamental Research Funds for the Central Universities

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**7. Acknowledgment** 

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**8. References** 

was deeply frequency fading in the bandwidth of the signal. It might explain the reason of BER performance degradation even though the 4-fold frequency diversities were used.

Fig. 22. The received signal (a) the received profile (b) the power spectral density of the received signal

## **6. Conclusion**

In this chapter, we first proposed two algorithms which simplify the modulation and demodulation of the conceptual CI/OFDM. Secondly, based on these algorithms and jointed with synchronization, channel estimation and equalization, we constructed CI/OFDM underwater acoustic communication systems. In the end, a number of experiments were carried out in the experimental pool and shallow waters in Xiamen of China to verify the performance of the system. Field results are as followed:

The BER of the uncoded CI/OFDM underwater acoustic communication system at the data rate 4.97kbps is lower than <sup>6</sup> 4 10 in the experimental pool (experiment I) and <sup>2</sup> 1.5 10 in Wuyuan Bay in Xiamen (experiment II). When 4-fold frequency diversity is applied, the data rate is 1.24kbps and the BER performance of the system is lower than <sup>3</sup> 6 10 in experiment II.

The BER of the uncoded 4-fold frequency diversity CI/OFDM acoustic communication system at the data rate 1.24kbps is lower than <sup>2</sup> 4 10 and <sup>2</sup> 7 10 in experiment III at Baicheng water in Xiamen. The BER of the coded frequency diversity CI/OFDM acoustic communication system at the data rate 620bps is almost zero in the short range and the long range.

A few problems exist in the system. The most important one is that the inherent frequency diversity of CI/OFDM did not play its due role in the system. According to our analysis, the orthogonality between the different symbols modulated on the same subcarrier will be destroyed if the phases were changed when signals transmitted in the channel. It means that the intersymbol interference cancels out the diversity combining gain. Future researches should focus on the optimization of the algorithms in order to take advantage of the inherent frequency diversity and other realizations based on the conceptual CI/OFDM.

## **7. Acknowledgment**

This work was supported by the Fundamental Research Funds for the Central Universities of China 2010121062.

## **8. References**

116 Underwater Acoustics

was deeply frequency fading in the bandwidth of the signal. It might explain the reason of BER performance degradation even though the 4-fold frequency diversities were used.

x 105

Fig. 22. The received signal (a) the received profile (b) the power spectral density of the

(a) (b)

In this chapter, we first proposed two algorithms which simplify the modulation and demodulation of the conceptual CI/OFDM. Secondly, based on these algorithms and jointed with synchronization, channel estimation and equalization, we constructed CI/OFDM underwater acoustic communication systems. In the end, a number of experiments were carried out in the experimental pool and shallow waters in Xiamen of China to verify the

The BER of the uncoded CI/OFDM underwater acoustic communication system at the data rate 4.97kbps is lower than <sup>6</sup> 4 10 in the experimental pool (experiment I) and <sup>2</sup> 1.5 10 in Wuyuan Bay in Xiamen (experiment II). When 4-fold frequency diversity is applied, the data rate is 1.24kbps and the BER performance of the system is lower than

The BER of the uncoded 4-fold frequency diversity CI/OFDM acoustic communication system at the data rate 1.24kbps is lower than <sup>2</sup> 4 10 and <sup>2</sup> 7 10 in experiment III at Baicheng water in Xiamen. The BER of the coded frequency diversity CI/OFDM acoustic communication system at the data rate 620bps is almost zero in the short range and the

0 1 2 3 4 5 6 7 8

Sample

performance of the system. Field results are as followed:

Received signal


received signal

**6. Conclusion** 

<sup>3</sup> 6 10 in experiment II.

long range.

Amplitude


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**7** 

*P.R.China* 

**Iterative Equalization and** 

Liang Zhao and Jianhua Ge

**Decoding Scheme for Underwater** 

**Acoustic Coherent Communications** 

*State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an,* 

Digital communications through underwater acoustic (UWA) channels differ from those in other media, such as radio channels, due to the high temporal and spatial variability of the acoustic channel which make the available bandwidth of the channel limited and dependent on both range and frequency. In order to overcome disadvantage factors and maximize performance to conduct real-time information understanding, underwater acoustic communications require the higher degree of information extraction and development from all kinds of onboard acoustic sensors and processing systems. A higher performance communication technology is needed in order to focus high-performance data processing on the problems and tasks faced by human operators and decision-makers. In order to establiseh reliable data commnication on the severely band-limited underwater acoustic channels, bandwidth-efficient modulation techniques (i.e. coherent communications) should be employed to overcome the inter-symbol interference (ISI) caused by channel multi-path propagation. The effective approach to eliminate the ISI caused by multipath propagation is that adaptive decision feedback equalizer (ADFE) integrates with spatial diversity. That is multi-channel adaptive decision feedback equalizer, which is applied in (Kilfoyle & Baggeroer, 2000; Stojanovic, 1996, 2005; Zhao et al., 2008) represents a more general

However, Single technique, such as equalizer, is difficult to obtain satisfied data transmission because of the complexity of UWA channel, especially in shallow water channel. In recent years, more and more attention has been paid to Turbo codes, including parallel concatenated convolutional code (PCCC) (Berrou et al., 1993) and serially concatenated convolutional code (SCCC) (Benedetto & Montorsi, 1996), because of its near-capacity gains. The range of applications of Turbo codes has expanded to many areas of communications. Trellis-Coded Modulation (TCM) (Ungerboeck, 1982) is a kind of design option combining coding with modulation. It can provide over 3 dB coding gain without bandwidth expansion. Especially, it is interesting to combine PCCC or SCCC with TCM in order to improve the transmission spectral efficiency (i.e. parallel concatenated trellis codes modulation (PCTCM) (Benedetto et al., 1996; Chung & Lou, 2000; Legoff et al., 1994; Yang & Ge, 2005) and serial concatenated trellis codes modulation (SCTCM)) (Benedetto et,al., 1997; Divsalar & Pollara, 1997; Ho, 1997;

Shohon et al., 2003) in order to improve the transmission spectral efficiency.

**1. Introduction** 

approach to spatial and temporal signal processing.

Xu, F. Xu, R., Zhang Y. H., Sun H. X. & Wang, D. Q. (2008), Design and test of a carrier interferometry OFDM system in underwater acoustic channels, *Proceedings of IEEE International Conference on Communications, Circuits and Systems,* ISBN 978-1-4244- 2063-6, Fujian, China, 25-27 May, 2008
