# Data Selective Rake Reception for Underwater Acoustic Communication in Strong Multipath Interference

Authors: Shingo Yoshizawa; Hiroshi Tanimoto; Takashi Saito
Journal: Journal of Electrical and Computer Engineering
 (2017)

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## Abstract

In underwater acoustic communication (UAC), very long delay waves are caused by reflection from water surfaces and bottoms and obstacles. Their waves interfere with desired waves and induce strong multipath interference. Use of a guard interval (GI) is effective for channel compensation in OFDM. However, a GI tends to be long in shallow-water environment because a guard time is determined by a delay time of multipath. A long GI produces a very long OFDM frame in several seconds, which is disadvantageous to a response speed of communication. This paper presents a method of keeping good communication performance even for a short GI. We discuss influence of intercarrier interference (ICI) in OFDM demodulation and propose a method of data selective rake reception (DSRake). The effectiveness of the proposed method is discussed by received signal distribution and confirmed by simulation results.


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## Body

## 1. Introduction

Remotely operated underwater vehicle (ROV) and autonomous underwater vehicle (AUV) are widely used in current marine surveys [1, 2]. Wireless communication is an important underlying technology in remote control and information gathering for ROV and AUV. Since light and electromagnetic waves have large attenuation in seawater, use of sound waves is suitable for long range communication. Underwater acoustic communication (UAC) has been studied for a long time as well as radio communication. For instance, a communication unit of single-sideband amplitude modulation (SSB-AM) was developed in the 1950s. Digital modulation schemes of spread spectrum [3, 4], OFDM [5–7], and MIMO [8, 9] have been studied in recent studies.Demodulation is affected by multipath interference and Doppler in UAC, which degrade communication performance. Doppler compensation has been discussed in [10–13]. We focus on the problem of multipath interference in this paper. Very long delay waves are caused by reflection from water surfaces and bottoms and obstacles. Their waves interfere with desired waves and induce strong multipath interference. For mitigation of multipath interference, OFDM with a guard interval (GI) (also named as a cyclic prefix (CP)) is adopted. As far as a delay time of multipath is less than a guard time, influence of delay waves can be expressed by channel coefficients for every frequency bin. These channel coefficients can be estimated and equalized by frequency domain equalization (FDE). Effectiveness of OFDM using a GI has been verified by sea trials in [5–7].The drawback of using a GI is decrease of communication efficiency because a GI itself is redundant. In shallow-water environment, a long GI is required when a guard time is determined by a delay time of multipath. The delay time ranges from several milliseconds to 100 milliseconds in underwater acoustic propagation, being dependent on surrounding environments. In the sea trial presented by Berger et al. [7], the GI and FFT length were set to 48 ms and 491 ms. OFDM frame duration runs up to 5.4 seconds, which would be undesirable in terms of a response speed of communication.This paper presents a method of keeping good communication performance even for a short GI. Strong multipath interference is assumed in our study, where arrival times of large delay waves exceed a guard time. First, we discuss the influence of interblock interference (IBI) and intercarrier interference (ICI) in received signal distribution. Although IBI always interferes with demodulation, ICI can be suppressed by taking an appropriate FFT window timing. Next, we propose a new idea of data selective rake reception (DSRake) according to the above discussion. DSRake takes multiple fingers by changing FFT window timing for every OFDM block. The best finger with the least ICI is selected by checking data errors for all fingers. With regard to QPSK modulation, the mitigation of ICI has an impact on avoiding error floor in BER performance. This paper discusses OFDM as communication scheme. As for single carrier frequency domain equalization (SC-FDE), we briefly report it in [14].This paper is organized as follows. Section2 discusses the influences of IBI and ICI by received signal distribution. Section 3 proposes DSRake for the mitigation of ICI. Section 4 reports simulation results evaluating DSRake in strong multipath interference. Section 5 summarizes our work.


## 2. Received Signal Distribution

### 2.1. OFDM Model

We discuss the influences of IBI and ICI by received signal distribution. Theoretical symbol error rates (SERs) of PSK and QAM can be obtained by probability density function (PDF) when we observe received signal amplitudes in noisy propagation channels. We use a basic OFDM model illustrated in Figure1. In the transmitter side, all transmitted data are set to zero, given by Am(n)=0 (0≤m≤M-1,0≤n≤N-1). m denotes a block number for M OFDM blocks. n is an subcarrier index for N OFDM subcarriers. A transmitted symbol becomes Bm(n)=1 after BPSK modulation. The transmitted symbol is converted into 1 or -1 by multiplying random patterns of Sm(n) in the scramble block, which becomes Xm(n). A time-domain signal block is given by xm(t) after IFFT operation, where t is a discrete sample time. A transmitted signal is expressed by x(t) after GI insertion and parallel to serial conversion. We presuppose that this GI is given by a cyclic prefix.Figure 1
Basic OFDM model.In the receiver side, a received signal block ofym(t) is obtained by cutting out a received signal of y(t) by a FFT window having a rectangular shape. A frequency domain signal block is given by Ym(n) after FFT operation. Cm(n) is obtained by multiplying the random patterns of Sm(n) used in transmitter side. Received data of Dm(n) are obtained after BPSK demodulation. We set lengths of a data block, GI, and OFDM block to T(=N), TG, and T+TG.We use a two-path channel model consisting of direct and delay waves. A relation between transmitted and received signals is expressed as(1)yt=xt+αxt-τ+nt,where α is a propagation channel coefficient (|α|<1) for the delay wave and τ is an arrival time difference between direct and delay waves. n(t) denotes noise signal component determined by a metric of the carrier to noise ratio (CNR).Figure2 shows an OFDM frame structure and timing positions for FFT windowing. This figure shows the case of receiving only a direct wave. When timing synchronization is perfect, their positions are the same of those of data blocks, not overlapping with GIs. The block boundary is emphasized between OFDM blocks.Figure 2
OFDM frame structure and timing positions for FFT windowing.The received signal distribution for a 30-dB CNR is shown in Figure3. We set a data block length and a guard time to T=256 and TG=64, respectively. The signal distribution for the received BPSK symbols of Cm(n) is plotted. The total number of received BPSK symbols is 256×20=5,120. In BPSK demodulation, a symbol error occurs when Cm(n) has a negative value. All the signals in Figure 3 locate around 1, which indicates the error-free demodulation of Cm(n)≈Bm(n).Figure 3
Received signal distribution for only direct wave.


### 2.2. Influence of Interblock Interference (IBI)

Let us consider the influence of IBI as a long delay wave overlaps with a direct wave. Figure4 shows the relations between direct and delay waves where their arrival time differences of τ=320 and τ=330. The propagation channel coefficient is set to α=0.7 for a delay wave. IBI happens due to the collision of different data blocks for direct and delay waves.Figure 4
Relations between direct and delay waves (τ=320 and τ=330).
(a)
α
=
0.7, τ=320, 30-dB CNR
(b)
α
=
0.7, τ=330, 30-dB CNRThe received signal distributions for Figure4(a) are shown in Figure 5. In Figure 4(a), (m-1)th block of the delay wave exactly overlaps with mth block of the direct wave in the FFT window period. The received symbol of Cm(n) can be introduced from the following equations, omitting the noise component of n(t).(2)ymt=xmt+αxm-1t(3)Ymn=Xmn+αXm-1n(4)Ymn=SmnBmn+αSm-1nBm-1n(5)Cmn=Bmn+αSmnSm-1nBm-1n.(6)Cmn=1+αSmnSm-1n.Since Sm(n) and Sm-1(n) are random patterns consisting of 1 or -1, (6) gives Cm(n)∈{0.3,1.7}. This signal distribution can be observed in Figure 5(a). Although the signal values of Cm(n) do not concentrate on 1, all of them are positive. A symbol error does not occur in Figure 4(a).Figure 5
Received signal distributions for long delay waves.
(a)
α
=
0.7, τ=320, 30-dB CNR
(b)
α
=
0.7, τ=330, 30-dB CNRIn Figure4(b), (m-1)th block of the delay wave is slightly deviated from mth block of the direct wave. Cm(n) can be introduced by(7)ymt=xmt+αxm-1t-τd(8)Ymn=Xmn+αXm-1nej2πnτd/N(9)ReCmn=ReBmn+αSmnSm-1nBm-1nej2πnτd/N(10)ReCmn=1+ReαSmnSm-1nej2πnτd/N,where we apply τd=τ-TG+T from circular shift property. The signal values of Re[Cm(n)] range from 0.3 to 1.7 as shown in Figure 5(b). This case also does not induce a symbol error.The IBI does not take a symbol error as long as a high CNR condition is kept as for this observation. The same phenomenon would be observed even in QPSK transmission. Improvement of SNR using antenna arrays is practical rather than keeping a high CNR, where Zheng presented MRC diversity in SIMO-OFDM as a measure against insufficient guard interval in [15].


### 2.3. Influence of Intercarrier Interference (ICI)

Let us consider the influence of ICI by giving another arrival time difference ofτ=300. The relation between direct and delay waves is shown in Figure 6. Different from Figure 4, (m-1)th data block and mth GI of the delay wave overlap with mth data block of the direct wave. This signal distribution is shown in Figure 7. Since some of Cm(n) have a negative value, a symbol error occurs.Figure 6
Relation between direct and delay waves (τ=300).Figure 7
Received signal distribution affected by ICI.We introduceCm(n) as well as Section 2.2. First, the received signal of ym(t) is given by(11)ymt=xmt+αum-1t+vmt.We decompose a received signal of the delay wave into um-1(t) and vm(t) as shown in Figure 6. Their functions are given by(12)um-1t=xm-1t-τd1if0≤t≤τd1-10ifτd1≤t≤N-1vmt=0if0≤t≤τd1-1xmt-τd2ifτd1≤t≤N-1,where we apply τd1=τ-TG and τd2=τd1-TG from circular shift property. um-1(t) can be replaced with xm-1(t-τd1)-um-1′(t). um-1′(t) is given by(13)um-1′t=0if0≤t≤τd1-1xm-1t-τd1ifτd1≤t≤N-1.Cm(n) can be expressed as(14)ymt=xmt+αxm-1t-τd1+α-um-1t+vmt(15)ReCmn=1+ReαSmnSm-1nej2πnτd1/N+ReαSmn-Um-1′n+Vmn.The received signal distribution of (15) would be almost the same as that of (10) if Um-1′(n) and Vm(n) are excluded. Um-1′(n) and Vm(n) can be expressed by using inverse discrete Fourier transform (IDFT) and DFT as(16)Um-1′n=∑t=τd1N-11N∑n=0N-1Sm-1nej2πtn/Ne-j2πτd2n/Ne-j2πnt/N(17)Vmn=∑t=τd1N-11N∑n=0N-1Smnej2πtn/Ne-j2πτd2n/Ne-j2πnt/N.The interferences of (16) and (17) are added for every subcarrier, which corresponds to ICI. Assuming that the average amplitude for the OFDM transmit signals after IDFT is 1/N (i.e., calculation within the square bracket in (16)), the average of deviations caused by Um-1′(n) and Vm(n) is roughly calculated as(18)±2αN-τd1N≃±0.11.These deviations would be observed by comparing the received signal distributions in Figures 5 and 7. The difference between Figures 4 and 6 is whether a block boundary is included within a FFT window.


### 2.4. Adjustment of FFT Window

The ICI can be avoided by changing FFT window timings, whose adjustment is illustrated in Figure8. The time positions of FFT windows have been shifted by 40 samples ahead. The block boundaries for the delay wave are not included for their FFT windows. Although this adjustment induces a phase rotation after FFT operation in frequency domain, the phase rotation can be detected and compensated by FDE. The received signal distribution after the FFT window adjustment is shown in Figure 9, where the phase rotation can be compensated before descramble. This distribution looks like Figure 5(b) owing to the ICI avoidance.Figure 8
Adjustment of FFT windowing.Figure 9
Received signal distribution after FFT window adjustment.


## 2.1. OFDM Model

We discuss the influences of IBI and ICI by received signal distribution. Theoretical symbol error rates (SERs) of PSK and QAM can be obtained by probability density function (PDF) when we observe received signal amplitudes in noisy propagation channels. We use a basic OFDM model illustrated in Figure1. In the transmitter side, all transmitted data are set to zero, given by Am(n)=0 (0≤m≤M-1,0≤n≤N-1). m denotes a block number for M OFDM blocks. n is an subcarrier index for N OFDM subcarriers. A transmitted symbol becomes Bm(n)=1 after BPSK modulation. The transmitted symbol is converted into 1 or -1 by multiplying random patterns of Sm(n) in the scramble block, which becomes Xm(n). A time-domain signal block is given by xm(t) after IFFT operation, where t is a discrete sample time. A transmitted signal is expressed by x(t) after GI insertion and parallel to serial conversion. We presuppose that this GI is given by a cyclic prefix.Figure 1
Basic OFDM model.In the receiver side, a received signal block ofym(t) is obtained by cutting out a received signal of y(t) by a FFT window having a rectangular shape. A frequency domain signal block is given by Ym(n) after FFT operation. Cm(n) is obtained by multiplying the random patterns of Sm(n) used in transmitter side. Received data of Dm(n) are obtained after BPSK demodulation. We set lengths of a data block, GI, and OFDM block to T(=N), TG, and T+TG.We use a two-path channel model consisting of direct and delay waves. A relation between transmitted and received signals is expressed as(1)yt=xt+αxt-τ+nt,where α is a propagation channel coefficient (|α|<1) for the delay wave and τ is an arrival time difference between direct and delay waves. n(t) denotes noise signal component determined by a metric of the carrier to noise ratio (CNR).Figure2 shows an OFDM frame structure and timing positions for FFT windowing. This figure shows the case of receiving only a direct wave. When timing synchronization is perfect, their positions are the same of those of data blocks, not overlapping with GIs. The block boundary is emphasized between OFDM blocks.Figure 2
OFDM frame structure and timing positions for FFT windowing.The received signal distribution for a 30-dB CNR is shown in Figure3. We set a data block length and a guard time to T=256 and TG=64, respectively. The signal distribution for the received BPSK symbols of Cm(n) is plotted. The total number of received BPSK symbols is 256×20=5,120. In BPSK demodulation, a symbol error occurs when Cm(n) has a negative value. All the signals in Figure 3 locate around 1, which indicates the error-free demodulation of Cm(n)≈Bm(n).Figure 3
Received signal distribution for only direct wave.


## 2.2. Influence of Interblock Interference (IBI)

Let us consider the influence of IBI as a long delay wave overlaps with a direct wave. Figure4 shows the relations between direct and delay waves where their arrival time differences of τ=320 and τ=330. The propagation channel coefficient is set to α=0.7 for a delay wave. IBI happens due to the collision of different data blocks for direct and delay waves.Figure 4
Relations between direct and delay waves (τ=320 and τ=330).
(a)
α
=
0.7, τ=320, 30-dB CNR
(b)
α
=
0.7, τ=330, 30-dB CNRThe received signal distributions for Figure4(a) are shown in Figure 5. In Figure 4(a), (m-1)th block of the delay wave exactly overlaps with mth block of the direct wave in the FFT window period. The received symbol of Cm(n) can be introduced from the following equations, omitting the noise component of n(t).(2)ymt=xmt+αxm-1t(3)Ymn=Xmn+αXm-1n(4)Ymn=SmnBmn+αSm-1nBm-1n(5)Cmn=Bmn+αSmnSm-1nBm-1n.(6)Cmn=1+αSmnSm-1n.Since Sm(n) and Sm-1(n) are random patterns consisting of 1 or -1, (6) gives Cm(n)∈{0.3,1.7}. This signal distribution can be observed in Figure 5(a). Although the signal values of Cm(n) do not concentrate on 1, all of them are positive. A symbol error does not occur in Figure 4(a).Figure 5
Received signal distributions for long delay waves.
(a)
α
=
0.7, τ=320, 30-dB CNR
(b)
α
=
0.7, τ=330, 30-dB CNRIn Figure4(b), (m-1)th block of the delay wave is slightly deviated from mth block of the direct wave. Cm(n) can be introduced by(7)ymt=xmt+αxm-1t-τd(8)Ymn=Xmn+αXm-1nej2πnτd/N(9)ReCmn=ReBmn+αSmnSm-1nBm-1nej2πnτd/N(10)ReCmn=1+ReαSmnSm-1nej2πnτd/N,where we apply τd=τ-TG+T from circular shift property. The signal values of Re[Cm(n)] range from 0.3 to 1.7 as shown in Figure 5(b). This case also does not induce a symbol error.The IBI does not take a symbol error as long as a high CNR condition is kept as for this observation. The same phenomenon would be observed even in QPSK transmission. Improvement of SNR using antenna arrays is practical rather than keeping a high CNR, where Zheng presented MRC diversity in SIMO-OFDM as a measure against insufficient guard interval in [15].


## 2.3. Influence of Intercarrier Interference (ICI)

Let us consider the influence of ICI by giving another arrival time difference ofτ=300. The relation between direct and delay waves is shown in Figure 6. Different from Figure 4, (m-1)th data block and mth GI of the delay wave overlap with mth data block of the direct wave. This signal distribution is shown in Figure 7. Since some of Cm(n) have a negative value, a symbol error occurs.Figure 6
Relation between direct and delay waves (τ=300).Figure 7
Received signal distribution affected by ICI.We introduceCm(n) as well as Section 2.2. First, the received signal of ym(t) is given by(11)ymt=xmt+αum-1t+vmt.We decompose a received signal of the delay wave into um-1(t) and vm(t) as shown in Figure 6. Their functions are given by(12)um-1t=xm-1t-τd1if0≤t≤τd1-10ifτd1≤t≤N-1vmt=0if0≤t≤τd1-1xmt-τd2ifτd1≤t≤N-1,where we apply τd1=τ-TG and τd2=τd1-TG from circular shift property. um-1(t) can be replaced with xm-1(t-τd1)-um-1′(t). um-1′(t) is given by(13)um-1′t=0if0≤t≤τd1-1xm-1t-τd1ifτd1≤t≤N-1.Cm(n) can be expressed as(14)ymt=xmt+αxm-1t-τd1+α-um-1t+vmt(15)ReCmn=1+ReαSmnSm-1nej2πnτd1/N+ReαSmn-Um-1′n+Vmn.The received signal distribution of (15) would be almost the same as that of (10) if Um-1′(n) and Vm(n) are excluded. Um-1′(n) and Vm(n) can be expressed by using inverse discrete Fourier transform (IDFT) and DFT as(16)Um-1′n=∑t=τd1N-11N∑n=0N-1Sm-1nej2πtn/Ne-j2πτd2n/Ne-j2πnt/N(17)Vmn=∑t=τd1N-11N∑n=0N-1Smnej2πtn/Ne-j2πτd2n/Ne-j2πnt/N.The interferences of (16) and (17) are added for every subcarrier, which corresponds to ICI. Assuming that the average amplitude for the OFDM transmit signals after IDFT is 1/N (i.e., calculation within the square bracket in (16)), the average of deviations caused by Um-1′(n) and Vm(n) is roughly calculated as(18)±2αN-τd1N≃±0.11.These deviations would be observed by comparing the received signal distributions in Figures 5 and 7. The difference between Figures 4 and 6 is whether a block boundary is included within a FFT window.


## 2.4. Adjustment of FFT Window

The ICI can be avoided by changing FFT window timings, whose adjustment is illustrated in Figure8. The time positions of FFT windows have been shifted by 40 samples ahead. The block boundaries for the delay wave are not included for their FFT windows. Although this adjustment induces a phase rotation after FFT operation in frequency domain, the phase rotation can be detected and compensated by FDE. The received signal distribution after the FFT window adjustment is shown in Figure 9, where the phase rotation can be compensated before descramble. This distribution looks like Figure 5(b) owing to the ICI avoidance.Figure 8
Adjustment of FFT windowing.Figure 9
Received signal distribution after FFT window adjustment.


## 3. Data Selective Rake Reception (DSRake)

The ICI avoidance is achieved when the arrival time of delay wave is perfectly known. Note that arrival times of individual delay waves are almost unknown in the actual environment. We introduce an OFDM rake reception as an alternative method, whose scheme is shown in Figure10. Since the arrival times (τ1 and τ2) and magnitude (α1 and α2) of delay waves are unknown, we take multiple FFT window timings for OFDM demodulation, that is, rake fingers.Figure 10
OFDM rake reception.Original rake reception itself is used as path diversity in spread spectrum [16]. In general, OFDM and rake reception for path diversity are not compatible. Received symbols in rake fingers have high correlation with each other as far as multipath delay time is less than a guard time. The improvement of received SNR is little considering increase of computational complexity in demodulation. We use the rake reception to find the best rake finger that is not affected by ICI so much. It does not aim at path diversity. The selection of rake fingers is achieved by checking data errors after demodulation, where the proposed scheme of data selective rake reception (DSRake) is shown in Figure 11. In the transmitter side, cyclic redundancy check (CRC) codes are inserted in binary data before forward error correcting (FEC) coding. In the receiver side, multiple OFDM demodulators accept received signals in rake fingers and output decoded data blocks. The best data block having no error is selected as final data by observing the CRC results in the data selection unit. If all fingers have data errors, the final data are generated by merging all decoded data in bit level.Figure 11
Data selective rake reception (DSRake).
(a)
Transmitter
(b)
ReceiverDSRake would not be adopted in general OFDM systems such as IEEE802 WLANs and LTE in RF communication due to considerable increase in computational complexity. Note that the bandwidth of UAC is much narrower than that of RF. The increase of computational complexity for UAC does not become a problem from the viewpoint of implementation in RF. The overhead of CRC is trivial because its length is enough for 16 bits (CRC-16) in typical usage.DSRake belongs to selection combining (SC) in diversity combining. Maximal ratio combining (MRC) should be discussed as another method. The alternative scheme of MRC rake reception (MRCRake) is shown in Figure12. The received symbols in rake fingers are synthesized after OFDM demodulation. Generally, a diversity gain of MRC is higher than that of SC. However, MRCRake is inferior to DSRake in terms of the mitigation of ICI. The synthesis of rake fingers takes in undesirable received symbols affected by ICI and the effect is limited. The superiority of DSRake will be confirmed by our simulation in the next section.Figure 12
MRC rake reception (MRCRake).
(a)
Transmitter
(b)
Receiver


## 4. Simulation

### 4.1. Channel Model

As an example of underwater acoustic propagation, we use two channel models measured in a swimming pool. The delay profiles were measured on the condition of horizontal link where one transmitter and four receiver hydrophones horizontally face each other. The location of hydrophones is drawn in Figure13. The pool length and width are 25 m and 13 m and the water depth is 1.2 m. The distances between transmitter and receiver hydrophones are 8 m and 20 m. The space of four hydrophones is 5 cm.Figure 13
Location of transmitter and receiver hydrophones.The delay profiles for 8 m and 20 m distances are shown in Figures14 and 15. A direct wave is located at 0 on the time axis and has normalized magnitude of 0 dB. Delay waves are expressed by individual values of relative magnitude and delay time. Several clusters of delay waves are periodically observed around 30 to 35 ms, 65 to 70 ms, and 97 to 102 ms in Figure 15. These clusters come from several round trip reflections at the side walls. The delay waves of more than −10 dB (i.e., less than 10 dB in desired to undesired signal ratio (DUR)) range from 0 seconds to 35 ms. Since we set a guard time to 12.8 ms in our simulation, the delay waves beyond the GI induce IBI and ICI. If a guard time is more than 110 ms (i.e., more than 20 dB DUR), the influences of IBI and ICI would be small. However, we must keep in mind that a long GI is undesirable in terms of a response speed of communication.Figure 14
Delay profile for 8 m distance.Figure 15
Delay profile for 20 m distance.Summary of the delay profiles is reported in Table1. The 20 m distance shows larger values in average delay time and RMS delay spread than the 8 m distance. The results of average delay time and RMS delay spread are different among receiver channels to some extent. The signal correlation among received antennas would not be very high as having different propagations. Space diversity using antenna arrays is effective to improve a received SNR in this case. RMS delay spread is helpful in the determination of a GI length as long as the magnitude of delay waves is exponentially decaying. However, the magnitude of delay waves does not always fade as time goes on as shown in Figures 14 and 15. Even though the RMS delay spread is less than the GI length, the strong interference of delay waves should be considered.Table 1
Results of delay profiles.
(a)
8-m distance
ch1
ch2
ch3
ch4
Ave. delay time [ms]
4.1
3.3
3.6
2.8
RMS delay spread [ms]
9.4
8.1
8.7
7.4
(b)
20-m distance
ch1
ch2
ch3
ch4
Ave. delay time [ms]
6.6
5.8
5.2
5.9
RMS delay spread [ms]
12.1
11.0
10.5
11.4


### 4.2. Simulation Parameters

The simulation parameters are enumerated in Table2. The baseband OFDM signals with a frequency band of -10kHz to 10kHz are modulated by a carrier wave of 50 kHz. One-tap frequency domain linear equalization based on MMSE criterion is used in channel equalization. The GI length is set to 12.8 ms, corresponding to 256 samples in baseband domain. Two training data blocks are added to the beginning of an OFDM frame, where the frame format is shown in Figure 16. The two long training fields (LTFs) are used for channel estimation. Since the LTFs are located at the head of frame, they do not have the influence of IBI and ICI. The number of rake fingers is set to 64 for DSRake and MRCRake. We have used convolutional coding with a coding rate of 1/2. The transmit data rate is about 13.3 kbps considering the overhead of LTFs and GIs. Although the overhead of CRC codes (CRC-16) might be counted for DSRake, this overhead is very small (less than 2%).Table 2
Simulation parameters.
Modulation
QPSK-OFDM
Sampling frequency [kHz]
200
Center frequency [kHz]
50
Frequency band [kHz]
40 to 60
FFT size
1024
Number of data subcarriers
1024
OFDM symbol length [ms]
51.2
GI [ms]
12.8
Number of OFDM symbols
10
Number of training OFDM symbols
2
OFDM frame length [ms]
768
OFDM frame data size [bytes]
1280
FEC
Convolutional coding & Viterbi decoding
Coding rate
0.5
Number of antennas
1 (TX)/4 (RX)
Number of OFDM rake fingers
64
Timing synchronization
Perfect
Number of evaluated OFDM frames
100Figure 16
OFDM frame format.We apply space diversity using array antennas for the mitigation of IBI. The scheme of OFDM space diversity is shown in Figure17. Space diversity combining based on MRC is performed after channel equalization. Space diversity combining and OFDM rake reception of DSRake or MRCRake are compatible. The diversity block is inserted into the OFDM demodulation units in Figures 11 and 12.Figure 17
OFDM space diversity.


### 4.3. Simulation Results

Bit error rates (BERs) for the 8 m and 20 m distances are plotted in Figures18 and 19. We have evaluated the schemes of single channel reception (average of four channels), space diversity, DSRake, and MRCRake. Both DSRake and MRCRake are given by the combination of space diversity and rake reception. The single channel reception has the BER floor of 10-2 due to strong multipath interference. The space diversity decreases the BER floor from 10-2 to 10-3 as shown in both figures. The influence of IBI would be decreased by space diversity combining to some extent. DSRake and MRCRake show further improvement of decreasing BER floor. DSRake is clearly superior to MRCRake from the BER results. The ICI mitigation contributes to the improvement of communication quality rather than taking path diversity. DSRake can eliminate a BER floor for the 8 m distance and decrease by up to 2×10-4 for the 20 m distance. The effectiveness of DSRake in strong multipath interference has been observed from this simulation.Figure 18
BER results for 8 m distance.Figure 19
BER results for 20 m distance.


## 4.1. Channel Model

As an example of underwater acoustic propagation, we use two channel models measured in a swimming pool. The delay profiles were measured on the condition of horizontal link where one transmitter and four receiver hydrophones horizontally face each other. The location of hydrophones is drawn in Figure13. The pool length and width are 25 m and 13 m and the water depth is 1.2 m. The distances between transmitter and receiver hydrophones are 8 m and 20 m. The space of four hydrophones is 5 cm.Figure 13
Location of transmitter and receiver hydrophones.The delay profiles for 8 m and 20 m distances are shown in Figures14 and 15. A direct wave is located at 0 on the time axis and has normalized magnitude of 0 dB. Delay waves are expressed by individual values of relative magnitude and delay time. Several clusters of delay waves are periodically observed around 30 to 35 ms, 65 to 70 ms, and 97 to 102 ms in Figure 15. These clusters come from several round trip reflections at the side walls. The delay waves of more than −10 dB (i.e., less than 10 dB in desired to undesired signal ratio (DUR)) range from 0 seconds to 35 ms. Since we set a guard time to 12.8 ms in our simulation, the delay waves beyond the GI induce IBI and ICI. If a guard time is more than 110 ms (i.e., more than 20 dB DUR), the influences of IBI and ICI would be small. However, we must keep in mind that a long GI is undesirable in terms of a response speed of communication.Figure 14
Delay profile for 8 m distance.Figure 15
Delay profile for 20 m distance.Summary of the delay profiles is reported in Table1. The 20 m distance shows larger values in average delay time and RMS delay spread than the 8 m distance. The results of average delay time and RMS delay spread are different among receiver channels to some extent. The signal correlation among received antennas would not be very high as having different propagations. Space diversity using antenna arrays is effective to improve a received SNR in this case. RMS delay spread is helpful in the determination of a GI length as long as the magnitude of delay waves is exponentially decaying. However, the magnitude of delay waves does not always fade as time goes on as shown in Figures 14 and 15. Even though the RMS delay spread is less than the GI length, the strong interference of delay waves should be considered.Table 1
Results of delay profiles.
(a)
8-m distance
ch1
ch2
ch3
ch4
Ave. delay time [ms]
4.1
3.3
3.6
2.8
RMS delay spread [ms]
9.4
8.1
8.7
7.4
(b)
20-m distance
ch1
ch2
ch3
ch4
Ave. delay time [ms]
6.6
5.8
5.2
5.9
RMS delay spread [ms]
12.1
11.0
10.5
11.4


## 4.2. Simulation Parameters

The simulation parameters are enumerated in Table2. The baseband OFDM signals with a frequency band of -10kHz to 10kHz are modulated by a carrier wave of 50 kHz. One-tap frequency domain linear equalization based on MMSE criterion is used in channel equalization. The GI length is set to 12.8 ms, corresponding to 256 samples in baseband domain. Two training data blocks are added to the beginning of an OFDM frame, where the frame format is shown in Figure 16. The two long training fields (LTFs) are used for channel estimation. Since the LTFs are located at the head of frame, they do not have the influence of IBI and ICI. The number of rake fingers is set to 64 for DSRake and MRCRake. We have used convolutional coding with a coding rate of 1/2. The transmit data rate is about 13.3 kbps considering the overhead of LTFs and GIs. Although the overhead of CRC codes (CRC-16) might be counted for DSRake, this overhead is very small (less than 2%).Table 2
Simulation parameters.
Modulation
QPSK-OFDM
Sampling frequency [kHz]
200
Center frequency [kHz]
50
Frequency band [kHz]
40 to 60
FFT size
1024
Number of data subcarriers
1024
OFDM symbol length [ms]
51.2
GI [ms]
12.8
Number of OFDM symbols
10
Number of training OFDM symbols
2
OFDM frame length [ms]
768
OFDM frame data size [bytes]
1280
FEC
Convolutional coding & Viterbi decoding
Coding rate
0.5
Number of antennas
1 (TX)/4 (RX)
Number of OFDM rake fingers
64
Timing synchronization
Perfect
Number of evaluated OFDM frames
100Figure 16
OFDM frame format.We apply space diversity using array antennas for the mitigation of IBI. The scheme of OFDM space diversity is shown in Figure17. Space diversity combining based on MRC is performed after channel equalization. Space diversity combining and OFDM rake reception of DSRake or MRCRake are compatible. The diversity block is inserted into the OFDM demodulation units in Figures 11 and 12.Figure 17
OFDM space diversity.


## 4.3. Simulation Results

Bit error rates (BERs) for the 8 m and 20 m distances are plotted in Figures18 and 19. We have evaluated the schemes of single channel reception (average of four channels), space diversity, DSRake, and MRCRake. Both DSRake and MRCRake are given by the combination of space diversity and rake reception. The single channel reception has the BER floor of 10-2 due to strong multipath interference. The space diversity decreases the BER floor from 10-2 to 10-3 as shown in both figures. The influence of IBI would be decreased by space diversity combining to some extent. DSRake and MRCRake show further improvement of decreasing BER floor. DSRake is clearly superior to MRCRake from the BER results. The ICI mitigation contributes to the improvement of communication quality rather than taking path diversity. DSRake can eliminate a BER floor for the 8 m distance and decrease by up to 2×10-4 for the 20 m distance. The effectiveness of DSRake in strong multipath interference has been observed from this simulation.Figure 18
BER results for 8 m distance.Figure 19
BER results for 20 m distance.


## 5. Conclusion

This paper presents a new method of OFDM rake reception in strong multipath interference. Very long delay waves beyond GI induce IBI and ICI. The influence of IBI and ICI is discussed by received signal distribution. Regarding ICI, we reported that the ICI avoidance can be achieved by changing FFT window timing. According to the idea of ICI avoidance, we have proposed DSRake as one of rake reception techniques. Original rake reception is used for obtaining path diversity. However, our rake reception aims at the mitigation of ICI. We have explained that selection combining by DSRake is superior to maximal ratio combining by MRCRake. The effectiveness of DSRkae has been confirmed by the simulation results based on actual underwater propagation models. In our future work, we will investigate communication performance of DSRake when Doppler effect is added.



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