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Multi-array iterative receiver for underwater acoustic OFDM communications with EXIT chart evaluation
Applied Acoustics 114 (2016) 307–316
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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Multi-array iterative receiver for underwater acoustic OFDM communications with EXIT chart evaluation Lan Zhang a, Xiaomei Xu a,⇑, Wei Feng b, Yougan Chen a a b
Key Laboratory of Underwater Acoustic Communication and Marine Information Technology (Xiamen University), Ministry of Education, Xiamen 361005, China College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
a r t i c l e
i n f o
Article history: Received 25 November 2015 Received in revised form 7 July 2016 Accepted 12 July 2016 Available online 16 August 2016 Keywords: OFDM Underwater acoustic communications Multi-array Iterative receiver LLR-combining EXIT chart
a b s t r a c t In this paper, a multi-array iterative receiver based on log-likelihood ratio (LLR)-combining detection involving joint sparse channel estimation and decoding is proposed for underwater acoustic OFDM communication. First, Extrinsic information transfer (EXIT) chart analysis is applied to evaluate the convergence behavior of the iterative receiver using the real data collected from the Kauai Acomms MURI 2011 (KAM11) experiment. This experiment was conducted in about 106 m-depth shallow water west of Kauai, HI, in June 2011, with a 20 kHz bandwidth (12–32 kHz) at range up to 3 km. It helps to explain the impact of different data configurations, detectors, and the diversity combinations in a highly inhomogeneous underwater environment and to predict the bit-error rate (BER) performance of the proposed receiver. Then the BERs as a function of the number of combined elements are illustrated to verify the prediction and analysis via the EXIT chart. Data transmission using 16QAM modulation achieves a BER of 104 at a data rate of 21 kb/s. The results provide guidance for the design of system parameters including the data configurations, the number of iterations for both iterative processing and low density parity check (LDPC) decoding, which are beneficial to achieve a good efficiency-performance tradeoff. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, underwater acoustic communication has been improved tremendously with the use of multi-carrier transmission, also known as orthogonal frequency division multiplexing (OFDM) [1–7]. It is advantageous to avoid complex channel equalization and block-by-block processing. In contrast to radio wireless channel, underwater acoustic (UWA) channel is very harsh as a result of its unique characteristics: large delay spread due to time-varying multi-path propagation causing significant inter-symbol interference, limited available bandwidth due to the frequency-selective attenuation, and strong spatial correlation [8,9]. Since underwater acoustic channel is a triple-selective fading channel in time, space and frequency, a robust receiver where channel estimation and decoding is performed jointly and iteratively is needed. The iterative processing, inspired by ‘‘Turbo Principle” [10], is often required to conquer the harshness of the underwater acoustic channel and to achieve satisfactory performance [11]. The Turbo principle was
⇑ Corresponding author. E-mail addresses: [email protected] (L. Zhang), [email protected] (X. Xu), [email protected] (W. Feng), [email protected] (Y. Chen). http://dx.doi.org/10.1016/j.apacoust.2016.07.008 0003-682X/Ó 2016 Elsevier Ltd. All rights reserved.
originally developed for decoding concatenated codes [12] and has been applied to direct-adaptation based turbo equalization (DA-TEQ) [13,14], channel-estimation based turbo equalization (CE-TEQ) [6,15–17] in the UWA communication community recently. Most of these methods are used in single-carrier UWA communication systems. Existing literature on iterative processing for underwater acoustic multi-carriers communication is still limited [18,19]. In [18], an iterative receiver incorporating multiple-input, multiple-output (MIMO) detection and sparse channel estimation techniques was proposed for UWA MIMOOFDM communications. The authors in [19] presented a linear turbo detection scheme for UWA MIMO-OFDM communications, without iterative channel estimation. Both of these two iterative receivers were designed for underwater acoustic MIMO-OFDM communications with experimental investigations. Such iterative processes are often analyzed using extrinsic information transfer (EXIT) charts [20]. EXIT chart, using the mutual information as a figure of merit, is a powerful semianalytical tool to analyze and optimize the convergence behavior of iterative systems. Early methods to evaluate the convergence behavior of the iterative decoder used the signal-to-noise ratio (SNR), the mean, the variance, the BER and the fidelity as a parameter of the chart [21]. The fidelity chart is also called the soft bit
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transfer (SOBIT) chart. In [22], the authors compared all these measures to describe the behavior of the soft-in soft-out decoder and found out that only the EXIT chart and the SOBIT chart could provide fairly accurate and robust explanation of the behavior of the iterative process. There is also another useful tool to study the convergence of iterative detection called density evolution [23]. It tracks the evolution of the distribution of extrinsic information in the iterative algorithm, which is mainly used for the analysis and optimization of LDPC codes. EXIT chart is a simplification of density evolution and is easier to program. The mutual information in the EXIT chart has the advantage of representing a common quantity in communication theory and provides additional insight of convergence prediction. Its accuracy is particularly impressive when the block-length of interleaver tends to be infinite. EXIT chart has become a preferable option because it has the ability to closely reflect the behavior of the iterative process and to evaluate the convergence of the entire iterative scheme without performing time consuming simulations. ten Brink [20] used extrinsic information transfer characteristics based on mutual information to describe the flow of extrinsic information through the soft-in/soft-out constituent decoders. This method provides an opportunity to predict the BER of a coded system and the iterative-processing system with substantial reduction in numerical complexity. Kang and Iltis [6] used the EXIT chart to optimize the power allocation between the pilot and data sub-carriers for iterative processing, but they used simulated data rather than experimental data from a real UWA channel. Wang et al. [24] utilized the EXIT chart to analyze the convergence property between the turbo equalizer and the decoder in the underwater acoustic single-carrier system. The first contribution of our paper is that we propose a multiarray iterative receiver performing sparse channel estimation and decoding jointly based on LLR-combining detection, instead of hard decision, for underwater acoustic OFDM communication. Note that the Gaussian assumption is mismatched by the coloring of the noise at the output of the hard-decision detector. We use extensive undersea trial data collected from KAM11 experiment conducted in shallow water to validate the performance of the proposed iterative receiver. The second contribution is that we give a deep insight on convergence behavior between the channel estimator and the LDPC decoder based on the EXIT chart using the experimental data rather than the simulated data. We consider the combination of diversity and the data configurations (the number of sub-carriers and the mapping scheme) affect the performance. Additionally, we extend the capabilities of the EXIT chart to predict BERs of the iterative receiver without extensive performance simulations or experimental data processing. Moreover, the EXIT analysis and prediction provides enlightenment into system parameter design for achieving a good tradeoff between the performance and the transmission efficiency. The rest of this paper is organized as follows. First, the system architecture consisting of transmitter and iterative receiver is displayed in Section 2, introducing the principle of iterative receiver and the flow of extrinsic information of the receiver. Then the EXIT evaluation on the iterative receiver based on the real data explains and predicts the performance of the iterative receiver in Section 3. Experimental results based on KAM11 experiment are subsequently exemplified in Section 4. Finally, conclusions are made in Section 5.
2. System architecture 2.1. Signal The specification for the underwater OFDM communication system considered in this paper is given in Table 1. The null
sub-carriers serve as a guard band and the pilot tones are nonuniformly allocated in one OFDM symbol. As shown in Fig. 1, the data packet consists of 100 ms chirp signal, 200 ms silence periods and 32 OFDM blocks. The chirp signal is used for synchronization and Doppler estimation. The data packets have 4 different configurations: 1024-QPSK, 1024-16QAM, 2048QPSK, and 2048-16QAM, specified as the number of sub-carrier and the modulation scheme. A data stream (a duration of 30 s) with 8 packets will be sent from the source to the vertical receiver array with 16 hydrophones over the underwater acoustic channel, where each kind of data packet repeats twice. 2.2. Transmitter T
As shown in Fig. 2, the bit sequence b ¼ ½b0 ; b1 ; . . . bMNd R1 is T
LDPC encoded to codewords c ¼ ½c0 ; c1 ; . . . cMNd 1 and the codewords are interleaved bit-wise. R is the code-rate and 2M is the order of the modulation. The interleaved codewords are mapped T
into data sub-carriers d ¼ ½d0 ; d1 ; . . . dNd 1 with Gray mapped QPSK or 16QAM, respectively. With the pilot tones p ¼ ½p0 ; p1 ; . . . pNp 1 T , the transmitted symbols in frequencydomain s ¼ ½s0 ; s1 ; . . . sNs 1 T can be expressed as the sum of orthogonal pilot tones and data sub-carriers, s ¼ p þ d, where pk dk ¼ 0 for 0 6 k 6 N s 1. In the guard band, pk ¼ dk ¼ 0. Then the time-domain transmitted symbol with CP x ¼ ½xNs Ng ; . . . xNs 1 ; x0 ; . . . xNs 1 T is generated by the ‘‘OFDM Modulator” consisting of parallel-serial converter, IFFT, CP adder and up-converter. There is negligible Doppler spread in the received data for there was no relative motion between the source and the multi-array receiver. With the effect of multipath propagation, the representation of the channel impulse response (CIR) is
hðs; tÞ ¼
L1 X Al ðtÞdðs sl ðtÞÞ
ð1Þ
l¼0
where L is the number of the multi-path of the channel, Al ðtÞ represents the real-valued gain of the l-th path, sl ðtÞ is the corresponding delay. The channel attenuation and delay spread is assumed to be invariant within one OFDM block, but varies block by block. The discrete-time baseband channel impulse response is rewritten as
hðnÞ ¼
L1 X Al dðn sl Þ
ð2Þ
l¼0
The multiple-receiving system will receive the data through the underwater acoustic channel like the Eq. (3):
yv ðnÞ ¼
L1 X Al;v xðn sl Þ þ gv ðnÞ; v ¼ 1; 2; . . . Nrx
ð3Þ
l¼0
where Nrx is the number of the receiving elements from bottom to top. g is assumed to be complex additive and independent on differ-
Table 1 OFDM specification. Number of sub-carriers Number of data sub-carriers Number of pilots Number of null sub-carriers Cyclic Prefix (CP) duration Symbol duration with CP Number of the samples of CP Subcarrier spacing LDPC decoder Uncoded data rate(QPSK/16QAM) Coded data rate(QPSK/16QAM)
N s ¼ 1024 N d ¼ 672 N p ¼ 256 N u ¼ 96 T g ¼ 12:8 ms T s ¼ 64 ms N g ¼ 256 Df ¼ 19:53 Hz (1344,672) LDPC 21 kbps/42 kbps 10.5 kbps/21 kbps
N s ¼ 2048 N d ¼ 1344 N p ¼ 512 N u ¼ 192 T g ¼ 25:6 ms T s ¼ 128 ms N g ¼ 512 Df ¼ 9:765 Hz (1344,672) LDPC 21 kbps/42 kbps 10.5 kbps/21 kbps
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2
32 blocks
OFDM
OFDM
OFDM
Silence Chirp
Chirp Silence 100ms 100ms
kN 1 1
j2p N k s 36 1 e s½kN1 6 kN 2 1 76 6 1 ej2p Ns k 76 6 . 6 . W¼6 76 . 56 .. 4 .. . 6. s½kNp 4 k
2
64ms/128ms
64ms/128ms
100ms 100ms
Np 1
1 ej2p Ns k
kN
1 ~L1 k
ej2p Ns e .. .
kN
j2p
2 ~L1 k Ns
.. . kN
p ~L1 k
3 7 7 7 7 7 7 7 7 5
ð6Þ
ej2p Ns
Packet duration=2.348s/4.396s
Fig. 1. The structure of data packet.
ent receiving-elements after noise pre-whitening. The ambient noise in underwater acoustic channel is typically modeled as a non-white Gaussian process and given as a linear combination of four independent noise sources: turbulence, shipping, waves, and thermal noise, which makes the equivalent noise more colored to mismatch the Gaussian assumption. Therefore, noise prewhitening is beneficial to facilitate iterative processing. The synchronization process at each receiving-element is achieved by matched filtering of chirp waveform. After baseband conversion, serial-parallel converter, CP removal and FFT, the received sequence over each element is
Y v ½k ¼ Hv ½ks½k þ W v ½k; k ¼ 0; 1; . . . Ns 1; v ¼ 1; 2; . . . Nrx
ð4Þ
where W is the FFT of the additive noise g, assumed to be independent on different elements and Gaussian distributed Nð0; r2w Þ. H is the channel frequency response (CFR) within one OFDM block on each receiving-element.
Based on the algorithm of OMP in [27], the estimated channel ^ p can be obtained. With pilot-based sparse impulse response h channel estimation, the estimated channel at other positions can be achieved by interpolation or discrete fourier transform (DFT):
^ v ½k ¼ H
~L1 X
Step2 Soft detection for each element: With the estimated CFR, it is traditional to utilize maximal ratio combining for hard detection in multiple receiving systems, which will make the noise at the output of the equalizer more colored. Instead, we calculate a posterior LLR value of the bit sequence as the output of each soft-detector. Leveraging on Bayes’ theorem, the a posterior LLR value is shown as follows:
LLRðbj jY v ½kÞ ¼ ln ¼ ln
In this section, we introduce how the iterative receiver works and describe the flow of extrinsic information through the channel estimator and LDPC decoder. As shown in Fig. 3, a block diagram of the receiver consists of six major components: pilot-based sparse channel estimator (CE), data-subcarrier-based channel estimator, LLR combiner, soft detector, LDPC decoder and symbol remapper. The multi-array iterative receiver incorporating joint channel estimator and decoding is summarized as in the following: Step1 Pilot-based Sparse Channel estimation: Since the underwater acoustic channel is sparse [25], we use sparse channel estimation with orthogonal matching pursuit (OMP) algorithm [26] in order to capture the sparsity of the channel. To estimate the path delays, the OMP channel estimator first selects a path delay grid such as h i l m T g Ns T s 2T s ~ TðkÞ ¼ 0; ; ; . . . T g , with length of L ¼ . k is an overTs
kNs
sampling factor, L ~ L for sparse recovery. For each receiving element, the initial sparse channel estimation based on pilot symbols in the vector-matrix form is
Yp ¼ Whp þ Wp
ð5Þ
where hp is the underwater acoustic channel impulse response
ð7Þ
l¼0
2.3. Iterative receiver structure
kNs
^ ej2pkNkls ; k ¼ 0; 1; . . . Ns 1; v ¼ 1; 2; . . . N rx h l
Prðbj ¼ 0jY v ½kÞ ; j ¼ 0; 1 . . . MNd R 1 Prðbj ¼ 1jY v ½kÞ PrðY v ½kjbj ¼ 0Þ Prðbj ¼ 0Þ þ ln ; PrðY v ½kjbj ¼ 1Þ Prðbj ¼ 1Þ
k ¼ kN1 ; kN2 . . . kNd P P dk ¼f ðb¼0Þ PrðY v ½kjdk Þ d ¼f ðb¼0Þ Prðdk Þ ¼ ln P þ ln P k ; PrðY ½kjd Þ v k dk ¼f ðb¼1Þ dk ¼f ðb¼1Þ Prðdk Þ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} LE;DET
LA;DET
v ¼ 1; 2; . . . Nrx
ð8Þ
where f is the Gray-Mapped QPSK or 16QAM. LA;DET is a priori LLR value of the detector and LE;DET is the extrinsic LLR value of the detector. On the basis of the assumption that the noise W is additive and Gaussian distributed, the conditional density for each receiving element is given as: ^ v ½kd j2 jY v ½kH k 2r2 w
PrðY v ½kjdk Þ ¼ e
; k ¼ kN1 ;kN2 ;. .. kNd ; v ¼ 1; 2;. .. Nrx
ð9Þ
Initially, the bit sequence is assumed to be equiprobable, so LA;DET ¼ 0. Step3 LLR combining: The error probability of one bit is assumed to be large for small magnitudes of its LLR values, and it is assumed to be small for large magnitudes of its corresponding LLR. Using the Jacobian logarithm [28] as follows
T
vector with entry of ½h0 ; h1 ; . . . h~L1 . W is the dictionary matrix with the size of N p ~L
lnða þ bÞ ¼ maxðA; BÞ þ lnð1 þ ejABj Þ
Pilot tones inseron p b
LDPC Encoder
c
Interleaver
M-ary Modulator
d
Fig. 2. Block diagram of the transmitter.
s
OFDM Modulator
x
ð10Þ
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Pilot-based Sparse CE
Y1
Soft Detector LE,DET
LA,LDPC
Deinterleaver
YNrx
Pilot-based Sparse CE
LDPC Decoder
Soft Detector
Symbol LAPP,LDPC + LA,DET Remapper
Datasubcarrier CE
bˆ
LE,LDPC
Interleaver
Fig. 3. Block diagram of the iterative receiver.
where A ¼ lna; B ¼ lnb, we can calculate the a posterior LLR of one bit from the detector for each element by substituting Eqs. (9) and (10) into Eq. (8). The LLR combiner will sum up the LLRs of receiving-elements from bottom to top:
LLRðbj Þ ¼
Nrx X
v ¼1
the next iteration. If the maximum iterations have not been reached, repeat steps 1, 2, 3 and 4. Otherwise, output the hard decision of the a posterior information. 3. EXIT chart evaluation
LLRðbj jY v ½kÞ; j ¼ 0; 1 . . . MN d R 1; k ¼ kN1 ; kN2 ; . . . kNd ð11Þ
Step4 Maximum a posterior (MAP) decoding for the LDPC decoder: A half-rate (1344,672) irregular LDPC code from the IEEE 802.16e standard is considered in this paper. The extrinsic LLR value from the detector LE;DET is used as a priori LLR for LDPC decoder LA;LDPC ; LE;DET ! LA;LDPC . After 25 iterations, a posterior LLR values of bits from the LDPC decoder LAPP;LDPC is achieved to make hard decisions to estimate the transmitted bit ^ Until now, one-direction detection is finished. sequence b. Step5 Symbol remapper: It is not easy to get a satisfactory performance by singleelement reception, as seen in [15]. If we want to get a more satisfactory performance, the multi-array iterative receiver incorporating joint channel estimation and decoding should be a promising method. With 25-iteration iterative decoding, the LDPC decoder yields the extrinsic LLR value LE;LDPC , which can feed back to the detector as its a priori LLR values: LE;LDPC ! LA;DET . However, the detector cannot get any gain from the iterative processing under Gray-mapping. Therefore the dashed line of Fig. 3 can be removed for Gray-mapping. Instead, we use a posterior LLR of the decoder LAPP;LDPC to calculate the probability of each bit:
Based on the mutual information transfer functions, the purpose of the EXIT chart is to visualize convergence behavior and to predict the performance of the iterative receiver between the soft information (LLR values) and the corresponding bits. Through the EXIT chart analysis, the exchange of extrinsic information between detector/channel estimator and LDPC decoder can be drawn in the same axis. On the ordinate, the extrinsic output of the detector IE;DET becomes a priori input of the LDPC decoder IA;LDPC . On the abscissa, the extrinsic output of the LDPC decoder IE;LDPC becomes a priori input of the detector IA;DET . Based on the definition of mutual information, the a priori mutual information IA;DET and extrinsic mutual information of the detector IE;DET can be expressed as:
IA;DET ¼ IðB; LA;DET Þ ¼ log 2
Z
þ1
1
PrA;DET ðnjB ¼ bÞ
2PrA;DET ðnjB ¼ bÞ dn Pr A;DET ðnjB ¼ 0Þ þ PrA;DET ðnjB ¼ 1Þ
IE;DET ¼ IðB; LE;DET Þ ¼ log 2
1X 2 0;1
1X 2 0;1
Z
þ1
1
ð17Þ
PrE;DET ðnjB ¼ bÞ
2PrE;DET ðnjB ¼ bÞ dn Pr E;DET ðnjB ¼ 0Þ þ PrE;DET ðnjB ¼ 1Þ
ð18Þ
Prðbj ¼ 1Þ ¼
eLAPP;LDPC ðbj Þ 1 þ eLAPP;LDPC ðbj Þ
ð12Þ
where PrA;DET and Pr E;DET are the probability density functions of LA;DET and LE;DET respectively.
Prðbj ¼ 0Þ ¼
1 1 þ eLAPP;LDPC ðbj Þ
ð13Þ
3.1. LLR distribution analysis
and we get the reliability value of the kth data symbol dk :
Prðdk Þ ¼
M Y
Prðbj Þ
ð14Þ
j¼1
Finally, we get the estimated data symbols with soft remapping:
^s ¼ d k
M X Prðdk ¼ ai Þai ; k ¼ kN1 ; kN2 ; . . . kNd
ð15Þ
i¼1
or hard remapping:
^h ¼ a ; i ¼ arg max Prðd ¼ a Þ; k ¼ kN ; kN ; . . . kN d i k i k 1 2 d i
ð16Þ
where ai are the constellation symbols. Then, we apply the remapped data sub-carriers as auxiliary pilots to get more accurate pilot-based channel estimation for
As seen in the Eq. (18), the extrinsic mutual information of the detector IE;DET depends on the distribution of the LLR values. In Figs. 4 and 5, we investigate the distribution of extrinsic LLR of the detector with the real data collected from the KAM11 experiment in 4 cases: 1024-QPSK, 1024-16QAM, 2048-QPSK and 2048-16QAM configurations. For all four cases, the reliability of the LLRs improves as the increase of the number of combined elements. The two LLR curves (b ¼ 0; b ¼ 1) will move apart and the overlapped part will decrease, giving more reliable soft information between detector and decoder. For 1024-QPSK configuration, the two curves become completely separated with combining 5 elements. For 2048-QPSK case, the two curves become nearly separated as a result of combining 2 elements. The correct bit values will be obtained by making decisions based upon the sign of the corresponding LLRs under these two cases. However, for 1024-16QAM and 204816QAM, the two curves still keep overlapped when all 16 elements
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311
Fig. 4. Left: 1024-QPSK LLR distribution; Right: 1024-16QAM LLR distribution.
Fig. 5. Left: 2048-QPSK LLR distribution; Right: 2048-16QAM LLR distribution.
are combined, which means we are not able to get error-free transmission even combining all 16 hydrophones. 3.2. EXIT chart evaluation and prediction Using the EXIT chart method, we are able to evaluate convergence and compare the iterative receiver under diverse combination and different data configurations. It is not difficult to calculate IE;DET using the empirical formulas in [29] for the distribution of the LLR value satisfying the consistency condition [22]. Although the actual LLR values of the detector are not always Gaussian distributed or do not satisfy the consistency condition due to the stochastic underwater acoustic channel, seen in Figs. 4 and 5, the EXIT chart still work well in a wide range of applications, e.g. [6,30]. The distributions of Pr E;DET in Eq. (18) are most conveniently determined by Monte Carlo simulation (histogram measurements). Generally, the analysis of EXIT chart is in agreement with the actual performance with 105 -bit interleaver size based on [20]. LDPC codes used here are rather short to facilitate underwater acoustic channels with long delay spread. The EXIT chart analysis for a short code is still valid, but the accuracy is limited. The EXIT curve of the LDPC decoder in Figs. 6–9 is obtained by running Mont Carlo simulation of LDPC codes with the code length 6
of 10 . As shown at the left part of Fig. 6, the extrinsic information will enlarge with the increase of the number of iterations at the same a priori information. 1 or 4-iteration decoding is not enough
for good performance, while 25-iteration is chosen for practical implementation without losing significant performance. Then we generate the EXIT curve of the estimator/detector for four cases. The EXIT chart in Fig. 6 (left) depicts the transfer function of 1024-QPSK detector and LDPC decoder. We compare the EXIT chart of the detector with a different number of the receiving elements combined. For 0 6 IA;DET 6 1; IE;DET is given as a monotonic function of IA;DET . The curve of detector is beneath the curve of decoder when combining 1 element. When combining 2 elements, the iterative receiver cannot get over the EXIT bottleneck, even though many iterations are provided. With the increase of the number of combined receiving-elements, the line of extrinsic information of the detector is becoming higher and higher. Under combining 5 elements, the EXIT curve of detector is totally above the curve of the decoder, meaning that we are able to get error-free correction. Each extrinsic output of the detector IE;DET is associated with BER prediction as shown at the right part of Fig. 6. We find that the LDPC coded BER with 102 can be achieved with combined 1 element when IE;DET 0:51 given IA;DET ¼ 1 and the coded BER with 103 can be achieved with combined 2 elements when IE;DET 0:62 with full a priori information. In addition, we can get the uncoded BER with 101 even with combined 5 elements when IE;DET 0:73 under IA;DET ¼ 1. And the coded BER is less than 104 corresponding to IE;DET 0:57 for IA;DET ¼ 0:1. The EXIT chart of 1024-16QAM detector and LDPC decoder is plotted at the left part of Fig. 7. We observe that the extrinsic
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Fig. 6. Left: EXIT chart for 1024-QPSK; Right: BER as a function of extrinsic information of the detector.
Fig. 7. Left: EXIT chart for 1024-16QAM; Right: BER as a function of extrinsic information of the detector.
Fig. 8. Left: EXIT chart for 2048-QPSK; Right: BER as a function of extrinsic information of the detector.
information of the detector increases with the number of combined elements, though all of them are under the LDPC decoder’s curve. There is no tunnel between the detector and the decoder, indicating that we are not able to acquire the error-free correction
even combining all 16 elements at the full a priori information. We can still make a prediction of BER at the right part with the corresponding IE;DET . With combined 4 elements, the LDPC coded BER with 101 can be obtained when IE;DET 0:51 given IA;DET ¼ 1. With
L. Zhang et al. / Applied Acoustics 114 (2016) 307–316
313
Fig. 9. Left: EXIT chart for 2048-16QAM; Right: BER as a function of extrinsic information of the detector.
combined 12 elements, the coded BER with 102 can be achieved when IE;DET 0:54 given IA;DET ¼ 1. Additionally, we can get the coded BER with 103 and the uncoded BER with 101 under all combined 16 elements when IE;DET 0:58 given IA;DET ¼ 1. We depict the EXIT chart of 2048-QPSK detector and LDPC decoder at the left of Fig. 8. As seen in its extrinsic LLR distribution in Fig.5, the curves of b ¼ 1 and b ¼ 0 nearly separate with combined 2 elements. Correspondingly, the EXIT curve of the detector is higher than the LDPC extrinsic curve, telling that it is easier to get successive detection with combined 2 elements in 2048QPSK, whose CP length is much higher than 1024-QPSK. Similarly, a prediction of the BER associated with the extrinsic information is provided at the right part. The LDPC coded BER with 102 can be attained with only 1 element corresponding to IE;DET 0:53 for IA;DET ¼ 1. With combined 2 elements, the coded BER with 102 can be achieved when IE;DET 0:57 given IA;DET ¼ 0:3. With the increase of a priori information, an error-free transmission is achievable with LDPC coding when IE;DET 0:64 given IA;DET ¼ 1. When combining 4 elements, the coded BER with 104 can be achieved when IE;DET 0:64 given IA;DET ¼ 0:2. With the increase of a priori information, an error-free transmission with LDPC coding and the uncoded BER with 101 is achievable corresponding to IE;DET 0:64 for full a priori information. We plot the EXIT chart of 2048-16QAM detector and the LDPC decoder at the left of Fig. 9. According to its extrinsic LLR distribution in Fig. 5, the curves of b ¼ 1 and b ¼ 0 slightly move apart with the increase of the number of combined receiving-elements, and they overlap partly even when combining all 16 elements. This means that the EXIT chart curves of the detector are all below the decoder’s. Meanwhile, a prediction of BER associated with the extrinsic information is provided at the right part. The coded BER with combining 2 elements is about 101 with its prediction corresponding to IE;DET 0:45 for IA;DET ¼ 1. When combining 8 elements, the coded BER is about 103 corresponding to IE;DET 0:58 given IA;DET ¼ 1. With combining 16 elements, the coded BER of 104 and the uncoded BER of 101 can be achieved corresponding to IE;DET 0:64 under IA;DET ¼ 1. 4. Experimental results 4.1. KAM11 experiment deployment The deployment on KAM11 experiment is shown at the left of Fig. 10. An eight-element source receiver array (SRA) was
suspended in about 102 m-depth water. The first transmitter was at about 90 m depth. The data stream was transmitted from the bottom Tx#1 to the top Tx#7, respectively for various transmitted positions. We are centered on the performance of Tx#1 here. The vertical receiver array (VRA) was used as the receiver, consisted of 16-elements spanning a 56 m aperture with 3.75 m interelement spacing, covering about half the water column. The data were received by the VRA at a distance of 3 km. The VRA had a sampling rate of 100 kHz per element. An example of estimated CIR by 100-ms chirp waveform from 12 to 32 kHz is shown at the right of Fig. 10, indicating that the maximum delay spread is about 15 ms and the level of sparseness of channel is spatialvarying. We also inserted two OFDM blocks of Golay sequence as preambles to estimate the CFR and found the UWA channel varied significantly block by block, which is not presented here. Therefore, channel updating block by block is necessary for a successful reception.
4.2. Performance results To investigate the impact of diversity combining on performance, BERs are shown as a function of the number of receivingelements combined to verify the prediction of the EXIT chart. As shown in Fig. 11, the BER curves converge with the increase of the number of the combined elements in non-iterative way (iter = 0), and the error-free correction can be attainable under combined 5 elements. However, the coded BER are close to about 105 not zero when combining 6, 7, 8, 9, 11, 12 elements. This is because the multipath in depth of 60–80 m is very severe, shown at the right part of Fig. 10. For the iterative detection, we see that the proposed receiver outperforms the non-iterative detection when combining less than 5 elements and converges to zero with more than 5 elements. The black curves are the predicted BERs based on the right part of Fig. 6 when IA;DET ¼ 1. We find that the uncoded BER with 5 iterations is very close to the predicted and the gap between the actual coded BER and the predicted is becoming smaller with the increase of the number of the combined elements and the iteration. Note that the iterative performance using soft remapping and hard remapping is comparable within 1 iteration. The right part of Fig. 11 further shows the convergence property of the iterative receiver. Generally, the Mean Square Error (MSE) of the iterative receiver decreases with the increase of the number of combined elements. The dash lines denote the MSEs of the iterative receiver with the transmitted symbols feeding back as
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95$ HOHPHQWV
65$ HOHPHQWV #P
5[
7[
P
5[ 'HSWK aP
7[
7[
# P
'HSWK aP
P …
7[
P
5[
P
NP
Fig. 10. Left: Schematic of the KAM11 SIMO-OFDM acoustic communication experiment; Right: An example of the CIR observed by the VRA at 3 km range showing a delay spread of about 15 ms.
Fig. 11. Left: BERs as function of the number of receiving-elements combined in 1024-QPSK; Right: MSE as function of the number of iterations in 1024-QPSK.
auxiliary pilots. When combining 2 elements, there is still a gap between the actual MSE and the perfect one. With the increase of the number of the combined elements, the gap is becoming smaller, and finally converges to zero when combing all 16 elements. The first iteration yields a significant performance improvement while there is almost no improvement for further iterations. Fig. 12 shows the BER versus the number of combined elements in 1024-16QAM. For the uncoded BER, it is matched to the predicted curve, which is based on the right part of Fig. 7 when IA;DET ¼ 1. For the coded BER, there is a performance gap between the actual BER and the predicted with full a priori information due to the errors of the initial channel estimation in the case that the length of CP (12.8 ms) is shorter than the maximum delay spread. Finally, the coded BER achieves 102 by combining all 16 elements after 5 iterations. With combining 11 elements, the BERs are slightly higher because the channel at the #11 hydrophone (at the depth of about 60 m) shows intensive multipath seen in Fig. 10. The right part of Fig. 12 further demonstrates the MSE versus the number of iterations. When combining 2 elements, the actual MSE is close to the perfect one (the dash line), denoting that the iterative processing would not further improve the performance of the system with the limited number of the combined elements. With the increase of the number of combined elements, the reducing of the MSE and the performance gap between the actual one and the perfect
one still exists, showing that the iterative performance cannot achieve the perfect performance in this data packet. Fig. 13 shows the BER versus the number of combined receiving-elements in 2048-QPSK. As wished in Fig. 8, we can obtain the coded BER about 103 with two-element reception and an error-free transmission under combining 3 elements after 2 iterations. The coded BER curve is highly close to the predicted curve with full a priori information. The right part of Fig. 13 further demonstrates the MSE versus the number of iterations. The iterative receiver generates a significant performance improvement with the increase of the number of iterations even combining only 2 elements. The actual MSE is highly approaching the perfect one (the dash line) and the proposed approach for 2048-QPSK configuration achieves its performance bound possibly because the 2048-QPSK configuration has longer CP than the 1024-QPSK configuration at the same data rate. The BER as a function of the number of combined receivingelements in 2048-16QAM is illustrated in Fig. 14. It can be observed that the coded BER of 104 can be obtained by combining 16 elements and 5 iterations, which is matched to the BER prediction denoted by black curves. The coded BER with combined 11 elements also shows slightly higher because the level of sparseness of the channel at the #11 hydrophone (at the depth of about 60 m) is very dense as seen in Fig. 10. Similarly, the right part of Fig. 14 further demonstrates the MSE versus the number of iterations.
L. Zhang et al. / Applied Acoustics 114 (2016) 307–316
315
Fig. 12. Left: BERs as function of the number of receiving-elements combined in 1024-16QAM; Right: MSE as function of the number of iterations in 1024-16QAM.
Fig. 13. Left: BERs as function of the number of receiving-elements combined in 2048-QPSK; Right: MSE as function of the number of iterations in 2048-QPSK.
The MSE has no decrease with combining 2 and 4 elements, and there is a big gap between the actual MSE and the perfect MSE marked by dash lines. With the increase of the number of the combined elements, the MSE reduces with three iterations nevertheless there is almost no big improvement for the further
iterations, and the actual MSE is highly approaching to the perfect one when combining all 16 elements. The 2048-16QAM configuration outperforms the 1024-16QAM configuration with the same frequency efficiency and has a trade-off between the transmission efficiency and the reliability.
Fig. 14. Left: BERs as function of the number of receiving-elements combined in 2048-16QAM; Right: MSE as function of the number of iterations in 2048-16QAM.
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5. Conclusions In this paper, a multi-array iterative receiver involving joint sparse channel estimation and decoding based on LLR-combining detection was proposed and its performance was investigated using data from KAM11 experiment conducted in shallow water. The processing results showed the proposed receiver worked very well and significantly outperformed the conventional non-iterative detection. The data transmission with a BER of 104 using 16QAM can be achievable at a data rate of 21 kbps. Moreover, we demonstrated the use of the EXIT chart to analyze the convergence property of iterative processing and to predict BER performance based on real data sets with different data configurations, different diversity combining and different numbers of the iteration. We wanted to provide enlightenment into the system parameter design for achieving a good trade-off among the performance and the transmission efficiency. Transmission over MIMO technique in timevarying underwater acoustic channels will be also considered for further research. Acknowledgments The KAM11 experiment was supported by the Office of Naval Research. We want to thank Dr. Hee-chun Song in Scripps Institution of Oceanography for the field test. This research is supported by the National Natural Science Foundation of China under Grants No. 41376040, 41476026, the Fundamental Research Funds for the Central Universities under Grants No. 20720140506 and China Scholarship Council. References [1] Stojanovic M. Low complexity OFDM detector for underwater acoustic channels. OCEANS 2006;2006:1–6. http://dx.doi.org/10.1109/ OCEANS.2006.307057. [2] Kang T, Song HC, Hodgkiss WS. Long-range multi-carrier acoustic communication in deep water using a towed horizontal array. J Acoust Soc Am 2012;131(6):4665–71. http://dx.doi.org/10.1121/1.4711009. [3] Radosevic A, Ahmed R, Duman T, Proakis J, Stojanovic M. Adaptive OFDM modulation for underwater acoustic communications: design considerations and experimental results. IEEE J Oceanic Eng 2014;39(2):357–70. http://dx.doi. org/10.1109/JOE.2013.2253212. [4] Kang T, Iltis R. Fast-varying doppler compensation for underwater acoustic OFDM systems. In: 2008 42nd Asilomar conference on signals, systems and computers. p. 933–7. http://dx.doi.org/10.1109/ACSSC.2008.5074548. [5] Wan L. Underwater acoustic OFDM: algorithm design, DSP implementation, and field performance. University of Connecticut; 2014. [6] Kang T, Iltis R. Iterative carrier frequency offset and channel estimation for underwater acoustic OFDM systems. IEEE J Sel Areas Commun 2008;26 (9):1650–61. http://dx.doi.org/10.1109/JSAC.2008.081205. [7] Zhang L, Kang T, Song H, Hodgkiss W, Xu X. MIMO-OFDM acoustic communication in shallow water. In: Oceans – San Diego, vol. 2013; 2013. p. 1–4. [8] Yang TC. Properties of underwater acoustic communication channels in shallow water. J Acoust Soc Am 2012;131(1):129–45. http://dx.doi.org/ 10.1121/1.3664053. [9] Stojanovic M. On the relationship between capacity and distance in an underwater acoustic communication channel. ACM SIGMOBILE Mob Comput Commun Rev 2007;11(4):34–43.
[10] Tuchler M, Koetter R, Singer A. Turbo equalization: principles and new results. IEEE Trans Commun 2002;50(5):754–67. http://dx.doi.org/10.1109/ TCOMM.2002.1006557. [11] Tuchler M, Singer A. Turbo equalization: an overview. IEEE Trans Inf Theory 2011;57(2):920–52. http://dx.doi.org/10.1109/TIT.2010.2096033. [12] Berrou C, Glavieux A. Near optimum error correcting coding and decoding: turbo-codes. IEEE Trans Commun 1996;44(10):1261–71. http://dx.doi.org/ 10.1109/26.539767. [13] Yellepeddi A, Preisig J. Adaptive equalization in a turbo loop. IEEE Trans Wireless Commun 2015;14(9):5111–22. http://dx.doi.org/10.1109/ TWC.2015.2432764. [14] Choi JW, Riedl T, Kim K, Singer A, Preisig J. Adaptive linear turbo equalization over doubly selective channels. IEEE J Oceanic Eng 2011;36(4):473–89. http:// dx.doi.org/10.1109/JOE.2011.2158013. [15] Kang T, Song HC, Hodgkiss WS, Soo Kim J. Long-range multi-carrier acoustic communications in shallow water based on iterative sparse channel estimation. J Acoust Soc Am 2010;128(6):EL372–7. http://dx.doi.org/ 10.1121/1.3514157. [16] Yang Z, Zheng Y. Iterative channel estimation and turbo equalization for multiple-input multiple-output underwater acoustic communications. IEEE J PP Oceanic Eng 2015(99). http://dx.doi.org/10.1109/JOE.2015.2398731. 1–1. [17] Zhang J, Zheng Y. Frequency-domain turbo equalization with soft successive interference cancellation for single carrier MIMO underwater acoustic communications. IEEE Trans Wireless Commun 2011;10(9):2872–82. http:// dx.doi.org/10.1109/TWC.2011.072511.100324. [18] Huang J, Huang J, Berger CR, Zhou S, Willett P. Iterative sparse channel estimation and decoding for underwater MIMO-OFDM. EURASIP J Adv Signal Process 2010;2010:1. [19] Tao J, Zheng Y. Turbo detection for MIMOOFDM underwater acoustic communications. Int J Wireless Inf Netw 2013;20(1):27–38. http://dx.doi. org/10.1007/s10776-012-0182-4. [20] ten Brink S. Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Trans Commun 2001;49(10):1727–37. http://dx.doi.org/10.1109/ 26.957394. [21] Hagenauer J. The exit chart-introduction to extrinsic information transfer in iterative processing. In: Proc 12th European signal processing conference (EUSIPCO). p. 1541–8. [22] Tuchler M, Brink ST, Hagenauer J. Measures for tracing convergence of iterative decoding algorithms. In: Proc 4th IEEE/ITG conf on source and channel coding. p. 53–60. [23] Divsalar D, Dolinar S, Pollara F. Iterative turbo decoder analysis based on density evolution. IEEE J Sel Areas Commun 2001;19(5):891–907. http://dx. doi.org/10.1109/49.924873. [24] Wang L, Tao J, Zheng YR. Single-carrier frequency-domain turbo equalization without cyclic prefix or zero padding for underwater acoustic communications. J Acoust Soc Am 2012;132(6):3809–17. http://dx.doi.org/ 10.1121/1.4763987. [25] Berger C, Wang Z, Huang J, Zhou S. Application of compressive sensing to sparse channel estimation. IEEE Commun Mag 2010;48(11):164–74. http://dx. doi.org/10.1109/MCOM.2010.5621984. [26] Kang T, Iltis R. Matching pursuits channel estimation for an underwater acoustic OFDM modem. In: IEEE international conference on acoustics, speech and signal processing, 2008. ICASSP 2008. p. 5296–9. http://dx.doi.org/ 10.1109/ICASSP.2008.4518855. [27] Berger C, Zhou S, Preisig J, Willett P. Sparse channel estimation for multicarrier underwater acoustic communication: from subspace methods to compressed sensing. IEEE Trans Signal Process 2010;58(3):1708–21. [28] Robertson P, Villebrun E, Hoeher P. A comparison of optimal and sub-optimal map decoding algorithms operating in the log domain. IEEE international conference on communications, 1995. ICC ’95 Seattle, ‘Gateway to Globalization’, 1995, vol. 2. p. 1009–13. http://dx.doi.org/10.1109/ ICC.1995.524253. [29] ten Brink S, Kramer G, Ashikhmin A. Design of low-density parity-check codes for modulation and detection. IEEE Trans Commun 2004;52(4):670–8. http:// dx.doi.org/10.1109/TCOMM.2004.826370. [30] Hou J, Siegel P, Milstein L. Design of multi-input multi-output systems based on low-density parity-check codes. IEEE Trans Commun 2005;53(4):601–11. http://dx.doi.org/10.1109/TCOMM.2005.844972.
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Multi-array iterative receiver for underwater acoustic OFDM communications with EXIT chart evaluation Lan Zhang a, Xiaomei Xu a,⇑, Wei Feng b, Yougan Chen a a b
Key Laboratory of Underwater Acoustic Communication and Marine Information Technology (Xiamen University), Ministry of Education, Xiamen 361005, China College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
a r t i c l e
i n f o
Article history: Received 25 November 2015 Received in revised form 7 July 2016 Accepted 12 July 2016 Available online 16 August 2016 Keywords: OFDM Underwater acoustic communications Multi-array Iterative receiver LLR-combining EXIT chart
a b s t r a c t In this paper, a multi-array iterative receiver based on log-likelihood ratio (LLR)-combining detection involving joint sparse channel estimation and decoding is proposed for underwater acoustic OFDM communication. First, Extrinsic information transfer (EXIT) chart analysis is applied to evaluate the convergence behavior of the iterative receiver using the real data collected from the Kauai Acomms MURI 2011 (KAM11) experiment. This experiment was conducted in about 106 m-depth shallow water west of Kauai, HI, in June 2011, with a 20 kHz bandwidth (12–32 kHz) at range up to 3 km. It helps to explain the impact of different data configurations, detectors, and the diversity combinations in a highly inhomogeneous underwater environment and to predict the bit-error rate (BER) performance of the proposed receiver. Then the BERs as a function of the number of combined elements are illustrated to verify the prediction and analysis via the EXIT chart. Data transmission using 16QAM modulation achieves a BER of 104 at a data rate of 21 kb/s. The results provide guidance for the design of system parameters including the data configurations, the number of iterations for both iterative processing and low density parity check (LDPC) decoding, which are beneficial to achieve a good efficiency-performance tradeoff. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, underwater acoustic communication has been improved tremendously with the use of multi-carrier transmission, also known as orthogonal frequency division multiplexing (OFDM) [1–7]. It is advantageous to avoid complex channel equalization and block-by-block processing. In contrast to radio wireless channel, underwater acoustic (UWA) channel is very harsh as a result of its unique characteristics: large delay spread due to time-varying multi-path propagation causing significant inter-symbol interference, limited available bandwidth due to the frequency-selective attenuation, and strong spatial correlation [8,9]. Since underwater acoustic channel is a triple-selective fading channel in time, space and frequency, a robust receiver where channel estimation and decoding is performed jointly and iteratively is needed. The iterative processing, inspired by ‘‘Turbo Principle” [10], is often required to conquer the harshness of the underwater acoustic channel and to achieve satisfactory performance [11]. The Turbo principle was
⇑ Corresponding author. E-mail addresses: [email protected] (L. Zhang), [email protected] (X. Xu), [email protected] (W. Feng), [email protected] (Y. Chen). http://dx.doi.org/10.1016/j.apacoust.2016.07.008 0003-682X/Ó 2016 Elsevier Ltd. All rights reserved.
originally developed for decoding concatenated codes [12] and has been applied to direct-adaptation based turbo equalization (DA-TEQ) [13,14], channel-estimation based turbo equalization (CE-TEQ) [6,15–17] in the UWA communication community recently. Most of these methods are used in single-carrier UWA communication systems. Existing literature on iterative processing for underwater acoustic multi-carriers communication is still limited [18,19]. In [18], an iterative receiver incorporating multiple-input, multiple-output (MIMO) detection and sparse channel estimation techniques was proposed for UWA MIMOOFDM communications. The authors in [19] presented a linear turbo detection scheme for UWA MIMO-OFDM communications, without iterative channel estimation. Both of these two iterative receivers were designed for underwater acoustic MIMO-OFDM communications with experimental investigations. Such iterative processes are often analyzed using extrinsic information transfer (EXIT) charts [20]. EXIT chart, using the mutual information as a figure of merit, is a powerful semianalytical tool to analyze and optimize the convergence behavior of iterative systems. Early methods to evaluate the convergence behavior of the iterative decoder used the signal-to-noise ratio (SNR), the mean, the variance, the BER and the fidelity as a parameter of the chart [21]. The fidelity chart is also called the soft bit
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transfer (SOBIT) chart. In [22], the authors compared all these measures to describe the behavior of the soft-in soft-out decoder and found out that only the EXIT chart and the SOBIT chart could provide fairly accurate and robust explanation of the behavior of the iterative process. There is also another useful tool to study the convergence of iterative detection called density evolution [23]. It tracks the evolution of the distribution of extrinsic information in the iterative algorithm, which is mainly used for the analysis and optimization of LDPC codes. EXIT chart is a simplification of density evolution and is easier to program. The mutual information in the EXIT chart has the advantage of representing a common quantity in communication theory and provides additional insight of convergence prediction. Its accuracy is particularly impressive when the block-length of interleaver tends to be infinite. EXIT chart has become a preferable option because it has the ability to closely reflect the behavior of the iterative process and to evaluate the convergence of the entire iterative scheme without performing time consuming simulations. ten Brink [20] used extrinsic information transfer characteristics based on mutual information to describe the flow of extrinsic information through the soft-in/soft-out constituent decoders. This method provides an opportunity to predict the BER of a coded system and the iterative-processing system with substantial reduction in numerical complexity. Kang and Iltis [6] used the EXIT chart to optimize the power allocation between the pilot and data sub-carriers for iterative processing, but they used simulated data rather than experimental data from a real UWA channel. Wang et al. [24] utilized the EXIT chart to analyze the convergence property between the turbo equalizer and the decoder in the underwater acoustic single-carrier system. The first contribution of our paper is that we propose a multiarray iterative receiver performing sparse channel estimation and decoding jointly based on LLR-combining detection, instead of hard decision, for underwater acoustic OFDM communication. Note that the Gaussian assumption is mismatched by the coloring of the noise at the output of the hard-decision detector. We use extensive undersea trial data collected from KAM11 experiment conducted in shallow water to validate the performance of the proposed iterative receiver. The second contribution is that we give a deep insight on convergence behavior between the channel estimator and the LDPC decoder based on the EXIT chart using the experimental data rather than the simulated data. We consider the combination of diversity and the data configurations (the number of sub-carriers and the mapping scheme) affect the performance. Additionally, we extend the capabilities of the EXIT chart to predict BERs of the iterative receiver without extensive performance simulations or experimental data processing. Moreover, the EXIT analysis and prediction provides enlightenment into system parameter design for achieving a good tradeoff between the performance and the transmission efficiency. The rest of this paper is organized as follows. First, the system architecture consisting of transmitter and iterative receiver is displayed in Section 2, introducing the principle of iterative receiver and the flow of extrinsic information of the receiver. Then the EXIT evaluation on the iterative receiver based on the real data explains and predicts the performance of the iterative receiver in Section 3. Experimental results based on KAM11 experiment are subsequently exemplified in Section 4. Finally, conclusions are made in Section 5.
2. System architecture 2.1. Signal The specification for the underwater OFDM communication system considered in this paper is given in Table 1. The null
sub-carriers serve as a guard band and the pilot tones are nonuniformly allocated in one OFDM symbol. As shown in Fig. 1, the data packet consists of 100 ms chirp signal, 200 ms silence periods and 32 OFDM blocks. The chirp signal is used for synchronization and Doppler estimation. The data packets have 4 different configurations: 1024-QPSK, 1024-16QAM, 2048QPSK, and 2048-16QAM, specified as the number of sub-carrier and the modulation scheme. A data stream (a duration of 30 s) with 8 packets will be sent from the source to the vertical receiver array with 16 hydrophones over the underwater acoustic channel, where each kind of data packet repeats twice. 2.2. Transmitter T
As shown in Fig. 2, the bit sequence b ¼ ½b0 ; b1 ; . . . bMNd R1 is T
LDPC encoded to codewords c ¼ ½c0 ; c1 ; . . . cMNd 1 and the codewords are interleaved bit-wise. R is the code-rate and 2M is the order of the modulation. The interleaved codewords are mapped T
into data sub-carriers d ¼ ½d0 ; d1 ; . . . dNd 1 with Gray mapped QPSK or 16QAM, respectively. With the pilot tones p ¼ ½p0 ; p1 ; . . . pNp 1 T , the transmitted symbols in frequencydomain s ¼ ½s0 ; s1 ; . . . sNs 1 T can be expressed as the sum of orthogonal pilot tones and data sub-carriers, s ¼ p þ d, where pk dk ¼ 0 for 0 6 k 6 N s 1. In the guard band, pk ¼ dk ¼ 0. Then the time-domain transmitted symbol with CP x ¼ ½xNs Ng ; . . . xNs 1 ; x0 ; . . . xNs 1 T is generated by the ‘‘OFDM Modulator” consisting of parallel-serial converter, IFFT, CP adder and up-converter. There is negligible Doppler spread in the received data for there was no relative motion between the source and the multi-array receiver. With the effect of multipath propagation, the representation of the channel impulse response (CIR) is
hðs; tÞ ¼
L1 X Al ðtÞdðs sl ðtÞÞ
ð1Þ
l¼0
where L is the number of the multi-path of the channel, Al ðtÞ represents the real-valued gain of the l-th path, sl ðtÞ is the corresponding delay. The channel attenuation and delay spread is assumed to be invariant within one OFDM block, but varies block by block. The discrete-time baseband channel impulse response is rewritten as
hðnÞ ¼
L1 X Al dðn sl Þ
ð2Þ
l¼0
The multiple-receiving system will receive the data through the underwater acoustic channel like the Eq. (3):
yv ðnÞ ¼
L1 X Al;v xðn sl Þ þ gv ðnÞ; v ¼ 1; 2; . . . Nrx
ð3Þ
l¼0
where Nrx is the number of the receiving elements from bottom to top. g is assumed to be complex additive and independent on differ-
Table 1 OFDM specification. Number of sub-carriers Number of data sub-carriers Number of pilots Number of null sub-carriers Cyclic Prefix (CP) duration Symbol duration with CP Number of the samples of CP Subcarrier spacing LDPC decoder Uncoded data rate(QPSK/16QAM) Coded data rate(QPSK/16QAM)
N s ¼ 1024 N d ¼ 672 N p ¼ 256 N u ¼ 96 T g ¼ 12:8 ms T s ¼ 64 ms N g ¼ 256 Df ¼ 19:53 Hz (1344,672) LDPC 21 kbps/42 kbps 10.5 kbps/21 kbps
N s ¼ 2048 N d ¼ 1344 N p ¼ 512 N u ¼ 192 T g ¼ 25:6 ms T s ¼ 128 ms N g ¼ 512 Df ¼ 9:765 Hz (1344,672) LDPC 21 kbps/42 kbps 10.5 kbps/21 kbps
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2
32 blocks
OFDM
OFDM
OFDM
Silence Chirp
Chirp Silence 100ms 100ms
kN 1 1
j2p N k s 36 1 e s½kN1 6 kN 2 1 76 6 1 ej2p Ns k 76 6 . 6 . W¼6 76 . 56 .. 4 .. . 6. s½kNp 4 k
2
64ms/128ms
64ms/128ms
100ms 100ms
Np 1
1 ej2p Ns k
kN
1 ~L1 k
ej2p Ns e .. .
kN
j2p
2 ~L1 k Ns
.. . kN
p ~L1 k
3 7 7 7 7 7 7 7 7 5
ð6Þ
ej2p Ns
Packet duration=2.348s/4.396s
Fig. 1. The structure of data packet.
ent receiving-elements after noise pre-whitening. The ambient noise in underwater acoustic channel is typically modeled as a non-white Gaussian process and given as a linear combination of four independent noise sources: turbulence, shipping, waves, and thermal noise, which makes the equivalent noise more colored to mismatch the Gaussian assumption. Therefore, noise prewhitening is beneficial to facilitate iterative processing. The synchronization process at each receiving-element is achieved by matched filtering of chirp waveform. After baseband conversion, serial-parallel converter, CP removal and FFT, the received sequence over each element is
Y v ½k ¼ Hv ½ks½k þ W v ½k; k ¼ 0; 1; . . . Ns 1; v ¼ 1; 2; . . . Nrx
ð4Þ
where W is the FFT of the additive noise g, assumed to be independent on different elements and Gaussian distributed Nð0; r2w Þ. H is the channel frequency response (CFR) within one OFDM block on each receiving-element.
Based on the algorithm of OMP in [27], the estimated channel ^ p can be obtained. With pilot-based sparse impulse response h channel estimation, the estimated channel at other positions can be achieved by interpolation or discrete fourier transform (DFT):
^ v ½k ¼ H
~L1 X
Step2 Soft detection for each element: With the estimated CFR, it is traditional to utilize maximal ratio combining for hard detection in multiple receiving systems, which will make the noise at the output of the equalizer more colored. Instead, we calculate a posterior LLR value of the bit sequence as the output of each soft-detector. Leveraging on Bayes’ theorem, the a posterior LLR value is shown as follows:
LLRðbj jY v ½kÞ ¼ ln ¼ ln
In this section, we introduce how the iterative receiver works and describe the flow of extrinsic information through the channel estimator and LDPC decoder. As shown in Fig. 3, a block diagram of the receiver consists of six major components: pilot-based sparse channel estimator (CE), data-subcarrier-based channel estimator, LLR combiner, soft detector, LDPC decoder and symbol remapper. The multi-array iterative receiver incorporating joint channel estimator and decoding is summarized as in the following: Step1 Pilot-based Sparse Channel estimation: Since the underwater acoustic channel is sparse [25], we use sparse channel estimation with orthogonal matching pursuit (OMP) algorithm [26] in order to capture the sparsity of the channel. To estimate the path delays, the OMP channel estimator first selects a path delay grid such as h i l m T g Ns T s 2T s ~ TðkÞ ¼ 0; ; ; . . . T g , with length of L ¼ . k is an overTs
kNs
sampling factor, L ~ L for sparse recovery. For each receiving element, the initial sparse channel estimation based on pilot symbols in the vector-matrix form is
Yp ¼ Whp þ Wp
ð5Þ
where hp is the underwater acoustic channel impulse response
ð7Þ
l¼0
2.3. Iterative receiver structure
kNs
^ ej2pkNkls ; k ¼ 0; 1; . . . Ns 1; v ¼ 1; 2; . . . N rx h l
Prðbj ¼ 0jY v ½kÞ ; j ¼ 0; 1 . . . MNd R 1 Prðbj ¼ 1jY v ½kÞ PrðY v ½kjbj ¼ 0Þ Prðbj ¼ 0Þ þ ln ; PrðY v ½kjbj ¼ 1Þ Prðbj ¼ 1Þ
k ¼ kN1 ; kN2 . . . kNd P P dk ¼f ðb¼0Þ PrðY v ½kjdk Þ d ¼f ðb¼0Þ Prðdk Þ ¼ ln P þ ln P k ; PrðY ½kjd Þ v k dk ¼f ðb¼1Þ dk ¼f ðb¼1Þ Prðdk Þ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} LE;DET
LA;DET
v ¼ 1; 2; . . . Nrx
ð8Þ
where f is the Gray-Mapped QPSK or 16QAM. LA;DET is a priori LLR value of the detector and LE;DET is the extrinsic LLR value of the detector. On the basis of the assumption that the noise W is additive and Gaussian distributed, the conditional density for each receiving element is given as: ^ v ½kd j2 jY v ½kH k 2r2 w
PrðY v ½kjdk Þ ¼ e
; k ¼ kN1 ;kN2 ;. .. kNd ; v ¼ 1; 2;. .. Nrx
ð9Þ
Initially, the bit sequence is assumed to be equiprobable, so LA;DET ¼ 0. Step3 LLR combining: The error probability of one bit is assumed to be large for small magnitudes of its LLR values, and it is assumed to be small for large magnitudes of its corresponding LLR. Using the Jacobian logarithm [28] as follows
T
vector with entry of ½h0 ; h1 ; . . . h~L1 . W is the dictionary matrix with the size of N p ~L
lnða þ bÞ ¼ maxðA; BÞ þ lnð1 þ ejABj Þ
Pilot tones inseron p b
LDPC Encoder
c
Interleaver
M-ary Modulator
d
Fig. 2. Block diagram of the transmitter.
s
OFDM Modulator
x
ð10Þ
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Pilot-based Sparse CE
Y1
Soft Detector LE,DET
LA,LDPC
Deinterleaver
YNrx
Pilot-based Sparse CE
LDPC Decoder
Soft Detector
Symbol LAPP,LDPC + LA,DET Remapper
Datasubcarrier CE
bˆ
LE,LDPC
Interleaver
Fig. 3. Block diagram of the iterative receiver.
where A ¼ lna; B ¼ lnb, we can calculate the a posterior LLR of one bit from the detector for each element by substituting Eqs. (9) and (10) into Eq. (8). The LLR combiner will sum up the LLRs of receiving-elements from bottom to top:
LLRðbj Þ ¼
Nrx X
v ¼1
the next iteration. If the maximum iterations have not been reached, repeat steps 1, 2, 3 and 4. Otherwise, output the hard decision of the a posterior information. 3. EXIT chart evaluation
LLRðbj jY v ½kÞ; j ¼ 0; 1 . . . MN d R 1; k ¼ kN1 ; kN2 ; . . . kNd ð11Þ
Step4 Maximum a posterior (MAP) decoding for the LDPC decoder: A half-rate (1344,672) irregular LDPC code from the IEEE 802.16e standard is considered in this paper. The extrinsic LLR value from the detector LE;DET is used as a priori LLR for LDPC decoder LA;LDPC ; LE;DET ! LA;LDPC . After 25 iterations, a posterior LLR values of bits from the LDPC decoder LAPP;LDPC is achieved to make hard decisions to estimate the transmitted bit ^ Until now, one-direction detection is finished. sequence b. Step5 Symbol remapper: It is not easy to get a satisfactory performance by singleelement reception, as seen in [15]. If we want to get a more satisfactory performance, the multi-array iterative receiver incorporating joint channel estimation and decoding should be a promising method. With 25-iteration iterative decoding, the LDPC decoder yields the extrinsic LLR value LE;LDPC , which can feed back to the detector as its a priori LLR values: LE;LDPC ! LA;DET . However, the detector cannot get any gain from the iterative processing under Gray-mapping. Therefore the dashed line of Fig. 3 can be removed for Gray-mapping. Instead, we use a posterior LLR of the decoder LAPP;LDPC to calculate the probability of each bit:
Based on the mutual information transfer functions, the purpose of the EXIT chart is to visualize convergence behavior and to predict the performance of the iterative receiver between the soft information (LLR values) and the corresponding bits. Through the EXIT chart analysis, the exchange of extrinsic information between detector/channel estimator and LDPC decoder can be drawn in the same axis. On the ordinate, the extrinsic output of the detector IE;DET becomes a priori input of the LDPC decoder IA;LDPC . On the abscissa, the extrinsic output of the LDPC decoder IE;LDPC becomes a priori input of the detector IA;DET . Based on the definition of mutual information, the a priori mutual information IA;DET and extrinsic mutual information of the detector IE;DET can be expressed as:
IA;DET ¼ IðB; LA;DET Þ ¼ log 2
Z
þ1
1
PrA;DET ðnjB ¼ bÞ
2PrA;DET ðnjB ¼ bÞ dn Pr A;DET ðnjB ¼ 0Þ þ PrA;DET ðnjB ¼ 1Þ
IE;DET ¼ IðB; LE;DET Þ ¼ log 2
1X 2 0;1
1X 2 0;1
Z
þ1
1
ð17Þ
PrE;DET ðnjB ¼ bÞ
2PrE;DET ðnjB ¼ bÞ dn Pr E;DET ðnjB ¼ 0Þ þ PrE;DET ðnjB ¼ 1Þ
ð18Þ
Prðbj ¼ 1Þ ¼
eLAPP;LDPC ðbj Þ 1 þ eLAPP;LDPC ðbj Þ
ð12Þ
where PrA;DET and Pr E;DET are the probability density functions of LA;DET and LE;DET respectively.
Prðbj ¼ 0Þ ¼
1 1 þ eLAPP;LDPC ðbj Þ
ð13Þ
3.1. LLR distribution analysis
and we get the reliability value of the kth data symbol dk :
Prðdk Þ ¼
M Y
Prðbj Þ
ð14Þ
j¼1
Finally, we get the estimated data symbols with soft remapping:
^s ¼ d k
M X Prðdk ¼ ai Þai ; k ¼ kN1 ; kN2 ; . . . kNd
ð15Þ
i¼1
or hard remapping:
^h ¼ a ; i ¼ arg max Prðd ¼ a Þ; k ¼ kN ; kN ; . . . kN d i k i k 1 2 d i
ð16Þ
where ai are the constellation symbols. Then, we apply the remapped data sub-carriers as auxiliary pilots to get more accurate pilot-based channel estimation for
As seen in the Eq. (18), the extrinsic mutual information of the detector IE;DET depends on the distribution of the LLR values. In Figs. 4 and 5, we investigate the distribution of extrinsic LLR of the detector with the real data collected from the KAM11 experiment in 4 cases: 1024-QPSK, 1024-16QAM, 2048-QPSK and 2048-16QAM configurations. For all four cases, the reliability of the LLRs improves as the increase of the number of combined elements. The two LLR curves (b ¼ 0; b ¼ 1) will move apart and the overlapped part will decrease, giving more reliable soft information between detector and decoder. For 1024-QPSK configuration, the two curves become completely separated with combining 5 elements. For 2048-QPSK case, the two curves become nearly separated as a result of combining 2 elements. The correct bit values will be obtained by making decisions based upon the sign of the corresponding LLRs under these two cases. However, for 1024-16QAM and 204816QAM, the two curves still keep overlapped when all 16 elements
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311
Fig. 4. Left: 1024-QPSK LLR distribution; Right: 1024-16QAM LLR distribution.
Fig. 5. Left: 2048-QPSK LLR distribution; Right: 2048-16QAM LLR distribution.
are combined, which means we are not able to get error-free transmission even combining all 16 hydrophones. 3.2. EXIT chart evaluation and prediction Using the EXIT chart method, we are able to evaluate convergence and compare the iterative receiver under diverse combination and different data configurations. It is not difficult to calculate IE;DET using the empirical formulas in [29] for the distribution of the LLR value satisfying the consistency condition [22]. Although the actual LLR values of the detector are not always Gaussian distributed or do not satisfy the consistency condition due to the stochastic underwater acoustic channel, seen in Figs. 4 and 5, the EXIT chart still work well in a wide range of applications, e.g. [6,30]. The distributions of Pr E;DET in Eq. (18) are most conveniently determined by Monte Carlo simulation (histogram measurements). Generally, the analysis of EXIT chart is in agreement with the actual performance with 105 -bit interleaver size based on [20]. LDPC codes used here are rather short to facilitate underwater acoustic channels with long delay spread. The EXIT chart analysis for a short code is still valid, but the accuracy is limited. The EXIT curve of the LDPC decoder in Figs. 6–9 is obtained by running Mont Carlo simulation of LDPC codes with the code length 6
of 10 . As shown at the left part of Fig. 6, the extrinsic information will enlarge with the increase of the number of iterations at the same a priori information. 1 or 4-iteration decoding is not enough
for good performance, while 25-iteration is chosen for practical implementation without losing significant performance. Then we generate the EXIT curve of the estimator/detector for four cases. The EXIT chart in Fig. 6 (left) depicts the transfer function of 1024-QPSK detector and LDPC decoder. We compare the EXIT chart of the detector with a different number of the receiving elements combined. For 0 6 IA;DET 6 1; IE;DET is given as a monotonic function of IA;DET . The curve of detector is beneath the curve of decoder when combining 1 element. When combining 2 elements, the iterative receiver cannot get over the EXIT bottleneck, even though many iterations are provided. With the increase of the number of combined receiving-elements, the line of extrinsic information of the detector is becoming higher and higher. Under combining 5 elements, the EXIT curve of detector is totally above the curve of the decoder, meaning that we are able to get error-free correction. Each extrinsic output of the detector IE;DET is associated with BER prediction as shown at the right part of Fig. 6. We find that the LDPC coded BER with 102 can be achieved with combined 1 element when IE;DET 0:51 given IA;DET ¼ 1 and the coded BER with 103 can be achieved with combined 2 elements when IE;DET 0:62 with full a priori information. In addition, we can get the uncoded BER with 101 even with combined 5 elements when IE;DET 0:73 under IA;DET ¼ 1. And the coded BER is less than 104 corresponding to IE;DET 0:57 for IA;DET ¼ 0:1. The EXIT chart of 1024-16QAM detector and LDPC decoder is plotted at the left part of Fig. 7. We observe that the extrinsic
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Fig. 6. Left: EXIT chart for 1024-QPSK; Right: BER as a function of extrinsic information of the detector.
Fig. 7. Left: EXIT chart for 1024-16QAM; Right: BER as a function of extrinsic information of the detector.
Fig. 8. Left: EXIT chart for 2048-QPSK; Right: BER as a function of extrinsic information of the detector.
information of the detector increases with the number of combined elements, though all of them are under the LDPC decoder’s curve. There is no tunnel between the detector and the decoder, indicating that we are not able to acquire the error-free correction
even combining all 16 elements at the full a priori information. We can still make a prediction of BER at the right part with the corresponding IE;DET . With combined 4 elements, the LDPC coded BER with 101 can be obtained when IE;DET 0:51 given IA;DET ¼ 1. With
L. Zhang et al. / Applied Acoustics 114 (2016) 307–316
313
Fig. 9. Left: EXIT chart for 2048-16QAM; Right: BER as a function of extrinsic information of the detector.
combined 12 elements, the coded BER with 102 can be achieved when IE;DET 0:54 given IA;DET ¼ 1. Additionally, we can get the coded BER with 103 and the uncoded BER with 101 under all combined 16 elements when IE;DET 0:58 given IA;DET ¼ 1. We depict the EXIT chart of 2048-QPSK detector and LDPC decoder at the left of Fig. 8. As seen in its extrinsic LLR distribution in Fig.5, the curves of b ¼ 1 and b ¼ 0 nearly separate with combined 2 elements. Correspondingly, the EXIT curve of the detector is higher than the LDPC extrinsic curve, telling that it is easier to get successive detection with combined 2 elements in 2048QPSK, whose CP length is much higher than 1024-QPSK. Similarly, a prediction of the BER associated with the extrinsic information is provided at the right part. The LDPC coded BER with 102 can be attained with only 1 element corresponding to IE;DET 0:53 for IA;DET ¼ 1. With combined 2 elements, the coded BER with 102 can be achieved when IE;DET 0:57 given IA;DET ¼ 0:3. With the increase of a priori information, an error-free transmission is achievable with LDPC coding when IE;DET 0:64 given IA;DET ¼ 1. When combining 4 elements, the coded BER with 104 can be achieved when IE;DET 0:64 given IA;DET ¼ 0:2. With the increase of a priori information, an error-free transmission with LDPC coding and the uncoded BER with 101 is achievable corresponding to IE;DET 0:64 for full a priori information. We plot the EXIT chart of 2048-16QAM detector and the LDPC decoder at the left of Fig. 9. According to its extrinsic LLR distribution in Fig. 5, the curves of b ¼ 1 and b ¼ 0 slightly move apart with the increase of the number of combined receiving-elements, and they overlap partly even when combining all 16 elements. This means that the EXIT chart curves of the detector are all below the decoder’s. Meanwhile, a prediction of BER associated with the extrinsic information is provided at the right part. The coded BER with combining 2 elements is about 101 with its prediction corresponding to IE;DET 0:45 for IA;DET ¼ 1. When combining 8 elements, the coded BER is about 103 corresponding to IE;DET 0:58 given IA;DET ¼ 1. With combining 16 elements, the coded BER of 104 and the uncoded BER of 101 can be achieved corresponding to IE;DET 0:64 under IA;DET ¼ 1. 4. Experimental results 4.1. KAM11 experiment deployment The deployment on KAM11 experiment is shown at the left of Fig. 10. An eight-element source receiver array (SRA) was
suspended in about 102 m-depth water. The first transmitter was at about 90 m depth. The data stream was transmitted from the bottom Tx#1 to the top Tx#7, respectively for various transmitted positions. We are centered on the performance of Tx#1 here. The vertical receiver array (VRA) was used as the receiver, consisted of 16-elements spanning a 56 m aperture with 3.75 m interelement spacing, covering about half the water column. The data were received by the VRA at a distance of 3 km. The VRA had a sampling rate of 100 kHz per element. An example of estimated CIR by 100-ms chirp waveform from 12 to 32 kHz is shown at the right of Fig. 10, indicating that the maximum delay spread is about 15 ms and the level of sparseness of channel is spatialvarying. We also inserted two OFDM blocks of Golay sequence as preambles to estimate the CFR and found the UWA channel varied significantly block by block, which is not presented here. Therefore, channel updating block by block is necessary for a successful reception.
4.2. Performance results To investigate the impact of diversity combining on performance, BERs are shown as a function of the number of receivingelements combined to verify the prediction of the EXIT chart. As shown in Fig. 11, the BER curves converge with the increase of the number of the combined elements in non-iterative way (iter = 0), and the error-free correction can be attainable under combined 5 elements. However, the coded BER are close to about 105 not zero when combining 6, 7, 8, 9, 11, 12 elements. This is because the multipath in depth of 60–80 m is very severe, shown at the right part of Fig. 10. For the iterative detection, we see that the proposed receiver outperforms the non-iterative detection when combining less than 5 elements and converges to zero with more than 5 elements. The black curves are the predicted BERs based on the right part of Fig. 6 when IA;DET ¼ 1. We find that the uncoded BER with 5 iterations is very close to the predicted and the gap between the actual coded BER and the predicted is becoming smaller with the increase of the number of the combined elements and the iteration. Note that the iterative performance using soft remapping and hard remapping is comparable within 1 iteration. The right part of Fig. 11 further shows the convergence property of the iterative receiver. Generally, the Mean Square Error (MSE) of the iterative receiver decreases with the increase of the number of combined elements. The dash lines denote the MSEs of the iterative receiver with the transmitted symbols feeding back as
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L. Zhang et al. / Applied Acoustics 114 (2016) 307–316
95$ HOHPHQWV
65$ HOHPHQWV #P
5[
7[
P
5[ 'HSWK aP
7[
7[
# P
'HSWK aP
P …
7[
P
5[
P
NP
Fig. 10. Left: Schematic of the KAM11 SIMO-OFDM acoustic communication experiment; Right: An example of the CIR observed by the VRA at 3 km range showing a delay spread of about 15 ms.
Fig. 11. Left: BERs as function of the number of receiving-elements combined in 1024-QPSK; Right: MSE as function of the number of iterations in 1024-QPSK.
auxiliary pilots. When combining 2 elements, there is still a gap between the actual MSE and the perfect one. With the increase of the number of the combined elements, the gap is becoming smaller, and finally converges to zero when combing all 16 elements. The first iteration yields a significant performance improvement while there is almost no improvement for further iterations. Fig. 12 shows the BER versus the number of combined elements in 1024-16QAM. For the uncoded BER, it is matched to the predicted curve, which is based on the right part of Fig. 7 when IA;DET ¼ 1. For the coded BER, there is a performance gap between the actual BER and the predicted with full a priori information due to the errors of the initial channel estimation in the case that the length of CP (12.8 ms) is shorter than the maximum delay spread. Finally, the coded BER achieves 102 by combining all 16 elements after 5 iterations. With combining 11 elements, the BERs are slightly higher because the channel at the #11 hydrophone (at the depth of about 60 m) shows intensive multipath seen in Fig. 10. The right part of Fig. 12 further demonstrates the MSE versus the number of iterations. When combining 2 elements, the actual MSE is close to the perfect one (the dash line), denoting that the iterative processing would not further improve the performance of the system with the limited number of the combined elements. With the increase of the number of combined elements, the reducing of the MSE and the performance gap between the actual one and the perfect
one still exists, showing that the iterative performance cannot achieve the perfect performance in this data packet. Fig. 13 shows the BER versus the number of combined receiving-elements in 2048-QPSK. As wished in Fig. 8, we can obtain the coded BER about 103 with two-element reception and an error-free transmission under combining 3 elements after 2 iterations. The coded BER curve is highly close to the predicted curve with full a priori information. The right part of Fig. 13 further demonstrates the MSE versus the number of iterations. The iterative receiver generates a significant performance improvement with the increase of the number of iterations even combining only 2 elements. The actual MSE is highly approaching the perfect one (the dash line) and the proposed approach for 2048-QPSK configuration achieves its performance bound possibly because the 2048-QPSK configuration has longer CP than the 1024-QPSK configuration at the same data rate. The BER as a function of the number of combined receivingelements in 2048-16QAM is illustrated in Fig. 14. It can be observed that the coded BER of 104 can be obtained by combining 16 elements and 5 iterations, which is matched to the BER prediction denoted by black curves. The coded BER with combined 11 elements also shows slightly higher because the level of sparseness of the channel at the #11 hydrophone (at the depth of about 60 m) is very dense as seen in Fig. 10. Similarly, the right part of Fig. 14 further demonstrates the MSE versus the number of iterations.
L. Zhang et al. / Applied Acoustics 114 (2016) 307–316
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Fig. 12. Left: BERs as function of the number of receiving-elements combined in 1024-16QAM; Right: MSE as function of the number of iterations in 1024-16QAM.
Fig. 13. Left: BERs as function of the number of receiving-elements combined in 2048-QPSK; Right: MSE as function of the number of iterations in 2048-QPSK.
The MSE has no decrease with combining 2 and 4 elements, and there is a big gap between the actual MSE and the perfect MSE marked by dash lines. With the increase of the number of the combined elements, the MSE reduces with three iterations nevertheless there is almost no big improvement for the further
iterations, and the actual MSE is highly approaching to the perfect one when combining all 16 elements. The 2048-16QAM configuration outperforms the 1024-16QAM configuration with the same frequency efficiency and has a trade-off between the transmission efficiency and the reliability.
Fig. 14. Left: BERs as function of the number of receiving-elements combined in 2048-16QAM; Right: MSE as function of the number of iterations in 2048-16QAM.
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5. Conclusions In this paper, a multi-array iterative receiver involving joint sparse channel estimation and decoding based on LLR-combining detection was proposed and its performance was investigated using data from KAM11 experiment conducted in shallow water. The processing results showed the proposed receiver worked very well and significantly outperformed the conventional non-iterative detection. The data transmission with a BER of 104 using 16QAM can be achievable at a data rate of 21 kbps. Moreover, we demonstrated the use of the EXIT chart to analyze the convergence property of iterative processing and to predict BER performance based on real data sets with different data configurations, different diversity combining and different numbers of the iteration. We wanted to provide enlightenment into the system parameter design for achieving a good trade-off among the performance and the transmission efficiency. Transmission over MIMO technique in timevarying underwater acoustic channels will be also considered for further research. Acknowledgments The KAM11 experiment was supported by the Office of Naval Research. We want to thank Dr. Hee-chun Song in Scripps Institution of Oceanography for the field test. This research is supported by the National Natural Science Foundation of China under Grants No. 41376040, 41476026, the Fundamental Research Funds for the Central Universities under Grants No. 20720140506 and China Scholarship Council. References [1] Stojanovic M. Low complexity OFDM detector for underwater acoustic channels. OCEANS 2006;2006:1–6. http://dx.doi.org/10.1109/ OCEANS.2006.307057. [2] Kang T, Song HC, Hodgkiss WS. Long-range multi-carrier acoustic communication in deep water using a towed horizontal array. J Acoust Soc Am 2012;131(6):4665–71. http://dx.doi.org/10.1121/1.4711009. [3] Radosevic A, Ahmed R, Duman T, Proakis J, Stojanovic M. Adaptive OFDM modulation for underwater acoustic communications: design considerations and experimental results. IEEE J Oceanic Eng 2014;39(2):357–70. http://dx.doi. org/10.1109/JOE.2013.2253212. [4] Kang T, Iltis R. Fast-varying doppler compensation for underwater acoustic OFDM systems. In: 2008 42nd Asilomar conference on signals, systems and computers. p. 933–7. http://dx.doi.org/10.1109/ACSSC.2008.5074548. [5] Wan L. Underwater acoustic OFDM: algorithm design, DSP implementation, and field performance. University of Connecticut; 2014. [6] Kang T, Iltis R. Iterative carrier frequency offset and channel estimation for underwater acoustic OFDM systems. IEEE J Sel Areas Commun 2008;26 (9):1650–61. http://dx.doi.org/10.1109/JSAC.2008.081205. [7] Zhang L, Kang T, Song H, Hodgkiss W, Xu X. MIMO-OFDM acoustic communication in shallow water. In: Oceans – San Diego, vol. 2013; 2013. p. 1–4. [8] Yang TC. Properties of underwater acoustic communication channels in shallow water. J Acoust Soc Am 2012;131(1):129–45. http://dx.doi.org/ 10.1121/1.3664053. [9] Stojanovic M. On the relationship between capacity and distance in an underwater acoustic communication channel. ACM SIGMOBILE Mob Comput Commun Rev 2007;11(4):34–43.
[10] Tuchler M, Koetter R, Singer A. Turbo equalization: principles and new results. IEEE Trans Commun 2002;50(5):754–67. http://dx.doi.org/10.1109/ TCOMM.2002.1006557. [11] Tuchler M, Singer A. Turbo equalization: an overview. IEEE Trans Inf Theory 2011;57(2):920–52. http://dx.doi.org/10.1109/TIT.2010.2096033. [12] Berrou C, Glavieux A. Near optimum error correcting coding and decoding: turbo-codes. IEEE Trans Commun 1996;44(10):1261–71. http://dx.doi.org/ 10.1109/26.539767. [13] Yellepeddi A, Preisig J. Adaptive equalization in a turbo loop. IEEE Trans Wireless Commun 2015;14(9):5111–22. http://dx.doi.org/10.1109/ TWC.2015.2432764. [14] Choi JW, Riedl T, Kim K, Singer A, Preisig J. Adaptive linear turbo equalization over doubly selective channels. IEEE J Oceanic Eng 2011;36(4):473–89. http:// dx.doi.org/10.1109/JOE.2011.2158013. [15] Kang T, Song HC, Hodgkiss WS, Soo Kim J. Long-range multi-carrier acoustic communications in shallow water based on iterative sparse channel estimation. J Acoust Soc Am 2010;128(6):EL372–7. http://dx.doi.org/ 10.1121/1.3514157. [16] Yang Z, Zheng Y. Iterative channel estimation and turbo equalization for multiple-input multiple-output underwater acoustic communications. IEEE J PP Oceanic Eng 2015(99). http://dx.doi.org/10.1109/JOE.2015.2398731. 1–1. [17] Zhang J, Zheng Y. Frequency-domain turbo equalization with soft successive interference cancellation for single carrier MIMO underwater acoustic communications. IEEE Trans Wireless Commun 2011;10(9):2872–82. http:// dx.doi.org/10.1109/TWC.2011.072511.100324. [18] Huang J, Huang J, Berger CR, Zhou S, Willett P. Iterative sparse channel estimation and decoding for underwater MIMO-OFDM. EURASIP J Adv Signal Process 2010;2010:1. [19] Tao J, Zheng Y. Turbo detection for MIMOOFDM underwater acoustic communications. Int J Wireless Inf Netw 2013;20(1):27–38. http://dx.doi. org/10.1007/s10776-012-0182-4. [20] ten Brink S. Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Trans Commun 2001;49(10):1727–37. http://dx.doi.org/10.1109/ 26.957394. [21] Hagenauer J. The exit chart-introduction to extrinsic information transfer in iterative processing. In: Proc 12th European signal processing conference (EUSIPCO). p. 1541–8. [22] Tuchler M, Brink ST, Hagenauer J. Measures for tracing convergence of iterative decoding algorithms. In: Proc 4th IEEE/ITG conf on source and channel coding. p. 53–60. [23] Divsalar D, Dolinar S, Pollara F. Iterative turbo decoder analysis based on density evolution. IEEE J Sel Areas Commun 2001;19(5):891–907. http://dx. doi.org/10.1109/49.924873. [24] Wang L, Tao J, Zheng YR. Single-carrier frequency-domain turbo equalization without cyclic prefix or zero padding for underwater acoustic communications. J Acoust Soc Am 2012;132(6):3809–17. http://dx.doi.org/ 10.1121/1.4763987. [25] Berger C, Wang Z, Huang J, Zhou S. Application of compressive sensing to sparse channel estimation. IEEE Commun Mag 2010;48(11):164–74. http://dx. doi.org/10.1109/MCOM.2010.5621984. [26] Kang T, Iltis R. Matching pursuits channel estimation for an underwater acoustic OFDM modem. In: IEEE international conference on acoustics, speech and signal processing, 2008. ICASSP 2008. p. 5296–9. http://dx.doi.org/ 10.1109/ICASSP.2008.4518855. [27] Berger C, Zhou S, Preisig J, Willett P. Sparse channel estimation for multicarrier underwater acoustic communication: from subspace methods to compressed sensing. IEEE Trans Signal Process 2010;58(3):1708–21. [28] Robertson P, Villebrun E, Hoeher P. A comparison of optimal and sub-optimal map decoding algorithms operating in the log domain. IEEE international conference on communications, 1995. ICC ’95 Seattle, ‘Gateway to Globalization’, 1995, vol. 2. p. 1009–13. http://dx.doi.org/10.1109/ ICC.1995.524253. [29] ten Brink S, Kramer G, Ashikhmin A. Design of low-density parity-check codes for modulation and detection. IEEE Trans Commun 2004;52(4):670–8. http:// dx.doi.org/10.1109/TCOMM.2004.826370. [30] Hou J, Siegel P, Milstein L. Design of multi-input multi-output systems based on low-density parity-check codes. IEEE Trans Commun 2005;53(4):601–11. http://dx.doi.org/10.1109/TCOMM.2005.844972.