色噪声下多载波水声通信的高阶调制和软检测

doi:10.12305/j.issn.1001-506X.2026.05.30

Abstract

Abstract:

In the field of underwater acoustic communication, orthogonal frequency division multiplexing （OFDM） combined with bit-interleaved coded modulation technology can effectively mitigate frequency-selective fading in underwater acoustic channels. However, due to incomplete acquisition of channel state information and noise interference, higher-order modulation schemes aimed at achieving higher communication rates are more sensitive to channel mismatches. To enhance decoding performance and communication reliability, this study delves into the statistical characteristics of channel estimation errors and proposes a maximum likelihood-based decoding metric design, which modifies the likelihood function used in the decoding process. Simultaneously, considering the characteristics of real-world noise, the channel estimation error correction decoding metric is further optimized under the colored noise assumption. The method estimates noise information for each subcarrier with the colored noise hypothesis and corrects the channel estimates based on the statistical characteristics of channel estimation errors, thereby reducing the impact of channel estimation errors on the output soft information in the presence of colored noise. The simulation results show that the color noise assumption (channel estimation error correction) decoding metric achieves a higher performance upper bound and offers a 5-6 dB improvement over the traditional (channel estimation error ignored) decoding metric, while providing a 1.4 dB enhancement compared to the white noise assumption (channel estimation error correction) decoding metric. Under the conditions of the deepest 900 m deep-sea vertical communication test, it was verified that the noise spectral density fluctuation in the frequency domain can reach 12 dB. The proposed method effectively improves decoding performance for OFDM signals with up to 256-order quadrature amplitude modulation (QAM) and a transmission rate of 8.84 kbps. At a communication distance of up to 4772 m, reliable OFDM underwater acoustic communication was achieved with a transmission rate of 4.42 kbps using 16QAM modulation.

Key words: underwater acoustic communication, orthogonal frequency division multiplexing （OFDM）, colored noise, channel estimation, log-likelihood ratio

CLC Number:

TB 567

Rui XU, Yanbo WU, Min ZHU. High-order modulation and soft detection of multi-carrier underwater acoustic communication with colored noise[J]. Systems Engineering and Electronics, 2026, 48(5): 1752-1764.

Figures/Tables 22

Fig.1

Table 1

Fig.2

Fig.3

Fig.4

Table 2

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 3

Fig.11

Fig.12

Fig.13

Table 4

Fig.14

Fig.15

Fig.16

Fig.17

Table 5

References 28

1	JUNEJO N U, SATTAR M, ADNAN S, et al. A survey on physical layer techniques and challenges in underwater communication systems[J]. Journal of Marine Science and Engineering, 2023, 11 (4): 885. doi: 10.3390/jmse11040885
2	朱敏, 武岩波. 水声通信技术进展[J]. 中国科学院院刊, 2019, 34 (3): 289- 296.
	ZHU M, WU Y B. Advances in underwater acoustic communication technology[J]. Bulletin of Chinese Academy of Sciences, 2019, 34 (3): 289- 296.
3	张舒然, 武岩波, 朱敏. 基于MCMC采样器的簇稀疏水声信道估计方法[J]. 仪器仪表学报, 2019, 40 (8): 201- 212.
	ZHANG S R, WU Y B, ZHU M. An estimation method of clustered sparsity underwater acoustic channel based on MCMC sampler[J]. Chinese Journal of Scientific Instrument, 2019, 40 (8): 201- 212.
4	BELLO O, ZEADALLY S. Internet of underwater things communication: architecture, technologies, research challenges and future opportunities[J]. Ad Hoc Networks, 2022, 135, 102933. doi: 10.1016/j.adhoc.2022.102933
5	WEN M Q, HE C L, XING S Y. A bit-interleaved coded modulation scheme based on the polar code in underwater acoustic OFDM communication system[C]//Proc. of the 5th International Conference on Electronic Engineering and Informatics, 2023: 316−321.
6	PFLETSCHINGER S, DIETL G. Performance evaluation of compansion-based clipped OFDM systems[J]. EURASIP Journal on Wireless Communications and Networking, 2024, 83.
7	ZHAN J, WANG L, KATZ M, et al. A differential chaotic bit-interleaved coded modulation system over multipath Rayleigh channels[J]. IEEE Trans. on Communications, 2017, 65 (12): 5257- 5265. doi: 10.1109/TCOMM.2017.2719030
8	XU Z P, CHEN Q W, LI Y, et al. Designing protograph LDPC codes for differential chaotic bit-interleaved coded modulation system for underwater acoustic communications[J]. Journal of Marine Science and Engineering, 2023, 11 (5): 914. doi: 10.3390/jmse11050914
9	ABOTABL A A, NOSRATINIA A. Broadcast coded modulation: multilevel and bit interleaved construction[J]. IEEE Trans. on Communications, 2016, 65 (3): 969- 980.
10	JIANG W H, DIAMANT R. Long-range underwater acoustic channel estimation[J]. IEEE Trans. on Wireless Communications, 2023, 22 (9): 6267- 6282. doi: 10.1109/TWC.2023.3241230
11	CHEN W X, TAO J, MA L, et al. Vector-approximate-message-passing-based channel estimation for MIMO-OFDM underwater acoustic communications[J]. IEEE Journal of Oceanic Engineering, 2024, 49 (2): 496- 506. doi: 10.1109/JOE.2023.3337349
12	JIA S Y, ZOU S C, ZHANG X C, et al. Underwater acoustic channel estimation based on sparse Bayesian learning algorithm[J]. IEEE Access, 2023, 11, 7829- 7836. doi: 10.1109/ACCESS.2023.3238100
13	YANG Z G, WANG X D. A sequential Monte Carlo blind receiver for OFDM systems in frequency-selective fading channels[J]. IEEE Trans. on Signal Processing, 2002, 50 (2): 271- 280. doi: 10.1109/78.978382
14	HUANG Y H, RITCEY J A. 16-QAM BICM-ID in fading channels with imperfect channel state information[J]. IEEE Trans. on Wireless Communications, 2003, 2 (5): 1000- 1007. doi: 10.1109/TWC.2003.817432
15	GARG P, MALLIK R K, GUPTA H M. Performance analysis of space-time coding with imperfect channel estimation[J]. IEEE Trans. on Wireless Communications, 2005, 4 (1): 257- 265. doi: 10.1109/TWC.2004.840202
16	GOLDSMITH A. Wireless communications[M]. Cambridge: Cambridge University Press, 2005.
17	WANG M M, XIAO W M, BROWN T. Soft decision metric generation for QAM with channel estimation error[J]. IEEE Trans. on Communications, 2002, 50 (7): 1058- 1061. doi: 10.1109/TCOMM.2002.800828
18	ESPLUGA L O, AUBAULT-ROUDIER M, POULLIAT C, et al. LLR approximation for fading channels using a Bayesian approach[J]. IEEE Communications Letters, 2020, 24 (6): 1244- 1248. doi: 10.1109/LCOMM.2020.2978832
19	MORELLI M, MORETTI M. Improved decoding of BICM-OFDM transmissions plagued by narrowband interference[J]. IEEE Trans. on Wireless Communications, 2010, 10 (1): 20- 26.
20	YUAN H F, KAM P Y. The LLR metric for q-ary LDPC codes with MPSK modulation over Rayleigh channels with imperfect CSI[J]. IEEE Trans. on Communications, 2012, 60 (7): 1793- 1799. doi: 10.1109/TCOMM.2012.050812.110129
21	MARTINEZ A, I FABREGAS A G, CAIRE G, et al. Bit-interleaved coded modulation revisited: a mismatched decoding perspective[J]. IEEE Trans. on Information Theory, 2009, 55 (6): 2756- 2765. doi: 10.1109/TIT.2009.2018177
22	JALDEN J, FERTL P, MATZ G. On the generalized mutual information of BICM systems with approximate demodulation[C]//Proc. of the IEEE Information Theory Workshop on Information Theory, 2010.
23	NGUYEN T T, LAMPE L. Bit-interleaved coded modulation with mismatched decoding metrics[J]. IEEE Trans. on Communications, 2010, 59 (2): 437- 447.
24	陶笃纯. 按辐射噪声平均功率谱形状识别船舶目标[J]. 声学学报, 1981, (4): 219- 228.
	TAO D C. Recognition of ship targets according to the shape of average power spectrum of radiated noise[J]. Acta Acustica, 1981, (4): 219- 228.
25	姚帅, 方世良, 王晓燕. 有色噪声背景下的水声跳频信号参数估计[J]. 东南大学学报（自然科学版）, 2014, 44 (1): 12- 18.
	YAO S, FANG S L, WANG X Y. Parameter estimation of underwater acoustic frequency-hopping signals in colored noise[J]. Journal of Southeast University （Natural Science Edition）, 2014, 44 (1): 12- 18.
26	YANG H, LI L L, LI G H. A new denoising method for underwater acoustic signal[J]. IEEE Access, 2020, 8, 201874- 201888. doi: 10.1109/ACCESS.2020.3035403
27	BERGER C R, CHEN W A, ZHOU S L, et al. A simple and effective noise whitening method for underwater acoustic orthogonal frequency division multiplexing[J]. The Journal of the Acoustical Society of America, 2010, 127 (4): 2358- 2367. doi: 10.1121/1.3309452
28	GALLAGER R G. Information theory and reliable communication[M]. New York: Wiley, 1968.

试验参数	数值
中心频率$ {f_c} $/kHz	10
带宽$ B $/kHz	5
采样频率$ {f_s} $/kHz	80
调制阶数	16QAM/64QAM
映射方式	格雷
系统总载波数$ {N_s} $	480
导频子载波数$ {N_p} $	160
空子载波数$ {N_n} $	40
编码速率$ R $	0.5
蒙特卡罗次数	100

试验参数	数值
发射深度SD/m	50
接收深度SR/m	30
传输距离L/m	300
水深D/m	100
海底形状	平坦底面
海底介质密度/（g/cm³）	1.84
声线发射角度	[−30°，30°]

试验参数	数值
中心频率${f_c}$/ kHz	10
带宽$B$/ kHz	5
采样频率${f_s}$/ kHz	80
调制格式	QPSK/16QAM/64QAM/256QAM
系统总载波数${N_s}$	480
导频子载波数${N_p}$	160
空子载波数${N_n}$	40

点位	水平距离/m	通信距离/m	SNR/dB	最大译码阶数	校验通过帧数（传统失配度量）	校验通过帧数（改进译码度量）
1	102	3 681	23.6	16QAM	20	20
2	500	3 714	27.3	16QAM	20	20
3	1 062	3 830	27.9	16QAM	20	20
4	1 809	4 101	25.1	16QAM	20	20
5	2 529	4 465	23.2	16QAM	12	15
6	3 038	4 772	21.4	16QAM	10	13

[1]	Haiyuan PENG, Yu LI, Yu’nan ZHU, Zhanqing PU, Wei WANG. GPU-based fast Doppler estimation method for DSSS underwater acoustic communication [J]. Systems Engineering and Electronics, 2026, 48(6): 2105-2112.
[2]	Guangping WANG, Zhiquan BAI, Jian DAI, Heng WANG, Xinhong HAO, Xiaopeng YAN. Design of dual-mode 3D OFDM index modulation scheme and low complexity detection [J]. Systems Engineering and Electronics, 2026, 48(4): 1422-1430.
[3]	Yan LIANG, Weiyang TU, Junqing WANG, Fei LI. IRS assisted millimeter wave massive MIMO channel estimation based on TS-OMP [J]. Systems Engineering and Electronics, 2026, 48(3): 1083-1090.
[4]	Yan LIANG, Baolong LI, Haozhang WEI, Fei LI. Double IRS-assisted wideband channel estimation scheme for terahertz massive MIMO systems [J]. Systems Engineering and Electronics, 2026, 48(1): 361-371.
[5]	Ce JI, Xiangyu MA, Xiaoyu MU, Jiayi ZHAO. TS-GRU-VTA: vehicle channel estimation scheme based on deep learning [J]. Systems Engineering and Electronics, 2025, 47(9): 3093-3098.
[6]	Yongxing FAN, Yangfan ZHANG, Haining HUANG. Modulation method suitable for underwater acoustic mobile communication [J]. Systems Engineering and Electronics, 2025, 47(8): 2727-2736.
[7]	Bo GAO, Youhua FU, Chen LIU. Terahertz extremely large-scale MIMO hybrid field channel estimation [J]. Systems Engineering and Electronics, 2025, 47(8): 2744-2752.
[8]	Lin CHENG, Wei GE, Wei MEN. MIMO spread spectrum deep-sea underwater acoustic communication method based on M-ary cyclic shift keying [J]. Systems Engineering and Electronics, 2025, 47(3): 1010-1018.
[9]	Haiyuan PENG, Wei WANG, Derui LI, Yanjun LIU, Yu LI, Cheng CHI, Yanan TIAN. GPU-based parallel implementation of M-ary despreading algorithm for OMCSS underwater acoustic communication [J]. Systems Engineering and Electronics, 2025, 47(3): 978-986.
[10]	Gang TAN, Shefeng YAN, Linlin MAO, Jirui YANG. Joint channel and impulsive noise estimation for underwater acoustic OFDM systems based on sparse Bayesian learning [J]. Systems Engineering and Electronics, 2025, 47(10): 3482-3491.
[11]	Ting LI, Chunjie ZHANG, Shanglong LIU, Peizhong XIE. Joint domain channel estimation in UCA-OAM communication system [J]. Systems Engineering and Electronics, 2025, 47(10): 3492-3503.
[12]	Mingxiu MO, Lei YUAN, Yan LEI, Huahua YUAN. Impact of imperfect hardware implementation on downlink NOMA short packet communication [J]. Systems Engineering and Electronics, 2025, 47(1): 296-306.
[13]	Yongqi SHAO, Lihua YANG, Ao CHANG, Lulu REN. Time-varying channel estimation in RIS-assisted OFDM system [J]. Systems Engineering and Electronics, 2025, 47(1): 324-331.
[14]	Fangzheng LIU, Ruiqi ZENG, Yang GONG, Zhenzhong HAN. ZC-OFDM-based radar interference integrated waveform design and processing method [J]. Systems Engineering and Electronics, 2024, 46(9): 2999-3011.
[15]	Gang TAN, Shefeng YAN, Zihao YE, Jirui YANG. Iterative impulsive noise mitigation and channel estimation method for OFDM system [J]. Systems Engineering and Electronics, 2024, 46(8): 2841-2849.

High-order modulation and soft detection of multi-carrier underwater acoustic communication with colored noise

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 22

References 28

Related Articles 15

Recommended Articles

Metrics

Comments

方案	QPSK	16QAM	64QAM	256QAM
失配度量（500 m）	20	20	17	6
改进软译码度量I （500 m）	20	20	19	13
失配度量（900 m）	20	20	14	4
改进软译码度量I （900 m）	20	20	17	9