Signal design and iterative channel estimation method oriented to deep sea underwater sound OFDM (Orthogonal Frequency Division Multiplexing) communication

Abstract

The invention relates to a signal design and iterative channel estimation method for deep sea underwater sound OFDM communication. The method comprises the following steps: step 1, establishing a ZP-OFDM communication system model; and 2, carrying out iterative channel estimation based on a channel cluster structure. According to the method, a channel cluster structure is fully utilized, a channel is divided into a plurality of clusters to be processed respectively, the iterative channel estimation and pilot frequency design technology is combined, channel parameters can be accurately estimated under the complex interference condition, and compared with a traditional method, the channel estimation performance is better, so that the reliability of a communication system is remarkably improved; aiming at serious IBI and ICI in a deep sea underwater acoustic channel, through iterative channel estimation and pilot frequency design, the interference influence is effectively inhibited, especially in a fast time-varying channel environment, stable estimation performance can still be maintained, it is ensured that communication quality is not significantly influenced by interference factors, and the method has efficient interference elimination capability and can be widely applied to the field of underwater acoustic communication. And the method has higher practical value in a dynamic deep sea environment.

Description

Technical Field

[0001] The present invention relates to a signal design and iterative channel estimation method for OFDM communication, and more specifically to a signal design and iterative channel estimation method for deep sea acoustic OFDM communication. Background Art

[0002] With the rapid development of society and the increasing frequency of production activities, humanity's demand for resources continues to increase. Land resource development has reached saturation, and marine resources have become a new frontier for human exploration. To meet the needs of marine environmental monitoring and resource exploration, establishing a stable and reliable underwater communication network is crucial. In underwater communications, electromagnetic waves are significantly attenuated by the conductivity of seawater, and light waves are significantly scattered by plankton and suspended particles. Therefore, sound waves have become the primary choice for underwater communication.

[0003] The attenuation characteristics of sound waves in seawater are closely related to frequency. High-frequency sound waves attenuate rapidly over short distances, while low-frequency sound waves can propagate farther. Consequently, the available bandwidth for underwater acoustic communications is extremely limited. In this context, Orthogonal Frequency Division Multiplexing (OFDM) technology, due to its high spectrum utilization and resistance to frequency-selective fading, has become a key technology of choice for underwater acoustic communications. Research on stable and reliable underwater acoustic OFDM communications is crucial.

[0004] The underwater acoustic channel is one of the most complex channels, and its unique physical properties bring many challenges to the design and implementation of underwater acoustic communication systems. First, the underwater acoustic channel has significant time-varying characteristics, and the propagation environment is strongly affected by ocean dynamic processes. For example, the dynamic changes in ocean currents, waves, and thermoclines can lead to instability in the sound propagation path, which in turn leads to a severe Doppler effect. Second, the underwater acoustic channel has a large delay spread. During propagation, sound waves experience seabed reflection, sea surface reflection, and water scattering, generating a large number of multipath signals. Low-speed sound waves and multipath effects can cause significant channel delay spread. Faced with the severe challenges of underwater acoustic channels, studying the characteristics of underwater acoustic channels and performing accurate channel estimation are important research topics.

[0005] In recent years, with the advancement of underwater acoustic communications, high-speed, stable, and reliable OFDM communication systems have been initially implemented in shallow water environments. However, OFDM communication in deep-sea acoustic channels still faces many challenges. Compared to shallow-sea acoustic channels, deep-sea acoustic channels exhibit greater delay spread, more severe Doppler spread, and a more pronounced clustering structure. Deep-sea acoustic channels are characterized by large delay spread, consisting of multiple, widely separated clusters. The first cluster consists primarily of direct paths and has a smaller delay spread; the second cluster primarily consists of single-reflection paths, with larger delay spread and severe Doppler spread; the third and further clusters consist of multiple-reflection paths, typically with far less energy than the first two clusters and thus negligible. There are two main traditional approaches to addressing the extreme delay spread in deep-sea acoustic channels: one is to set a guard interval greater than the channel delay spread to avoid inter-block interference (IBI). However, the channel delay spread can reach the order of seconds, severely impacting communication rates. The other approach utilizes the channel clustering structure to design the guard interval length, transforming the large delay spread channel into a quasi-synchronous channel with a two-minute delay spread. To avoid a reduction in communication rate, even with the second approach, few studies have considered the impact of IBI on the measurement matrix used in channel estimation. Furthermore, given the severe Doppler spread in deep-sea acoustic channels, most studies assume the Doppler spread of each raypath is identical. After Doppler compensation, the residual Doppler shift is treated as noise, ignoring inter-carrier interference (ICI). However, due to the significant variation in Doppler spread across different raypaths in deep-sea environments, this can severely degrade communication performance.

[0006] Many scholars have published papers on underwater acoustic channel estimation. In order to take advantage of channel sparsity, Berger et al. introduced compressed sensing (CS) technology into underwater acoustic channel estimation (Berger CR, Zhou S, Preisig JC, et al. Sparse channel estimation for multicarrier underwater acoustic communication: From subspace methods to compressed sensing [J]. IEEE Transactions on Wireless Communications, 2010; 58(3): 1708-1721).

[0007] For fast time-varying scenarios, Huang et al. proposed an inter-carrier interference (ICI)-aware channel estimation method (Huang J, Zhou S, Huang J, et al. Progressive inter-carrier interference equalization for OFDM transmission over time-varying underwater acoustic channels[J]. IEEE Journal of Selected Topics in Signal Processing, 2011; 5(8): 1524-1536).

[0008] In order to utilize the coherence and cluster structure of the channel, Wang et al. proposed an adaptive inter-block iterative estimation based on cluster structure (Wang Z, Zhou S, Preisig JC, et al. Clustered adaptation for estimation of time-varying underwater acoustic channels[J]. IEEE Transactions on SignalProcessing, 2012; 60(6): 3079-3091).

[0009] To address the problem of poor robustness of CS-based algorithms, sparse Bayesian learning (SBL) (Wipf D, Rao B D. Sparse Bayesian learning for basis selection [J]. IEEE Transactions on Signal Processing, 2004; 52(8): 2153-2164) and its extended methods were described (Zhang Z, Rao B D. Sparse signal recovery with temporally correlated source vectors using sparse Bayesian learning [J]. IEEE Journal of Selected Topics in Signal Processing, 2011; 5(5): 912-926; Al-Shoukairi M, Schniter P, Rao BD. A GAMP based low complexity sparse Bayesian learning algorithm [J]. IEEE Transactions on Signal Processing, 2018; 66(2): 294-308); and was also introduced into underwater acoustic channel estimation (Qiao G, Song Q, Ma L, et al. Sparse Bayesian learning for channel estimation intime-varying underwater acoustic OFDM communication[J]. IEEE Access, 2018; 6:56675-56684.; Feng

[0010] Previous studies have mainly focused on shallow waters. In shallow water acoustic communications, the channel delay spread is smaller than the symbol duration, and inter-block interference (IBI) can be avoided by using a guard interval that is larger than the delay spread.

[0011] In recent years, with the increasing demand for underwater broadcasting networks, deep-water acoustic communications have attracted increasing attention. Wang et al. obtained channel cluster information through cluster detection technology to improve the performance of channel estimation (Wang D, Zhang Y, Tai Y, et al. Cluster-aware channel estimation with deep learning method in deep-water acoustic communications. The Journal of the Acoustical Society of America, 2023; 154(3): 1757-1769).

[0012] In order to utilize the coherence of deep-sea channels, Wang et al. proposed an inter-block iterative channel estimation method based on sparse time-varying channel modeling (Wang Yueyue, Wang Haibin, Tai Yupeng, et al. Inter-block iterative sparse channel estimation method for deep-sea long-range orthogonal frequency division multiplexing water acoustic communication [J]. Acta Acoustics, 2023; 48(01): 16-26).

[0013] However, these methods still use a guard interval larger than the channel delay spread when transmitting signals, resulting in low communication rates and the impact of residual ICI in the received signal after Doppler compensation is not considered. To address the large delay spread in deep-sea channels, Wang et al. used a channel cluster structure to transform the large delay spread channel into two quasi-synchronous channels with smaller delay spread by designing the length of the guard interval (Wang Z, Zhou S, Catipovic J, et al. Factor-graph-based joint IBI / ICI mitigation for OFDM in underwater acoustic multipath channels with long-separated clusters[J]. IEEE Journal of Oceanic Engineering, 2012; 37(4): 680-694).

[0014] The above method does not consider the impact of IBI on channel estimation. In order to avoid loss of communication rate, this invention patent application adopts a method similar to that of reference

[11] , which introduces IBI into the received signal, resulting in deterioration of the measurement matrix.

[0015] In wireless communications, the problem of measurement matrix degradation is mainly addressed through pilot design. Qi et al. proposed a deterministic pilot design scheme for single-input single-output and multiple-input multiple-output systems by minimizing the coherence of the measurement matrix (QiC, Yue G, Wu L, et al. Pilot design schemes for sparse channel estimation in OFDM systems [J]. IEEE Transactions on Vehicular Technology, 2015; 64(4): 1493-1505).

[0016] Mohammadian et al. proposed a deterministic pilot design suitable for multiple-input single-output systems by minimizing the coherence of the Fourier matrix (Mohammadian R, Amini A, Khalaj B H. Deterministic pilot design for sparse channel estimation in Miso / Multi-user OFDM systems[J]. IEEE Transactions on Wireless Communications, 2017; 16(1): 129-140).

[0017] In existing technologies to date, traditional channel estimation research has avoided IBI caused by delay spread in deep-sea channels by setting a guard interval greater than the channel delay spread. However, the delay spread of deep-sea acoustic channels can reach the second level, and this approach can seriously affect communication rates. To address the inter-carrier interference caused by the severe Doppler spread of deep-sea channels, traditional channel estimation research assumes that the Doppler spread of each acoustic path is the same. After performing two-step Doppler compensation, the residual inter-carrier interference is treated as noise. However, the obvious cluster structure of deep-sea acoustic channels leads to large differences in Doppler spread between different paths, resulting in poor channel estimation performance.

[0018] In the prior art disclosed so far, no research has been found to propose a pilot design suitable for deep sea acoustic communication. Summary of the Invention

[0019] The signal design and iterative channel estimation method for deep sea acoustic OFDM communication of the present invention comprises the following steps:

[0020] Step 1. Establish a ZP-OFDM communication system model;

[0021] Step 2. Iterative channel estimation based on channel cluster structure.

[0022] Furthermore, the iterative channel estimation based on the channel cluster structure in step 1 includes the following specific steps:

[0023] Step 1.1 Send passband transmission signal:

[0024] Consider a ZP-OFDM communication system, let T denote the OFDM symbol duration, T g Represents the zero-filled guard interval length, then the duration of an OFDM block is expressed as T bl =T+T g , let K represent the number of subcarriers, Δf = 1 / T represent the subcarrier spacing, f c If represents the center frequency, then the signal bandwidth is B = KΔf, and the frequency of the kth subcarrier is as follows:

[0025]

[0026] In the above formula: K subcarriers are decomposed into a set of pilot subcarriers Data subcarrier set and the set of empty subcarriers And satisfy Let d[k;n] represent the data of the kth subcarrier of the nth transmission block, and the nth transmission block of the baseband transmission signal is expressed as follows:

[0027]

[0028] In the above formula: is the set of active subcarriers, h(t) is a rectangular pulse shaping filter that is not zero in [0,T], and its Fourier transform is:

[0029]

[0030] The nth transmission block of the passband transmission signal is expressed as:

[0031]

[0032] The transmission signal consisting of N OFDM blocks is expressed as:

[0033]

[0034] Step 1.2 Channel model based on channel cluster structure:

[0035] The path-based channel model of deep sea acoustic channel is expressed as follows:

[0036]

[0037] In the above formula: N pa Indicates the total number of sound lines, Ap (t) and τ p (t) denotes the amplitude and delay of the pth path, respectively. In deep sea acoustic channels, the delay between two clusters reaches the order of seconds, which is several times the length of the transmitted block. This leads to IBI at the receiver. To model the IBI at the receiver, the inter-cluster delay between the first and second clusters is decomposed into:

[0038] τ 1,2 =γT bl +ξ,

[0039] In the above formula: γ is an integer, ξ is The channel model is rewritten as the sum of the impulse responses of the two clusters:

[0040] h(t,τ)=h (1) (t,τ)+h (2) (t,τ-γT bl ),

[0041] In the above formula: h (i) (t,τ) represents the channel impulse response of the i-th cluster, and each cluster is expressed as:

[0042]

[0043] In the above formula: and represent the amplitude and delay of the pth path of the ith cluster, respectively. represents the number of paths in cluster i; assuming that the path amplitude and Doppler factor remain unchanged during the duration of a receiving block, that is, in, and denote the amplitude, initial delay and Doppler factor of the pth path of the ith cluster respectively. The impulse response of the ith cluster is rewritten as follows:

[0044]

[0045] Step 1.3 OFDM guard interval design and received signal:

[0046] Let χ i represents the delay spread of cluster i. For the nth receiving block, if ξ≥0, then h (2) (t,τ;n) lags behind h (1) (t,τ; n), then the delay extension length of the two impulse responses after quasi-synchronization is max{χ1,ξ+χ2}; on the contrary, if ξ<0, it means h (1) (t,τ;n) lags behind h (2)(t,τ; n), at this time, after quasi-synchronization, the delay spread length of the two impulse responses is max{χ1+ξ,χ2}, assuming that χ i , γ and ξ are known, and these prior information are obtained in advance through the cluster detection method, from which the guard interval T is derived g The conditions that need to be met are:

[0047]

[0048] By setting the guard interval to satisfy the above equation, the received signal is blocked without considering the blocking caused by intra-cluster delay spread. The nth block of the received passband signal is expressed as follows:

[0049]

[0050] In the above formula: Represents the environmental noise, and performs two-step Doppler compensation on the received signal. The receiver first resamples the received block to remove the influence of the dominant Doppler. After resampling, we get in, is the resampling factor, and after down-conversion and low-pass filtering, the baseband signal is obtained Then the baseband signal y(t;n) is combined with Multiply to compensate for residual Doppler, where Indicates the carrier frequency offset compensation factor;

[0051] After sampling at baseband rate 1 / B and Fourier transform, the m-th subcarrier of the n-th block is expressed as follows:

[0052]

[0053] In the above formula: w[m;n] is the environmental noise, the channel coefficient H (i) [m, k; n] is expressed as follows:

[0054]

[0055] In the above formula:

[0056]

[0057] The length L of each cluster of channel taps is expressed as follows:

[0058]

[0059] The vectors and matrices involved above are defined as follows:

[0060]

[0061] In the above formula, y n Represents the vector composed of subcarrier data of the received signal, x n Represents the vector composed of subcarrier data of the transmitted signal, Λ τ represents the diagonal matrix composed of Fourier transform corresponding to the time delay τ, w n represents the noise vector;

[0062] As above, the frequency domain input and output relationship can be expressed in the form of matrices and vectors as follows:

[0063]

[0064] Furthermore, the iterative channel estimation based on the channel cluster structure in step 2 includes the following specific steps:

[0065] Step 2.1 Pilot signal design based on minimization of measurement matrix coherence:

[0066] Γ b,∈ It reveals the interference of adjacent subcarriers on the current subcarrier, and the interference decays as the subcarrier spacing increases. Here, only the interference of D adjacent subcarriers is considered, that is, the ICI depth is D, and Γ is defined b,∈ is the following formula:

[0067]

[0068] When the residual ICI after Doppler compensation is ignored, D = 0, is the unit matrix, and the frequency domain input-output relationship is rewritten as follows:

[0069]

[0070] In the above formula: X n By x n The diagonal matrix is composed of K×L discrete Fourier transform (DFT) submatrix. is The L×1 vector formed;

[0071] Let K p represents the number of pilot subcarriers. When only pilot subcarriers are considered, the frequency domain input and output relationship is as follows:

[0072]

[0073] In the above formula: Φ n is the measurement matrix when the nth receiving block ICI is ignored, h n is a sparse vector composed of two clusters of impulse responses when ICI is ignored. The sparse vector uses the sparse signal reconstruction algorithm to estimate the channel.p,n A vector of noise components representing the pilot positions;

[0074] Due to the same pilot position of each block and the existence of IBI, a sufficient condition for the stable reconstruction of sparse vectors is that the measurement matrix satisfies the Restricted Isometry Property (RIP). The RIP criterion states that for the measurement matrix Φ and the vector with sparsity k, if there exists a constant δ k , so that for all k sparse vectors x, the following equation is satisfied:

[0075]

[0076] Then any k-sparse vector x can be recovered. Considering that the detection measurement matrix satisfies RIP, the measurement matrix coherence minimization is used instead, and the measurement matrix Φ n The coherence of is defined as follows:

[0077]

[0078] In the above formula: β i Represents Φ n Column i of represents the pilot position, express In order to utilize the cyclic properties of the DFT matrix, the relationship between the pilots corresponding to the two clusters is designed as follows:

[0079]

[0080] Assuming that each pilot power is the same, then Φ n The coherence is further expressed as follows:

[0081]

[0082] In the above formula:

[0083] φ1=X p,n F p ,

[0084] φ2=X p,n-γ F p ,

[0085]

[0086] For simplicity, it is defined as follows:

[0087]

[0088] In the above formula, P represents the set of pilot positions, and the pilot design is transformed into the following optimization problem:

[0089]

[0090] In the above formula:

[0091]

[0092] In order to find the optimal solution of the pilot, a method for finding the optimal pilot design by random order search is proposed. The optimal pilot design method contains three layers of loops. Let I α , I out and I in Represent the number of first, second and third layer loops respectively. In each iteration of the first layer loop, The internal order of generating the value of α, where is a set of optional values of α. According to the cyclic shift characteristics of the DFT matrix, the following formula is obtained:

[0093]

[0094] In each iteration of the second-level loop, an optional set of pilot positions is used The elements in the random number K are generated p The pilot position set P is used for the third-layer loop. In each iteration of the third-layer loop, the elements of the pilot position set are modified in turn, and the position set with the minimum coherence is recorded, as shown in the following formula:

[0095]

[0096] In the above formula: Represents the set after P removes an element;

[0097] Step 2.2 Inter-carrier interference-aware iterative channel estimation:

[0098] When ICI is considered, the ICI depth D is greater than 0, and the residual Doppler factor is defined and path delay The dictionary of atoms b and τ is as follows:

[0099] b∈{-b max ,-b max +Δb,…,b max},

[0100]

[0101] In the above formula: Δb is the Doppler factor resolution, is the maximum value of the optional Doppler factor, and it increases with the increase of ICI depth D, so the channel matrix composed of dictionary atoms is It is expressed as the following formula:

[0102]

[0103] The frequency domain input-output relationship is rewritten as follows:

[0104]

[0105] In the above formula: Let x n Estimates It is expressed as the following formula:

[0106]

[0107] In the above formula: Representing the decoding result of the previous iteration, the frequency domain input and output relationship is simplified in the form of matrix and vector as follows:

[0108]

[0109] In the above formula: A n is the measurement matrix of the nth receiving block ICI perception, η n It is a sparse vector composed of channel coefficients corresponding to different dictionary atoms during ICI perception. The sparse vector uses the sparse signal reconstruction algorithm for channel estimation;

[0110] As above, the ICI-aware iterative channel estimation is obtained. The channel estimation process of the nth receiving block is as follows:

[0111] Parameter input: frequency domain received signal y n , the diagonal matrix X formed by the two clusters of corresponding pilots p,n and X p,n-γ , maximum ICI depth D max , the length of each channel tap L, the Doppler factor resolution Δb, the carrier frequency offset compensation factor

[0112] Step a: Use sparse signal reconstruction algorithm to estimate the channel and obtain h n or η n , the channel matrix is calculated based on the channel estimation results

[0113] Step b, noise variance update, based on the received signal at the empty subcarrier position and the channel matrix Update noise variance

[0114]

[0115] Step c: channel equalization and decoding, after decoding, the data symbol detection result is obtained

[0116] Step d, iterative termination judgment, if D=D max Then terminate the iteration. Otherwise D=D+1, update x n Estimates And jump to step b.

[0117] The superior technical effects of the present invention are as follows:

[0118] 1. The signal design and iterative channel estimation method for deep-sea underwater acoustic OFDM communication of the present invention fully utilizes the channel cluster structure, divides the channel into multiple clusters for separate processing, and combines iterative channel estimation and pilot design technology to accurately estimate channel parameters under complex interference conditions. Compared with traditional methods, the channel estimation performance of the present invention is superior, significantly improving the reliability of the communication system.

[0119] 2. The signal design and iterative channel estimation method for deep-sea ocean acoustic OFDM communication in the present invention effectively suppresses the interference effects of severe IBI and ICI in deep-sea ocean acoustic channels through iterative channel estimation and pilot design. Especially in fast time-varying channel environments, it can still maintain stable estimation performance, ensuring that communication quality is not significantly affected by interference factors. It has efficient interference cancellation capabilities and has higher practical value in dynamic deep-sea environments.

[0120] 3. The signal design and iterative channel estimation method for deep-sea acoustic OFDM communication in the present invention optimizes the communication rate. Traditional methods usually require a long guard interval to avoid IBI, which significantly reduces the communication rate. The present invention avoids the need for an excessively long guard interval through the application of a channel cluster structure and the optimization of the pilot design, significantly improving the data transmission rate while ensuring the accuracy of the channel estimation. This feature is particularly important for deep-sea application scenarios that require efficient communication.

[0121] 4. The signal design and iterative channel estimation method for deep-sea ocean acoustic OFDM communication in the present invention demonstrates strong robustness. The dynamic changing characteristics of deep-sea ocean acoustic channels pose challenges to communication systems. The present invention can adapt to slow and fast time-varying channel environments, maintain stable performance, and effectively respond to any changes in channel conditions. It is widely applicable to various deep-sea communication scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] Figure 1 is a schematic diagram of two clusters of deep sea acoustic channels, where Figure 1a is a large delay spread channel with two long separated clusters; Figure 1b Two quasi-synchronous channels with small delay spread;

[0123] Figure 2 When ξ>0, the receiving block is indicated;

[0124] Figure 3 Schematic diagram of the channel estimation process for the nth receiving block;

[0125] Figure 4 is the sound velocity profile used in the simulation, where: Figure 4a is a diagram of the relationship between depth and sound speed. Figure 4b A schematic diagram of the depth-distance relationship. Figure 4c Schematic diagram of normalized amplitude-time relationship;

[0126] Figure 5 shows the delay-Doppler response of two clusters of channels corresponding to the channel, where Figure 5a is the delay-Doppler response of the first cluster of channels, Figure 5b is the delay-Doppler response of the second cluster channel;

[0127] Figure 6 The normalized mean square error is used to compare the v = 0.1m / s slow time-varying channel when the signal-to-noise ratio is 3 to 8dB;

[0128] Figure 7 is σ v = 0.1m / s BER comparison diagram of different channel estimates;

[0129] Figure 8 shows σ v =0.5m / s, where Figure 8a shows the delay-Doppler response of the first cluster of channels; Figure 8b shows the delay-Doppler response of the second cluster of channels;

[0130] Figure 9 The NMSE performance of different channel estimates is compared;

[0131] Figure 10 The BER performance of different channel estimations is compared. DETAILED DESCRIPTION

[0132] To design a high-speed and reliable deep-sea acoustic communication system, this patent application adopts a channel model based on a channel cluster structure. By setting an appropriate guard interval length, a large delay spread channel is converted into two quasi-synchronous channels. Based on this, a signal design and iterative channel estimation method for deep-sea acoustic OFDM communication is proposed. By utilizing the channel cluster structure, accurate channel estimation can be performed in the presence of both IBI and ICI without affecting the communication rate. The iterative channel estimation based on the channel cluster structure is divided into two parts: ICI-aware iterative channel estimation and pilot design based on minimizing the coherence of the measurement matrix. To address the residual ICI after Doppler compensation, the ICI-aware iterative channel estimation uses all subcarrier information decoded in the previous iteration as prior information for the current iteration to estimate the interference of adjacent subcarriers on the current subcarrier. To address the problem of IBI degrading the measurement matrix, a measurement matrix coherence minimization-based pilot design (MMCM-PD) is proposed. The relationship between the designed pilot positions and the corresponding pilots in the two clusters is searched in a random order to find a solution with the minimum coherence of the measurement matrix.

[0133] The specific implementation scheme of the signal design and iterative channel estimation method for deep sea water acoustic OFDM communication according to the present invention is described in detail below with reference to the accompanying drawings.

[0134] Example

[0135] The signal design and iterative channel estimation method for deep sea acoustic OFDM communication of the present invention comprises the following steps:

[0136] Step 1. Establish the ZP-OFDM communication system model:

[0137] Step 1.1 Send passband transmission signal:

[0138] Consider a ZP-OFDM communication system, let T denote the OFDM symbol duration, T g Represents the zero-filled guard interval length, then the duration of an OFDM block is expressed as T bl =T+T g , let K represent the number of subcarriers, Δf = 1 / T represent the subcarrier spacing, f c If represents the center frequency, then the signal bandwidth is B = KΔf, and the frequency of the kth subcarrier is as follows:

[0139]

[0140] In the above formula: K subcarriers can be decomposed into a set of pilot subcarriers Data subcarrier set and the set of empty subcarriers And satisfy Let d[k;n] represent the data of the kth subcarrier of the nth transmission block, and the nth transmission block of the baseband transmission signal is expressed as follows:

[0141]

[0142] In the above formula: is the set of active subcarriers, g(t) is a rectangular pulse shaping filter that is not zero in [0,T], and its Fourier transform is:

[0143]

[0144] The nth transmission block of the passband transmission signal is expressed as:

[0145]

[0146] The transmission signal consisting of N OFDM blocks is expressed as:

[0147]

[0148] Step 1.2 Channel model based on channel cluster structure:

[0149] The path-based channel model of deep sea acoustic channel is expressed as follows:

[0150]

[0151] In the above formula: N pa Indicates the total number of sound lines, A p (t) and τ p (t) denotes the amplitude and delay of the pth path, respectively. In deep sea acoustic channels, the delay between two clusters reaches the order of seconds, which is several times the length of the transmitted block. This leads to IBI at the receiver. To model the IBI at the receiver, the inter-cluster delay between the first and second clusters is decomposed into:

[0152] τ 1,2 =γT bl +ξ,

[0153] In the above formula: γ is an integer, ξ is The channel model is rewritten as the sum of the impulse responses of the two clusters:

[0154] h(t,τ)=h (1) (t,τ)+h (2) (t,τ-γT bl ),

[0155] In the above formula: h (i)(t,τ) represents the channel impulse response of the i-th cluster, as shown in Figure 1. Each cluster is represented as:

[0156]

[0157] In the above formula: and represent the amplitude and delay of the pth path of the ith cluster, respectively. represents the number of paths in cluster i; assuming that the path amplitude and Doppler factor remain unchanged during the duration of a receiving block, that is, in, and denote the amplitude, initial delay and Doppler factor of the pth path of the ith cluster respectively. The impulse response of the ith cluster is rewritten as follows:

[0158]

[0159] Step 1.3 OFDM guard interval design and received signal:

[0160] Let χ i represents the delay spread of the i-th cluster. As shown in Figure 1, for the n-th receiving block, if ξ ≥ 0, then h (2) (t,τ;n) lags behind h (1) (t,τ; n), then the delay extension length of the two impulse responses after quasi-synchronization is max{χ1,ξ+χ2}; on the contrary, if ξ<0, it means h (1) (t,τ;n) lags behind h (2) (t,τ; n), at this time, after quasi-synchronization, the delay spread length of the two impulse responses is max{χ1+ξ,χ2}, assuming X i , γ and ξ are known, and these prior information are obtained in advance through the cluster detection method, from which the guard interval T is derived g The conditions that need to be met are:

[0161]

[0162] like Figure 2 As shown, by setting the guard interval to satisfy the above formula, the received signal is blocked without considering the blocking caused by intra-cluster delay spread. After that, the nth block of the received passband signal is expressed as follows:

[0163]

[0164] In the above formula: Represents the environmental noise, and performs two-step Doppler compensation on the received signal. The receiver first resamples the received block to remove the influence of the dominant Doppler. After resampling, we get in, is the resampling factor, and after down-conversion and low-pass filtering, the baseband signal is obtained Then the baseband signal y(t;n) is combined with Multiply to compensate for residual Doppler, where Indicates the carrier frequency offset compensation factor;

[0165] After sampling at baseband rate 1 / B and Fourier transform, the m-th subcarrier of the n-th block is expressed as follows:

[0166]

[0167] In the above formula: w[m;n] is the environmental noise, the channel coefficient H (i) [m, k; n] can be expressed as follows:

[0168]

[0169] In the above formula:

[0170]

[0171]

[0172] The length L of each cluster of channel taps is expressed as follows:

[0173]

[0174] Some vector and matrix definitions are as follows:

[0175]

[0176] In the above formula, y n Represents the vector composed of subcarrier data of the received signal, x n Represents the vector composed of subcarrier data of the transmitted signal, Λ τ represents the diagonal matrix composed of Fourier transform corresponding to the time delay τ, w n represents the noise vector;

[0177] As above, the frequency domain input and output relationship can be expressed in the form of matrices and vectors as follows:

[0178]

[0179] Step 2 Iterative channel estimation based on channel cluster structure:

[0180] Step 2.1 Pilot signal design based on minimization of measurement matrix coherence:

[0181] Γ b,∈It reveals the interference of adjacent subcarriers on the current subcarrier, and the interference decays as the subcarrier spacing increases. Here, only the interference of D adjacent subcarriers is considered, that is, the ICI depth is D, and Γ is defined b,∈ is the following formula:

[0182]

[0183] When the residual ICI after Doppler compensation is ignored, D = 0, is the unit matrix, and the frequency domain input-output relationship is rewritten as follows:

[0184]

[0185] In the above formula: X n By x n The diagonal matrix is composed of K×L discrete Fourier transform (DFT) submatrix. is The L×1 vector formed;

[0186] Let K p represents the number of pilot subcarriers. When only pilot subcarriers are considered, the frequency domain input and output relationship is as follows:

[0187]

[0188] In the above formula: Φ n is the measurement matrix when the nth receiving block ICI is ignored, h n It is a sparse vector composed of two clusters of impulse responses when ICI is ignored. The sparse vector uses the sparse signal reconstruction algorithm for channel estimation;

[0189] Due to the same pilot position of each block and the existence of IBI, a sufficient condition for the stable reconstruction of sparse vectors is that the measurement matrix satisfies the Restricted Isometry Property (RIP). The RIP criterion states that for the measurement matrix Φ and the vector with sparsity k, if there exists a constant δ k , so that for all k sparse vectors x, the following equation is satisfied:

[0190]

[0191] Then any k-sparse vector x can be recovered. Considering that the detection measurement matrix satisfies RIP, the measurement matrix coherence minimization is used instead, and the measurement matrix Φ n The coherence of is defined as follows:

[0192]

[0193] In the above formula: β i Represents Φ n Column i of represents the pilot position, express In order to utilize the cyclic properties of the DFT matrix, the relationship between the pilots corresponding to the two clusters is designed as follows:

[0194]

[0195] Assuming that each pilot power is the same, then Φ n The coherence is further expressed as follows:

[0196]

[0197] In the above formula:

[0198] φ1=X p,n F p ,

[0199] φ2=X p,n-γ F p ,

[0200]

[0201]

[0202] For simplicity, it is defined as follows:

[0203]

[0204] In the above formula, P represents the set of pilot positions, and the pilot design is transformed into the following optimization problem:

[0205]

[0206] In the above formula:

[0207]

[0208] In order to find the optimal solution of the pilot, the present application proposes a method for finding the optimal pilot design by random order search. The optimal pilot design method includes three layers of loops. Let I α , I out and I in Represent the number of first, second and third layer loops respectively. In each iteration of the first layer loop, The internal order of generating the value of α, where is a set of optional values of α. According to the cyclic shift characteristics of the DFT matrix, the following formula is obtained:

[0209]

[0210] In each iteration of the second-level loop, an optional set of pilot positions is used The elements in the random number K are generated p The pilot position set P is used for the third-layer loop. In each iteration of the third-layer loop, the elements of the pilot position set are modified in turn, and the position set with the minimum coherence is recorded, as shown in the following formula:

[0211]

[0212] In the above formula: P represents the set after removing an element. The MMCM-PD algorithm is shown in Table 1 below:

[0213] Table 1 MMCM-PD algorithm

[0214]

[0215]

[0216] Step 2.2 Inter-carrier interference-aware iterative channel estimation:

[0217] When ICI is considered, the ICI depth D is greater than 0, and the residual Doppler factor is defined and path delay The dictionary of atoms b and τ is as follows:

[0218] b∈{-b max ,-b max +Δb,…,b max},

[0219]

[0220] In the above formula: Δb is the Doppler factor resolution, is the maximum value of the optional Doppler factor, and it increases with the increase of ICI depth D, so the channel matrix composed of dictionary atoms is It is expressed as the following formula:

[0221]

[0222] The frequency domain input-output relationship is rewritten as follows:

[0223]

[0224] In the above formula: Let x n Estimates It is expressed as the following formula:

[0225]

[0226] In the above formula: Representing the decoding result of the previous iteration, the frequency domain input and output relationship is simplified in the form of matrix and vector as follows:

[0227]

[0228] In the above formula: A n is the measurement matrix of the nth receiving block ICI perception, η n It is a sparse vector composed of channel coefficients corresponding to different dictionary atoms during ICI perception. The sparse vector uses the sparse signal reconstruction algorithm for channel estimation;

[0229] As above, the ICI-aware iterative channel estimation is obtained, such as Figure 3 As shown, the channel estimation process of the nth receiving block is as follows:

[0230] Parameter input: frequency domain received signal y n , the diagonal matrix X formed by the two clusters of corresponding pilots p,n and X p,n-γ , maximum ICI depth D max , the length of each channel tap L, the Doppler factor resolution Δb, the carrier frequency offset compensation factor

[0231] Step a: Use sparse signal reconstruction algorithm to estimate the channel and obtain h n or η n , the channel matrix is calculated based on the channel estimation results

[0232] Step b, noise variance update, based on the received signal at the empty subcarrier position and the channel matrix Update noise variance

[0233]

[0234] Step c: channel equalization and decoding, after decoding, the data symbol detection result is obtained

[0235] Step d, iterative termination judgment, if D=D max Then terminate the iteration. Otherwise D=D+1, update x n Estimates And jump to step b.

[0236] Experimental example

[0237] The signal design and iterative channel estimation method for deep-sea acoustic OFDM communications described in this invention further validates the algorithm and superior technical effects of the method described in this invention through experimental examples. The performance of the proposed algorithm is verified by combining iterative channel estimation based on a channel cluster structure with the OMP algorithm and the GGAMP-SBL algorithm, and comparing their performance with traditional channel estimation algorithms. Furthermore, the performance of the channel estimation when the proposed pilot design is used and when not is compared, thereby verifying the performance of the proposed algorithm.

[0238] The simulation parameters of the deep sea acoustic channel are shown in Table 2. The transmitter and receiver are set at a water depth of 1100m, a horizontal distance of 20km, and a seabed density of 1.8g / cm 3 The speed of sound on the seabed is 1600 m / s; the maximum height of the seabed mountain is 20 m, and each mountain is 200 m long. The sea surface wind speed is 10 m / s, the sea surface height changes by 0.1 m, the expansion factor is 1.7, the number of scattering micropaths is 10, and the channel delay spread is 1 second.

[0239] Table 2 Simulation parameters of deep sea water acoustic channel

[0240]

[0241] The sound velocity profiles used for verification were drawn by Dushaw based on the temperature, pressure, and salinity data of the 2009 World Ocean Atlas in summer (56.5°N, 11.5°W) (Li B, Zhou S, Stojanovic M, et al. Multicarrier Communication Over Underwater Acoustic Channels With Nonuniform DopplerShifts[J]. IEEE Journal of Oceanic Engineering, 2008, 33(2): 198-209) and Qarabaqi P, Stojanovic M. Statistical Characterization and Computationally Efficient Modeling of a Class of Underwater Acoustic Communication Channels[J]. IEEE Journal of Oceanic Engineering, 2013, 38(4): 701–717).

[0242] As shown in Figure 4(a), we first generate random seabed and sea surface according to the literature (MOROZS N, GORMA W, HENSON BT, et al. Channel modeling for underwater acoustic network simulation[J]. IEEE Access, 2020, 8: 136151-136175) and ([MOROZS N, GORMA W, HENSON BT, et al. Channel modeling for underwater acoustic network simulation[J]. IEEE Access, 2020, 8: 136151-136175). Then, we use the ray acoustics software Bellhop to generate a deterministic deep-sea acoustic channel. The ray tracing diagram and channel impulse response are shown in Figures 4(b) and 4(c). In order to consider the influence of random environmental fluctuations, the channel impulse response is input into the statistical channel simulator (Qarabaqi P, Stojanovic M. Statistical Characterization and Computationally Efficient Modeling of a Class of Underwater Acoustic Communication Channels[J]. IEEE Journal of Oceanic Engineering, 2013, 38(4):701–717) to obtain a dynamic channel;

[0243] In addition, in order to simulate a more complex deep sea acoustic channel, different velocities are added to each path, and the velocities are selected from a uniformly distributed velocity set. Randomly selected from the set of speeds satisfy Since the influence of the movement of the transceiver will be eliminated by Doppler compensation, the relative movement of the transceiver is not considered in the simulation.

[0244] The verification example uses the ZP-OFDM communication system. In the iterative channel estimation simulation based on the channel cluster structure, an OFDM block consists of 512 subcarriers, including 336 data subcarriers, 128 pilot subcarriers, and 48 null subcarriers. The guard interval length is set to 0.0625s. In the simulation of traditional channel estimation, an OFDM block consists of 2048 subcarriers, including 1344 data subcarriers, 512 pilot subcarriers, and 192 null subcarriers. The guard interval length is set to 0.75s. The data symbols are obtained through 1 / 2 code rate convolution coding, interleaving and QPSK modulation. The communication rate is calculated as follows:

[0245]

[0246] In the above formula: r c is the channel coding rate, K d is the number of data subcarriers, M is the constellation size, the number of time domain taps per cluster is L=100, and the signal simulation parameters are shown in Table 3:

[0247] Table 3 ZP-OFDM signal simulation parameters

[0248]

[0249] First, in σ v The performance of different channel estimations is compared in a slowly time-varying channel with a velocity of 0.1 m / s. Under the channel cluster structure model, the delay-Doppler responses of the two corresponding clusters of channels are shown in Figure 5. It can be seen that the motion of the sound line produces a large Doppler spread. In addition, due to differences in propagation environment and velocity, the Doppler spread of different sound lines varies significantly. The first cluster of channels consists of relatively stable direct paths and has a relatively small Doppler spread, while the second cluster consists of reflected paths and has a relatively severe Doppler spread.

[0250] Figure 6 The normalized mean square error (NMSE) was used to compare the v =0.1m / s slow time-varying channel when the signal-to-noise ratio is 3 to 8dB. The calculation formula of NMSE is In the formula, H and represent the true and estimated channel frequency domain responses, respectively.

[0251] Figure 7 The bit error rate (BER) performance of different channel estimations is compared. In the "GGAMP-SBL" and "OMP" scenarios, this application uses a traditional channel estimation method, which avoids inter-block interference by using a guard interval larger than the channel delay spread.

[0252] In the "CCS-based GGAMP-SBL" and "CCS-based OMP" scenarios, iterative channel estimation based on the channel cluster structure is used, but the pilot design uses the random pilot design commonly used in underwater acoustic communication; in the "CCS-based GGAMP-SBL with MMCM-PD" and "CCS-based OMP with MMCM-PD" scenarios, iterative channel estimation based on the channel cluster structure and MMCM-PD are used; in the iterative channel estimation, the maximum ICI depth D maxSet to 2, the Doppler factor resolution is Δb = 10 -3 , the maximum selectable Doppler factor is from Figure 6 and Figure 7 It can be seen that the performance of iterative channel estimation based on the channel cluster structure is significantly better than that of traditional channel estimation. This is because it incorporates ICI into the range of channel estimation through iteration, thereby improving the performance of channel estimation. By utilizing the channel cluster structure, iterative channel estimation has lower requirements for channel time-varying than traditional channel estimation and can achieve higher communication rates. In addition, MMCM-PD solves the problem of measurement matrix degradation and further improves the performance of iterative channel estimation. Taking SNR = 7dB as an example, compared with "GGAMP-SBL" and "OMP", the channel estimation NMSE gains of "CCS-based GGAMP-SBL" and "CCS-based OMP" are 4.75dB and 1.76dB, and the bit error rate gains are 5.31dB and 2.83dB, respectively. Compared with "CCS-based GGAMP-SBL" and "CCS-based OMP", the channel estimation NMSE gains of "CCS-based GGAMP-SBL with MMCM-PD" and "CCS-based OMP with MMCM-PD" are 4.52dB and 1.87dB, and the bit error rate gains are 8.45dB and 5.16dB, respectively.

[0253] In order to verify the performance of iterative channel estimation based on channel cluster structure in fast time-varying deep sea acoustic channel, it is applied to σ v = 0.5m / s fast time-varying channel. Figure 8 shows σ v = 0.5m / s, the delay-Doppler response of the deep sea acoustic channel can be seen, compared with σ v =0.1m / s slow time-varying channel, the two clusters of channels corresponding to this channel both show severe Doppler spread.

[0254] Figure 9 and Figure 10 The NMSE and BER performance of different channel estimates are compared. Figure 9 and Figure 10It is clear that iterative channel estimation based on the channel cluster structure maintains good performance in fast time-varying channels, and pilot design further improves channel estimation performance, while traditional channel estimation cannot accurately estimate the channel. Taking an SNR of 11dB as an example, compared with "CCS-based GGAMP-SBL" and "CCS-based OMP", the channel estimation NMSE gains of "CCS-based GGAMP-SBL with MMCM-PD" and "CCS-based OMP with MMCM-PD" are 1.82dB and 2.15dB, respectively, and the bit error rate gains are 8.51dB and 9.89dB, respectively.

[0255] The present invention is not limited to the above-mentioned embodiments. Any modification, improvement, or substitution that can be conceived by those skilled in the art without departing from the essential content of the present invention shall fall within the scope of protection of the claims of the present invention.

Claims

1. A signal design and iterative channel estimation method for deep sea acoustic OFDM communication, comprising the following steps: Step 1. Establish a ZP-OFDM communication system model; Step 2. Iterative channel estimation based on channel cluster structure.

2. According to the signal design and iterative channel estimation method for deep sea acoustic OFDM communication according to claim 1, the ZP-OFDM communication system model is established in step 1. Furthermore, the iterative channel estimation based on the channel cluster structure in step 2 includes the following specific steps: Step 1.1 Send passband transmission signal: Consider a ZP-OFDM communication system, let T denote the OFDM symbol duration, T g Represents the zero-filled guard interval length, then the duration of an OFDM block is expressed as T bl =T+T g , let K represent the number of subcarriers, Δf = 1 / T represent the subcarrier spacing, f c If represents the center frequency, then the signal bandwidth is B = KΔf, and the frequency of the kth subcarrier is as follows: In the above formula: K subcarriers can be decomposed into a set of pilot subcarriers Data subcarrier set and the set of empty subcarriers And satisfy Let d[k;n] represent the data of the kth subcarrier of the nth transmission block, and the nth transmission block of the baseband transmission signal is expressed as follows: In the above formula: is the set of active subcarriers, g(t) is a rectangular pulse shaping filter that is not zero in [0,T], and its Fourier transform is: The nth transmission block of the passband transmission signal is expressed as: The transmission signal consisting of N OFDM blocks is expressed as: Step 1.2 Channel model based on channel cluster structure: The path-based channel model of deep sea acoustic channel is expressed as follows: In the above formula: N pa Indicates the total number of sound lines, A p (t) and τ p (t) denotes the amplitude and delay of the pth path, respectively. In deep sea acoustic channels, the delay between two clusters reaches the order of seconds, which is several times the length of the transmitted block. This leads to IBI at the receiver. To model the IBI at the receiver, the inter-cluster delay between the first and second clusters is decomposed into: t 1,2 =γT bl +ξ, In the above formula: γ is an integer, ξ is The channel model is rewritten as the sum of the impulse responses of the two clusters: h(t,τ)=h (1) (t,τ)+h (2) (t,τ-γT bl ), In the above formula: h (i) (t,τ) represents the channel impulse response of the i-th cluster, as shown in Figure 1. Each cluster is represented as: In the above formula: and represent the amplitude and delay of the pth path of the ith cluster, respectively. represents the number of paths in cluster i; Assume that the path amplitude and Doppler factor remain constant during the duration of a reception block, i.e. in, and denote the amplitude, initial delay and Doppler factor of the pth path of the ith cluster respectively. The impulse response of the ith cluster is rewritten as follows: Step 1.3 OFDM guard interval design and received signal: Let χ i represents the delay spread of cluster i. For the nth receiving block, if ξ≥0, then h (2) (t,τ;n) lags behind h (1) (t,τ; n), then the delay extension length of the two impulse responses after quasi-synchronization is max{χ1,ξ+χ2}; on the contrary, if ξ<0, it means h (1) (t,τ;n) lags behind h (2) (t,τ; n), at this time, after quasi-synchronization, the delay spread length of the two impulse responses is max{χ1+ξ,χ2}, assuming that χ i , γ and ξ are known, and these prior information are obtained in advance through the cluster detection method, from which the guard interval T is derived g The conditions that need to be met are: By setting the guard interval to satisfy the above equation, the received signal is blocked without considering the blocking caused by intra-cluster delay spread. The nth block of the received passband signal is expressed as follows: In the above formula: Represents the environmental noise, and performs two-step Doppler compensation on the received signal. The receiver first resamples the received block to remove the influence of the dominant Doppler. After resampling, we get in, is the resampling factor, and after down-conversion and low-pass filtering, the baseband signal is obtained Then the baseband signal y(t;n) is combined with Multiply to compensate for residual Doppler, where Indicates the carrier frequency offset compensation factor; After sampling at baseband rate 1 / B and Fourier transform, the m-th subcarrier of the n-th block is expressed as follows: In the above formula: w[m;n[ is the environmental noise, the channel coefficient H (i) [m, k; n] is expressed as follows: In the above formula: The length L of each cluster of channel taps is expressed as follows: Some of the vectors and matrices involved are defined as follows: Among them, y n Represents the vector composed of subcarrier data of the received signal, x n Represents the vector composed of subcarrier data of the transmitted signal, Λ τ represents the diagonal matrix composed of Fourier transform corresponding to the time delay τ, w n represents the noise vector As above, the frequency domain input and output relationship can be expressed in the form of matrices and vectors as follows:

3. According to the signal design and iterative channel estimation method for deep sea acoustic OFDM communication according to claim 1, the iterative channel estimation based on the channel cluster structure in step 2 comprises the following specific steps: Step 2.1 Pilot signal design based on minimization of measurement matrix coherence: Γ b,∈ The interference of adjacent subcarriers on the current subcarrier is revealed, and the interference decays as the subcarrier spacing increases. Here, only the interference of D adjacent subcarriers is considered, that is, the ICI depth is D, and Γ is defined b,∈ is the following formula: When the residual ICI after Doppler compensation is ignored, D = 0, is the unit matrix, and the frequency domain input-output relationship is rewritten as follows: In the above formula: X n By x n The diagonal matrix is composed of, F is the K×L Discrete Fourier Transform (DFT) submatrix, is The L×1 vector formed; Let K p represents the number of pilot subcarriers. When only the pilot subcarriers are considered, the frequency domain input and output relationship is as follows: In the above formula: Φ n is the measurement matrix when the nth receiving block ICI is ignored, h n is a sparse vector composed of two clusters of impulse responses when ICI is ignored. The sparse vector uses the sparse signal reconstruction algorithm to estimate the channel. p,n A vector of noise components representing the pilot positions; Due to the same pilot position of each block and the existence of IBI, a sufficient condition for the stable reconstruction of sparse vectors is that the measurement matrix satisfies the restricted isometry property (RIP). The RIP criterion shows that for the measurement matrix Φ and the vector with sparsity k, if there exists a constant δ k , so that for all k sparse vectors x, the following equation is satisfied: Then any k-sparse vector x can be recovered. Considering that the detection measurement matrix satisfies RIP, the measurement matrix coherence minimization is used instead, and the measurement matrix Φ n The coherence of is defined as follows: In the above formula: β i Represents Φ n Column i of represents the pilot position, express In order to utilize the cyclic properties of the DFT matrix, the relationship between the pilots corresponding to the two clusters is designed as follows: Assuming that each pilot power is the same, then Φ n The coherence is further expressed as follows: In the above formula: φ1=X p,n F p , φ2=X p,n-γ F p , For simplicity, it is defined as follows: In the above formula, P represents the set of pilot positions, and the pilot design is transformed into the following optimization problem: In the above formula: In order to find the optimal solution of pilot, a method of finding the optimal pilot design by random order search is proposed. The optimal pilot design method contains three layers of loops. Let I α , I out and I in Represent the number of cycles of the first, second and third layers respectively; Step 2.2 Inter-carrier interference-aware iterative channel estimation: When ICI is considered, the ICI depth D is greater than 0, and the residual Doppler factor is defined and path delay The dictionary of atoms b and τ is as follows: b∈{-b max ,-b max +Δb,…,b max }, In the above formula: Δb is the Doppler factor resolution, is the maximum value of the optional Doppler factor, and it increases with the increase of ICI depth D, so the channel matrix composed of dictionary atoms is It is expressed as the following formula: The frequency domain input-output relationship is rewritten as follows: In the above formula: Let x n Estimates It is expressed as the following formula: In the above formula: Representing the decoding result of the previous iteration, the frequency domain input and output relationship is simplified in the form of matrix and vector as follows: In the above formula: A n is the measurement matrix of the nth receiving block ICI perception, η n It is a sparse vector composed of channel coefficients corresponding to different dictionary atoms during ICI perception. The sparse vector uses the sparse signal reconstruction algorithm to perform channel estimation to obtain the iterative channel estimation of ICI perception. The channel estimation procedure of the nth receiving block is as follows: Before using the sparse signal reconstruction algorithm for channel estimation, the input frequency domain received signal y n , the diagonal matrix X formed by the two corresponding pilots p,n and X p,n-γ , maximum ICI depth D max , length of each channel tap L, Doppler factor resolution Δb, carrier frequency offset compensation factor Parameters, the specific steps are as follows; Step a: Use sparse signal reconstruction algorithm to estimate the channel and obtain h n or η n , the channel matrix is calculated based on the channel estimation results Step b, noise variance update, based on the received signal at the empty subcarrier position and the channel matrix Update noise variance Step c: channel equalization and decoding, after decoding, the data symbol detection result is obtained Step d, iterative termination judgment, if D=D max Then terminate the iteration, otherwise D=D+1, update x n Estimates And jump to step b.

4. According to the signal design and iterative channel estimation method for deep sea acoustic OFDM communication according to claim 1, in step 2.1, the number of first, second and third layer loops are expressed as follows: In each iteration of the first-level loop, The internal order of generating the value of α, where is a set of optional values of α. According to the cyclic shift characteristics of the DFT matrix, the following formula is obtained: In each iteration of the second-level loop, an optional set of pilot positions is used The elements in the random number K are generated p The pilot position set P is used for the third layer cycle; In each iteration of the third-layer loop, the elements of the pilot position set are modified in turn, and the position set with the minimum coherence is recorded, as follows: In the above formula: Represents the set after P removes an element.

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