Underwater Acoustic OFDM Communication Array Signal Combining Method in the Presence of Spatial Correlated Noise

Abstract

Underwater acoustic OFDM communication array signal combining method in the presence of spatially correlated noise, which belongs to the field of underwater acoustic communication technology. The purpose of the present invention is to improve the signal-to-noise ratio gain of the combined signal. The method of the present invention is as follows: Step 1, for any symbol e in the OFDM signal transmitted by the transmitting end, use the receiving array to receive symbol e; after processing the signals received by each array element respectively, obtain the processed signals corresponding to each array element; then obtain the channel parameters corresponding to each array element according to the processed signals; Step 2, construct the signal-to-noise ratio according to the covariance matrix of the noise between different array elements and the channel parameters, and calculate the weighted vector when the signal-to-noise ratio reaches the maximum value; Step 3, use the calculated weighted vector to combine the received signals of each array element to obtain the combined received signal; then decode the combined received signal to obtain the original bits transmitted by the transmitting end. The method of the present invention can be applied to the field of underwater acoustic communication technology.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic communication, and particularly relates to a method for combining underwater acoustic OFDM (Orthogonal Frequency Division Multiplexing) communication array signals in spatially correlated noise. Background Technique

[0002] Underwater acoustic communication technology has been widely studied and applied in the fields of underwater sensor networks, ocean environment observation, ocean engineering construction, etc. Since the underwater acoustic channel has obvious multipath and fast time-varying characteristics, and the underwater noise field is complex and diverse, it is very difficult to achieve stable and high-speed underwater acoustic communication.

[0003] In an underwater acoustic communication system, for a traditional SISO (Single input Single output) underwater acoustic communication system, the low signal-to-noise ratio problem caused by long-distance transmission makes underwater acoustic communication decoding extremely difficult. The SIMO (Singleinput Multi output) underwater acoustic communication system well solves this problem. The SIMO underwater acoustic communication system arranges an M-element hydrophone array at the receiving end, and through signal combination, an array gain of 10log 10 (M) decibels can be brought, which greatly improves the received signal-to-noise ratio of underwater acoustic signals. During the process of combining the received array signals in the SIMO underwater acoustic communication system, it is usually assumed that the channels of the signals received by each array element are independent of each other and the noises are uncorrelated. However, in the measured ocean noise field, the channels and noises between array elements often have spatial correlation.

[0004] The patent application with the publication number CN116366170A proposes a signal combination processing method based on the noise correlation between the sound pressure and vibration velocity channels of a vector hydrophone, and uses the guard interval of the OFDM signal to estimate the correlation coefficient of the noise between channels, but this method is not applicable to large-scale underwater acoustic arrays and fast time-varying underwater noise fields.

[0005] The patent application with the publication number CN102778676A proposes a signal detection method in a fast-changing underwater acoustic channel. This signal detection and combination method considers the fast time-varying characteristics of the underwater acoustic channel and noise of the underwater acoustic receiving array, and considers the influence of the correlated channel, but does not consider the influence brought by noise correlation.

[0006] In summary, since the existing methods do not consider the influence of noise correlation when combining the received array signals, it is very necessary to propose a new method for combining array signals to further improve the signal-to-noise ratio gain of the combined signals. Summary of the Invention

[0007] The object of the present invention is to improve the signal-to-noise ratio gain of the combined signal, and a method for combining underwater acoustic OFDM communication array signals in spatially correlated noise is proposed. By considering the spatial noise correlation between array elements, signals are combined to obtain a higher signal-to-noise ratio gain and achieve stable long-distance underwater acoustic communication.

[0008] The technical solution adopted by the present invention to solve the above technical problems is: a method for combining underwater acoustic OFDM communication array signals in spatially correlated noise, and the method specifically includes the following steps:

[0009] Step 1: For any symbol e in the OFDM signal transmitted by the transmitter, use a receiving array composed of K receiving elements to receive symbol e;

[0010] After processing the signals received by each element respectively, the processed signals corresponding to each element are obtained; then, channel estimation is performed based on the processed signals, and the channel parameters corresponding to each element are obtained respectively;

[0011] Step 2: For the m-th data subcarrier, denote the channel parameter of the k-th element on the m-th data subcarrier as H k [m], k = 1, 2,..., K; then the channel parameter vector on the m-th data subcarrier is H[m], and H[m] = [H1[m], H2[m], …, H K [m]] T , where the superscript T represents transpose;

[0012] Construct a signal-to-noise ratio based on the covariance matrix Q[m] of the noise between different elements on the m-th data subcarrier and the channel parameter vector H[m], and calculate the weighting vector when the signal-to-noise ratio reaches the maximum value;

[0013] Step 3: Use the weighting vector calculated in Step 2 to combine the received signals of each element on the m-th data subcarrier to obtain the combined received signal;

[0014] Then decode the combined received signal to obtain the original bits transmitted by the transmitter;

[0015] Step 4: For each symbol in the OFDM signal transmitted by the transmitter, perform the processes of Step 1 to Step 3 to complete signal reception.

[0016] Furthermore, the specific process of processing the signals received by each element respectively is:

[0017] For the signals received by each element, perform LFM synchronization, down-conversion, Doppler estimation and compensation, and FFT processing.

[0018] Furthermore, the signal-to-noise ratio γ(W) is:

[0019]

[0020] Among them, E[·] represents the expectation, Var[·] represents the variance, and |x[m]| 2 =|W[m] T H[m]| 2 , where W[m] is the weighting vector on the m-th subcarrier, and W[m]=[w1[m], w2[m]…W K [m]] T , W k [m] is the complex weighting factor of the k-th array element on the m-th data subcarrier, and Var[n[m]]=W[m] T Q[m]W[m] * , [·] * represents the conjugate calculation;

[0021] Omitting the subcarrier serial number [m], that is, simply denoting W[m] as W, H[m] as H, and Q[m] as Q, then the signal-to-noise ratio is re-denoted as γ oC (W):

[0022]

[0023] Diagonalize Q to D -1 QD = A, where A is a K×K diagonal matrix, and A H =A, [·] H represents the conjugate transpose calculation. The k-th diagonal element of matrix A is the k-th eigenvalue of Q, and D is a unitary matrix composed of the eigenvectors of Q, with D H =D -1 ;

[0024] Let P = D H , then Q = p H Λ 2 p, where p H =P -1 , A = Λ 2 and Λ H =Λ;

[0025] Then the denominator of Equation (2) is written as:

[0026]

[0027] where ||·||2 is the 2-norm;

[0028] Define Equation (4):

[0029] [(ΛP * ) T -1 ​=(P H Λ T ) -1 =(P -1 Λ) -1 =Λ -1 P(4)

[0030] Among them, the superscript -1 represents the inverse of the matrix;

[0031] Then write the numerator of Equation (2) as:

[0032] W T H = W T (ΛP * ) T ·[(ΛP * ) T ) -1 H = W T p H Λ·v -1 PH=(ΛPW*) H (Λ -1 PH)(5).

[0033] Furthermore, the calculation makes the weight vector when the signal-to-noise ratio reaches the maximum value; specifically:

[0034] Step 2-1. Obtained from the Cauchy-Schwarz inequality:

[0035]

[0036] When and only when Equation (7) is satisfied, the equal sign of Equation (6) holds:

[0037] ΛPW * =Λ -1 PH(7)

[0038] That is, when Equation (7) is satisfied, γ OC (W) reaches the maximum value, and the signal-to-noise ratio gain γ OC (W) MAX :

[0039]

[0040] Step 2-2. Solve the weighted vector in Equation (7) to obtain:

[0041] W * =(ΛP) -1 Λ -1 PH(9)

[0042] Then the weighted vector W when the signal-to-noise ratio reaches the maximum value is:

[0043] W=(P H Λ-2 P) * H * =(Q * ) -1 H * (10).

[0044] Furthermore, the calculation method of the covariance matrix Q is as follows:

[0045] n l [m′]n k [m′] * =Y l [m′]Y k [m′] * (11)

[0046] where n k [m′] is the noise signal of the k-th array element on the m′-th null subcarrier, n l [m′] is the noise signal of the l-th array element on the m′-th null subcarrier, Y k [m′] is the output signal of the k-th array element branch on the m′-th null subcarrier, Y l [m′] is the output signal of the l-th array element branch on the m′-th null subcarrier;

[0047] Then the noise covariance q of the k-th array element branch and the l-th array element branch kl is:

[0048]

[0049] where M is the number of null subcarriers included in each OFDM symbol;

[0050] Then the covariance matrix Q is:

[0051]

[0052] Furthermore, the output signal of the k-th array element branch on the m′-th null subcarrier is:

[0053] Y k [m′]=H k [m′]s[m′]+n k [m′], k ∈ 1, 2,..., K (14)

[0054] where s[m′] is the symbol modulated on the m′-th null subcarrier, H k [m′] is the channel parameter of the k-th array element on the m′-th null subcarrier.

[0055] Even further, the output signal of the l-th array element branch on the m′-th null subcarrier is:

[0056] Y l [m′] = H l [m′]s[m′] + n l [m′], l ∈ 1, 2, …, K (15)

[0057] Among them, H l [m′] is the channel parameter of the l-th array element on the m′-th null subcarrier.

[0058] The beneficial effects of the present invention are as follows:

[0059] 1. The array signal combining method of the underwater acoustic OFDM system proposed by the present invention is based on the assumption that there is correlation between the spatial noises among the arrays. Based on the maximum average signal-to-noise ratio criterion, the weighted combining method of the signals of each array element is derived, which conforms to the actual ocean noise field situation and has more application value;

[0060] 2. The method for estimating the spatial noise correlation coefficient matrix proposed by the present invention has extremely high estimation accuracy for the spatial noise correlation coefficient matrix within each OFDM symbol and is applicable to the fast time-varying ocean noise field;

[0061] 3. When there is spatial noise correlation among the array elements in the array, compared with the traditional optimal MRC combining method, the combining method proposed by the present invention improves the received signal-to-noise ratio gain without increasing the receiver complexity and greatly reduces the bit error rate (BER) of the communication system. Description of the Drawings

[0062] Figure 1 is the processing flow chart of the combining receiver considering the spatial noise correlation;

[0063] Figure 2 is the performance comparison diagram between the combining receiver of the present invention and the traditional MRC combining receiver in a system with 4 array elements at the receiving end;

[0064] Figure 3 is the normalized mean square error of the present invention using null subcarriers to estimate different correlation coefficients. Detailed Embodiments

[0065] Detailed Embodiment 1: Combined with Figure 1 This embodiment is described. An underwater acoustic OFDM communication array signal combining method with spatially correlated noise according to this embodiment specifically includes the following steps:

[0066] Step 1. For any symbol e in the OFDM signal sent by the transmitter, since the duration of each symbol in the OFDM signal is short, it can be considered that the spatial noise correlation coefficient matrix within each symbol is stable. Use a receiving array composed of K receiving elements (any array with correlated spatial noise between elements can be used as the receiving array of the present invention) to receive symbol e;

[0067] After processing the signals received by each element respectively, the processed signals corresponding to each element are obtained; then, according to the processed signals, channel estimation is performed to obtain the channel parameters corresponding to each element respectively (i.e., the channel parameters of each element on each data subcarrier and the channel parameters of each element on each null subcarrier);

[0068] Step 2. For the m-th data subcarrier, denote the channel parameter of the k-th element on the m-th data subcarrier as H k [m], k = 1, 2,..., K, and H k [m] is the channel parameter obtained in Step 1; then the channel parameter vector on the m-th data subcarrier is H[m], and H[m] = [H1[m], H2[m], …, H K [m]] T , where the superscript T represents transpose;

[0069] Construct the signal-to-noise ratio according to the covariance matrix Q[m] of the noise between different elements on the m-th data subcarrier and the channel parameter vector H[m], and calculate the weighted vector when the signal-to-noise ratio reaches the maximum value;

[0070] Step 3. Use the weighted vector calculated in Step 2 to combine the received signals of each element on the m-th data subcarrier (i.e., perform weighted summation processing on the received signals of each element in the array), and obtain the combined received signal;

[0071] Then decode the combined received signal to obtain the original bits sent by the transmitter;

[0072] Step 4. For each symbol in the OFDM signal sent by the transmitter, perform the processes of Step 1 to Step 3 to complete the reception of the signal.

[0073] The time-varying characteristics of the ocean noise field cause the noise correlation coefficient to change at all times. In the case of correlated noise between elements, the noise correlation between elements can be used to combine signals to obtain a higher signal-to-noise ratio gain, solving the influence of correlated noise on the array reception performance. By improving the received signal-to-noise ratio, stable and reliable long-distance underwater acoustic communication is thus achieved. Moreover, the method of the present invention is applicable to the array signal combination of underwater acoustic communication systems with a large number of elements.

[0074] Embodiment 2: The difference between this embodiment and Embodiment 1 is that the signals received by each array element are processed as follows:

[0075] For the signals received by each array element, LFM (Linear Frequency Modulation) synchronization, down-conversion, Doppler estimation and compensation, and FFT (Fast Fourier Transform) processing are all performed.

[0076] Other steps and parameters are the same as those in Embodiment 1.

[0077] Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that the signal-to-noise ratio gain γ(W) is:

[0078]

[0079] where E[·] represents expectation, Var[·] represents variance, and |x[m]| 2 = |W[m] T H[m]| 2 , W[m] is the weighting vector on the m-th subcarrier, W[m] = [w1[m], w2[m]…W K [m]] T , W k [m] is the complex weighting factor of the k-th array element on the m-th data subcarrier, Var[n[m]] = W[m] T Q[m]W[m] * , [·] * represents conjugate calculation;

[0080] Omitting the subcarrier serial number [m], that is, simply denoting W[m] as W, H[m] as H, and Q[m] as Q, then the signal-to-noise ratio is re-denoted as γ OC (W):

[0081]

[0082] Since the noise covariance matrix Q is a positive definite Hermitian matrix, diagonalize Q as D -1 QD = A, where A is a K×K diagonal matrix, and there is A H = A, [·] H represents conjugate transpose calculation, the k-th diagonal element of matrix A is the k-th eigenvalue of Q, and D is a unitary matrix composed of the eigenvectors of Q, and there is D H = D -1 ;

[0083] Let P = D H , then there is Q = p H Λ 2p, where p H = P -1 , A = Λ 2 and Λ H = Λ;

[0084] Then write the denominator of Equation (2) as:

[0085]

[0086] where ||·||2 is the 2-norm;

[0087] Define Equation (4):

[0088] [(ΛP * ) T -1 = (P H Λ T ) -1 = (P -1 Λ) -1 = Λ -1 P (4)

[0089] where the superscript -1 represents the inverse of the matrix;

[0090] Then write the numerator of Equation (2) as:

[0091] W T H = W T (ΛP * ) T ·[(ΛP * ) T -1 H = W T P H Λ·Λ -1 PH = (ΛPW*) H (Λ -1 PH) (5).

[0092] Other steps and parameters are the same as those in the first or second specific implementation manner.

[0093] The output signal of the m-th subcarrier and K receiving array element branches can be expressed as:

[0094] y[m] = x[m] + z[m]

[0095] where

[0096]

[0097]

[0098] s[m] is the modulation symbol on the m-th subcarrier of the baseband, and n[m] is the relevant noise on the m-th subcarrier;​​

[0099] E{n[m]} = 0, E{s[m]n[m]} = 0

[0100] s[m] and n[m] satisfy: The noise n[m] and the signal s[m] are relatively independent, that is, the noise n[m] and the signal s[m] are uncorrelated, and the noise n[m] still has a zero mean value.

[0101] Specific Embodiment Four: The difference between this embodiment and any one of Embodiments One to Three is that the weight vector when the signal-to-noise ratio reaches the maximum value is calculated; specifically:

[0102] Step 2-1: According to the Cauchy-Schwarz inequality:

[0103]

[0104] Based on the maximum average signal-to-noise ratio criterion, the equality in Equation (6) holds if and only if Equation (7) is satisfied:

[0105] ΛPW * = Λ -1 PH (7)

[0106] That is, when Equation (7) is satisfied, γ OC (W) reaches the maximum value, and the signal-to-noise ratio gain γ OC (W) MAX :

[0107]

[0108] Step 2-2: Solve the weighted vector in Equation (7) to obtain:

[0109] W * = (ΛP) -1 Λ -1 PH (9)

[0110] Then the weighted vector W when the signal-to-noise ratio reaches the maximum value is:

[0111] W = (P H Λ -2 P) * H * = (Q * ) -1 H * (10)

[0112] Other steps and parameters are the same as any one of Embodiments One to Three.

[0113] Specific Embodiment Five: The difference between this embodiment and any one of Embodiments One to Four is that the calculation method of the covariance matrix Q is:

[0114] n l [m′]n k [m′] * =Y l [m′]Y k [m′] * (11)

[0115] Among them, n k [m′] is the noise signal of the k-th array element on the m′-th null subcarrier (the subcarrier with modulation symbol s[m′]=0 is the null subcarrier), n l [m′] is the noise signal of the l-th array element on the m′-th null subcarrier, Y k [m′] is the output signal of the k-th array element branch on the m′-th null subcarrier, Y l [m′] is the output signal of the l-th array element branch on the m′-th null subcarrier;

[0116] Then the noise covariance q of the k-th array element branch and the l-th array element branch kl is:

[0117]

[0118] Among them, M is the number of null subcarriers included in each OFDM symbol, and the M null subcarriers are evenly distributed within each OFDM symbol block;

[0119] Then the covariance matrix Q is:

[0120]

[0121] Other steps and parameters are the same as those in any one of the specific embodiments one to four.

[0122] Substitute the estimated noise covariance matrix Q into Equation (10), and the weighted vector can be obtained. It should be noted that for the received symbol e, the noise covariance matrix on each data subcarrier is the same.

[0123] To more intuitively show the correlation of noise between different array elements, the correlation coefficient matrix R after energy normalization can be used to represent the noise correlation between channels. According to formulas (11) to (13), the spatial noise correlation coefficient between the k-th array element branch and the l-th array element branch can be expressed as:

[0124]

[0125] The noise energy of different array element branches can be considered to be stationary, so the noise energy |n k | 2 , |n l | 2It can be obtained from the estimation of the null carrier, that is, the correlation coefficient matrix R of the spatial noise between different receiving array elements can be expressed as:

[0126]

[0127] Such as Figure 3 As shown, it is the estimation result obtained by using the method of this embodiment, indicating that the estimation method of this embodiment has excellent estimation performance.

[0128] Specific Embodiment Six: Different from any one of Specific Embodiments One to Five, the output signal of the k-th element branch on the m'-th null subcarrier is:

[0129] Y k [m′] = H k [m′]s[m′] + n k [m′], k ∈ 1, 2,..., K (14)

[0130] Wherein, s[m′] is the symbol modulated on the m'-th null subcarrier, and H k [m′] is the channel parameter of the k-th element on the m'-th null subcarrier.

[0131] Other steps and parameters are the same as any one of Specific Embodiments One to Five.

[0132] Specific Embodiment Seven: Different from any one of Specific Embodiments One to Six, the output signal of the l-th element branch on the m'-th null subcarrier is:

[0133] Y l [m′] = H l [m′]s[m′] + n l [m′], l ∈ 1, 2,..., K (15)

[0134] Wherein, H l [m′] is the channel parameter of the l-th element on the m'-th null subcarrier.

[0135] Other steps and parameters are the same as any one of Specific Embodiments One to Six.

[0136] The maximum signal-to-noise ratio gain obtained by using the method of the present invention is:

[0137]

[0138] For a system adopting the MRC (Maximum Ratio Combining) method, its SNR can be expressed as:

[0139]

[0140] It can be obtained from the Cauchy-Schwarz inequality:

[0141]

[0142] Then, under the optimal combining weight, the maximum signal-to-noise ratio gain of the system with the MRC combining method is:

[0143]

[0144] Then, the difference between the maximum signal-to-noise ratio gain obtained by the method of the present invention and the signal-to-noise ratio gain of the MRC combining method is:

[0145]

[0146] As Figure 2 shown, it is a performance comparison diagram of the combining receiver of the present invention and the traditional MRC combining receiver, indicating that the performance of the combining receiver of the present invention is better.

[0147] The above numerical examples of the present invention are only used to illustrate in detail the calculation model and calculation process of the present invention, rather than limiting the implementation manner of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation manners here. Any obvious changes or modifications derived from the technical solutions of the present invention still fall within the protection scope of the present invention.

Claims

1. An underwater acoustic OFDM communication array signal combining method under spatially correlated noise, characterized in that, The method specifically includes the following steps: Step 1: For any symbol e in the OFDM signal sent by the transmitting end, use a receiving array composed of K receiving elements to receive symbol e; After processing the signals received by each element respectively, obtain the processed signals corresponding to each element; then perform channel estimation based on the processed signals to obtain the channel parameters corresponding to each element respectively; Step 2: For the m-th data subcarrier, denote the channel parameter of the k-th array element on the m-th data subcarrier as H k [m], where k = 1, 2, …, K; then the channel parameter vector on the m-th data subcarrier is H[m], and H[m] = [H1[m], H2[m], …, H K [m]] T , where the superscript T represents transpose; Construct a signal-to-noise ratio according to the covariance matrix Q[m] of the noise between different elements on the m-th data subcarrier and the channel parameter vector H[m], and calculate the weighted vector when the signal-to-noise ratio reaches the maximum value; The signal-to-noise ratio is: where, Var[·] represents variance, |x[m]| 2 = |W[m] T H[m]| 2 , W[m] is the weighting vector on the m-th subcarrier, W[m] = [w1[m], w2[m]…w K [m]] T , w k [m] is the complex weighting factor of the k-th array element on the m-th data subcarrier, Var[n[m]] = W[m] T Q[m]W[m] * , [·] * represents conjugate calculation; γ(W) represents signal-to-noise ratio; Omit the subcarrier serial number [m], that is, simply denote W[m] as W, H[m] as H, and Q[m] as Q, and then re-denote the signal-to-noise ratio as γ OC (W): Diagonalize Q to D -1 QD = A, where A is a K×K diagonal matrix with A H = A, [·] H denotes the conjugate transpose calculation. The k-th diagonal element of matrix A is the k-th eigenvalue of Q, and D is a unitary matrix composed of the eigenvectors of Q, with D H = D -1 ; Let P = D H , then Q = P H Λ 2 P, where P H = P -1 , A = Λ 2 and Λ H = Λ; Then write the denominator of Equation (2) as: where, ||·||2 is the 2-norm; Define Equation (4): [(ΛP * )] T -1 =(P H Λ T ) -1 =(P -1 Λ) -1 =Λ -1 P (4)​ where, the superscript -1 represents the inverse of the matrix; Then write the numerator of Equation (2) as: W T H = W T (ΛP * ) T ·[(ΛP * ) T -1 H = W T P H Λ·Λ -1 PH = (ΛPW * ) H (Λ -1 PH)(5)​ The calculation of the weighted vector when the signal-to-noise ratio reaches the maximum value; specifically: Step 2-1: Obtain from the Cauchy-Schwarz inequality: The equal sign of Equation (6) holds if and only if Equation (7) is satisfied: ΛPW * = Λ -1 PH (7) That is, when the formula (7) is satisfied, γ OC (W) obtains the maximum value, and the signal-to-noise ratio gain γ OC (W) MAX : Step 2-2: Solve the weighted vector in Equation (7) to obtain: W * = (ΛP) -1 Λ -1 PH (9) Then the weighted vector W when the signal-to-noise ratio reaches the maximum value is: W = (P H Λ -2 P) * H * = (Q * ) -1 H * (10) The calculation method of the covariance matrix Q is: n l [m']n k [m'] * = Y l [m']Y k [m'] * (11) where n k [m'] is the noise signal of the k-th array element on the m'-th empty subcarrier, n l [m'] is the noise signal of the l-th array element on the m'-th empty subcarrier, Y k [m'] is the output signal of the k-th array element branch on the m'-th empty subcarrier, Y l [m'] is the output signal of the l-th array element branch on the m'-th empty subcarrier; Then the noise covariance q between the k-th and l-th array element branches kl is as follows: where, M is the number of empty subcarriers included in each OFDM symbol; Then the covariance matrix Q is: Step 3: Use the weighted vector calculated in Step 2 to combine the received signals of each element on the m-th data subcarrier to obtain the combined received signal; Then decode the combined received signal to obtain the original bits sent by the transmitting end; Step 4: For each symbol in the OFDM signal sent by the transmitting end, perform the processes of Step 1 to Step 3 to complete the reception of the signal.

2. The underwater acoustic OFDM communication array signal combining method for spatially correlated noise according to claim 1, wherein The specific process of processing the signals received by each element respectively is: For the signal received by each element, perform LFM synchronization, down-conversion, Doppler estimation and compensation, and FFT processing.

3. The underwater acoustic OFDM communication array signal combining method for spatially correlated noise according to claim 2, wherein The output signal of the k-th element branch on the m'-th empty subcarrier is: Y k [m'] = H k [m']s[m'] + n k [m'], k ∈ 1, 2, …, K (14) where s[m'] is the symbol modulated on the m'-th null subcarrier, and H k [m'] is the channel parameter of the k-th array element on the m'-th null subcarrier.

4. The underwater acoustic OFDM communication array signal combining method for spatially correlated noise according to claim 3, characterized in that The output signal of the l-th element branch on the m'-th empty subcarrier is: Y l [m'] = H l [m']s[m'] + n l [m'], l ∈ 1, 2, …, K (15) Among them, H l [m'] is the channel parameter of the l-th array element on the m'-th null subcarrier.

Images