Optimal paired pilot design method in filter bank multi-carrier communication system

Abstract

This invention discloses an optimal pairwise pilot design method for a filter bank multicarrier communication system. First, based on the pairwise pilot channel estimation method, a pilot optimization model is established, and expressions for inherent interference and prototype filters are given in the model. Then, using differentiation analysis, the optimal pilot values ​​are determined under constraint boundary conditions, thus transforming the constraints of the pilot optimization model into equality constraints. Finally, optimal pairwise pilot structures applicable to different prototype filters are provided, and these structures are used as pilot designs for the pairwise pilot channel estimation method. Using this method, only two columns of pilot symbols are needed for channel estimation, and different pilot structures are adopted according to the type of prototype filter, thereby reducing pilot load while adapting to different communication scenarios.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to an optimal pair pilot design method in a filter bank multicarrier communication system. Background Technology

[0002] Currently, pilot-based channel estimation methods are widely used in filter bank multicarrier communication systems. However, data symbols in these systems inherently interfere with pilot symbols, complicating pilot symbol design and reducing channel estimation performance. To address this inherent interference in pilot design, the interference approximation method improves channel estimation performance by approximating the inherent interference experienced by pilot symbols. However, the advantages of the interference approximation method—strong noise immunity and high estimation accuracy—are achieved at the cost of adding two columns of zero-value pilot symbols, resulting in additional resource overhead. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide an optimal pair of pilot design method in a filter bank multicarrier communication system. Using the method of the present invention, only two columns of pilot symbols are needed for channel estimation, and different pilot structures are adopted according to the type of prototype filter, thereby reducing pilot load while adapting to different communication scenarios.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0005] According to the present invention, an optimal pairwise pilot design method for a filter bank multicarrier communication system is proposed. First, based on the pairwise pilot channel estimation method, a pilot optimization model is established, and the expressions for inherent interference and prototype filters in the pilot optimization model are given. Then, the optimal pilot value is determined under the constraint boundary conditions by using the differentiation analysis method, thereby transforming the constraints of the pilot optimization model into equality constraints. Finally, the optimal pairwise pilot structure applicable to different prototype filters is given, and the pilot structure is used as the pilot design for the pairwise pilot channel estimation method.

[0006] As a further optimization scheme for the optimal paired pilot design method in the filter bank multicarrier communication system described in this invention, the specific steps are as follows:

[0007] Step A: In a filter bank multicarrier communication system, a pilot optimization model A1 is established based on the paired pilot channel estimation method. Model A1 is as follows:

[0008]

[0009] Limited by: -(2 r -1)≤p m ≤2 r -1, m∈[0,M-1]

[0010] Where, p m It is the pilot symbol on subcarrier m; G0(...) is the pilot symbol on p m The function is a variable; M is the number of subcarriers in the system, r is an integer, and r is the logarithm of the modulation order N of the QAM signal, i.e., r = log₄N; I m,0 It is the inherent interference experienced by subcarrier m and the pilot at time 0, I m,0 The expression is:

[0011] I m,0 =p <m+1> (β-α)+p <m>< / m> γ-p <m-1>< / m-1> (β+α)

[0012] Where the subscript <·> indicates a circular index, that is:

[0013]

[0014] Where l is an integer, It is a set of integers, and mod() is the modulo operation;

[0015] The expressions for α, β, and γ are as follows:

[0016]

[0017] Where g[k] is the impulse response coefficient of the prototype filter in the filter bank multicarrier communication system, (·) * The conjugate operation is represented; the system uses N-order QAM modulation, where k is a natural number, e is the natural base, and j is the imaginary unit;

[0018] Step B: Solve for the boundary conditions of the optimal solution of model A1. The specific steps are as follows:

[0019] Step B-1: Simplify model A1 to obtain the inherent disturbance optimization model B1:

[0020]

[0021] Limited by: -(2 r -1)≤p m ≤2 r -1, m∈[0,M-1]

[0022] Step B-2: Calculate G(p0,p1,…,p) m ,…,p M-1 Regarding p m First-order partial derivatives:

[0023]

[0024] Among them, I ＜m-1>,0 I m,0 and I <m+1>,0 The first-order partial derivatives of the three terms are:

[0025]

[0026] We obtain G(p0,p1,…,p) m ,...,p M-1 Regarding p m The expression for the first-order partial derivative is:

[0027]

[0028] Calculate G(p0,p1,...,p) M-1 Regarding p m The second-order partial derivatives are used to obtain the M×M order Hessian matrix H. G The elements in are

[0029]

[0030] The objective function in model B1 is rewritten as follows:

[0031]

[0032] Where G1(p) is a function with p as the variable, p is the pilot symbol vector, p = [p0, p1, ..., p M-1 ] T The symbol T represents the transpose of a vector;

[0033] Step B-3: Simplify the objective function G1(p) to

[0034]

[0035] in, Therefore A function with variables; It is the k0th element pilot symbol vector,

[0036]

[0037] Step B-4: Transform the aforementioned model B1 into an optimized model B2:

[0038]

[0039] Limited by :p m =±(2) r -1), m∈[0,M-1)

[0040] Step C: Determine the optimal paired pilot signals. The specific steps are as follows:

[0041] Step C-1: Let X and Y represent the two values ​​of the optimal paired pilot, i.e., X = 2. r -1、Y=-(2 r -1);

[0042] Step C-2: Calculate β 2 -α 2 -αγ, if (β) 2 -α 2 If -αγ)>0, then the optimal paired pilot arrangement is the repetition of two columns of XXYY; if (β 2 -γ 2 -αγ)≤0, the optimal pairwise pilot arrangement is the repetition of two columns XYXY.

[0043] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0044] The method of this invention first establishes a pilot optimization model based on the pairwise pilot channel estimation method, and gives the expressions for inherent interference and prototype filters in the pilot optimization model. Then, using differentiation analysis, the optimal pilot values ​​are determined under the constraint boundary conditions, thereby transforming the constraints of the pilot optimization model into equality constraints. Finally, the optimal pairwise pilot structure applicable to different prototype filters is given, and this pilot structure is used as the pilot design for the pairwise pilot channel estimation method. Using this method, only two columns of pilot symbols are needed for channel estimation, and different pilot structures are used depending on the type of prototype filter, thus reducing pilot load while adapting to different communication scenarios. Attached Figure Description

[0045] Figure 1 For (β) 2 -α 2 System frame structure when -αγ)>0.

[0046] Figure 2 For (β) 2 -γ 2 System frame structure when -αγ)≤0. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] This invention presents an optimal paired pilot design method for filter bank multi-carrier communication systems. The method, targeting filter bank multi-carrier communication systems, optimizes pilot design by maximizing the noise impact factor in paired pilot channel estimation methods as the objective function, and provides expressions for inherent interference and prototype filters in the pilot optimization model. First, a corresponding mathematical optimization model is established, determining that the optimal pilot design value should exist on the boundary conditions of the constraints, thus transforming the constraints of the pilot optimization model into equality constraints. Based on the boundary conditions of the optimal solution, optimal pilot structures applicable to different prototype filters are proposed. Using this method, only two columns of pilot symbols are needed for channel estimation, and different pilot structures are adopted according to the type of prototype filter, thereby reducing pilot load while adapting to different communication scenarios.

[0049] To better illustrate the method of the present invention, more detailed examples are provided below:

[0050] In a filter bank multicarrier visible light communication system based on pilot-based channel estimation, the number of subcarriers in the system is M, y m,n It is the subcarrier m and the received signal at time n, p m,n H represents the subcarrier m and the pilot signal at time n. m It is the channel frequency response at the m-th subcarrier, I m,n The inherent interference experienced by subcarrier m and the pilot at time n, η m,n This is the noise-related term after demodulation at the receiving end. Where m∈[0,M-1].

[0051] The first step, without considering the impact of noise, is to obtain the received signal for the pairwise pilot channel estimation method.

[0052]

[0053] in, These are the subcarrier m1 and the received signal at time n1. These are the subcarrier m2 and the received signal at time n2.

[0054] The second step is to use... and They represent The real and imaginary parts are used and They represent The real and imaginary parts of the frequency response; λ is the ratio between the imaginary and real parts of the channel frequency response; and yes The real and imaginary parts, and yes The real and imaginary parts of the received signal are then expressed as:

[0055]

[0056] The third step involves linearly combining the real and imaginary parts of the received signal. This is typically done using two consecutive pilot signals that are adjacent in frequency. Therefore, it is assumed that the channel frequency response at the corresponding frequency grid point is constant. It can be obtained

[0057]

[0058] The fourth step is to obtain the ratio λ between the imaginary and real parts of the channel frequency response, which can be expressed as:

[0059]

[0060] Thus, the frequency response of the channel is obtained as

[0061]

[0062] Fifth, considering the impact of noise, in order to improve the accuracy of the paired pilot channel estimation method, the expression needs to be satisfied.

[0063]

[0064] Where μ is the noise impact factor, expressed as:

[0065]

[0066] η1 and η2 are the noise terms at each pilot position, respectively

[0067]

[0068] Considering that the inherent interference is mainly concentrated in the first-order neighborhood, two consecutive columns of pilot symbols should be placed to better utilize the inherent interference. Furthermore, the pilot symbols... and These are considered as two pilot symbols on the same subcarrier, and have the same value, i.e. The absolute value of the noise impact factor μ can be expressed as:

[0069] |μ|=|p m I m,1 -p m I m,0 |=|p m |×|I m,1 -I m,0 |

[0070] Where |·| represents taking the absolute value.

[0071] Step 6: Let α, β, and γ represent the inherent interference coefficients generated by the pilot symbols to adjacent time points and adjacent subcarrier symbols, respectively. Then I m,0 and I m,1 It can be represented as

[0072] I m,0 =(p <m+1> -p <m-1>< / m-1> )β+p m γ-(p <m+1> +p <m-1>< / m-1> )α

[0073] I m,1 =(p <m-1>< / m-1> -p <m++1> )β-p m γ+(p <m+1> +p <m-1>< / m-1> )α

[0074] Therefore, we can obtain I m,0 =-I m,1 Therefore, the absolute value of the noise impact factor μ can be further rewritten as:

[0075] |μ|=2|p m |×|I m,0 |=2|p m |×|I m,1 |

[0076] Step 7: Establish pilot optimization model A1 for the pairwise pilot channel estimation method in the DCO-FBMC system:

[0077]

[0078] Limited by: -(2 r -1)≤p m ≤2 r -1, m∈[0,M-1]

[0079] The design and channel estimation process for the optimal pilot is as follows:

[0080] Step 1: Solve the boundary conditions for the optimal solution of the pilot optimization model A1 of the pairwise pilot channel estimation method in the DCO-FBMC system. The specific steps are as follows:

[0081] Step 1-1: The optimal value of each variable needs to be obtained on the boundary of the constraints, at which point the corresponding value is... This is also the maximum value, which simplifies optimization model A1 to obtain inherent disturbance optimization model B1:

[0082]

[0083] Limited by: -(2 r -1)≤p m ≤2 r -1, m∈[0,M-1]

[0084] The integer r is the logarithm of the modulation order N of the QAM signal, that is, r = log₄N;

[0085] Steps 1-2: G(p0,p1,...,p M-1 For p m The first-order partial derivatives are calculated as follows:

[0086]

[0087] Of these, only I ＜m-1>,0 I m,0 and I <m+1>,0 The three items will be affected by pilot p m The effect of this is shown in the following calculation of its first-order partial derivative:

[0088]

[0089] We can obtain G(p0,p1,...,p) M-1 For p m The expression for the first-order partial derivative is:

[0090]

[0091] Further analysis of G(p0,p1,…,p) M-1 By taking the second-order partial derivative, we can obtain the Hessian matrix H. G The element expression for each line is:

[0092]

[0093] The objective function in optimization model B1 is rewritten as follows:

[0094]

[0095] Where G1(p) is a function with p as the variable, p is the pilot symbol vector, p = [p0, p1, ..., p M-1 ] T The symbol T represents the transpose of the vector; the objective function G1(p) is convex, and the optimal solution p * It will be obtained at the boundary, i.e., p * There exists at least one Make or

[0096] Steps 1-3: The initial objective function with M variables can be simplified to an objective function with M-1 variables:

[0097]

[0098] G3(p3) is a function with p3 as the variable. G3(p3) is also convex, and the optimal solution of the objective function G3(p3) is... It is still obtained at the boundary, that is There exist at least k1∈[0,M-1], (k1≠k0) such that or

[0099] Steps 1-4: Repeat steps 1-3 to simplify the objective function G1(p) to

[0100]

[0101] in, Therefore A function with variables; The k0th element is pilot symbol vector,

[0102] Steps 1-4: The inherent disturbance optimization model B1 can be transformed into B2:

[0103]

[0104] Limited by :p m =±(2) r -1), m∈[0,M-1)

[0105] Step 2: Design pilots based on the boundary conditions of the optimal solution, and provide the optimal paired pilots for different prototype filters. The specific steps are as follows:

[0106] Step 2-1: Let X and Y represent the two possible values ​​of the optimal paired pilot, i.e., X = 2. r -1、Y=-(2 r -1);

[0107] Steps 2-3: Under different paired pilot arrangements, |I m,0 There are four possible values: γ+2β, γ+2α, |γ-2β| and |γ-2α|. In order to design the optimal paired pilots, we choose to retain the larger inherent interferences γ+2β and γ+2α, and discard the smaller inherent interferences |γ-2β| and |γ-2α|. Then the optimal pilot arrangement is a repetition of XYXY or XXYY.

[0108] Step 2-2: Calculate β 2-α 2 -αγ, if (β) 2 -α 2 -αγ)>0, the optimal pairwise pilot arrangement is the repetition of two columns of XXYY. Figure 1 (β) is given 2 -α 2 When -αγ)>0, the system frame structure inserts two pilot columns in the frame header. The pilot structure is a repetition of XXYY, and the second pilot column is the same as the first pilot column. If (β) 2 -γ 2 -αγ)≤0, the optimal paired pilot arrangement is the repetition of two columns XYXY. Figure 2 (β) is given 2 -γ 2 When -αγ)≤0, the system frame structure inserts two columns of pilots in the frame header. The pilot symbol structure is a repetition of XXYY, and the second column of pilots is the same as the first column of pilots.

[0109] Step 3: Obtain the real part of the channel frequency response using the pairwise pilot channel estimation method. and the virtual part and The expression is:

[0110]

[0111] Where λ is the ratio between the imaginary and real parts of the channel frequency response; It is the real part of the subcarrier m and the received signal at time 0. It is the imaginary part of the subcarrier m and the received signal at time 0.

[0112] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. An optimal pair of pilot design method in a filter bank multicarrier communication system, characterized in that, First, based on the pairwise pilot channel estimation method, a pilot optimization model is established, and the expressions for inherent interference and prototype filters in the pilot optimization model are given. Then, using differentiation analysis, the optimal pilot values ​​are determined under the constraint boundary conditions, thus transforming the constraints of the pilot optimization model into equality constraints. Finally, the optimal pairwise pilot structure applicable to different prototype filters is given, and this pilot structure is used as the pilot design for the pairwise pilot channel estimation method. The specific steps are as follows: Step A: In a filter bank multicarrier communication system, a pilot optimization model A1 is established based on the paired pilot channel estimation method. Model A1 is as follows: ； in, In subcarrier Pilot symbols on; Therefore A function with variables; It is the number of subcarriers in the system. The integer is the modulation order of the QAM signal. The logarithm, that is ; It is a subcarrier The inherent interference experienced by the pilot at time 0, The expression is: ； Among them, subscript This represents a circular index, i.e.: ， in, It is an integer. It is a set of integers, and mod() is the modulo operation; , and The expression is as follows: ， ， ； in, These are the impulse response coefficients of the prototype filter in a filter bank multicarrier communication system. Represents conjugate operation; the system uses QAM modulation, It is a natural number. It is the natural base. It is the imaginary unit; Step B: Solve for the boundary conditions of the optimal solution of model A1. The specific steps are as follows: Step B-1: Simplify model A1 to obtain the inherent disturbance optimization model B1: ； Step B-2: Calculation about First-order partial derivatives: ， in, , and The first-order partial derivatives of the three terms are: ， get about The expression for the first-order partial derivative is: ， calculate about The second-order partial derivatives are obtained. Hessian matrix of order The elements in are , The objective function in model B1 is rewritten as follows: ； in, Therefore A function of variables It is the pilot symbol vector. ,symbol Represents the transpose of a vector; Step B-3: Set the objective function Simplified to : ， in, Therefore A function with variables; It is the first element pilot symbol vector, , ; Step B-4: Transform the aforementioned model B1 into an optimized model B2: ； Step C: Determine the optimal paired pilot signals. The specific steps are as follows: Step C-1: Use and These represent the two values ​​of the optimal paired pilot, i.e. , ; Step C-2: Calculation ,if The optimal pairwise pilot arrangement is two columns. The repetition; if The optimal pairwise pilot arrangement is two columns. The repetition.

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