A method for maximum likelihood channel estimation of a visible light communication system

Abstract

The application discloses a maximum likelihood channel estimation method for a visible light communication system, and relates to the technical field of visible light communication, and establishes a channel estimation model for the visible light communication system; in order to meet the constraint that the time domain response of visible light is a real number, the real part and the imaginary part of a frequency domain receiving signal are split and combined into a new matrix; then the maximum likelihood channel estimation model is converted into solving a linear equation set; and then a method based on GS iteration is used to solve the linear equation set, and the output after iteration termination is the maximum likelihood estimation value of the channel time domain response of the visible light communication system. By using the method, the maximum likelihood estimation value of the visible light channel can meet the real number constraint, and the accurate matrix inversion operation is not needed, so that the complexity of channel estimation is reduced.

Description

Technical Field

[0001] This invention relates to the field of visible light communication technology, and in particular to a maximum likelihood channel estimation method for visible light communication systems. Background Technology

[0002] Visible Light Communication (VLC) systems employ intensity modulation / direct detection technology, using light intensity as the signal transmission carrier. This system uses DCO-OFDM (Direct Current Biased Optical OFDM) modulation. Currently, most channel estimation algorithms for VLC systems directly apply channel estimation algorithms from radio frequency communication to VLC systems, without considering the constraint that the time-domain response of the visible light communication channel is a real number. This can lead to incorrect estimations or low estimation accuracy. When the noise in the system follows a Gaussian distribution, the maximum likelihood estimation problem of the visible light channel is equivalent to solving a system of linear equations. The main computational complexity lies in the inversion of an L×L matrix, where L is the maximum length of the time-domain response of the visible light communication channel. Accurate matrix inversion methods, such as the Cholesky decomposition method, have a complexity of O(L×L). 3 The complexity is relatively high. The Gauss-Seidel (GS) iterative method is used to solve the linear equation system, avoiding the high complexity of exact matrix inversion, achieving a complexity of O(L...). 2 ). 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 a maximum likelihood channel estimation method for visible light communication systems. The method of the present invention can not only make the maximum likelihood estimate of the visible light channel satisfy the real number constraint, but also reduce the complexity of channel estimation without the need for precise matrix inversion.

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

[0005] According to the maximum likelihood channel estimation method for visible light communication systems proposed in this invention, a channel estimation model is established for the visible light communication system. This model satisfies the constraint that the visible light time-domain response is a real number by splitting and combining the real and imaginary parts of the frequency-domain received signal into a new matrix. Then, the maximum likelihood channel estimation model is transformed into solving a system of linear equations. Finally, a GS-based iterative method is used to solve the system of linear equations, and the output after the iteration terminates is the maximum likelihood estimate of the channel time-domain response of the visible light communication system.

[0006] As a further optimization of the maximum likelihood channel estimation method for a visible light communication system described in this invention, the specific steps are as follows:

[0007] Step A: Establish the channel estimation model A1 for the visible light communication system:

[0008] Y = XBh + W

[0009] Where Y represents the N×1 dimensional frequency domain received signal, N represents the number of subcarriers; X represents the N×N diagonal matrix formed by the frequency domain transmitted signal; B represents the N×L DFT transform matrix, and L represents the maximum length of the channel time domain response of the visible light communication system. This represents the time-domain response of a visible light communication system. Represents the real number field; W represents N×1 dimensional complex Gaussian white noise;

[0010] Step B: Solve the channel estimation model A1. The specific steps are as follows:

[0011] Step B-1: After splitting and combining the real and imaginary parts of the frequency domain received signal in the channel estimation model A1 into a new matrix, the channel estimation model A1 is transformed into model B1:

[0012]

[0013] Where Re(·) represents the real part operation and Im(·) represents the imaginary part operation;

[0014] Step B-2: For model B1 obtained in step B-1, let... Then model B1 is equivalent to model B2:

[0015]

[0016] in, Θ represents a 2N×1 dimensional real vector; Θ represents a 2N×L order real matrix; Represents a 2N×1 dimensional real vector;

[0017] Step B-3: Solve for the maximum likelihood channel estimate of model B2 to obtain model B3:

[0018]

[0019] in(·) T Indicates transpose. The maximum likelihood estimator of h;

[0020] Step B-4: For model B3 obtained in step B-3, let A = Θ T Θ and A are L×L symmetric positive definite matrices. b is an L×1 dimensional real vector; therefore, solving model B3 is transformed into solving model B4:

[0021] Ah = b

[0022] Step B-5: Solve model B4 using GS iteration, and decompose matrix A:

[0023] A = D + L + L T

[0024] Among them, D, L and L T These represent the diagonal, lower triangular, and upper triangular components of A, respectively; the initial solution h used for iteration. 0 =D -1 b; the output h of the i-th iteration i for:

[0025] h i =(Λ+L) -1 (bL T h i-1 )

[0026] Where i represents the number of iterations;

[0027] Step B-6: When ||h i -h i-1 The iteration terminates when ||2 is less than the threshold ε, yielding the channel time-domain response h = h of the visible light communication system. i , where ·2 represents the 2-norm operation; otherwise, proceed to the next iteration.

[0028] As a further optimization of the maximum likelihood channel estimation method for a visible light communication system described in this invention, the threshold value ε in step B-6 is 10. -3 .

[0029] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0030] This invention addresses visible light communication systems by establishing a channel estimation model. To satisfy the constraint that the visible light time-domain response is real, the real and imaginary parts of the received frequency-domain signal are split and combined into a new matrix. The maximum likelihood channel estimation model is then transformed into solving a system of linear equations. A GS-based iterative method is then used to solve these linear equations, and the output after iteration is complete is the maximum likelihood estimate of the visible light communication system's channel time-domain response. This invention not only ensures that the maximum likelihood estimate of the visible light channel satisfies the real number constraint but also eliminates the need for precise matrix inversion, thus reducing the complexity of channel estimation. Attached Figure Description

[0031] Figure 1 This is a block diagram of a DCO-OFDM visible light communication system. Detailed Implementation

[0032] 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.

[0033] like Figure 1 The DCO-OFDM visible light communication system shown has N OFDM subcarriers, all of which are used for pilot transmission. The transmitter has one LED, and the receiver has one PD.

[0034] The first step is to write the frequency domain transmitted signal into an N×N diagonal matrix form:

[0035]

[0036] Where X has non-zero elements only on its diagonal, and all other elements are 0; X0, X1, ..., X N-1 Transmit data in the frequency domain on N subcarriers;

[0037] The second step is to define h = [h0, h1, ..., h...]. L-1 ] T This represents the channel time-domain response of the visible light communication system, and Where L represents the maximum length of the channel time-domain response of the visible light communication system, (·) T Indicates transpose. Represents the real number domain; the frequency domain response of the visible light channel is H = [H0, H1, ..., H]. N-1 ] T After performing a DFT transformation on h, we obtain:

[0038] H = Bh

[0039] Where B is an N×L order DFT transformation matrix:

[0040]

[0041] The third step is to establish the channel estimation model A1 for the visible light communication system:

[0042] Y = XBh + W

[0043] Where Y represents the N×1 dimensional frequency domain received signal; X represents the N×N order diagonal matrix composed of the frequency domain transmitted signal; B represents the N×L order DFT transform matrix; h represents the channel time domain response of the visible light communication system; W represents N×1 dimensional complex Gaussian white noise; the channel estimation problem is to estimate h from Y;

[0044] The specific steps for solving the channel estimation model A1 are as follows:

[0045] Step 1: After splitting and combining the real and imaginary parts of the frequency domain received signal in the channel estimation model A1 into a new matrix, the channel estimation model A1 is transformed into model B1:

[0046]

[0047] Where Re represents the real part extraction operation and Im represents the imaginary part extraction operation;

[0048] Step 2: For model B1 obtained in Step 1, let... Then model B1 is equivalent to model B2:

[0049]

[0050] in, Θ represents a 2N×1 dimensional real vector; Θ represents a 2N×L order real matrix; Represents a 2N×1 dimensional real vector;

[0051] Step 3: Solve for the maximum likelihood channel estimate of model B2 to obtain model B3:

[0052]

[0053] Step 4: For model B3 obtained in step 3, let A = Θ T Θ is an L×L symmetric positive definite matrix. Given an L×1 dimensional real vector, solving model B3 is transformed into solving model B4:

[0054] Ah = b

[0055] Step 5: Solve model B4 using GS iteration, and decompose matrix A:

[0056] A = D + L + L T

[0057] Where D, L and L T These represent the diagonal, lower triangular, and upper triangular components of A, respectively; the initial solution h used for iteration. 0 =D -1 b; The output of the i-th iteration is:

[0058] h i =(Λ+L) -1 (bL T h i-1 )

[0059] Step 6: When h i -h i-1 Less than the threshold value ε = 10 -3When the iteration terminates, the estimated value of the channel time domain response of visible light communication system 2 is output. Where ‖·2‖ represents the 2-norm operation; otherwise, proceed to the next iteration.

[0060] 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. A maximum likelihood channel estimation method for a visible light communication system, characterized in that, For visible light communication systems, a channel estimation model was established. To satisfy the constraint that the visible light time-domain response is real, the real and imaginary parts of the received frequency-domain signal were split and combined into a new matrix. Then, the maximum likelihood channel estimation model was transformed into solving a system of linear equations. Finally, a GS-based iterative method was used to solve the system of linear equations, and the output after the iteration terminated was the maximum likelihood estimate of the channel time-domain response of the visible light communication system. The specific steps are as follows: Step A: Establish the channel estimation model A1 for the visible light communication system: Y = XBh + W Where Y represents the N×1 dimensional frequency domain received signal, N represents the number of subcarriers; X represents the N×N diagonal matrix formed by the frequency domain transmitted signal; B represents the N×L DFT transform matrix, and L represents the maximum length of the channel time domain response of the visible light communication system. The channel time-domain response of a visible light communication system is represented by R, which represents the real number domain; W represents N×1 dimensional complex Gaussian white noise. Step B: Solve the channel estimation model A1. The specific steps are as follows: Step B-1: After splitting and combining the real and imaginary parts of the frequency domain received signal in the channel estimation model A1 into a new matrix, the channel estimation model A1 is transformed into model B1: Where Re(×) represents the real part operation and Im(×) represents the imaginary part operation; Step B-2: For model B1 obtained in step B-1, let... Then model B1 is equivalent to model B2: in, Θ represents a 2N×1 dimensional real vector; Θ represents a 2N×L order real matrix; Represents a 2N×1 dimensional real vector; Step B-3: Solve for the maximum likelihood channel estimate of model B2 to obtain model B3: in(·) T Indicates transpose. The maximum likelihood estimator of h; Step B-4: For model B3 obtained in step B-3, let A = Θ T Θ and A are L×L symmetric positive definite matrices. b is an L×1 dimensional real vector; therefore, solving model B3 is transformed into solving model B4: Ah = b Step B-5: Solve model B4 using GS iteration, and decompose matrix A: A=D+L+L T Among them, D, L and L T These represent the diagonal, lower triangular, and upper triangular components of A, respectively; the initial solution h used for iteration. 0 =D -1 b; the output h of the i-th iteration i for: h i =(Λ+L) -1 (b-L T h i-1 ) Where i represents the number of iterations; Step B-6: When ||h i -h i-1 The iteration terminates when ||2 is less than the threshold ε, yielding the channel time-domain response h = h of the visible light communication system. i , where ||·||2 represents the 2-norm operation; otherwise, proceed to the next iteration.

2. The maximum likelihood channel estimation method for a visible light communication system according to claim 1, characterized in that, The threshold value ε mentioned in step B-6 is 10. -3 .

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