CN108092714A - Support the ofdm system of color adjustment and the detection of CSK planispheres - Google Patents

Abstract

Support that color adjusts and the ofdm system of CSK planispheres detection, its advantage are the present invention provides a kind of：1) existing PM CCSK OFDM schemes are improved, by transmitting terminal to carrying out color adjustment by the modulated signals of OOFDM, can modifying factor OOFDM modulated process and the optical signal color displacement that generates, it is ensured that the light color needed for presentation user；2) in the case of the STO and without knowledge of noise covariance of CSK ofdm systems, realize the estimation to unknown parameter, and the species for sending CSK planispheres is recognized accurately, and the planisphere based on identification completes symbol demodulation.Therefore, method provided by the invention can be suitable for the scene of multiple target color change.

Description

OFDM system supporting color adjustment and CSK constellation diagram detection

Technical Field

The invention relates to the technical field of visible light communication, in particular to an OFDM system supporting color adjustment and CSK constellation diagram detection.

Background

In recent years, Visible Light Communication (VLC) has been widely studied because of its many advantages, such as efficient widening of spectrum resources, green energy saving, and high security [1 ]. In VLC systems, Color Shift Keying (CSK) is a commonly used modulation technique. The VLC system based on the CSK modulation mode has higher modulation bandwidth, and further can realize high-speed signal transmission [2] [3 ].

Existing studies on CSK are generally conducted from two aspects.

On one hand, from the perspective of the optimal design of the CSK modulation scheme, the CSK constellation diagram can be optimally designed under the constraint of color balance by using a spherical algorithm [4] and an interior point method [5 ]; and a CSK modulation scheme based on a four-color lamp (quad LED, QLED) 6 can also be adopted, so that the transmission reliability of the system is improved.

On the other hand, it is conceivable to design CSK in combination with other modulation schemes. For example, designs may be made in conjunction with Pulse Position Modulation (PPM) to form a more efficient Modulation scheme [7] [8 ]. In addition, the characteristic of Orthogonal Frequency Division Multiplexing (OFDM) to effectively combat Inter Symbol Interference (ISI) can be utilized, and Polar Modulation (PM) complex CSK-OFDM hybrid scheme (PM-CCSK-OFDM) [9] is adopted to achieve high transmission rate. However, in the current PM-CCSK-OFDM scheme, the OFDM-modulated signal generates a color shift, i.e., the color obtained by using the current PM-CCSK-OFDM scheme is different from the color required by the user. Further, in a scene with multiple target color changes, such as a scene of a sporting event, a dance design, and the like related to entertainment, a target color required by a user is constantly changing, which means that a constellation diagram of a transmitter needs to be correspondingly transformed, and the PM-CCSK-OFDM scheme cannot automatically detect and identify the change of the constellation diagram type and adjust a demodulation mode of a receiver, thereby inevitably resulting in a great reduction in system performance. In such a multi-target color case, the existing scheme needs to consume additional bit information to indicate the selected CSK constellation type.

Aiming at the defects of the existing PM-CCSK-OFDM scheme, the invention provides an OFDM system which simultaneously supports color adjustment and CSK constellation diagram detection. The system has the following characteristics:

firstly, at a transmitting end, according to a constellation diagram type selected by a user, color adjustment is performed on a signal modulated by Optical OFDM (Optical OFDM, OOFDM);

secondly, aiming at a scene of multi-target color change, an Automatic Modulation Recognition (AMR) technology is introduced, so that a receiving end can automatically recognize the type of the constellation diagram under the condition that a user replaces the CSK constellation diagram with different target colors.

For the second point described above, AMR algorithms are generally classified into likelihood function [10] based and feature extraction [11] based algorithms. For AMR algorithms based on feature extraction, the recognition performance often depends on the extraction method of the received signal features. According to the features extracted from the signal, a Neural Network (NN) or a Support Vector Machine (SVM) is often used as a classifier to accurately identify the modulation mode. The invention introduces AMR technology based on maximum Expectation (EM) algorithm of likelihood function on the basis of PM-CCSK-OFDM scheme, and identifies CSK constellation diagrams of different target colors under the condition that system STO and receiver noise variance are unknown, thereby ensuring that a receiving end can normally demodulate information in a scene of multi-target color change.

Disclosure of Invention

The invention aims to provide an OFDM system supporting color adjustment and CSK constellation detection.

In order to realize the purpose, the technical scheme is as follows:

a color keying constellation diagram and symbol timing deviation and noise variance joint estimation system, which carries out color adjustment at a transmitting end and CSK constellation diagram detection at a receiving end;

firstly, color adjustment is carried out at a sending end

S1, supposing that the selected p-th constellation diagram isWherein p is more than or equal to 1 and less than or equal to N_type，N_typeRepresenting the number of types of constellation, s_pu＝[s_puR,s_puG,s_puB]^TIs the u-th constellation point, M on the constellation diagram_pThe number of signal points contained in the p-th constellation diagram; defining I E { R, G, B }, wherein R, G, B represents three color channels of CSK modulation; calculating an I-path signal x in the time domain signal subjected to OOFDM operation by utilizing a majority theorem_IProbability density function of

S2, when the p-th constellation diagram is adopted, the corresponding I-path signal x in the time domain signal_IThe optical power of (a) is expressed as:

s3, specifying light intensity P_tarIn the case of (1), let the p-th constellation diagram S_pThe target color ratio is [ Avg_pR,Avg_pG,Avg_pB]^TWhereinThe ratio of the three colors meets the Avg_pR+Avg_pG+Avg_pB1 is ═ 1; then to maintain the original target color fraction, the pth constellation S_pThe time domain signal of (a) needs to be multiplied by a color adjustment factor:

wherein, Avg_pIRepresenting the target color ratio, s, of the p-th constellation diagram I way_puII-way coordinate values representing the u-th constellation point of the p-th constellation diagram;

according to the above operation, R, G, B three color adjustment factors α are obtained_pR、α_pGand alpha_pB(ii) a Further obtaining the p-th constellation diagram S_pThen, the corresponding color adjustment matrix is:

α_p＝diag([α_pR,α_pG,α_pB])

secondly, detecting CSK constellation diagram at receiving end

A) Let the data vector received by the receiver beThe class of the transmission constellation is Z ═ γ_p；

B) Setting an estimation accuracy epsilon of a symbol timing offset in an iterative process_δNoise variance estimation accuracyPrecision epsilon of EM algorithm_emIn the iteration process, the maximum iteration times L of the current estimation value of the symbol timing deviation is obtained by utilizing a Newton method, and the maximum iteration times L of the current estimation value of the noise variance is obtained by utilizing the Newton method_NTSolving the maximum iteration number L of the current estimated value of the noise variance by using a gradient descent method_GRMaximum iteration number q of EM algorithm_maxand adjustment factors lambda, β for the gradient descent algorithm;

C) selecting an initial value of the symbol timing deviation: signal x [ n + delta ] with delta timing offset in time domain]After FFT transformation of OFDM modulation, for k_cFrequency domain signal X k on sub-carrier_c]Will generateMagnitude of phase deviation, i.e. frequency domain signal becomingDue to the symmetry of the frequency domain symbols of the PM-CCSK modulation, i.e.Therefore it has the advantages of

Wherein k is_cA sub-carrier number is indicated,denotes the kth_cPM-CCSK symbols sent on the subcarriers;

thus, it can be seen that the range of symbol timing offsets that can be identified is:in the process of selecting the initial value of STO, every otherSampling symbol timing deviation once in each period, wherein N is_spIs the number of samples in one sampling period; and using the obtained sample value as the initial value of symbol timing deviationIs at a candidate value ofWill have a range ofThe candidate value can be expressed as:

using these candidate values to perform a grid search for the number no of the best candidate value_ptSo that it satisfies:

then the initial value of the symbol timing offset is obtained as

In the above scheme, N_cLength of FFT transform for OFDM modulation; y is_2k-1Representing the kth useful data in the OFDM symbol Y obtained by the receiver; x_pvDenotes the v symbol, H, on the p PM-CCSK constellation_2k-1Representing a channel gain matrix corresponding to the 2k-1 th subcarrier;

D) selecting an initial value of the noise variance: random assignment of noise varianceFurther construct the initial valueSubstituting the formula to calculate the received signal Y from the Z-Y_pProbability of constellation-like:

whereinFurther, it is possible to obtain:

wherein,expressed in the system parameter ofWhen the received signal Y is obtained, the system transmits the Z-Y_pProbability of constellation-like maps;expressed in the system parameter ofIn case of (1), the transmission Z ═ γ_pProbability of constellation-like and received signal being Y;expressed in the system parameter ofThe probability that the received signal is Y; p is a radical of_optA number representing the optimal constellation type selected in the initial value selection process;

the initial value of the noise variance can be updated as:

wherein N is_typeRepresenting the number of CSK constellation diagram types, v is more than or equal to 1 and less than or equal to M_cp， The constellation diagram type selected in the initial value selection process is p_optThe corresponding color adjustment matrix in the case of (2),the constellation diagram type selected in the initial value selection process is p_optThe v-th symbol in the corresponding PM-CCSK constellation in case (a);

E) selectingSetting the initial value of q to 0;

F) at the current parameterCalculating the data received by the receiverProbability from pth constellation:

wherein

G) SelectingAs x_lThe initial value of (a) is set to 0; using Newton's method, as per steps G1) -G4) to solve

G1) Using x_lDetermining the first derivativeWhereinIs a core function of EM algorithm and is defined asRequired in the iterative solution processThe first derivative for δ can be calculated as follows:

wherein:

wherein (·)^HRepresents a conjugate transpose operation, Im (·) represents an imaginary part operation; in the formula for defining the kernel function, Z is an implicit layer variable, and here, the constellation type Z ═ γ is specifically referred to_p(ii) a θ is the system parameter matrix, θ ═ δ, σ²)；

G2) If g | | |_δ||＜ε_δOr L is more than L, stopping the current Newton method to solve the iteration to obtainThe step H) is executed in a loop out of the step G); otherwise step G3) is performed.

G3) Using x_lDetermining the second derivativeIn which what is required during the iterative solution of Newton's methodThe second derivative for δ can be calculated as follows:

whereinRe (-) represents the operation of the extraction part;

G4) order toJuxtaposing l ═ l +1, go to step G1);

H) the following iterative solution is carried out according to steps H1) -H8) by using a Newton method or a gradient descent methodWherein the steps H1) -H5) are solved iteratively by Newton's methodIf the abnormity occurs, the steps H6) -H8) are used for switching and iterating by using a gradient descent method; in iterative solution of noise variance, variable substitution is usedAs an intermediate variable of the noise variance update iteration; let initial step length d of Newton's method_NT,0Infinity, initial step size d of gradient descent method_GR,00; l placing_NTLet iteration start value equal to 0

H1) By usingDetermining the first derivativeWherein required in the iterative solution processThe first derivative for t can be calculated asThe following:

wherein

H2) If it isOr l_NT＞L_NTStopping the current Newton method iteration solution to obtainThe step I) is executed in a loop out of the step H); otherwise, step H3 is executed);

H3) by usingDetermining the second derivativeWherein required in the iterative solution processThe second derivative for t can be calculated as follows:

H4) computing

H5) If it isThen put it in_NT＝l_NT+1, go to step H1); otherwise, jumping out of the Newton method solving cycle, and switching to use the gradient descent method to iteratively solveJuxtaposition of_GRThe initial value of the iterative solution of the gradient descent method is 0Performing step H6);

H6) by usingDetermining first derivative information

H7) If it isOr l_GR＞L_GRThen stop the current cycle to getThe step I) is executed in a loop out of the step H); otherwise, step H8 is executed);

H8) updatingAndjuxtaposition of_GR＝l_GR+1 and step H6 is performed);

I) updatingAnd calculating the difference

J) If it isOr q > q_maxThen, the loop is skipped to obtain the estimated valuePerforming step K); otherwise, setting q to q +1, and executing the step F);

K) according toSolving for I.e. an estimate of the CSK constellation class.

Compared with the prior art, the invention has the beneficial effects that:

1) the method improves the prior PM-CCSK-OFDM scheme, and can correct the color deviation of optical signals generated in the OOFDM modulation process by adjusting the color of signals modulated by the OOFDM at a sending end so as to ensure that the light color required by a user is presented;

2) under the condition that STO and noise variance of the CSK-OFDM system are unknown, estimation of unknown parameters is achieved, the type of a CSK constellation diagram is accurately identified, and symbol demodulation is completed based on the identified constellation diagram. Therefore, the method provided by the invention can be suitable for scenes with multiple target color changes.

Drawings

FIG. 1 is a schematic diagram of a system provided by the present invention.

Fig. 2 is a schematic flow chart of the system for detecting the CSK constellation diagram provided by the present invention.

Fig. 3 is a comparison chart of probability distribution of three-color light intensity ratios before and after color adjustment (taking the 5 th constellation diagram as an example).

Fig. 4 is a diagram illustrating the recognition rate of the CSK constellation diagram.

FIG. 5 is a plot of the mean square error performance of the STO estimate.

Figure 6 is a plot of the mean square error performance of the noise variance estimation.

FIG. 7 is a system performance pairSensitivity analysis chart of initial value.

Fig. 8 is a graph comparing system BLER performance.

Detailed Description

The drawings are for illustrative purposes only and are not to be construed as limiting the patent;

the invention is further illustrated below with reference to the figures and examples.

Example 1

Fig. 1 is a schematic diagram of an OFDM system supporting color adjustment and CSK constellation detection provided in the present invention, wherein a gray module is the invention of the present application. The transmitter of the system provided by the invention can use the N pre-designated in the system for each OFDM symbol based on a certain strategy_typeOne of the CSK constellations performs CSK modulation. Therefore, it is required to be able to accurately identify the type of the CSK constellation at the receiving end.

The system provided by the invention mainly comprises two processes, namely a color adjustment process and a CSK constellation diagram detection process.

Firstly, color adjustment is carried out at a sending end

After the OOFDM operation, the color balance of the visible light signal will change, and it needs to go through the design adjustment step of the present invention to restore it to the preset desired color. I ∈ { R, G, B } is defined, where R, G, B represents the three color channels of the CSK modulation. The process of color adjustment is set forth below.

First, the Probability Density Function (PDF) of the time domain signal needs to be calculated according to the selected OOFDM scheme. If ACO-OFDM is adopted, the p-th constellation diagram is supposed to be transmittedWherein p is more than or equal to 1 and less than or equal to N_type，s_pu＝[s_puR,s_puG,s_puB]^TIs the u-th constellation point, M, on the original constellation diagram_pFor the number of signal points included in the p-th constellation diagram, the probability density function of the time domain signal is [12 ] obtained by utilizing the logarithm theorem][13]：

Where u (w) and δ (w) are a step function and an impulse function, respectively, σ_pIFor cutting off signal x by way of I_pIAnd satisfies the following criteria:wherein X_pIIs a PM-CCSK symbol X_pI way data of (i.e. X)_pI∈{±s_pmI±j·s_pnI|1≤m,n≤M_pTherefore, the optical power of the I-path ACO-OFDM signal is:

at a given light intensity P_tarIn the case of (1), a p-th constellation S selected in advance is set_pThe target color ratio is [ Avg_pR,Avg_pG,Avg_pB]^TWhereinThe ratio of the three colors satisfies

Avg_pR+Avg_pG+Avg_pB1. Then to maintain the original target color ratio, the ACO-OFDM time domain signal needs to be multiplied by a color adjustment factor:

according to the above operation, R, G, B three color adjustment factors α can be obtained_pR、α_pGand alpha_pB. Further, the p-th constellation S in the selected transmission can be obtained_pWhen the corresponding color adjustment matrix is

α_p＝diag([α_pR,α_pG,α_pB])

Second, CSK constellation diagram detection process based on EM algorithm

For a CSK-OFDM system in which a constellation is not known at a receiver, in a probability-based constellation identification process, a likelihood function needs to be constructed based on information of symbol timing deviation and receiver noise. In addition, the performance of system demodulation also depends on the accurate acquisition of STO. In OFDM systems, Particle Filter (PF) [14 ] is typically used][15]To obtain the STO parameter δ (representing the deviation of δ sampling intervals) and to Estimate the (CESE) based on a Complex Essential Supremum Estimate [16][17]To estimate the noise variance σ². However, the STO estimation scheme based on PF is prone to fall into degradation problem and waste system computing power due to the self-disadvantage of the algorithm; the noise variance estimation scheme based on CESE inevitably reduces the transmission efficiency of the system because the estimation is performed by using the sparsity of the OFDM signal. Therefore, the invention provides a CSK constellation diagram detection method based on an EM algorithm, which realizes the estimation of STO and noise varianceAnd completes the detection of constellation diagram and symbol demodulation at the same time. And the existing method [11]]Compared with the prior art, the method has the advantages that the recognition rate is obviously improved, and the problems of constellation diagram recognition and symbol demodulation under the condition that system parameters are unknown can be effectively solved.

As shown in fig. 2, the overall processing flow of the CSK constellation detection process based on the EM algorithm proposed by the present invention is as follows:

A) let the data vector received by the receiver beThe class of the transmission constellation is Z ═ γ_p；

B) Setting an estimation accuracy epsilon of a symbol timing offset in an iterative process_δNoise variance estimation accuracyPrecision epsilon of EM algorithm_emIn the iteration process, the maximum iteration times L of the current estimation value of the symbol timing deviation is obtained by utilizing a Newton method, and the maximum iteration times L of the current estimation value of the noise variance is obtained by utilizing the Newton method_NTSolving the maximum iteration number L of the current estimated value of the noise variance by using a gradient descent method_GRMaximum iteration number q of EM algorithm_maxand adjustment factors lambda, β for the gradient descent algorithm;

C) selecting an initial value of the symbol timing deviation: signal x [ n + delta ] with delta timing offset in time domain]After FFT transformation of OFDM modulation, for k_cFrequency domain signal X k on sub-carrier_c]Will generateMagnitude of phase deviation, i.e. frequency domain signal becomingDue to the symmetry of the frequency domain symbols of the PM-CCSK modulation, i.e.Therefore it has the advantages of

Wherein k is_cA sub-carrier number is indicated,denotes the kth_cPM-CCSK symbols sent on the subcarriers;

thus, it can be seen that the range of symbol timing offsets that can be identified is:in the process of selecting the initial value of STO, every otherSampling symbol timing deviation once in each period, wherein N is_spIs the number of samples in one sampling period; and using the obtained sample value as the initial value of symbol timing deviationIs at a candidate value ofWill have a range ofThe candidate value can be expressed as:

using these candidate values to perform a grid search for the number no of the best candidate value_ptSo that it satisfies:

then the initial value of the symbol timing offset is obtained as

In the above scheme, N_cLength of FFT transform for OFDM modulation; y is_2k-1Representing the kth useful data in the OFDM symbol Y obtained by the receiver; x_pvDenotes the v symbol, H, on the p PM-CCSK constellation_2k-1Representing a channel gain matrix corresponding to the 2k-1 th subcarrier;

D) selecting an initial value of the noise variance: random assignment of noise varianceFurther construct the initial valueSubstituting the formula to calculate the received signal Y from the Z-Y_pProbability of constellation-like:

whereinFurther, it is possible to obtain:

wherein,expressed in the system parameter ofWhen the received signal Y is obtained, the system transmits the Z-Y_pProbability of constellation-like maps;expressed in the system parameter ofIn case of (1), the transmission Z ═ γ_pProbability of constellation-like and received signal being Y;expressed in the system parameter ofThe probability that the received signal is Y; p is a radical of_optA number representing the optimal constellation type selected in the initial value selection process;

the initial value of the noise variance can be updated as:

wherein N is_typeRepresenting the number of CSK constellation diagram types, v is more than or equal to 1 and less than or equal to M_cp， The constellation diagram type selected in the initial value selection process is p_optThe corresponding color adjustment matrix in the case of (2),the constellation diagram type selected in the initial value selection process is p_optThe v-th symbol in the corresponding PM-CCSK constellation in case (a);

E) selectingSetting the initial value of q to 0;

F) at the current parameterCalculating the data received by the receiverProbability from pth constellation:

wherein

G) SelectingAs x_lThe initial value of (a) is set to 0; using Newton's method, as per steps G1) -G4) to solve

G1) Using x_lDetermining the first derivativeWhereinIs a core function of EM algorithm and is defined asRequired in the iterative solution processThe first derivative for δ can be calculated as follows:

wherein:

wherein (·)^HRepresents a conjugate transpose operation, Im (·) represents an imaginary part operation; in the formula for defining the kernel function, Z is an implicit layer variable, and here, the constellation type Z ═ γ is specifically referred to_p(ii) a θ is the system parameter matrix, θ ═ δ, σ²)；

G2) If g | | |_δ||＜ε_δOr L is more than L, stopping the current Newton method to solve the iteration to obtainThe step H) is executed in a loop out of the step G); otherwise step G3) is performed.

G3) Using x_lDetermining the second derivativeIn which what is required during the iterative solution of Newton's methodThe second derivative for δ can be calculated as follows:

whereinRe (-) represents the operation of the extraction part;

G4) order toJuxtaposing l ═ l +1, go to step G1);

H) the following iterative solution is carried out according to steps H1) -H8) by using a Newton method or a gradient descent methodWherein the steps H1) -H5) are solved iteratively by Newton's methodIf the abnormity occurs, the steps H6) -H8) are used for switching and iterating by using a gradient descent method; in iterative solution of noise variance, variable substitution is usedAs an intermediate variable of the noise variance update iteration; let initial step length d of Newton's method_NT,0Infinity, initial step size d of gradient descent method_GR,00; l placing_NTLet iteration start value equal to 0

H1) By usingDetermining the first derivativeWherein required in the iterative solution processThe first derivative for t can be calculated as follows:

wherein

H2) If it isOr l_NT＞L_NTStopping the current Newton method iteration solution to obtainThe step I) is executed in a loop out of the step H); otherwise, step H3 is executed);

H3) by usingDetermining the second derivativeWherein required in the iterative solution processThe second derivative for t can be calculated as follows:

H4) computing

H5) If it isThen put it in_NT＝l_NT+1, go to step H1); otherwise, jumping out of the Newton method solution cycle,switching uses gradient descent method iterative solutionJuxtaposition of_GRThe initial value of the iterative solution of the gradient descent method is 0Performing step H6);

H6) by usingDetermining first derivative information

H7) If it isOr l_GR＞L_GRThen stop the current cycle to getThe step I) is executed in a loop out of the step H); otherwise, step H8 is executed);

H8) updatingAndjuxtaposition of_GR＝l_GR+1 and step H6 is performed);

I) updatingAnd calculating the difference

J) If it isOr q > q_maxThen, the loop is skipped to obtain the estimated valuePerforming step K); otherwise, setting q to q +1, and executing the step F);

K) according toSolving for I.e. an estimate of the CSK constellation class.

After the algorithm flow is executed, the estimated value of the CSK constellation diagram category selected by the transmitter can be obtained, and then the CSK symbol is demodulated according to the constellation diagram, and finally the estimated value of the original sending information can be obtained.

Example 2

To more fully illustrate the benefits of the present invention, the following simulation analysis and results of one embodiment further illustrate the effectiveness and advancement of the present invention.

First, according to document [5]]The method provided selects N_typeAs alternative constellation schemes to be transmitted, 5 8-CSK constellations with different target colors are used, and their constellation point coordinates and target color coordinates are listed in table 1. On the other hand, ACO-OFDM is selected as the OOFDM scheme of this embodiment, and the number of subcarriers is set to N_c64. The simulation system selects a typical indoor room model, the dimension of the room is 4m multiplied by 3m, the midpoint of the room is a coordinate origin, and the position coordinates of the user terminal are assumed to be [0m,0m,0.85m ]]. The VLC channel model uses classical lightLine tracking model [18 ]]The time resolution is set to Δ_tThe maximum number of reflections is set to 3 for 4 ns. Further, assume that the systematic symbol timing offset STO is atIs randomly selected. EM algorithm parameter settingε_em＝(10^-5,10^-5)；L＝1，L_NT＝L_GR＝5，q_max＝10；λ＝β＝0.5；

Table 1: the constellation point coordinates and target color coordinates of the 5 constellation diagrams used in this embodiment

According to the above simulation parameter settings, fig. 3 shows the probability distribution contrast of the light intensity ratios of R, G, B before and after color adjustment, by taking the class 5 constellation diagram as an example, where the black vertical line represents the light intensity ratios of R, G, B three colors under the set target color condition. As can be seen from FIG. 3, after the PM-CCSK signal based on the constellation diagram of class 5 is subjected to ACO-OFDM modulation, the colors presented by the signal are biased and distributed in [0.34,0.19,0.47 ]]^TNearby. As can be seen from FIG. 3, after color adjustment, the color of the signal is corrected and distributed over the target colors [0.32,0.16,0.52 ]]^TAnd (4) surrounding.

In addition, the method provided by the invention can be used for obtaining the CSK constellation diagram recognition rate curve shown in fig. 4. The present embodiment also provides a traditional neural network-based recognition scheme [11](NN) for comparison. The recognition rate is defined asWherein N is_sFor transmitting the total number of OFDM symbols, and N_rIt means that the number of OFDM symbols of the selected CSK constellation type is successfully and accurately identified. The experimental result of fig. 4 shows that, compared with the recognition scheme based on the neural network, the CSK constellation detection algorithm based on the EM algorithm provided by the method of the present invention has superior performance. For example, in the case of signal-to-noise ratio exceedingAnd the recognition rate can reach 100 percent.

FIG. 5 shows the Mean Square Error (MSE) performance of the STO estimate. It can be seen from fig. 5 that the MSE of the STO estimation approaches zero with increasing signal-to-noise ratio, i.e. the STO estimation tends to be accurate with increasing signal-to-noise ratio, and the estimation performance is better than the conventional STO estimation scheme based on PF, where the parameter N in fig. 5 represents the number of particles.

Fig. 6 shows the comparison result of the MSE performance of the method provided by the present invention and the conventional CESE-based noise variance estimation scheme. The noise variance estimation scheme based on CESE estimates by using the sparsity of the OFDM signal, and does not need the signal model information of the transmission signal, i.e., the performance of the estimation is related to the sparsity of the signal itself, and is not related to the constellation type of the transmission signal and the size of the system STO. The sparsity of the OFDM signal can be characterized by a parameter d, representing the usage of the OFDM subcarriers. As can be seen from fig. 6, the proposed scheme provides a better MSE performance than the conventional CESE noise variance estimation method.

FIG. 7 then analyzesThe influence of the initial value of (A) on the system performance respectively shows that the system is different when the signal-to-noise ratio is 5dB, 10dB and 15dBVariation of constellation recognition rate, STO estimation performance, noise variance estimation performance and EM algorithm convergence speed under valueAnd (4) transforming. As can be seen from FIG. 7, the system performance is pairedThe values of (a) are not sensitive. Therefore, the scheme pairThe initial value of (A) is selected without special requirements, and has better robustness.

The invention applies the constellation recognition technology based on the EM algorithm to the CSK-OFDM system with multiple target colors, so as to realize accurate estimation of the system STO and the noise variance and automatically detect the CSK constellation type selected by the user, thereby finally completing the demodulation of the information symbol. Fig. 8 shows a Block Error Rate (BLER) performance curve of the CSK-OFDM system using the scheme provided by the present invention, and is compared with other schemes. In the figure delta is the true value of STO,representing an estimate of STO. Wherein:

1) the curve referring to the system PM-CCSK-OFDM is the performance assuming that the constellation class and STO are known to the receiver, and thus can be considered the system performance that can be achieved in an ideal situation.

2) Furthermore, because the constellation identification technique based on neural networks cannot estimate STO while identifying the constellation type, the performance curve of the system based on neural networks shown in the triangular legend in fig. 8 is obtained assuming that STO is known.

3) In comparison, a BLER curve of a constellation diagram detection system based on a neural network when STO values have errors of 0.5% and 1% is also given.

According to the above simulation parameter settings, it can be seen from fig. 8 that the scheme based on the present invention can achieve the system BLER performance close to the ideal case.

Reference to the literature

[1].T.Komine and M.Nakagawa,“Fundamental analysis for visible-lightcommunication system using LED lights,”IEEE transactions on ConsumerElectronics.,vol.50,no.1,pp.100-107,Feb.2014.

[2].E.Monteiro and S.Hranilovic,“Design and implementation of color-shift keying for visible light communications,”Journal of LightwaveTechnology,vol.32,no.10,pp.2053-2060,May 15,2014.

[3].IEEE Standard for Local and Metropolitan Area Networks—Part15.7:Short-Range Wireless Optical Communication Using Visible Light,IEEEStandard 802.15.7-2011,Sep.2011,pp.1-309.

[4].R.J.Drost and B.M.Sadler,“Constellation design for color-shiftkeying using billiards algorithms,”GLOBECOM Workshops,2010,pp.980-984.

[5].E.Monteiro and S.Hranilovic,“Constellation design for color-shiftkeying using interior point methods,”Globecom Workshops,2012,pp.1224-1228.

[6].R.Singh,T.O’Farrell and J.P.R.David,“An enhanced color shiftkeying modulation scheme for high-speed wireless visible lightcommunications,”Journal of Lightwave Technology,vol.32,no.14,pp.2582-2592,2014.

[7].J.M.Luna-Rivera,R.Perez-Jimenez,V.Guerra-Yanez and F.A.Delgado-Rajo,“Combined CSK and pulse position modulation scheme for indoor visiblelight communications,”Electronics Letters,vol.50,no.10,pp.762-764,2014.

[8].F.A.D.Rajo,V.Guerra,J.A.R.Borges,J.R.Torres and R.Perez-Jimenez,“Color shift keying communication system with a modified PPM synchronizationscheme,”IEEE Photonics Technology Letters,vol.26,no.18,pp.1851-1854,Sep.2014.

[9].Y.Chen,M.Jiang,L.Zhang and X.Chen,“Polarity Modulation ComplexColour Shift Keying for OFDM-based Visible Light Communication,”inProceedings of the 2017 IEEE/CIC International Conference on Communicationsin China(ICCC 2017),Qingdao,China,Oct.2017,pp.22-24.

[10].Bayer and M.“Joint space time block code and modulationclassification for MIMO systems,”IEEE Wireless Communications Letters,vol.6,no.1,pp.62-65,2017.

[11].X.Zhu,Y.Lin and Z.Dou,“Automatic recognition of communicationsignal modulation based on neural network,”Electronic Information andCommunication Technology(ICEICT)IEEE International Conference on,Harbin,China,Mar.2016,pp.223-226.

[12].L.Chen,B.Krongold and J.Evans,“Performance analysis for opticalOFDM transmission in short-range IM/DD systems,”Journal of LightwaveTechnology,vol.30,no.7,pp.974-983,Feb.2012.

[13].X.Li,R.Mardling and J.Armstrong,“Channel capacity of IM/DDoptical communication systems and of ACO-OFDM,”in Proc.IEEE Int.Conf.Commun.(IEEE ICC),Glasgow,U.K.,Jun.2007,pp.2128-2133.

[14].P.M.Djuric,I.H.Kotecha,J.Zhang,Y.Huang,T.Ghirmai,M.F.Bugallo andJ.Miguez,“Particle filtering,”IEEE Signal Processing Magazine,vol.20,no.5,pp.19-38,Sep.2003.

[15].H.Huang,C.Yin and G.Yue,“Symbol Timing Estimation for OFDMSystems Using Particle Filtering,”Anti-counterfeiting,Security,Identification,IEEE International Workshop on,Xiamen,China,Apr.2007,pp.386-389.

[16].F.X.Socheleau,D.Pastor,A.Aissa-El-Bey,and S.Houcke,“Blind noisevariance estimation for OFDMA signals,”in Proc.IEEE Int.Confe.Acoust.,Speech,Signal Process.(ICASSP),Taipei,Taiwan,May 2009,pp.2581-2584.

[17].D.Pastor and A.Amehraye,“Algorithms and Applications forEstimating the Standard Deviation of AWGN when Observations are not Signal-Free,”Journal of Computers,vol.2,no.7,pp.1-10,Sept.2007.

[18].J.R.Barry,J.M.Kahn,W.J.Krause,E.A.Lee,and D.G.Messerschmitt,“Simulation of Multipath Impulse Response for Indoor Wireless OpticalChannels,”IEEE Journal on Selected Areas in Communications,vol.11,no.3,pp.367-379,Apr.1993.

It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (1)

1. The OFDM system supporting color adjustment and CSK constellation diagram detection is characterized in that: carrying out color adjustment at a transmitting end and CSK constellation diagram detection at a receiving end;

firstly, color adjustment is carried out at a sending end

S1, supposing that the selected p-th constellation diagram isWherein p is more than or equal to 1 and less than or equal to N_type，N_typeRepresenting the number of types of constellation, s_pu＝[s_puR,s_puG,s_puB]^TIs the u-th constellation point, M on the constellation diagram_pThe number of signal points contained in the p-th constellation diagram; defining I E { R, G, B }, wherein R, G, B represents three color channels of CSK modulation; calculating an I-path signal x in the time domain signal subjected to OOFDM operation by utilizing a majority theorem_IProbability density function of

S2, when the p-th constellation diagram is adopted, the corresponding I-path signal x in the time domain signal_IThe optical power of (a) is expressed as:

<mrow> <msub> <mi>P</mi> <mi>I</mi> </msub> <mo>=</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>I</mi> </msub> <mo>&amp;rsqb;</mo> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>&amp;infin;</mi> </msubsup> <mi>w</mi> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>x</mi> <mi>I</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>w</mi> </mrow>

s3, specifying light intensity P_tarIn the case of (1), let the p-th constellation diagram S_pThe target color ratio is [ Avg_pR,Avg_pG,Avg_pB]^TWhereinThe ratio of the three colors meets the Avg_pR+Avg_pG+Avg_pB1 is ═ 1; then to maintain the original target color fraction, the pth constellation S_pThe time domain signal of (a) needs to be multiplied by a color adjustment factor:

<mrow> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>p</mi> <mi>I</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>a</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>Avg</mi> <mrow> <mi>p</mi> <mi>I</mi> </mrow> </msub> </mrow> <msub> <mi>P</mi> <mi>I</mi> </msub> </mfrac> </mrow>

wherein, Avg_pIRepresenting the target color ratio, s, of the p-th constellation diagram I way_puII-way coordinate values representing the u-th constellation point of the p-th constellation diagram;

according to the above operation, R, G, B three color adjustment factors α are obtained_pR、α_pGand alpha_pB(ii) a Further obtaining the p-th constellation diagram S_pThen, the corresponding color adjustment matrix is:

α_p＝diag([α_pR,α_pG,α_pB])

secondly, detecting CSK constellation diagram at receiving end

A) Let Y be [ Y ] as the data vector received by the receiver₀,Y₁,...,Y_kc,...,Y_Nc-1]The class of the transmission constellation is Z ═ γ_p；

B) Setting an estimation accuracy epsilon of a symbol timing offset in an iterative process_δNoise variance estimation accuracyPrecision epsilon of EM algorithm_emIn the iteration process, the maximum iteration times L of the current estimation value of the symbol timing deviation is obtained by utilizing a Newton method, and the maximum iteration times L of the current estimation value of the noise variance is obtained by utilizing the Newton method_NTSolving the maximum iteration number L of the current estimated value of the noise variance by using a gradient descent method_GRMaximum iteration number q of EM algorithm_maxand adjustment factors lambda, β for the gradient descent algorithm;

C) selecting an initial value of the symbol timing deviation: signal x [ n + delta ] with delta timing offset in time domain]After FFT transformation of OFDM modulation, for k_cFrequency domain signal X k on sub-carrier_c]Will generateMagnitude of phase deviation, i.e. frequency domain signal becomingDue to the symmetry of the frequency domain symbols of the PM-CCSK modulation, i.e.Therefore it has the advantages of

<mrow> <msup> <mi>e</mi> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;k</mi> <mi>c</mi> </msub> <mi>&amp;delta;</mi> </mrow> <msub> <mi>N</mi> <mi>c</mi> </msub> </mfrac> </msup> <msub> <mi>X</mi> <msub> <mi>k</mi> <mi>c</mi> </msub> </msub> <mo>=</mo> <msup> <mi>e</mi> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;k</mi> <mi>c</mi> </msub> <mi>&amp;delta;</mi> </mrow> <msub> <mi>N</mi> <mi>c</mi> </msub> </mfrac> </msup> <mo>&amp;CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <msub> <mi>k</mi> <mi>c</mi> </msub> <mi>&amp;pi;</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> <msub> <mi>X</mi> <msub> <mi>k</mi> <mi>c</mi> </msub> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;k</mi> <mi>c</mi> </msub> </mrow> <msub> <mi>N</mi> <mi>c</mi> </msub> </mfrac> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>+</mo> <mfrac> <msub> <mi>N</mi> <mi>c</mi> </msub> <mn>4</mn> </mfrac> <mo>)</mo> </mrow> </mrow> </msup> <msub> <mi>X</mi> <msub> <mi>k</mi> <mi>c</mi> </msub> </msub> </mrow>

Wherein k is_cA sub-carrier number is indicated,denotes the kth_cPM-CCSK symbols sent on the subcarriers;

thus, it can be seen that the range of symbol timing offsets that can be identified is:in the process of selecting the initial value of STO, every otherSampling symbol timing deviation once in each period, wherein N is_spIs the number of samples in one sampling period; and using the obtained sample value as the initial value of symbol timing deviationIs at a candidate value ofWill have a range ofThe candidate value can be expressed as:

<mrow> <msub> <mi>&amp;delta;</mi> <mi>n</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mrow> <mi>s</mi> <mi>p</mi> </mrow> </msub> </mfrac> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mfrac> <mrow> <msub> <mi>N</mi> <mrow> <mi>s</mi> <mi>p</mi> </mrow> </msub> <msub> <mi>N</mi> <mi>c</mi> </msub> </mrow> <mn>4</mn> </mfrac> </mrow>

using these candidate values to perform a grid search for the number no of the best candidate value_ptSo that it satisfies:

<mrow> <msub> <mi>n</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <munder> <mrow> <mi>arg</mi> <mi>min</mi> </mrow> <mi>n</mi> </munder> <mrow> <mo>(</mo> <munder> <mi>min</mi> <mi>p</mi> </munder> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mfrac> <msub> <mi>N</mi> <mi>c</mi> </msub> <mn>4</mn> </mfrac> </munderover> <munder> <mi>min</mi> <mi>v</mi> </munder> <mo>|</mo> <mo>|</mo> <msub> <mi>Y</mi> <mrow> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;&amp;delta;</mi> <mi>n</mi> </msub> </mrow> <msub> <mi>N</mi> <mi>c</mi> </msub> </mfrac> </mrow> </msup> <msub> <mi>H</mi> <mrow> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>&amp;alpha;</mi> <mi>p</mi> </msub> <msub> <mi>X</mi> <mrow> <mi>p</mi> <mi>v</mi> </mrow> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

then the initial value of the symbol timing offset is obtained as

In the above scheme, N_cLength of FFT transform for OFDM modulation; y is_2k-1Representing the kth useful data in the OFDM symbol Y obtained by the receiver; x_pvDenotes the v symbol, H, on the p PM-CCSK constellation_2k-1Representing a channel gain matrix corresponding to the 2k-1 th subcarrier;

D) selecting an initial value of the noise variance: random assignment of noise varianceFurther construct the initial valueSubstituting the formula to calculate the received signal Y from the Z-Y_pProbability of constellation-like:

whereinFurther, it is possible to obtain:

<mrow> <msub> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <munder> <mrow> <mi>arg</mi> <mi>max</mi> </mrow> <mi>p</mi> </munder> <mi>P</mi> <mrow> <mo>(</mo> <mi>Z</mi> <mo>=</mo> <msub> <mi>&amp;gamma;</mi> <mi>p</mi> </msub> <mo>|</mo> <mi>Y</mi> <mo>,</mo> <msup> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow>

wherein,expressed in the system parameter ofWhen the received signal Y is obtained, the system transmits the Z-Y_pProbability of constellation-like maps;expressed in the system parameter ofIn case of (1), the transmission Z ═ γ_pProbability of constellation-like and received signal being Y;expressed in the system parameter ofThe probability that the received signal is Y; p is a radical of_optA number representing the optimal constellation type selected in the initial value selection process;

the initial value of the noise variance can be updated as:

<mrow> <msup> <mover> <mi>&amp;sigma;</mi> <mo>^</mo> </mover> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mrow> </msup> <mo>=</mo> <mfrac> <mn>4</mn> <msub> <mi>N</mi> <mi>c</mi> </msub> </mfrac> <mrow> <mo>(</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mfrac> <msub> <mi>N</mi> <mi>c</mi> </msub> <mn>4</mn> </mfrac> </munderover> <munder> <mi>min</mi> <mi>v</mi> </munder> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>|</mo> <mo>|</mo> <msub> <mi>Y</mi> <mrow> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <msup> <mover> <mi>&amp;delta;</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msup> </mrow> <msub> <mi>N</mi> <mi>c</mi> </msub> </mfrac> </mrow> </msup> <msub> <mi>H</mi> <mrow> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>&amp;alpha;</mi> <msub> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </msub> <msub> <mi>X</mi> <mrow> <msub> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mi>v</mi> </mrow> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

wherein N is_typeRepresenting the number of CSK constellation diagram types, v is more than or equal to 1 and less than or equal to M_cp， The constellation diagram type selected in the initial value selection process is p_optThe corresponding color adjustment matrix in the case of (2),the constellation diagram type selected in the initial value selection process is p_optThe v-th symbol in the corresponding PM-CCSK constellation in case (a);

E) selectingSetting the initial value of q to 0;

F) at the current parameterCalculating the data received by the receiverProbability from pth constellation:

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mi>P</mi> <mrow> <mo>(</mo> <mi>Z</mi> <mo>=</mo> <msub> <mi>&amp;gamma;</mi> <mi>p</mi> </msub> <mo>|</mo> <mi>Y</mi> <mo>,</mo> <msup> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>Y</mi> <mo>,</mo> <mi>Z</mi> <mo>=</mo> <msub> <mi>&amp;gamma;</mi> <mi>p</mi> </msub> <mo>|</mo> <msup> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>Y</mi> <mo>|</mo> <msup> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mrow> <mfrac> <mn>1</mn> <msub> <mi>N</mi> <mrow> <mi>t</mi> <mi>y</mi> <mi>p</mi> <mi>e</mi> </mrow> </msub> </mfrac> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mfrac> <msub> <mi>N</mi> <mi>c</mi> </msub> <mn>4</mn> </mfrac> </munderover> <mfrac> <mn>1</mn> <msub> <mi>M</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>v</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>M</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> </munderover> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;pi;</mi> <msup> <mover> <mi>&amp;sigma;</mi> <mo>^</mo> </mover> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </msup> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mfrac> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mi>&amp;zeta;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>p</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mrow> <mi>t</mi> <mi>y</mi> <mi>p</mi> <mi>e</mi> </mrow> </msub> </munderover> <mfrac> <mn>1</mn> <msub> <mi>N</mi> <mrow> <mi>t</mi> <mi>y</mi> <mi>p</mi> <mi>e</mi> </mrow> </msub> </mfrac> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mfrac> <msub> <mi>N</mi> <mi>c</mi> </msub> <mn>4</mn> </mfrac> </munderover> <mfrac> <mn>1</mn> <msub> <mi>M</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>v</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>M</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> </munderover> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;pi;</mi> <msup> <mover> <mi>&amp;sigma;</mi> <mo>^</mo> </mover> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </mrow> </msup> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mfrac> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mi>&amp;zeta;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>p</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

wherein

G) SelectingAs x_lThe initial value of (a) is set to 0; using Newton's method, as per steps G1) -G4) to solve

G1) Using x_lDetermining the first derivativeWhereinIs a core function of EM algorithm and is defined asRequired in the iterative solution processThe first derivative for δ can be calculated as follows:

wherein:

<mrow> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>p</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mover> <mi>&amp;sigma;</mi> <mo>^</mo> </mover> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </mrow> </msup> <msub> <mi>N</mi> <mi>c</mi> </msub> </mrow> </mfrac> <mi>Im</mi> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>&amp;delta;</mi> </mrow> <msub> <mi>N</mi> <mi>c</mi> </msub> </mfrac> </mrow> </msup> <msubsup> <mi>Y</mi> <mrow> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>H</mi> </msubsup> <msub> <mi>H</mi> <mrow> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>&amp;alpha;</mi> <mi>p</mi> </msub> <msub> <mi>X</mi> <mrow> <mi>p</mi> <mi>v</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>

wherein (·)^HRepresents a conjugate transpose operation, Im (·) represents an imaginary part operation; in the formula for defining the kernel function, Z is an implicit layer variable, and here, the constellation type Z ═ γ is specifically referred to_p(ii) a θ is the system parameter matrix, θ ═ δ, σ²)；

G2) If g | | |_δ||＜ε_δOr L is more than L, stopping the current Newton method to solve the iteration to obtainThe step H) is executed in a loop out of the step G); otherwise step G3) is performed.

G3) Using x_lDetermining the second derivativeIn which what is required during the iterative solution of Newton's methodThe second derivative for δ can be calculated as follows:

whereinRe (-) represents the operation of the extraction part;

G4) order toJuxtaposing l ═ l +1, go to step G1);

H) the following iterative solution is carried out according to steps H1) -H8) by using a Newton method or a gradient descent methodWherein the steps H1) -H5) are solved iteratively by Newton's methodIf the abnormity occurs, the steps H6) -H8) are used for switching and iterating by using a gradient descent method; in iterative solution of noise variance, variable substitution is usedAs an intermediate variable of the noise variance update iteration; let initial step length d of Newton's method_NT,0Infinity, initial step size d of gradient descent method_GR,00; l placing_NTLet iteration start value equal to 0

H1) By usingDetermining the first derivativeWhere it is required in the iterative solution processTo be requiredThe first derivative for t can be calculated as follows:

wherein

H2) If it isOr l_NT＞L_NTStopping the current Newton method iteration solution to obtainThe step I) is executed in a loop out of the step H); otherwise, step H3 is executed);

H3) by usingDetermining the second derivativeWherein required in the iterative solution processThe second derivative for t can be calculated as follows:

H4) computing

H5) If it isThen put it in_NT＝l_NT+1, go to step H1); otherwise, jumping out of the Newton method solving cycle, and switching to use the gradient descent method to iteratively solveJuxtaposition of_GRThe initial value of the iterative solution of the gradient descent method is 0Performing step H6);

H6) by usingDetermining first derivative information

H7) If it isOr l_GR＞L_GRThen stop the current cycle to getThe step I) is executed in a loop out of the step H); otherwise, step H8 is executed);

H8) updatingAndjuxtaposition of_GR＝l_GR+1 and step H6 is performed);

I) updatingAnd calculating the difference

J) If it isOr q > q_maxThen, the loop is skipped to obtain the estimated valuePerforming step K); otherwise, setting q to q +1, and executing the step F);

K) according toSolving for I.e. an estimate of the CSK constellation class.