CN108092714B - OFDM system supporting color adjustment and CSK constellation diagram detection - Google Patents

OFDM system supporting color adjustment and CSK constellation diagram detection Download PDF

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CN108092714B
CN108092714B CN201711386552.0A CN201711386552A CN108092714B CN 108092714 B CN108092714 B CN 108092714B CN 201711386552 A CN201711386552 A CN 201711386552A CN 108092714 B CN108092714 B CN 108092714B
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constellation
constellation diagram
initial value
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CN108092714A (en
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江明
林泽锋
陈贤煜
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National Sun Yat Sen University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/11—Arrangements specific to free-space transmission, i.e. transmission through air or vacuum
    • H04B10/114—Indoor or close-range type systems
    • H04B10/116—Visible light communication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/50—Transmitters
    • H04B10/516—Details of coding or modulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/60—Receivers
    • H04B10/66—Non-coherent receivers, e.g. using direct detection
    • H04B10/69—Electrical arrangements in the receiver
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0012—Modulated-carrier systems arrangements for identifying the type of modulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems

Abstract

The invention provides an OFDM system supporting color adjustment and CSK constellation diagram detection, which 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.

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) that effectively combats Inter Symbol Interference (ISI) can be utilized to realize high transmission rate by adopting Polar Modulation (PM) complex CSK-OFDM hybrid scheme (PM-CCSK-OFDM) [9 ]. 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 is
Figure GDA0002773866640000022
Wherein
Figure GDA0002773866640000023
Are all constellation point symbols, p is more than or equal to 1 and less than or equal to Ntype，NtypeRepresenting the number of types of constellation, spu＝[spuR,spuG,spuB]TIs the u-th constellation point, M on the constellation diagrampThe 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 theoremIProbability density function fxI(w)；
S2, when the p-th constellation diagram is adopted, the corresponding I-path signal x in the time domain signalIThe optical power of (a) is expressed as:
Figure GDA0002773866640000021
s3, specifying light intensity PtarIn the case of (1), let the p-th constellation diagram SpThe target color ratio is [ AvgpR,AvgpG,AvgpB]TWherein
Figure GDA0002773866640000031
The ratio of the three colors meets the AvgpR+AvgpG+Avg pB1 is ═ 1; then to maintain the original target color fraction, the pth constellation SpThe time domain signal of (a) needs to be multiplied by a color adjustment factor:
Figure GDA0002773866640000032
wherein, AvgpIRepresenting the target color ratio, s, of the p-th constellation diagram I waypuII-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 alpha are obtainedpR、αpGAnd alphapB(ii) a Further obtaining the p-th constellation diagram SpThen, the corresponding color adjustment matrix is:
αp＝diag([αpR,αpG,αpB])
secondly, detecting CSK constellation diagram at receiving end
A) Let the data vector received by the receiver be
Figure GDA0002773866640000033
The class of the transmission constellation is Z ═ γp(ii) a Wherein
Figure GDA0002773866640000034
Indicating the kth received by the receivercA received symbol, kc＝0,1,...,Nc-1，NcLength of FFT transform for OFDM modulation; gamma raypNumbering the constellation map types;
B) setting an estimation accuracy epsilon of a symbol timing offset in an iterative processδNoise variance estimation accuracy
Figure GDA0002773866640000035
Precision epsilon of EM algorithmemIn 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 methodNTSolving the maximum iteration number L of the current estimated value of the noise variance by using a gradient descent methodGRMaximum iteration number q of EM algorithmmax(ii) a And adjustment factors lambda, beta of 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 kcFrequency domain signal X k on sub-carrierc]Will generate
Figure GDA0002773866640000036
Magnitude of phase deviation, i.e. frequency domain signal becoming
Figure GDA0002773866640000037
Due to the symmetry of the frequency domain symbols of the PM-CCSK modulation, i.e.
Figure GDA0002773866640000038
Therefore it has the advantages of
Figure GDA0002773866640000039
Wherein k iscA sub-carrier number is indicated,
Figure GDA00027738666400000310
denotes the kthcPM-CCSK symbols sent on the subcarriers;
thus, it can be seen that the range of symbol timing offsets that can be identified is:
Figure GDA0002773866640000041
in the process of selecting the initial value of STO, every other
Figure GDA0002773866640000042
Sampling symbol timing deviation once in each period, wherein N isspIs the number of samples in one sampling period; and using the obtained sample value as the initial value of symbol timing deviation
Figure GDA0002773866640000043
Is at a candidate value of
Figure GDA0002773866640000044
Will have a range of
Figure GDA0002773866640000045
The candidate value can be expressed as:
Figure GDA0002773866640000046
using these candidate values to perform a grid search for the number n of the best candidate valueoptSo that it satisfies:
Figure GDA0002773866640000047
then the initial value of the symbol timing offset is obtained as
Figure GDA0002773866640000048
In the above scheme, NcLength of FFT transform for OFDM modulation; y is2k-1Representing the kth useful data in the OFDM symbol Y obtained by the receiver; xpvDenotes the v symbol, H, on the p PM-CCSK constellation2k-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 variance
Figure GDA0002773866640000049
Further construct the initial value
Figure GDA00027738666400000410
Substituting the formula to calculate the received signal Y from the Z-YpProbability of constellation-like:
Figure GDA00027738666400000411
wherein
Figure GDA00027738666400000412
Further, it is possible to obtain:
Figure GDA0002773866640000051
wherein the content of the first and second substances,
Figure GDA0002773866640000052
expressed in the system parameter of
Figure GDA0002773866640000053
When the received signal Y is obtained, the system transmits the Z-YpProbability of constellation-like maps;
Figure GDA0002773866640000054
expressed in the system parameter of
Figure GDA0002773866640000055
In case of (1), the transmission Z ═ γpProbability of constellation-like and received signal being Y;
Figure GDA0002773866640000056
expressed in the system parameter of
Figure GDA0002773866640000057
The probability that the received signal is Y; p is a radical ofoptIndicating selection during initial value selectionThe number of the best constellation type;
the initial value of the noise variance is updated as follows:
Figure GDA0002773866640000058
wherein N istypeRepresenting the number of CSK constellation diagram types, v is more than or equal to 1 and less than or equal to Mcp，
Figure GDA0002773866640000059
Figure GDA00027738666400000510
The constellation diagram type selected in the initial value selection process is poptThe corresponding color adjustment matrix in the case of (2),
Figure GDA00027738666400000511
the constellation diagram type selected in the initial value selection process is poptThe v-th symbol in the corresponding PM-CCSK constellation in case (a);
E) selecting
Figure GDA00027738666400000512
Setting the initial value of q to 0;
F) at the current parameter
Figure GDA00027738666400000513
Calculating the data received by the receiver
Figure GDA00027738666400000520
Probability from pth constellation:
Figure GDA00027738666400000514
wherein
Figure GDA00027738666400000515
G) Selecting
Figure GDA00027738666400000516
As xlThe initial value of (a) is set to 0; using Newton's method, as per steps G1) -G4) to solve
Figure GDA00027738666400000517
G1) Using xlDetermining the first derivative
Figure GDA00027738666400000518
Wherein
Figure GDA00027738666400000519
Is a core function of EM algorithm and is defined as
Figure GDA0002773866640000061
Required in the iterative solution process
Figure GDA0002773866640000062
The first derivative for δ can be calculated as follows:
Figure GDA0002773866640000063
wherein:
Figure GDA0002773866640000064
Figure GDA0002773866640000065
wherein epsilonδFor the accuracy of the estimation of the symbol timing offset in the iterative process, (.)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 top(ii) a θ is the system parameter matrix, θ ═ δ, σ2)；
G2) If g | | |δ||＜εδOr L is more than L, stopping the current Newton method to solve the iteration to obtain
Figure GDA0002773866640000066
The step H) is executed in a loop out of the step G); otherwise, executing step G3);
G3) using xlDetermining the second derivative
Figure GDA0002773866640000067
In which what is required during the iterative solution of Newton's method
Figure GDA0002773866640000068
The second derivative for δ can be calculated as follows:
Figure GDA0002773866640000069
wherein
Figure GDA00027738666400000610
Re (-) represents the operation of the extraction part;
G4) order to
Figure GDA00027738666400000611
Juxtaposing 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 method
Figure GDA00027738666400000612
Wherein the steps H1) -H5) are solved iteratively by Newton's method
Figure GDA00027738666400000613
If 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 used
Figure GDA0002773866640000071
As noiseUpdating an intermediate variable of iteration by the variance; let initial step length d of Newton's methodNT,0Infinity, initial step size d of gradient descent method GR,00; l placingNTLet iteration start value equal to 0
Figure GDA0002773866640000072
H1) By using
Figure GDA00027738666400000715
Determining the first derivative
Figure GDA0002773866640000073
Wherein required in the iterative solution process
Figure GDA0002773866640000074
The first derivative for t can be calculated as follows:
Figure GDA0002773866640000075
wherein
Figure GDA0002773866640000076
H2) If it is
Figure GDA0002773866640000077
Or lNT＞LNTStopping the current Newton method iteration solution to obtain
Figure GDA0002773866640000078
The step I) is executed in a loop out of the step H); otherwise, step H3 is executed);
H3) by using
Figure GDA00027738666400000716
Determining the second derivative
Figure GDA0002773866640000079
Wherein required in the iterative solution process
Figure GDA00027738666400000710
The second derivative for t can be calculated as follows:
Figure GDA00027738666400000711
H4) computing
Figure GDA00027738666400000712
H5) If it is
Figure GDA00027738666400000717
Then put it inNT＝lNT+1, go to step H1); otherwise, jumping out of the Newton method solving cycle, and switching to use the gradient descent method to iteratively solve
Figure GDA00027738666400000713
Juxtaposition ofGRThe initial value of the iterative solution of the gradient descent method is 0
Figure GDA00027738666400000718
Performing step H6);
H6) by using
Figure GDA00027738666400000719
Determining first derivative information
Figure GDA00027738666400000714
H7) If it is
Figure GDA0002773866640000081
Or lGR＞LGRThen stop the current cycle to get
Figure GDA0002773866640000082
The step I) is executed in a loop out of the step H); otherwise, step H8 is executed);
H8) updating
Figure GDA0002773866640000083
And
Figure GDA0002773866640000084
juxtaposition ofGR＝lGR+1 and step H6 is performed);
I) updating
Figure GDA0002773866640000085
And calculating the difference
Figure GDA0002773866640000086
J) If it is
Figure GDA0002773866640000087
Or q > qmaxThen, the loop is skipped to obtain the estimated value
Figure GDA0002773866640000088
Performing step K); otherwise, setting q to q +1, and executing the step F);
K) according to
Figure GDA0002773866640000089
Solving for
Figure GDA00027738666400000810
Figure GDA00027738666400000811
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 pair
Figure GDA00027738666400000812
Sensitivity 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 strategytypeOne 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 transmitted
Figure GDA0002773866640000091
Wherein
Figure GDA0002773866640000092
Are all constellation point symbols, p is more than or equal to 1 and less than or equal to Ntype，spu＝[spuR,spuG,spuB]TIs the u-th constellation point, M, on the original constellation diagrampFor 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]：
Figure GDA0002773866640000093
Where u (w) and δ (w) are step and impulse functions, σ, respectivelypIFor cutting off signal x by way of IpIAnd satisfies the following criteria:
Figure GDA0002773866640000094
wherein XpIIs a PM-CCSK symbol XpI way data of (i.e. X)pI∈{±spmI±j·spnI|1≤m,n≤MpTherefore, the optical power of the I-path ACO-OFDM signal is:
Figure GDA0002773866640000095
at a given light intensity PtarIn the case of (1), a p-th constellation S selected in advance is setpThe target color ratio is [ AvgpR,AvgpG,AvgpB]TWherein
Figure GDA0002773866640000101
The ratio of the three colors meets the AvgpR+AvgpG+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:
Figure GDA0002773866640000102
according to the above operation, R, G, B three color adjustment factors α can be obtainedpR、αpGAnd alphapB. Further, the p-th constellation S in the selected transmission can be obtainedpWhen the corresponding color adjustment matrix is
αp＝diag([αpR,αpG,αpB])
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 variance and completes the detection of the 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 be
Figure GDA0002773866640000103
The class of the transmission constellation is Z ═ γp(ii) a Wherein
Figure GDA0002773866640000104
Indicating the kth received by the receivercA received symbol, kc＝0,1,...,Nc-1，NcLength of FFT transform for OFDM modulation; gamma raypNumbering the constellation map types;
B) setting an estimation accuracy epsilon of a symbol timing offset in an iterative processδNoise variance estimation accuracy
Figure GDA0002773866640000105
Precision epsilon of EM algorithmemIn 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 methodNTSolving the maximum iteration number L of the current estimated value of the noise variance by using a gradient descent methodGRMaximum iteration number q of EM algorithmmax(ii) a And adjustment factors lambda, beta of 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 kcFrequency domain signal X k on sub-carrierc]Will generate
Figure GDA0002773866640000111
Magnitude of phase deviation, i.e. frequency domain signal becoming
Figure GDA0002773866640000112
Due to the symmetry of the frequency domain symbols of the PM-CCSK modulation, i.e.
Figure GDA0002773866640000113
Therefore it has the advantages of
Figure GDA0002773866640000114
Wherein k iscA sub-carrier number is indicated,
Figure GDA0002773866640000115
denotes the kthcPM-CCSK symbols sent on the subcarriers;
thus, it can be seen that the range of symbol timing offsets that can be identified is:
Figure GDA0002773866640000116
in the process of selecting the initial value of STO, every other
Figure GDA0002773866640000117
Sampling symbol timing deviation once in each period, wherein N isspIs the number of samples in one sampling period; and using the obtained sample value as the initial value of symbol timing deviation
Figure GDA0002773866640000118
Is at a candidate value of
Figure GDA0002773866640000119
Will have a range of
Figure GDA00027738666400001110
The candidate value can be expressed as:
Figure GDA00027738666400001111
using these candidate values to perform a grid search for the number n of the best candidate valueoptSo that it satisfies:
Figure GDA00027738666400001112
then the initial value of the symbol timing offset is obtained as
Figure GDA00027738666400001113
In the above scheme, NcLength of FFT transform for OFDM modulation; y is2k-1Representing the kth useful data in the OFDM symbol Y obtained by the receiver; xpvDenotes the v symbol, H, on the p PM-CCSK constellation2k-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 variance
Figure GDA0002773866640000121
Further construct the initial value
Figure GDA0002773866640000122
Substituting the formula to calculate the received signal Y from the Z-YpProbability of constellation-like:
Figure GDA0002773866640000123
wherein
Figure GDA0002773866640000124
Further, it is possible to obtain:
Figure GDA0002773866640000125
wherein the content of the first and second substances,
Figure GDA0002773866640000126
expressed in the system parameter of
Figure GDA0002773866640000127
When the received signal Y is obtained, the system transmits the Z-YpProbability of constellation-like maps;
Figure GDA0002773866640000128
expressed in the system parameter of
Figure GDA0002773866640000129
In case of (1), the transmission Z ═ γpProbability of constellation-like and received signal being Y;
Figure GDA00027738666400001210
expressed in the system parameter of
Figure GDA00027738666400001211
The probability that the received signal is Y; p is a radical ofoptA number representing the optimal constellation type selected in the initial value selection process;
the initial value of the noise variance is updated as follows:
Figure GDA00027738666400001212
wherein N istypeRepresenting the number of CSK constellation diagram types, v is more than or equal to 1 and less than or equal to Mcp，
Figure GDA00027738666400001213
Figure GDA00027738666400001214
The constellation diagram type selected in the initial value selection process is poptThe corresponding color adjustment matrix in the case of (2),
Figure GDA00027738666400001215
the constellation diagram type selected in the initial value selection process is poptThe v-th symbol in the corresponding PM-CCSK constellation in case (a);
E) selecting
Figure GDA00027738666400001216
Setting the initial value of q to 0;
F) at the current parameter
Figure GDA00027738666400001217
Calculating the data received by the receiver
Figure GDA00027738666400001218
Probability from pth constellation:
Figure GDA0002773866640000131
wherein
Figure GDA0002773866640000132
G) Selecting
Figure GDA0002773866640000133
As xlThe initial value of (a) is set to 0; using Newton's method, as per steps G1) -G4) to solve
Figure GDA0002773866640000134
G1) Using xlDetermining the first derivative
Figure GDA0002773866640000135
Wherein
Figure GDA0002773866640000136
Is a core function of EM algorithm and is defined as
Figure GDA0002773866640000137
Required in the iterative solution process
Figure GDA0002773866640000138
The first derivative for δ can be calculated as follows:
Figure GDA0002773866640000139
wherein:
Figure GDA00027738666400001310
Figure GDA00027738666400001311
wherein epsilonδFor the accuracy of the estimation of the symbol timing offset in the iterative process, (.)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 top(ii) a θ is the system parameter matrix, θ ═ δ, σ2)；
G2) If g | | |δ||＜εδOr L is more than L, stopping the current Newton method to solve the iteration to obtain
Figure GDA00027738666400001312
The step H) is executed in a loop out of the step G); otherwise, executing step G3);
G3) using xlDetermining the second derivative
Figure GDA00027738666400001313
In which what is required during the iterative solution of Newton's method
Figure GDA00027738666400001314
The second derivative for δ can be calculated as follows:
Figure GDA0002773866640000141
wherein
Figure GDA0002773866640000142
Re (-) represents the operation of the extraction part;
G4) order to
Figure GDA0002773866640000143
Juxtaposing 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 method
Figure GDA0002773866640000144
Wherein the steps H1) -H5) are solved iteratively by Newton's method
Figure GDA0002773866640000145
If 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 used
Figure GDA0002773866640000146
As an intermediate variable of the noise variance update iteration; let initial step length d of Newton's methodNT,0Infinity, initial step size d of gradient descent method GR,00; l placingNTLet iteration start value equal to 0
Figure GDA0002773866640000147
H1) By using
Figure GDA00027738666400001415
Determining the first derivative
Figure GDA0002773866640000148
Wherein required in the iterative solution process
Figure GDA0002773866640000149
The first derivative for t can be calculated as follows:
Figure GDA00027738666400001410
wherein
Figure GDA00027738666400001411
H2) If it is
Figure GDA00027738666400001416
Or lNT＞LNTStopping the current Newton method iteration solution to obtain
Figure GDA00027738666400001412
The step I) is executed in a loop out of the step H); otherwise, step H3 is executed);
H3) by using
Figure GDA00027738666400001417
Determining the second derivative
Figure GDA00027738666400001413
Wherein required in the iterative solution process
Figure GDA00027738666400001414
The second derivative for t can be calculated as follows:
Figure GDA0002773866640000151
H4) computing
Figure GDA0002773866640000152
H5) If it is
Figure GDA00027738666400001517
Then put it inNT＝lNT+1, go to step H1); otherwise, jumping out of the Newton method solving cycle, and switching to use the gradient descent method to iteratively solve
Figure GDA0002773866640000153
Juxtaposition ofGRThe initial value of the iterative solution of the gradient descent method is 0
Figure GDA0002773866640000154
Performing step H6);
H6) by using
Figure GDA00027738666400001518
Determining first derivative information
Figure GDA0002773866640000155
H7) If it is
Figure GDA0002773866640000156
Or lGR＞LGRThen stop the current cycle to get
Figure GDA0002773866640000157
The step I) is executed in a loop out of the step H); otherwise, step H8 is executed);
H8) updating
Figure GDA0002773866640000158
And
Figure GDA0002773866640000159
juxtaposition ofGR＝lGR+1 and step H6 is performed);
I) updating
Figure GDA00027738666400001510
And calculating the difference
Figure GDA00027738666400001511
J) If it is
Figure GDA00027738666400001512
Or q > qmaxThen, the loop is skipped to obtain the estimated value
Figure GDA00027738666400001513
Performing step K); otherwise, setting q to q +1, and executing the step F);
K) according to
Figure GDA00027738666400001514
Solving for
Figure GDA00027738666400001515
Figure GDA00027738666400001516
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 NtypeAs 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 Nc64. 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 adopts a classical ray tracing model [18 ]]The time resolution is set to ΔtThe maximum number of reflections is set to 3 for 4 ns. Further, assume that the systematic symbol timing offset STO is at
Figure GDA0002773866640000161
Is randomly selected. EM algorithm parameter setting
Figure GDA0002773866640000162
εem＝(10-5,10-5)；L＝1，LNT＝LGR＝5，qmax＝10；λ＝β＝0.5；
Figure GDA0002773866640000163
Table 1: the constellation point coordinates and target color coordinates of the 5 constellation diagrams used in this embodiment
Figure GDA0002773866640000164
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 as
Figure GDA0002773866640000171
Wherein N issFor transmitting the total number of OFDM symbols, and NrIt 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 exceeding
Figure GDA0002773866640000172
And 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 analyzes
Figure GDA0002773866640000173
The 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 15dB
Figure GDA0002773866640000174
And the constellation diagram identification rate, STO estimation performance, noise variance estimation performance and the change of the convergence speed of the EM algorithm under the value taking. As can be seen from FIG. 7, the system performance is paired
Figure GDA0002773866640000175
The values of (a) are not sensitive. Therefore, the scheme pair
Figure GDA0002773866640000176
The 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 the Block error rate (Block) of the CSK-OFDM system using the scheme provided by the present inventionError Rate, BLER) performance curves and compared to other schemes. In the figure delta is the true value of STO,
Figure GDA0002773866640000177
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
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[2].E.Monteiro and S.Hranilovic,“Design and implementation of color-shift keying for visible light communications,”Journal of Lightwave Technology,vol.32,no.10,pp.2053-2060,May 15,2014.
[3].IEEE Standard for Local and Metropolitan Area Networks—Part 15.7:Short-Range Wireless Optical Communication Using Visible Light,IEEE Standard 802.15.7-2011,Sep.2011,pp.1-309.
[4].R.J.Drost and B.M.Sadler,“Constellation design for color-shift keying using billiards algorithms,”GLOBECOM Workshops,2010,pp.980-984.
[5].E.Monteiro and S.Hranilovic,“Constellation design for color-shift keying using interior point methods,”Globecom Workshops,2012,pp.1224-1228.
[6].R.Singh,T.O’Farrell and J.P.R.David,“An enhanced color shift keying modulation scheme for high-speed wireless visible light communications,”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 visible light 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 synchronization scheme,”IEEE Photonics Technology Letters,vol.26,no.18,pp.1851-1854,Sep.2014.
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[10].
Figure GDA0002773866640000191
Bayer and M.
Figure GDA0002773866640000192
“Joint space time block code and modulation classification 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 communication signal modulation based on neural network,”Electronic Information and Communication Technology(ICEICT)IEEE International Conference on,Harbin,China,Mar.2016,pp.223-226.
[12].L.Chen,B.Krongold and J.Evans,“Performance analysis for optical OFDM transmission in short-range IM/DD systems,”Journal of Lightwave Technology,vol.30,no.7,pp.974-983,Feb.2012.
[13].X.Li,R.Mardling and J.Armstrong,“Channel capacity of IM/DD optical 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 and J.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 OFDM Systems 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 noise variance 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 for Estimating the Standard Deviation of AWGN when Observations are not Signal-Free,”Journal of Computers,vol.2,no.7,pp.1-10,Sept.2007.
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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 is
Figure FDA0002773866630000011
Wherein
Figure FDA0002773866630000012
Are all constellation point symbols, p is more than or equal to 1 and less than or equal to Ntype，NtypeRepresenting the number of types of constellation, spu＝[spuR,spuG,spuB]TIs the u-th constellation point, M on the constellation diagrampThe 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 theoremIProbability density function of
Figure FDA0002773866630000013
S2, when the p-th constellation diagram is adopted, the corresponding I-path signal x in the time domain signalIThe optical power of (a) is expressed as:
Figure FDA0002773866630000014
s3, specifying light intensity PtarIn the case of (1), let the p-th constellation diagram SpThe target color ratio is [ AvgpR,AvgpG,AvgpB]TWherein
Figure FDA0002773866630000015
The ratio of the three colors meets the AvgpR+AvgpG+AvgpB1 is ═ 1; then to maintain the original target color occupancyP-th constellation diagram SpThe time domain signal of (a) needs to be multiplied by a color adjustment factor:
Figure FDA0002773866630000016
wherein, AvgpIRepresenting the target color ratio, s, of the p-th constellation diagram I waypuII-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 alpha are obtainedpR、αpGAnd alphapB(ii) a Further obtaining the p-th constellation diagram SpThen, the corresponding color adjustment matrix is:
αp＝diag([αpR,αpG,αpB])
secondly, detecting CSK constellation diagram at receiving end
A) Let the data vector received by the receiver be
Figure FDA0002773866630000017
The class of the transmission constellation is Z ═ γp(ii) a Wherein
Figure FDA0002773866630000018
Indicating the kth received by the receivercA received symbol, kc＝0,1,...,Nc-1，NcLength of FFT transform for OFDM modulation; gamma raypNumbering the constellation map types;
B) setting an estimation accuracy epsilon of a symbol timing offset in an iterative processδNoise variance estimation accuracy
Figure FDA0002773866630000021
Precision epsilon of EM algorithmemIn 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 methodNTSolving the current noise variance by using a gradient descent methodMaximum number of iterations L of the estimated valueGRMaximum iteration number q of EM algorithmmax(ii) a And adjustment factors lambda, beta of 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 kcFrequency domain signal X k on sub-carrierc]Will generate
Figure FDA0002773866630000022
Magnitude of phase deviation, i.e. frequency domain signal becoming
Figure FDA0002773866630000023
Due to the symmetry of the frequency domain symbols of the PM-CCSK modulation, i.e.
Figure FDA0002773866630000024
Therefore it has the advantages of
Figure FDA0002773866630000025
Wherein k iscA sub-carrier number is indicated,
Figure FDA0002773866630000026
denotes the kthcPM-CCSK symbols sent on the subcarriers;
thus, it can be seen that the range of symbol timing offsets that can be identified is:
Figure FDA0002773866630000027
in the process of selecting the initial value of STO, every other
Figure FDA0002773866630000028
Sampling symbol timing deviation once in each period, wherein N isspIs the number of samples in one sampling period; and using the obtained sample value as the initial value of symbol timing deviation
Figure FDA0002773866630000029
Is at a candidate value of
Figure FDA00027738666300000210
Will have a range of
Figure FDA00027738666300000211
The candidate value can be expressed as:
Figure FDA00027738666300000212
using these candidate values to perform a grid search for the number n of the best candidate valueoptSo that it satisfies:
Figure FDA00027738666300000213
then the initial value of the symbol timing offset is obtained as
Figure FDA00027738666300000214
In the above scheme, NcLength of FFT transform for OFDM modulation; y is2k-1Representing the kth useful data in the OFDM symbol Y obtained by the receiver; xpvDenotes the v symbol, H, on the p PM-CCSK constellation2k-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 variance
Figure FDA0002773866630000031
Further construct the initial value
Figure FDA0002773866630000032
Substituting the formula to calculate the received signal Y from the Z-YpOf constellation-like diagramsProbability:
Figure FDA0002773866630000033
wherein
Figure FDA0002773866630000034
Further, it is possible to obtain:
Figure FDA0002773866630000035
wherein the content of the first and second substances,
Figure FDA0002773866630000036
expressed in the system parameter of
Figure FDA0002773866630000037
When the received signal Y is obtained, the system transmits the Z-YpProbability of constellation-like maps;
Figure FDA0002773866630000038
expressed in the system parameter of
Figure FDA0002773866630000039
In case of (1), the transmission Z ═ γpProbability of constellation-like and received signal being Y;
Figure FDA00027738666300000310
expressed in the system parameter of
Figure FDA00027738666300000311
The probability that the received signal is Y; p is a radical ofoptA number representing the optimal constellation type selected in the initial value selection process;
the initial value of the noise variance is updated as follows:
Figure FDA00027738666300000312
wherein N istypeRepresenting the number of CSK constellation diagram types, v is more than or equal to 1 and less than or equal to Mcp，
Figure FDA00027738666300000313
Figure FDA00027738666300000314
The constellation diagram type selected in the initial value selection process is poptThe corresponding color adjustment matrix in the case of (2),
Figure FDA00027738666300000315
the constellation diagram type selected in the initial value selection process is poptThe v-th symbol in the corresponding PM-CCSK constellation in case (a);
E) selecting
Figure FDA00027738666300000316
Setting the initial value of q to 0;
F) at the current parameter
Figure FDA00027738666300000317
Calculating the data received by the receiver
Figure FDA0002773866630000041
Probability from pth constellation:
Figure FDA0002773866630000042
wherein
Figure FDA0002773866630000043
G) Selecting
Figure FDA0002773866630000044
As xlThe initial value of (a) is set to 0; using Newton's method, as per steps G1) -G4) to solve
Figure FDA0002773866630000045
G1) Using xlDetermining the first derivative
Figure FDA0002773866630000046
Wherein
Figure FDA0002773866630000047
Is a core function of EM algorithm and is defined as
Figure FDA0002773866630000048
Required in the iterative solution process
Figure FDA0002773866630000049
The first derivative for δ can be calculated as follows:
Figure FDA00027738666300000410
wherein:
Figure FDA00027738666300000411
Figure FDA00027738666300000412
wherein epsilonδFor the accuracy of the estimation of the symbol timing offset in the iterative process, (.)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 top(ii) a Theta is systemParameter matrix, θ ═ δ, σ2)；
G2) If g | | |δ||＜εδOr L is more than L, stopping the current Newton method to solve the iteration to obtain
Figure FDA00027738666300000413
The step H) is executed in a loop out of the step G); otherwise, executing step G3);
G3) using xlDetermining the second derivative
Figure FDA00027738666300000414
In which what is required during the iterative solution of Newton's method
Figure FDA0002773866630000051
The second derivative for δ can be calculated as follows:
Figure FDA0002773866630000052
wherein
Figure FDA0002773866630000053
Re (-) represents the operation of the extraction part;
G4) order to
Figure FDA0002773866630000054
Juxtaposing 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 method
Figure FDA0002773866630000055
Wherein the steps H1) -H5) are solved iteratively by Newton's method
Figure FDA0002773866630000056
If the abnormity occurs, the steps H6) -H8) are used for switching and iterating by using a gradient descent method; in the iterative solution of the noise variance, use is made ofVariable replacement
Figure FDA0002773866630000057
As an intermediate variable of the noise variance update iteration; let initial step length d of Newton's methodNT,0Infinity, initial step size d of gradient descent methodGR,00; l placingNTLet iteration start value equal to 0
Figure FDA0002773866630000058
H1) By using
Figure FDA0002773866630000059
Determining the first derivative
Figure FDA00027738666300000510
Wherein required in the iterative solution process
Figure FDA00027738666300000511
The first derivative for t can be calculated as follows:
Figure FDA00027738666300000512
wherein
Figure FDA00027738666300000513
H2) If it is
Figure FDA00027738666300000514
Or lNT＞LNTStopping the current Newton method iteration solution to obtain
Figure FDA00027738666300000515
The step I) is executed in a loop out of the step H); otherwise, step H3 is executed);
H3) by using
Figure FDA00027738666300000516
Determining the second derivative
Figure FDA00027738666300000517
Wherein required in the iterative solution process
Figure FDA0002773866630000061
The second derivative for t can be calculated as follows:
Figure FDA0002773866630000062
H4) computing
Figure FDA0002773866630000063
H5) If it is
Figure FDA0002773866630000064
Then put it inNT＝lNT+1, go to step H1); otherwise, jumping out of the Newton method solving cycle, and switching to use the gradient descent method to iteratively solve
Figure FDA0002773866630000065
Juxtaposition ofGRThe initial value of the iterative solution of the gradient descent method is 0
Figure FDA0002773866630000066
Performing step H6);
H6) by using
Figure FDA0002773866630000067
Determining first derivative information
Figure FDA0002773866630000068
H7) If it is
Figure FDA0002773866630000069
Or lGR＞LGRThen stop the current cycle to get
Figure FDA00027738666300000610
The step I) is executed in a loop out of the step H); otherwise, step H8 is executed);
H8) updating
Figure FDA00027738666300000611
And
Figure FDA00027738666300000612
juxtaposition ofGR＝lGR+1 and step H6 is performed);
I) updating
Figure FDA00027738666300000613
And calculating the difference
Figure FDA00027738666300000614
J) If it is
Figure FDA00027738666300000615
Or q > qmaxThen, the loop is skipped to obtain the estimated value
Figure FDA00027738666300000616
Performing step K); otherwise, setting q to q +1, and executing the step F);
K) according to
Figure FDA00027738666300000617
Solving for
Figure FDA00027738666300000618
Figure FDA00027738666300000619
I.e. the estimated value of CSK constellation diagram category。
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