CN112367123B - Light space-time keying modulation method suitable for turbulent flow channel - Google Patents

Light space-time keying modulation method suitable for turbulent flow channel Download PDF

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CN112367123B
CN112367123B CN202011245533.8A CN202011245533A CN112367123B CN 112367123 B CN112367123 B CN 112367123B CN 202011245533 A CN202011245533 A CN 202011245533A CN 112367123 B CN112367123 B CN 112367123B
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CN112367123A (en
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王惠琴
张悦
马雪梅
包仲贤
侯文斌
李文文
武宜雯
叶归清
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Lanzhou University of Technology
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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
    • H04B10/50—Transmitters
    • H04B10/516—Details of coding or modulation
    • H04B10/548—Phase or frequency modulation
    • H04B10/556—Digital modulation, e.g. differential phase shift keying [DPSK] or frequency shift keying [FSK]
    • 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
    • H04B10/61—Coherent receivers
    • H04B10/612—Coherent receivers for optical signals modulated with a format different from binary or higher-order PSK [X-PSK], e.g. QAM, DPSK, FSK, MSK, ASK
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention relates to the technical field of wireless optical communication, in particular to an optical space-time keying modulation method suitable for a turbulent flow channel. The method comprises the steps of carrying out space domain mapping on binary bit streams, detecting received signals and calculating the theoretical bound of the average bit error rate of an optical space-time keying modulation system. The space domain mapping maps the binary bit stream into an orthogonal space-time dispersion matrix block through a laser selection algorithm based on a channel norm maximization criterion, and the orthogonal space-time dispersion matrix block is transmitted by an optical antenna. And detecting the space-time dispersion matrix index by using an orthogonal matching pursuit decoding algorithm based on a threshold value at a receiving end, and recovering binary information through demapping. The average bit error rate of the optical space-time keying modulation is deduced by using a joint bound technology. The proposal greatly improves the transmission rate and the error code performance of the system on the premise of not increasing the cost, and promotes the application of the proposed system in the actual engineering.

Description

Light space-time keying modulation method suitable for turbulent flow channel
Technical Field
The invention relates to the technical field of wireless optical communication, in particular to an optical space-time keying modulation method suitable for a turbulent flow channel.
Background
Optical Spatial Modulation (OSM) is a novel Optical Multiple Input Multiple Output (OMIMO) technology, and is characterized in that only one laser is activated to transmit signals at a time, so that channel interference and channel synchronization problems in an OMIMO system can be effectively avoided. Particularly, the OSM adds an index map for activating the laser on the basis of the two-dimensional signal constellation map, so that the index number of the laser becomes a carrying mode of extra data information. Therefore, the information of the signal domain and the space domain can be simultaneously transmitted in each symbol period, and the system transmission rate and the spectrum efficiency can be improved by fully utilizing the space resources. Optical Space Shift Keying (OSSK), a special OSM, uses only the active laser index to transmit information, further reducing the complexity of the transceiver end design. Therefore, the device has the advantages of simple structure, low complexity and the like.
The increase of the transmission rate of the OSSK scheme is at the cost of the increase of the number of lasers, which limits the wide application of the OSSK scheme in practice. In order to further improve the transmission rate and the space resource utilization rate of the system without increasing the cost, Optical Generalized Space Shift Keying (OGSSK) is proposed. Although the transmission rate of the OGSSK scheme is improved to a certain extent, the transmission rate is at the cost of the loss of error code performance, and the improvement of the transmission rate is limited by the number of lasers, so that the requirements of users in the big data era on ultrahigh rate, ultra-large capacity and the like are difficult to meet.
Disclosure of Invention
Based on the above problems, the present invention provides an optical space-time keying modulation method suitable for a turbulent flow channel, which is combined with the OSSK by using the advantages of linear dispersion codes to construct an optical space-time keying method. The method provides a new way for improving the transmission rate and the error code performance of the wireless optical communication system, and has important application value.
The technical scheme adopted by the invention is as follows:
an optical space-time keying modulation method suitable for a turbulent flow channel, characterized by:
at a sending end: mapping a bit data block formed by binary bit streams into an orthogonal space-time dispersion matrix; selecting and sending signals in the orthogonal space-time dispersion matrix set;
during transmission: the signal passes through an atmospheric turbulence channel;
at the receiving end: after receiving the signal, recovering the original bit data block after the detection and the de-mapping of the orthogonal matching tracking decoding algorithm;
and (3) calculating: and (3) deriving the average bit error rate of the optical space-time keying modulation system under a turbulent flow channel by using a joint bound technology.
At the transmitting end, the binary bit stream is divided into bit data blocks with specific lengths after serial/parallel conversion.
And performing index mapping on the bit data block according to a diffusion matrix rank maximization criterion to activate the laser, wherein the mapping is an orthogonal space-time diffusion matrix.
Only one laser per column in the orthogonal space-time dispersion matrix is activated and each laser is activated only once in successive columns.
At the transmitting end, the selection signals in the orthogonal space-time dispersion matrix set are as follows: and selecting a transmission signal in the orthogonal space-time dispersion matrix set by utilizing a laser selection algorithm of a channel norm maximization criterion according to the channel state information.
At a receiving end, a photoelectric detector is adopted to receive signals, and the received signals are as follows:
Y＝ηP t HX+n
where eta is the photoelectric conversion efficiency, P t Is the peak power, n is the obedient mean μ n Variance is
Figure BDA0002769901260000022
White gaussian noise vector.
Figure BDA0002769901260000021
Is N r ×N t The channel fading coefficient matrix of (1).
The detection of the orthogonal matching pursuit decoding algorithm needs to be based on threshold detection.
The average bit error rate expression of the optical space-time keying modulation system under the turbulent flow channel is as follows:
Figure BDA0002769901260000031
in the formula (I), the compound is shown in the specification,
Figure BDA0002769901260000032
alpha and beta respectively represent large and small scale scattering coefficients; ρ represents the received signal-to-noise ratio; τ denotes
Figure BDA0002769901260000033
An arithmetic average of the number of occurrences is possible.
The invention has the beneficial effects that: binary bit data is mapped into an orthogonal space-time dispersion matrix index composed of laser serial numbers through a dispersion matrix rank maximization criterion, and therefore the space-time keying modulation method with high transmission rate is constructed. On the basis, the laser redundancy combination is fully utilized, the selection of the optimal laser combination is completed according to a laser selection algorithm of a channel norm maximization criterion, and the error code performance of the system is further improved. The orthogonal matching tracking decoding algorithm based on the threshold value is utilized at the receiving end, the calculation complexity of the system is effectively reduced, an effective way is provided for realizing the communication target of high speed, reliability and low energy consumption in the wireless optical communication, and the method has important value in practical application.
Drawings
FIG. 1 is a model of a space-time keying modulation system;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a comparison between the theoretical upper bound of the bit error rate and the simulation performance of the space-time keying modulation system;
FIG. 4 is a comparison of the performance of different detection algorithms;
FIG. 5 is a comparison of computational complexity of different detection algorithms;
FIG. 6 is a graph of the effect of different turbulence intensities on the performance of a space-time keying modulation system;
FIG. 7 is a comparison of performance for different modulation schemes;
Detailed Description
The technical scheme of the invention is further explained by specific embodiments in the following with the accompanying drawings:
to one has N t A Laser (LD) and N r The OSTSK system of each Photodetector (PD) is modeled as shown in FIG. 1. In fig. 1, a serial/parallel transformed binary bit stream is divided into data blocks of length l bits, and the l-bit blocks are mapped to an orthogonal space-time dispersion matrix. A laser selection algorithm that utilizes a channel norm maximization criterion selects a suitable signal in the set of orthogonal space-time dispersion matrices. The signal is transmitted by an optical antenna, received by a photoelectric detector after passing through an atmospheric turbulence channel, and then detected by an orthogonal matching tracking decoding algorithm based on a threshold value and de-mapped, so that an original bit data block can be recovered, and the specific step flow is shown in figure 2.
1. Transmit end signal mapping
At a sending end, firstly, the binary bit stream is subjected to space domain mapping, space and time resources are considered, and N is obtained according to a diffusion matrix rank maximization criterion t The indices of the individual lasers are mapped to an orthogonal space-time dispersion matrix X. The matrix is N with only one non-zero element in each row and column t ×N t Dimensional matrix, which can be expressed as
Figure BDA0002769901260000041
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002769901260000042
and
Figure BDA0002769901260000043
are all N t A vector of x 1 dimensions, and,
Figure BDA0002769901260000044
and
Figure BDA0002769901260000045
representing the location in the different columns where the laser is activated. N can be constructed due to different positions of non-zero elements in different symbol periods in X t | A An orthogonal space-time dispersion matrix, and a mapping set is recorded as
Figure BDA0002769901260000046
At the same time, the number of X's sent needs to be an integer power of 2, and will be collected
Figure BDA0002769901260000047
In selection
Figure BDA0002769901260000048
The seed X is transmitted, then the transmission rate of the OSTSK system is
Figure BDA0002769901260000049
bpcu. Simultaneous aggregation
Figure BDA00027699012600000410
Also exist in
Figure BDA00027699012600000411
The redundancy is not utilized.
Since the atmospheric channel is a time-varying fading channel, the transmission signal is affected differently when transmitted by different sub-channels. The method selects an active laser by adopting a laser selection algorithm based on a channel norm maximization criterion according to current channel state information, the essence of the method is to select a subchannel with the maximum channel norm to transmit information, and a corresponding mathematical expression of the algorithm is
Figure BDA00027699012600000412
Wherein | · | purple sweet F Is F norm, p represents from
Figure BDA00027699012600000413
Of the selected subset of the plurality of subsets,
Figure BDA00027699012600000414
is the channel fading matrix corresponding to p.
And (2) assuming that the channel state information of the receiving end is known, obtaining the index of the activated laser according to the calculation result of the formula (1), transmitting the result to the transmitting end through a high-quality feedback link, and activating the selected laser by the transmitting end to transmit signals.
2. Channel model
The modulated signal is emitted by the activated laser, and is received by the photoelectric detector after passing through the turbulent flow channel, and the received signal is
Y＝ηP t HX+n (2)
Where eta is the photoelectric conversion efficiency, P t Is the peak power, n is the obedient mean μ n Variance of
Figure BDA0002769901260000051
Gaussian white noise vector.
Figure BDA0002769901260000052
Is N r ×N t Under medium to strong turbulence conditions, the channel fading coefficient h ij Obeying a Gamma-Gamma distribution with a probability density function of
Figure BDA0002769901260000053
Wherein Gamma (·) is a Gamma function, and alpha and beta are respectively a large-scale scattering coefficient and a small-scale scattering coefficient. Alpha and beta can be respectively expressed as
Figure BDA0002769901260000054
In the formula (I), the compound is shown in the specification,
Figure BDA0002769901260000055
is the Rytov variance. Wherein the content of the first and second substances,
Figure BDA0002769901260000056
and k is 2 pi/lambda, lambda is the wavelength, and L is the transmission distance of the laser beam.
ML detection and bit error rate calculation
At the receiving end, when the channel state information is known, the index of the activation laser serial number can be obtained by maximum likelihood detection (ML) estimation, and the original bit information can be recovered after demapping. The maximum likelihood detection criterion is
Figure BDA0002769901260000057
Wherein the content of the first and second substances,
Figure BDA0002769901260000058
is the index of the detected active laser sequence number.
The theoretical upper bound of the error rate of the OSTSK system based on the maximum likelihood detection can be obtained by the combined bound technology
Figure BDA0002769901260000061
In the formula, d H (X i ,X j ) Presentation delivery message
Figure BDA0002769901260000062
Number X i And the estimated signal X j Hamming distance between them, PEP (X) i →X j | H) indicates that X is transmitted when CSI is known i And is erroneously detected as X j Pair-wise error probability. PEP (X) after normalized noise processing of equation (6) i →X j H) can be defined as
Figure BDA0002769901260000063
Due to the matrix X i Is characterized in that
Figure BDA0002769901260000064
Equation (7) can be reduced to
Figure BDA0002769901260000065
Wherein the content of the first and second substances,
Figure BDA0002769901260000066
and
Figure BDA0002769901260000067
is an independent co-distributed channel gain matrix.
Figure BDA0002769901260000068
And
Figure BDA0002769901260000069
are independent co-distributed channel gain vectors.
The formula (2) is changed into the formula (8), and the formula (8) can be simplified into
Figure BDA00027699012600000610
Suppose that
Figure BDA00027699012600000611
Delta is obedient mean value of E [ Delta ]]0, variance of
Figure BDA00027699012600000612
Gaussian random variable of (2). Thus obtaining
Figure BDA00027699012600000613
Wherein the content of the first and second substances,
Figure BDA00027699012600000614
is a function of the Q of the gaussian,
Figure BDA00027699012600000615
is a complementary error function.
Figure BDA00027699012600000616
Is the received signal-to-noise ratio. Tau is(2. ltoreq. tau. ltoreq. ξ) is
Figure BDA00027699012600000619
An arithmetic average of the number of occurrences is possible.
To calculate the Average Pairwise Error Probability (APEP), we define a variable
Figure BDA00027699012600000617
Wherein, it is made
Figure BDA00027699012600000618
Then its probability density function is
Figure BDA0002769901260000071
Further, let
Figure BDA0002769901260000072
Then gamma is kij Has a probability density function of
Figure BDA0002769901260000073
To calculate APEP, γ is first calculated kij Has a moment mother function of
Figure BDA0002769901260000074
Due to the fact that
Figure BDA0002769901260000075
Then
Figure BDA0002769901260000076
Obtained by using the calculation of the kirsch product
Figure BDA0002769901260000077
Wherein the content of the first and second substances,
Figure BDA0002769901260000078
and
Figure BDA0002769901260000079
denotes convolution operation. Therefore, the temperature of the molten metal is controlled,
Figure BDA00027699012600000715
can be determined by a probability density function of
Figure BDA00027699012600000710
Is obtained by laplace transformation
Figure BDA00027699012600000711
According to the formulas (15) and (16), we can calculate APEP as
Figure BDA00027699012600000712
Application relationship
Figure BDA00027699012600000713
APEP can be simplified into
Figure BDA00027699012600000714
Therefore, the average bit error rate of OSTSK obtained by substituting equation (18) into equation (6) is expressed as
Figure BDA0002769901260000081
Orthogonal matching pursuit decoding algorithm based on threshold value
Although the maximum likelihood detection algorithm is a receiver detection algorithm with the best performance, when the number of lasers at the transmitting end and the receiving end is large, the calculation complexity is high, and ML is generally used as a performance boundary to measure the performance of other decoding algorithms. Therefore, the invention introduces a compressive sensing theory aiming at the sparsity of the signals transmitted by the OSTSK system, provides a threshold-based orthogonal matching pursuit (T-OMP) algorithm, further reduces the computational complexity of the OSTSK system, and promotes the application of the system in practice. The specific decoding algorithm is as follows:
OSTSK- (T-OMP) algorithm process
Figure BDA0002769901260000082
Figure BDA0002769901260000091
Finally, will
Figure BDA0002769901260000092
And performing demapping to recover the original transmitted information bits.
To further illustrate the correctness of the method of the present invention, it was verified by simulation using Monte Carlo (Monte Carlo) method. In the simulation process, (N) is adopted for convenient identification t ,N r ) To label the parameters of the OSTSK system. The simulation parameters take the values as follows: eta 0.5, L1000 m, weak turbulence
Figure BDA0002769901260000093
Medium turbulence
Figure BDA0002769901260000094
And strong turbulence
Figure BDA0002769901260000095
Simulations were performed at medium turbulence, not specifically illustrated in the figures below.
FIG. 3 shows the theoretical upper bound of error code rate and Monte Carlo simulation performance when the OSTSK system adopts the ML detection algorithm. As can be seen from fig. 3: the theoretical upper bound curve of the error code rate is superposed with the actual curve at the time of high signal-to-noise ratio, and the correctness of theoretical derivation is proved. Since the transmission rate of the OSTSK increases with the number of lasers, the increase in the number of lasers leads to a loss of system error performance. Therefore, the increase in transmission rate of the OSTSK system comes at the cost of the loss of system performance.
Fig. 4 is a graph of the effect of different turbulence intensities on the error performance of an OSTSK system. As can be seen from fig. 4: the OSTSK-MLSD scheme loses about 9dB and 13.2dB more signal-to-noise ratio under weak turbulence conditions than under medium and strong turbulence conditions, respectively. That is, the OSTSK-MLSD scheme performs less under conditions of weak turbulence than under conditions of medium and strong turbulence. This is because the performance of the OSTSK-MLSD system depends on the difference between the channel gains. The larger the subchannel difference, the better the system performance. In addition, the OSST can effectively resist the influence of turbulence on the system error performance. Under the condition of strong turbulence, the OSTSK-OSST-MLSD scheme has BER of 1 × 10 -3 The error performance in time is improved by about 5dB over the OSTSK-MLSD scheme. Therefore, the introduction of OSST in the proposed solution is an effective measure against the turbulent effect.
Fig. 5 and 6 show the error performance and computational complexity of the OSTSK system when different decoding algorithms are used. As can be seen from fig. 4, when the T-OMP algorithm is used, the error performance decreases as θ increases. When theta is less than or equal to 1, the T-OMP algorithm approaches the maximum likelihood optimal detection, but the calculation complexity is reduced by 70.42 percent compared with ML; when θ is increased from 1 to 3, the system error performance is lost by 5dB, and the computational complexity is reduced by 30.42%. As can be seen from the above, as the threshold of the T-OMP algorithm increases, the system performance will be lost to some extent, but the decoding complexity will be reduced to a greater extent. Therefore, the reasonable selection of the threshold can make the system error rate and the calculation complexity reach an effective compromise.
FIG. 7 is a comparison of OSTSK versus OSSK and OGSSK system performance. As can be seen from fig. 7: under the condition that the spectral efficiency is 1bit/s/Hz, the error code performance of (4,4) OSTSK-MLSD is better than that of (2,4) OSSK-MLSD and (3,4) OGSSK-MLSD, and the transmission rate of the OSTSK-MLSD is improved by 3bpcu compared with that of the OSSK-MLSD. (II) under the same construction cost condition, (III)The error code performance of the 4,4) OSTSK-MLSD is better than that of the (4,4) OSSK-MLSD and the (4,4) OGSSK-MLSD, and the transmission rate of the OSTSK-MLSD is improved by 2bpcu compared with that of the OSSK-MLSD and the OGSSK-MLSD. And thirdly, a laser selection algorithm is introduced, so that the error code performance of the system can be greatly improved. When BER is 1 × 10 -3 And in time, the system performance is improved by 8dB after the laser selection algorithm is adopted. Therefore, the OSTSK-OSST-MLSD system has a higher transmission rate and an optimal bit error rate, but at the cost of increased system computational complexity. And fourthly, introducing a T-OMP algorithm in order to reduce the computational complexity of the OSTSK system. When BER is 1 × 10 -3 While the signal-to-noise ratio is lost by 1.3dB, its computational complexity is reduced by about 74.3%. .
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (4)

1. An optical space-time keying modulation method suitable for a turbulent flow channel, characterized by:
at a sending end: dividing a binary bit stream into bit data blocks with specific lengths after serial/parallel conversion, performing index mapping on the bit data blocks formed by the binary bit stream according to a diffusion matrix rank maximization criterion to activate lasers, mapping the bit data blocks into an orthogonal space-time diffusion matrix, wherein only one laser is activated in each column of the orthogonal space-time diffusion matrix, each laser is activated only once in a plurality of continuous columns, and selecting a transmission signal in an orthogonal space-time diffusion matrix set by using a laser selection algorithm of a channel norm maximization criterion according to channel state information;
during transmission: the signal passes through an atmospheric turbulence channel;
at the receiving end: after receiving the signal, recovering the original bit data block after the detection and the de-mapping of the orthogonal matching tracking decoding algorithm;
and (3) calculating: and (3) deriving the average bit error rate of the optical space-time keying modulation system under a turbulent flow channel by using a joint bound technology.
2. An optical space-time keying modulation method suitable for turbulent flow channels according to claim 1, characterized in that: at a receiving end, a photoelectric detector is adopted to receive signals, and the received signals are as follows:
Y＝ηP t HX+n
where eta is the photoelectric conversion efficiency, P t Is the peak power, n is the obedient mean μ n Variance is
Figure FDA0003612132030000011
The vector of white gaussian noise of (a),
Figure FDA0003612132030000012
is N r ×N t The channel fading coefficient matrix of (1).
3. An optical space-time keying modulation method suitable for turbulent flow channels according to claim 1, characterized in that: the detection of the orthogonal matching pursuit decoding algorithm needs to be based on threshold detection.
4. An optical space-time keying modulation method suitable for turbulent flow channels according to claim 1, characterized in that: the average bit error rate expression of the optical space-time keying modulation system under the turbulent flow channel is as follows:
Figure FDA0003612132030000013
in the formula (I), the compound is shown in the specification,
Figure FDA0003612132030000014
alpha and beta respectively represent large and small scale scattering coefficients; ρ represents the received signal-to-noise ratio; τ denotes
Figure FDA0003612132030000021
An arithmetic average of the number of occurrences is possible.
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