CN114448567B - Polarization coding cooperative communication method for FSO system - Google Patents
Polarization coding cooperative communication method for FSO system Download PDFInfo
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- H—ELECTRICITY
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- H04L1/00—Arrangements for detecting or preventing errors in the information received
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
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Abstract
The invention relates to the technical field of wireless communication, in particular to a polarization coding cooperative communication method facing an FSO system, which comprises a cooperative communication mode based on system polarization coding; the relay node uses a decoding forwarding cooperative protocol and sets a forwarding threshold value; the code length of the polarization code is increased, and a cooperative communication mode is used. The invention uses a cooperative communication mode based on system polarization coding, thereby realizing the improvement of the error rate and outage probability performance of the FSO communication system; the decoding forwarding cooperative protocol is used at the relay node, and the forwarding threshold value is set, so that the system performance loss caused by noise signals is effectively avoided; aiming at the problems of strong turbulence and obvious performance degradation of a long-distance communication system, the interference of atmospheric turbulence on the error rate and outage probability performance of the communication system can be restrained by increasing the code length of a polarization code and using a cooperative communication mode.
Description
Technical Field
The invention relates to the technical field of wireless communication, in particular to a polarization coding cooperative communication method facing an FSO system.
Background
The free space optical (FSO, free Space Optical) communication technology is used as a communication technology using light as an information transmission medium, and has the characteristics of large bandwidth, high speed and strong anti-interference performance. In particular, the technology does not need to use fixed frequency band communication, so that spectrum resources are saved to a certain extent. However, in the near-earth turbulence channel wireless optical communication system, when laser is transmitted in the atmosphere, the laser is easily affected by the atmospheric turbulence, so that the problems of light beam arrival angle change, light intensity fluctuation of a receiving end and the like are caused. To overcome the impact of atmospheric turbulence effects on FSO systems, cooperative communication techniques are applied to FSO communication systems that may create spatial diversity to improve system performance.
Document [1] (Han Lijiang, you Yahui. Study of all-optical free-space optical communication relay collaboration scheme [ J ]. Chinese laser, 2016,43 (10): 187-193) in an FSO communication system, the influence of a relay collaboration communication scheme on FSO link performance was analyzed using a Gamma-Gamma turbulence model in combination with a subcarrier intensity modulation direct detection (IM/DD) technique. To analyze the performance of FSO cooperative communication systems in detail, document [2] (Liu Wenya, wang Xiang, zhao Shanghong, mou Di. Hybrid RF/FSO aero communication system performance analysis under three-point cooperative architecture [ J ]. Laser and optoelectronics advances, 2020,57 (21): 129-136) analyzed the impact of turbulence intensity, modulation scheme and diversity communication scheme on the system Outage Probability (OP) and average Bit Error Rate (BER) for hybrid RF/FSO aero communication systems under three-point cooperative architecture. Document [3] (h.lei, h.luo, k. -H.Park, Z.Ren, G.Pan and m. -s.alouini, "Secrecy Outage Analysis of Mixed RF-FSO Systems With Channel Imperfection," in IEEE Photonics Journal, vol.10, no.3, pp.1-13,June 2018,Art no.7904113,doi:10.1109/jphot.2018.2835562) analyzed the privacy-interruption performance of a hybrid RF-FSO communication system under imperfect channel state information, deriving a closed expression for the privacy-interruption probability lower bound under fixed gain relay and variable gain relay. Document [4] (S.Sharma, A.S.Madhukumar and r.swaminothan, "Switching-based cooperative decode-and-forward relaying for hybrid FSO/RF networks," in Journal of Optical Communications and Networking, vol.11, no.6, pp.267-281,June 2019,doi:10.1364/jocn.11.000267) proposes a Switching scheme for an FSO/RF hybrid system that uses selective decoding forwarding relay networks and derives progressive outage probability and symbol error rate expressions with low computational complexity.
Although the above document applies the cooperative communication method to the FSO communication system to improve the performance of the FSO communication system, there is a certain improvement degree.
The coding is used as a key factor affecting the transmission efficiency, and the performance of the FSO cooperative communication system can be improved by selecting a proper coding scheme. Currently, polarization codes are always focused on as a coding method capable of reaching the shannon limit of binary discrete memory-free channels. Due to the low coding complexity and excellent performance, the method becomes a mainstream coding mode of a channel coding part in 5G and has very good development potential. In recent years, with the high-speed development of cooperative communication technology, the application of polarization codes in the cooperative communication field is also becoming more and more widespread. Document [5] (J.Fang et al., "Polar-coded MIMO FSO communication system over gamma-gamma turbulence channel with spatially correlated fading," in Journal of Optical Communications and Networking, vol.10, no.11, pp.915-923, nov.2018, doi: 10.1364/JOCN.10.000915) proposes a polarization-encoded multiple-input multiple-output (MIMO) FSO communication system to combat turbulence-induced fading, investigating the traversing ability of a gamma-gamma model atmospheric turbulence channel in the presence or absence of correlated fading. Document [6] (K.Ito, E.Okamoto, H.Takenaka, H.Kunimori and M.Toyoshima, "Application of polar codes for free space optical communication,"2017IEEE International Conference on Space Optical Systems and Applications (ICSOS), 2017, pp.183-187, doi: 10.1109/ICSOS.2017.8357232) has studied a method for selecting a polarization code freezing bit in an FSO communication system by evaluating the block error rate performance of the FSO communication system, thereby achieving the purpose of improving the performance of the FSO communication system. Document [7] (Chen Xuanxuan. Research on application of polarization codes in optical communication [ D ]. Western A electronics technology university, 2017) proves that the polarization codes can be applied to FSO communication systems, and the bit error rate performance of the polarization codes is superior to that of LDPC codes under the same condition. Document [8] (Shao Dong. Near-earth turbulence wireless optical communication polarization code space-time coding design and implementation [ D ]. Electronic technology university, 2020) applies the method for constructing the polarization code under the AWGN channel to the FSO communication system, researches the problems of single-chain error rate performance, coding mode and the like in the turbulence channel, and discusses the application of the polarization code in the free space optical communication MIMO system.
Cooperative communication modes and polarization encoding can be used in FSO communication systems for the ease of interruption events and the high bit error rate problems that exist in atmospheric turbulence channels. The invention provides an FSO cooperative communication transmission scheme based on system polarization coding. The scheme combines the system polarization code with the cooperative communication mode, and introduces a method for constructing the polarization code in the cooperative communication system.
Disclosure of Invention
The invention aims to provide a polarization coding cooperative communication method for an FSO system, which is used for solving the existing problems: the atmospheric turbulence channel is prone to interruption events and the high bit error rate problems that exist.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a polarization coding cooperative communication method facing FSO system includes the following steps:
s1, constructing an FSO cooperative communication transmission system model consisting of a source node S, a relay node R and a destination node D;
s2, encoding information bits of original information M of the source node S by using a system polarization encoding mode;
s3, during a first time slot:
assume that the information sequence after source node coding is x s ；
The source node S broadcasts a signal x to the relay node R and the destination node D, respectively s ；
The relay node R receives x s Then, decoding the bit error rate and calculating the bit error rate;
if the error rate is lower than the threshold value, extracting an intersection of the S-D direct transmission link frozen bit set and the S-R link information bit set, performing polarization coding on the intersection, and then sending the intersection to a destination node D;
s4. during the second time slot:
the relay node R sends a signal after system polarization coding to the destination node D;
the destination node D firstly uses the signal and the S-R link system polarization code frozen bit set to recover the information bit set of the S-R link to obtain information x r ；
Finally received signal x s And x r And combining by using an EGC mode, and decoding.
Furthermore, a half duplex communication mode is used among the source node S, the relay node R and the destination node D, and a transmission link accords with a gamma-gamma distribution model.
Further, in S3, the channel coefficient of the S-R link is h sr The channel coefficient of the S-D direct transmission link is h sd The received signals of the relay node R and the destination node D are expressed as:
y sr ＝h sr x s +n sr
y sd ＝h sd x s +n sd
wherein n is sr And n sd The mean value of the additive Gaussian white noise of the S-R link and the S-D link is zero, and the variance of each dimension is respectivelyAnd->
Further, in S4, the channel coefficient of the R-D link is h rd Signal y received by destination node D rd Expressed as:
y rd ＝h rd x r +n rd
wherein n is rd Is that the mean value of R-D link is zero and the variance of each dimension isIs added to the white gaussian noise.
Further, the probability density function of the channel state h of each branch is expressed as:
wherein: Γ (·) is a Gamma function, K v (. Cndot.) is a Bessel function of the second type, alpha and beta respectivelyCharacterizing the effective amount of large and small area vortices during scattering;
when the optical radiation at the receiving end is a plane wave, α and β can be expressed as:
wherein, the liquid crystal display device comprises a liquid crystal display device,for Rytov variance, defined as:
wherein, the liquid crystal display device comprises a liquid crystal display device,is the atmospheric refractive index structural constant, k=2pi/λ is the number of light waves, λ is the laser wavelength, and L is the transmission distance between adjacent nodes.
Further, the system polarization coding mode is based on the following principle:
assuming set a is the reliable channel set, then a is a subset of sets {1, …, N }, and the set of transmitted freeze bits may be complementary set a of a c A representation;
the coding mode of the polarization code with the code length of N is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,information bits, which are source information, ">Is the coded information bit, G N Is a generating matrix of order N;
splitting the source information and the generator matrix according to the reliability of the channel, i.eFormula (8) can be written as follows:
in equation (9), the encoded codewordSplit into->Wherein B is any subset of {1, …, N }, formula (9) can be represented by formula (10), formula (11):
wherein G is AB Represents G N Is a sub-matrix of (a);
in systematic polarization encoding, x B Is considered asPart of the data containing only information bits, +.>Is->ComprisesFreezing a portion of the bits.
Furthermore, the relay node R uses DF protocol, the source node S carries out cascade coding of cyclic redundancy check code and polarization code to the information source bit, and transmits the information source bit to the relay node R through S-R link.
Further, when cascade coding of cyclic redundancy check code and polarization code is performed, all information bits of the information source bits participate in CRC coding;
let the input information sequence information bit length be K, use v= { v 1 ,v 2 ,…,v K -representation;
after CRC encoding v, a sequence x with the code length of K+M is obtained i Where i ε {1,2, …, K+M };
then x is i Sending the information sequence into a system polarization code encoder to obtain an information sequence with a code length of NThe length of the frozen bit is N-K;
after passing through the atmospheric turbulence channel, is transmitted to the relay node R, the received signal sequence at R is +.>
Relay node R department pairDecoding to obtain a decoded sequence +.>
In a polar-coded symmetric decode-and-forward relay system, for a randomly degenerated relay channel with orthogonal receivers, only the code rate of the polar code is usedWherein->Is the symmetrical capacity of the system, there is always one polarization code sequence indexed by the block length N, which is for any +.>All have bit error rate +.>Where O (·) represents the asymptotic nature of the function and N is the code length of the polarization code.
Further, wherein S2 includes:
s21, constructing a system polarization code sequence reaching the channel capacity of an S-R link at a source node, wherein the code rate R of the system polarization code is less than I (W SR )，I(W SR ) For mutual information of the channel, assume thatAnd->The set of systematic polarization code freeze bits is defined as:
for a binary discrete memory-less channel, the average pasteurization parameter for the channel is:
wherein Y is the received signal of the channel, and Y is the received signal set;
order theIs F SR Is constructed to encode only the information symbol +.>For an S-D direct transmission link, the construction mode of a system polarization code is the same as that of an S-R link, and a frozen bit set of the S-D link is as follows:
s22, at the relay node, firstly decoding information from the source node, and then extracting to obtainPerforming systematic polarization code coding on the information bits to reach the capacity of an R-D link channel as an indexed information bit set, and finally transmitting the information bits to a destination node;
s23, the information decoded by the destination node comprises partial information sent to the relay node by the source node, namely
UsingAnd F SR Information bit set for recovering S-R link +.>
The destination node gathers the information bits of the S-R linkAnd information bit set of S-D direct transmission link +.>Equal gain combination and mergingAnd decoding the information after the decoding, so that the original information can be recovered.
The invention has at least the following beneficial effects:
the invention uses a cooperative communication mode based on system polarization coding, and realizes the improvement of the error rate and outage probability performance of the FSO communication system. And a decoding forwarding cooperative protocol is used at the relay node, and a forwarding threshold value is set, so that the system performance loss caused by noise signals is effectively avoided. Aiming at the problems of strong turbulence and obvious performance degradation of a long-distance communication system, the interference of atmospheric turbulence on the error rate and outage probability performance of the communication system can be restrained by increasing the code length of a polarization code and using a cooperative communication mode.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a basic system block diagram of a collaborative communication system;
FIG. 2 is a concatenated CRC-Polar code encoding and decoding flow chart;
FIG. 3 is a schematic diagram of bit error rates of a cooperative FSO communication system and a direct link under different turbulence intensities;
FIG. 4 is a schematic diagram of bit error rates of a cooperative FSO communication system and a direct link at different communication distances;
FIG. 5 is a schematic diagram of bit error rates of a collaborative FSO communication system under different code lengths;
FIG. 6 is a schematic representation of outage probabilities for a collaborative FSO communication system at different turbulence intensities;
fig. 7 is a schematic diagram of outage probability of a cooperative FSO communication system at different communication distances.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
1. System and channel model
A system model of the FSO cooperative communication transmission scheme under the system polarization coding is shown in fig. 1, wherein S, R, D is a source node, a relay node and a destination node of the cooperative communication system respectively. And each node uses a half-duplex communication mode, and the transmission link accords with a gamma-gamma distribution model. The source node S and the relay node R use a system polarization coding mode, and the destination node D uses a fast serial cancellation list decoding mode.
In half duplex mode, each node transmits and receives signals by dividing different time slots. In the present system, only information bits of the original information M are encoded using a system polarization encoding scheme. Assume that the information sequence after source node coding is x s During a first time slot of the FSO cooperative communication system, the source node S transmits a signal x to the relay node R and the destination node D, respectively s . The relay node receives x s And then decoding the bit error rate and calculating the bit error rate. If the error rate is lower than the threshold value, extracting an intersection of the S-D direct transmission link frozen bit set and the S-R link information bit set, performing polarization coding processing on the intersection, and then transmitting the intersection to a destination node. Wherein the channel coefficient of the S-R link is h sr The channel coefficient of the S-D link is h sd . The received signals of the relay node R and the destination node D can be expressed as:
y sr ＝h sr x s +n sr (1)
y sd ＝h sd x s +n sd (2)
wherein n is sr And n sd The mean value of the additive Gaussian white noise of the S-R link and the S-D link is zero, and the variance of each dimension is respectivelyAnd->During the second time slot, the relay node R broadcasts the system polarization encoded signal to the destination node D. The destination node D firstly uses the signal and the S-R link system polarization code frozen bit set to recover the information bit set of the S-R link to obtain information x r . Finally received signal x s And x r And combining by using an EGC mode, and decoding. The channel coefficient of the R-D link is h rd So the destination node D receives the signal y rd Can be expressed as:
y rd ＝h rd x r +n rd (3)
wherein n is rd Is that the mean value of R-D link is zero and the variance of each dimension isIs added to the white gaussian noise.
Since the FSO links all follow the gamma-gamma distribution, the Probability Density Function (PDF) of the channel state h of each branch can be expressed as:
wherein: Γ (·) is a Gamma function, K v (. Cndot.) is a Bessel function of the second type. Alpha and beta characterize the effective amount of large and small region vortices, respectively, during scattering. When the optical radiation at the receiving end is a plane wave, α and β can be expressed as:
in the formulas (5) and (6),for Rytov variance, defineThe method comprises the following steps:
wherein the method comprises the steps ofIs the atmospheric refractive index structural constant, k=2pi/λ is the number of light waves, λ is the laser wavelength, and L is the transmission distance between adjacent nodes.
2. System polarization code construction principle under cooperative communication
Since systematic polarization codes have better bit error rate performance than non-systematic polarization codes, systematic polarization coding modes are used in the system. Assuming set a is the reliable channel set, then a is a subset of sets {1, …, N }, and the set of transmitted freeze bits may be complementary set a of a c And (3) representing. The coding mode of the polarization code with the code length of N is as follows:
wherein the method comprises the steps ofInformation bits, which are source information, ">Is the coded information bit, G N Is an N-order generator matrix. The source information and the generator matrix can be split according to the reliability of the channel, i.e./or->Formula (8) can be written as follows:
in equation (9), the encoded codeword may be alsoSplit into->Where B is any subset of {1, …, N }. Formula (9) can be represented by formula (10) and formula (11):
wherein G is AB Can represent G N Is a sub-matrix of (c). In systematic polarization encoding, x B Can also be regarded asPart of the data containing only information bits, +.>Is->Including portions of frozen bits. For non-systematic polarization codes, there is a given parameter +.>Is a non-systematic decoder of (a); then for the system polarization code, if u A And x B Has a one-to-one correspondence with a given parameter +.>Is a system decoder of (a).
In the present system, the relay node uses the DF protocol. And the information source node S carries out cascade coding of check codes and polarization codes on the information source bits and transmits the information source bits to the relay node R through an S-R link. The two code words are cascaded to perform error checking at the relay node R, so that the error correction performance of the medium and short code long polarization codes can be effectively improved, and the error rate performance of the whole cooperative communication system is improved. The encoding and decoding flow of the CRC cascade polarization code is shown in figure 2:
when performing CRC and systematic polarization code cascade coding, all information bits of the source bits participate in CRC coding. The input information sequence has a bit length of K, and v= { v can be used 1 ,v 2 ,…,v K And } represents. After CRC encoding v, a sequence x with the code length of K+M is obtained i Where i ε {1,2, …, K+M }. Then x is i Sending the information sequence into a system polarization code encoder to obtain an information sequence with a code length of NThe frozen bit has a length of N-K. />After passing through the atmospheric turbulence channel, is transmitted to the relay node R, the received signal sequence at R is +.>Next, at the relay node R, p +.>Decoding to obtain a decoded sequence +.>By using CRC to assist in polarization code decoding, burst errors in the decoding process can be effectively detected, so that the decoding performance is improved.
In a polar-coded symmetric decode-and-forward relay system, for a randomly degenerated relay channel with orthogonal receivers, only the code rate of the polar code is usedIs the symmetric capacity of the system), there is always one polarized code sequence indexed by the block length NThe polarization code is for any +.>All have bit error rate +.>Where O (·) represents the asymptotic nature of the function and N is the code length of the polarization code.
The coding cooperation scheme based on the system polarization code comprises the following implementation steps:
at a source node, a system polarization code sequence is constructed which can reach the channel capacity of an S-R link, the code rate R of the system polarization code being less than I (W SR )，I(W SR ) Is the mutual information of the channel. Assume thatAnd->The set of systematic polarization code freeze bits is defined as:
is the average pasteurization parameter for that channel. For a binary discrete memoryless channel, the average papanicolaou parameters for this channel are:
where Y is the received signal of the channel and Y is the set of received signals.
Order theIs F SR Is a complement of (a). The structured systematic polarization code sequence encodes only the information symbols +.>For an S-D direct transmission link, the construction mode of a system polarization code is the same as that of an S-R link, and a frozen bit set of the S-D link is as follows:
secondly, at the relay node, firstly, information from the source node is decoded, and then extracted to obtainAnd (3) carrying out systematic polarization code coding on the information bits which can reach the channel capacity of the R-D link as an indexed information bit set, and finally transmitting the information bits to a destination node.
The information decoded by the destination node comprises partial information sent to the relay node by the source node, namelyA corresponding set of information bits. From literature [15]The frozen bit set of the S-R link of proposition 1 in (R.Blasco-Serrano, R.Thobaben, M.Andersson, V.Rathi and M.Skoglund, "Polar Codes for Cooperative Relaying," in IEEE Transactions on Communications, vol.60, no.11, pp.3263-3273,November 2012,doi:10.1109/TCOMM.2012.081412.110266)>So can useAnd F SR Information bit set for recovering S-R link +.>Finally, the destination node gathers the information bits of the S-R linkAnd S-DInformation bit set of direct transmission link->And performing equal gain combination, and decoding the combined information to recover the original information.
3. Interrupt probability and bit error rate analysis
3.1 outage probability analysis
In collaborative communication systems, a system outage occurs when the instantaneous transmission capacity of a channel is below the current transmission rate or the system signal-to-noise ratio is below a specified signal-to-noise ratio threshold. The probability of the interruption is the interruption probability of the system. This section mainly analyzes outage probabilities of collaborative systems under atmospheric turbulence channels, where R-D links and S-D links are independent of each other.
The point-to-point transmission is direct transmission link transmission in the cooperative communication system, and when interruption occurs, the signal to noise ratio of the link is lower than a specified signal to noise ratio threshold, and the interruption probability can be expressed as follows:
average signal to noise ratio for current linkγ th To specify a signal to noise ratio threshold.
According to document [17] (Li Xiaoyan. Reverse modulation free space optical communication performance under atmospheric turbulence study [ D ]. University of gilin, 2020):
so formula (4) can be written as:
further, it is obtained from the formula (2.13) in the document [17] (Li Xiaoyan. Study on the performance of reverse-modulated free-space optical communication under atmospheric turbulence [ D ]. Jilin university, 2020)
Formula (17) can be written in the following form:
bringing equation (19) into equation (15) yields a break probability for the link of:
in FSO system, average signal to noise ratio of channelAnd signal to noise threshold gamma th The relation between the channel states h isBy using this relationship, the right integral of expression (20) is subjected to integral transformation, and the result is:
from document [12] (B.Jiang, S.Yang, J.Bao, C.Liu, X.Tang and F.Zhu, "Optimized Polar Coded Selective Relay Cooperation With Iterative Threshold Decision of Pseudo Posterior Probability," in IEEE Access, vol.7, pp.53066-53078,2019, doi: 10.1109/ACCESS.2019.291172.) (2.29):
combining equations (20), (21) and (22), the outage probability of the direct link can be finally obtained as follows:
in the cooperative communication system consisting of the source node S, the relay node R and the destination node D, all branches participate in information transmission when information transmission is carried out, wherein the branches comprise a direct transmission link and a relay link, and finally all paths of signals are combined at the destination node D in an equal-gain combination mode. When the relay link is interrupted, the direct transmission link of the cooperative communication system can transmit information; when the direct link is interrupted, the cooperative communication system may transmit information through the relay link. Therefore, the use of cooperative communication reduces the probability of system disruption to some extent. In a cooperative communication system, when an interruption event occurs, the direct link must have the interruption event. Meanwhile, one of the S-R and R-D links must be interrupted. Thus, the outage probability of a cooperative FSO communication system can be expressed as:
P out ＝P S-R P S-D +(1-P S-R )P R-D P S-D
＝P S-R P S-D +P S-R P R-D -P S-R P R-D P S-D (24)
wherein P is S-R 、P R-D 、P S-D The outage probabilities for the S-R, R-D, S-D links, respectively, can be determined by equation (23).
4.2 System error Rate analysis
Let epsilon and epsilon SR 、ε RD Respectively represent eventsAnd error transmission of R-D link, wherein M is original information sent by source node,/or->For system output information->Is the decoded information at the relay node. Let epsilon C 、Are respective complementary events. The error rate of the cooperative FSO communication system of the system polarization coding is expressed as:
at the source node, the code rate R < I (W SR )，Pr(ε SR ) Is defined as the upper bound ofThe second term in formula (25) can be expressed as:
in the above formula ε SR And epsilon RD Are independent of each other. All the items are obtained in the system polarization code construction mode, so that the upper limit of all the items isBy substituting equation (26) into equation (25), the upper limit of the error rate of the cooperative FSO communication system with the system polarization coding can be obtained.
The average bit error rate of an IM/DD optical communication system using on-off keying (OOK) modulation can be expressed as:
P(e)＝P(0)P(e|0)+P(1)P(e|1) (27)
in the expression (27), P (0) and P (1) represent probabilities of transmitting "0" and "1", respectively, and P (e|0) and P (e|1) represent probabilities of errors occurring when "0" and "1" are transmitted, respectively. Since the system uses a binary coding scheme, the probabilities of transmitting 0 and 1 are equal, so that the scheme is not restrictedThe error probability under irradiance I conditions can be obtained as:
wherein eta is photoelectric conversion efficiency, N 0 Is the variance of gaussian white noise. Q (·) is a Gaussian Q function, defined as
Expressed as an error function
By averaging the irradiance I, the average bit error rate of the system can be expressed as:
based on irradiance I and end-to-end instantaneous signal-to-noise ratio gamma end The instantaneous signal-to-noise ratio at the current receiving node is:
the average bit error rate of the system can be expressed as the instantaneous signal-to-noise ratio at the receiving node:
according to a method of constructing a system polarization code in a cooperative communication system, expression (33) satisfies an upper limit of an error rate in expression (26).
4. Simulation results and analysis
Through system simulation, the error rate and the outage probability of the FSO cooperative communication system under the polarization coding are mainly analyzed in this section. Under the proposed system scheme, the system error rate and the outage probability are simulated for different turbulence intensities under the same communication distance and different communication distances under the same refractive index structural constant. The basic parameter settings for the simulation are shown in table 1:
Table 1 basic parametersettings of polarization coding cooperative FSO communication system simulation
in the polarization coding mode, aiming at turbulent flow channels with different intensities, the bit error rate performance of the FSO cooperative communication system is simulated. The code length of the polarization code is set to 1024, the code rate is 0.5, and the decoding mode uses fast serial cancellation list decoding (FastSCL) with CRC check. The relay node of the cooperative communication mode uses a Decoding Forwarding (DF) mode and sets the bit error rate threshold value as 10 -5 The simulation results are shown in fig. 3. Wherein the solid line indicates that a cooperative communication mode is used, and the dotted line indicates that there is no cooperation (i.e. a direct transmission link between the source node S and the destination node D). Simulation results show that the turbulence intensity is 0.3 and the system error rate is 10 -3 When the FSO cooperative communication system is improved by about 0.5dB compared with the direct transmission link, the FSO cooperative communication system shows better gain performance after the signal to noise ratio is greater than 13 dB; turbulence intensity of 0.7 and system error rate of 10 -3 When the FSO cooperative communication system is used, the performance of the FSO cooperative communication system is improved by about 1dB compared with that of a direct transmission link, and the higher the signal-to-noise ratio is, the more obvious the gain is; turbulence intensity of 1.0 and system error rate of 10 -2 When the FSO cooperative communication system is used, the performance of the FSO cooperative communication system is improved by about 1.5dB compared with that of a direct transmission link, and the higher the signal-to-noise ratio is, the more obvious the gain is. From the analysis, the cooperative communication mode can obviously improve the performance of the FSO system of polarization coding, and the stronger the turbulence is, the more obvious the improvement effect is.
Fixed refractive index structural constantThe effect of different communication distances between the source node S and the destination node D on the system error rate is shown in fig. 4. As can be seen from the figure, when the communication distance is 1000m and the system error rate is 10 -3 When the FSO cooperative communication system is used, the performance of the FSO cooperative communication system is improved by about 7dB compared with that of a direct transmission link; when the communication distance is 1500m and the system error rate is 10 -3 When the FSO cooperative communication system is used, the performance of the FSO cooperative communication system is improved by about 3dB compared with that of a direct transmission link; when the communication distance is 2000m and the system error rate is 10 -3 When the FSO cooperative communication system is used, the performance improvement effect of the FSO cooperative communication system is more obvious than that of a direct transmission link. The longer the communication distance, the stronger the intensity of the atmospheric turbulence, so the system error rate performance is slowly reduced. From the above analysis, it can be seen that for FSO communication systems with greater atmospheric turbulence intensity, the longer the communication distance, the more significant the improvement in system performance using cooperative communication means.
The effect of polarization codes of systems with different code lengths on the bit error rate of the FSO cooperative communication system under the same atmospheric turbulence intensity is shown in figure 5. It can be seen from the figure that the shorter the system polarization code length, the poorer the FSO cooperative communication system performance. When the signal-to-noise ratio of the system is lower than 8dB, the code length of the polarization code has little influence on the error rate of the system. After 8dB, the system polarization codes with the code lengths of 1024 and 2048 have similar improvement degree on the system error rate performance. When the error rate of the system is 10 -4 When the system polarization code with the code length 1024 is compared with the system polarization code with the code length 512, the system error rate is improved by about 0.7dB, and the system polarization code with the code length 4096 is improved by about 0.5dB. In the FSO cooperative communication system, decoding is performed at both the relay node R and the destination node D, and multiple decoding results in an increase in the system error rate. Therefore, the code length of the system polarization code is too long, and the improvement degree of the system error rate performance is reduced.
In the FSO communication system, the outage probability performance of the cooperative communication mode is superior to that of the direct transmission link. Fig. 6 compares outage probabilities for FSO cooperative communication systems at different turbulence intensities, and it can be seen from the graph that the system outage performance is best when the turbulence intensity is at a minimum. As the turbulence intensity increases, the system outage performance decreases.When the turbulence intensity is increased to a certain intensity, the FSO cooperative communication system can restrain the occurrence of interruption event under strong turbulence, and the interruption performance of the system is improved. For example, when the turbulence intensity increases from 1.35 to 2.35, the interruption performance of the system decreases; as the turbulence intensity continues to increase to 3.35, the interruption performance of the system improves. When the interruption probability of the system is 10 -4 When the turbulence intensity is increased from 2.35 to 2.85, the signal-to-noise ratio gain of the system is about 1.3 dB; the signal to noise ratio gain of the system is around 5dB when the turbulence intensity increases from 2.85 to 3.35.
At the same refractive index structure constantThe outage probability at different communication distances is shown in fig. 7. As can be seen from the figure, as the communication distance between the source node S and the destination node D increases, the interruption performance of the FSO cooperative communication system decreases. When the distance increases to a certain extent, the FSO cooperative communication system can suppress deterioration of the interruption performance. For example, when the communication distance increases from 1000m to 1500m, the outage probability of the FSO cooperative communication system increases by about 1 order of magnitude when the signal-to-noise ratio is 5dB. When the communication distance is more than 1500m, the interruption performance of the FSO cooperative communication system is improved. When the communication distance increases to 3000m, the outage probability of the FSO cooperative communication system even decreases to 10 -7 The following is given.
5. Summary
In order to improve the performance of the FSO communication system, a cooperative communication mode based on system polarization coding is used, so that the performance improvement of the error rate and the outage probability of the FSO communication system is realized. And a decoding forwarding cooperative protocol is used at the relay node, and a forwarding threshold value is set, so that the system performance loss caused by noise signals is effectively avoided. Aiming at the problems of strong turbulence and obvious performance degradation of a long-distance communication system, the interference of atmospheric turbulence on the error rate and outage probability performance of the communication system can be restrained by increasing the code length of a polarization code and using a cooperative communication mode. Simulation results show that the system polarization code is used for transmitting information bits by selecting channels with good channel quality, so that the error rate of the system can be reduced; the cooperative communication mode is used to obtain space diversity and reduce the error rate and interruption probability of the system. The cooperative communication scheme based on the system polarization coding can be effectively applied to the FSO communication system.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made therein without departing from the spirit and scope of the invention, which is defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (9)
1. The polarization coding cooperative communication method for the FSO system is characterized by comprising the following steps of:
s1, constructing an FSO cooperative communication transmission system model consisting of a source node S, a relay node R and a destination node D;
s2, encoding information bits of original information M of the source node S by using a system polarization encoding mode;
s3, during a first time slot:
assume that the information sequence after source node coding is x s ；
The source node S broadcasts a signal x to the relay node R and the destination node D, respectively s ；
The relay node R receives x s Then, decoding the bit error rate and calculating the bit error rate;
if the error rate is lower than the threshold value, extracting an intersection of the S-D direct transmission link frozen bit set and the S-R link information bit set, performing polarization coding on the intersection, and then sending the intersection to a destination node D;
s4. during the second time slot:
the relay node R sends a signal after system polarization coding to the destination node D;
the destination node D recovers the information of the S-R link by using the signal and the S-R link system polarization code frozen bit setBit set, get information x r ；
Finally received signal x s And x r And combining by using an EGC mode, and decoding.
2. The method for cooperative communication of polarization coding for FSO system according to claim 1, wherein a half duplex communication mode is used among the source node S, the relay node R and the destination node D, and the transmission link conforms to a gamma-gamma distribution model.
3. The polarization-encoded cooperative communication method for an FSO system according to claim 1, wherein in S3, a channel coefficient of an S-R link is h sr The channel coefficient of the S-D direct transmission link is h sd The received signals of the relay node R and the destination node D are expressed as:
y sr ＝h sr x s +n sr
y sd ＝h sd x s +n sd
wherein n is sr And n sd The mean value of the additive Gaussian white noise of the S-R link and the S-D link is zero, and the variance of each dimension is respectivelyAnd->
4. The polarization-encoded cooperative communication method for an FSO system according to claim 3, wherein in S4, the channel coefficient of the R-D link is h rd Signal y received by destination node D rd Expressed as:
y rd ＝h rd x r +n rd
wherein n is rd Is that the mean value of R-D link is zero and the variance of each dimension isIs added to the white gaussian noise.
5. The method for cooperative communication of polarization coding for FSO system according to claim 4, wherein probability density functions of channel states h of each branch are expressed as:
wherein: Γ (·) is a Gamma function, K v (. Cndot.) is a second class of Bessel functions, α and β characterizing the effective amount of large and small region vortices, respectively, during scattering;
when the optical radiation at the receiving end is a plane wave, α and β can be expressed as:
wherein, the liquid crystal display device comprises a liquid crystal display device,for Rytov variance, defined as:
wherein, the liquid crystal display device comprises a liquid crystal display device,is the atmospheric refractive index structural constant, k=2pi/λ is the number of light waves, λ is the laser wavelength, and L is the transmission distance between adjacent nodes.
6. The polarization coding cooperative communication method for the FSO system according to claim 1, wherein the system polarization coding mode is as follows:
assuming set a is the reliable channel set, then a is a subset of sets {1, …, N }, and the set of transmitted freeze bits may be complementary set a of a c A representation;
the coding mode of the polarization code with the code length of N is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,information bits, which are source information, ">Is the coded information bit, G N Is a generating matrix of order N;
splitting the source information and the generator matrix according to the reliability of the channel, i.eFormula (8) can be written as follows:
in equation (9), the encoded codewordSplit into->Wherein B is any subset of {1, …, N }, formula (9) may representFormula (10) and formula (11):
wherein G is AB Represents G N Is a sub-matrix of (a);
in systematic polarization encoding, x B Is considered asPart of the data containing only information bits, +.>Is->Including portions of frozen bits.
7. The cooperative communication method of polarization coding for FSO system according to claim 1, wherein the relay node R uses DF protocol, and the source node S performs cascade coding of cyclic redundancy check code and polarization code on the source bit, and transmits the cyclic redundancy check code and polarization code to the relay node R through the S-R link.
8. The cooperative communication method of polarization encoding for FSO system according to claim 7, wherein all information bits of the source bits participate in CRC encoding when performing cascade encoding of cyclic redundancy check code and polarization code;
let the input information sequence information bit length be K, use v= { v 1 ,v 2 ,…,v K -representation;
after CRC encoding v, a sequence x with the code length of K+M is obtained i Where i ε {1,2, …, K+M };
then x is i Sending the information sequence into a system polarization code encoder to obtain an information sequence with a code length of NThe length of the frozen bit is N-K;
after passing through the atmospheric turbulence channel, is transmitted to the relay node R, the received signal sequence at R is +.>
Relay node R department pairDecoding to obtain a decoded sequence +.>
In a polar-coded symmetric decode-and-forward relay system, for a randomly degenerated relay channel with orthogonal receivers, only the code rate of the polar code is usedWherein->Is the symmetrical capacity of the system, there is always one polarization code sequence indexed by the block length N, which is for any +.>All have bit error rate +.>Wherein O (·) represents the gradient of the functionFurther, N is the code length of the polarization code.
9. The FSO system oriented polarization coded cooperative communication method of claim 1, wherein S2 comprises:
s21, constructing a system polarization code sequence reaching the channel capacity of an S-R link at a source node, wherein the code rate R of the system polarization code is less than I (W SR )，I(W SR ) For mutual information of the channel, assume thatAnd->The set of systematic polarization code freeze bits is defined as:
for a binary discrete memory-less channel, the average pasteurization parameter for the channel is:
wherein Y is the received signal of the channel, and Y is the received signal set;
order theIs F SR Is constructed to encode only the information symbol +.>For S-D direct transmission chainThe construction mode of the system polarization code is the same as that of the S-R link, and the frozen bit set of the S-D link is as follows:
s22, at the relay node, firstly decoding information from the source node, and then extracting to obtainPerforming systematic polarization code coding on the information bits to reach the capacity of an R-D link channel as an indexed information bit set, and finally transmitting the information bits to a destination node;
s23, the information decoded by the destination node comprises partial information sent to the relay node by the source node, namely
UsingAnd F SR Information bit set for recovering S-R link +.>
The destination node gathers the information bits of the S-R linkAnd information bit set of S-D direct transmission link +.>And performing equal gain combination, and decoding the combined information to recover the original information.
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| CN107453807A (en) * | 2017-06-21 | 2017-12-08 | 西安电子科技大学 | A kind of polarization method, device and the electronic equipment of atmospheric optical communication channel model |
| US11063614B1 (en) * | 2019-11-21 | 2021-07-13 | Cadence Design Systems, Inc. | Polar decoder processor |
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