CN109586772B - Multi-antenna wireless relay MIMO system and transmission method thereof - Google Patents

Multi-antenna wireless relay MIMO system and transmission method thereof Download PDF

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CN109586772B
CN109586772B CN201910014842.5A CN201910014842A CN109586772B CN 109586772 B CN109586772 B CN 109586772B CN 201910014842 A CN201910014842 A CN 201910014842A CN 109586772 B CN109586772 B CN 109586772B
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relay node
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CN109586772A (en
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杨芷华
黄丽美
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Wuyi University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/14—Relay systems
    • H04B7/15—Active relay systems
    • H04B7/155—Ground-based stations

Abstract

The invention discloses a multi-antenna wireless relay MIMO system, comprising: a source node S, a relay node R and a destination node D; an orthogonal spatial modulation system is used for transmission between nodes S, R and R, D. Simulation experiments are carried out on the relay MIMO communication system based on the orthogonal space modulation under the amplifying and forwarding protocol and the decoding and forwarding protocol. The invention has the advantages that: has better error code performance.

Description

Multi-antenna wireless relay MIMO system and transmission method thereof
Technical Field
The invention relates to the technical field of wireless communication, in particular to a multi-antenna wireless relay MIMO system based on orthogonal space modulation and a transmission method thereof.
Background
Spatial Modulation (SM) to improve transmission performance in wireless communication systems[1-3]The antenna can not only transmit information by using modulation symbols, but also transmit information by using the spatial position of the antenna, which is a transmission scheme that people pay more and more attention to. Quadrature Spatial Modulation (QSM)[4]Is a novel space modulation technology which can eliminate the correlation of channels so as to improve the performance of the MIMO communication system[5-7]. The orthogonal space modulation divides a group of information bit stream into three parts in each transmission time slot, one part is mapped into corresponding M-QAM modulation symbols according to the adopted modulation mode, and the other two parts are respectively used for mapping the antenna positions of the real part and the imaginary part of the transmitted modulation symbols.
In wireless communication network, relay transmission mode can extend wireless coverage[8]Can improve the reliability of the wireless network[9]To improve transmission performance of a relay MIMO communication system [10]]A multi-relay AF-MISO communication system based on orthogonal spatial modulation is researched in a multi-relay wireless communication system; document [11]In order to improve the error code performance of a wireless relay system with a direct route between receiving and transmitting, a DF-MISO communication system based on orthogonal space modulation is researched; and document [12 ]]The error code performance of the two-way relay cooperative communication system based on orthogonal space modulation under the decoding forwarding protocol is researched. In the relay transmission system based on orthogonal spatial modulation in the wireless communication network, the relay node is a single antenna.
Reference to the literature
[1]Ganesan S,Mesleh R,Haas H,et al.On the Performance of Spatial Modulation OFDM[C]Signals,Systems and Computers,2006.ACSSC'06.Fortieth Asilomar Conference on.IEEE,2006:1825-1829；
[2]R.Mesleh,H.Haas,C.W.Ahn,and S.Yun,―Spatial modulation—A new low-complexity spectral efficiency enhancing technique,”in Proc.CHINACOM,Oct.25–27,2006,pp.1–5；
[3]R.Mesleh,H.Haas,C.W.Ahn,and S.Yun,―Spatial modulation–OFDM,”in Proc.11th InOWo,Aug.30–31,2006,pp.288–292；
[4]Mesleh R,Althunibat S,Younis A.Differential Quadrature Spatial Modulation[J].Etri Journal,2015,39(99):1-1；
[5]Mesleh R,Ikki S S.A High Spectral Efficiency Spatial Modulation Technique[C]Vehicular Technology Conference.IEEE,2014:1-5；
[6]Mesleh R,Ikki S S.On the impact of imperfect channel knowledge on the performance of quadrature spatial modulation[C]Wireless Communications and Networking Conference.IEEE,2015:534-538；
[7]Younis A,Mesleh R,Haas H.Quadrature Spatial Modulation Performance Over Nakagamim Fading Channels[J].IEEE Transactions on Vehicular Technology,2016,65(12):10227-10231；
[8]Dahlman E,Parkvall S,
Figure BDA0001938673530000031
J,et al.3G Evolution:HSPA and LTE for mobilebroadband[J].pp22,2008；
[9]Wang B,Zhang J,Host-Madsen A.On the capacity of MIMO relay channels[J].IEEE Transactions on Information Theory,2005,51(1):29-43；
[10]Afana A,Mesleh R,Ikki S,et al.Performance of Quadrature Spatial Modulation in Amplify-and-Forward Cooperative Relaying[J].IEEE Communications Letters,2016,20(2):240-243；
[11]Afana A,Erdogan E,Ikki S.Quadrature Spatial Modulation for Cooperative MIMO 5G Wireless Networks[C]GLOBECOM Workshops.IEEE,2017:1-5；
[12]Althunibat S,Mesleh R.Performance Analysis of Quadrature Spatial Modulation in Two-Way Relaying Cooperative Networks[J].Iet Communications,2017,12(4)。
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a multi-antenna wireless relay MIMO system and a transmission method thereof, which can effectively solve the problems in the prior art.
In order to realize the purpose, the technical scheme adopted by the invention is as follows:
a multi-antenna wireless relay MIMO system comprising: a source node S, a relay node R and a destination node D; an orthogonal spatial modulation system is used for transmission between nodes S, R and R, D.
The source node S, the relay node R and the destination node D are respectively provided with NS、NRAnd NDN is formed between root antenna and node S, RR×NSDimension channel matrix H, N formed between nodes R, DD×NRThe channel matrix G is maintained.
H. G is respectively represented as:
Figure BDA0001938673530000041
Figure BDA0001938673530000042
(1) in the formula
Figure BDA0001938673530000043
hji、glkAll obey a complex gaussian distribution with a mean of 0 and a variance of 1.
The quadrature space modulation system is provided with NtRoot transmitting antenna and NrA root receiving antenna; in each transmission period, the source is generated to a length of
Figure BDA0001938673530000044
Is divided into a stream of binary information bits c of length b1＝log2(M)、b2＝log2(Nt) And b3＝log2(Nt) C ofb1、cb2And cb3Three parts
Figure BDA0001938673530000045
Length b1Of the information bit stream cb1Constellation symbol set S ═ S in M-QAM modulation1,s2,...,sMMapping into modulation symbol s ═ s in }re+jsim(S ∈ S); length b2、b3Of the information bit stream cb2、cb3Respectively for use in NtSelecting the a-th transmitting antennaiRoot, ajRoot aerial emission sreAnd sim(ai,aj∈{1,2,...,Nt}). According to ai，ajIs mapped to form NtThe dimension transmit vector x has two cases:
①ai≠ajwhen the temperature of the water is higher than the set temperature,
Figure BDA0001938673530000046
②ai＝ajwhen the temperature of the water is higher than the set temperature,
Figure BDA0001938673530000047
sending vector x via Nr×NtThe dimensional channel matrix H reaches the receiving end, and the receiving end receives NrThe x 1-dimensional signal y is:
y＝Hx+n (4)
(4) in the formula
Figure BDA0001938673530000048
(4) The column vector by H in the formula can be written as:
Figure BDA0001938673530000051
assuming that the receiving end knows the channel matrix H, the maximum likelihood detection (ML) algorithm is adopted to detect the channel matrix H according to the H and the received vector y
Figure BDA0001938673530000052
And recovering a bit stream of length b
Figure BDA0001938673530000053
Figure BDA0001938673530000054
(6) In the formula | · | non-conducting phosphor2Is Frobenius norm.
Based on the transmission method of the multi-antenna relay MIMO system, in a transmission time slot of the system, orthogonal space modulation transmission is adopted between the node S, R and the node R, D, and the whole communication process is divided into two stages: the first stage is that the source node S sends a signal to the relay node R; in the second stage, the relay node R forwards the received signal to the destination node D according to two processing modes.
The first processing mode is QSM-AF-MIMO
In the first phase of each transmission time slot, the information bit stream of the source node S reaches the relay node R according to the transmission vector x generated by the orthogonal space modulation transmission scheme from the transmission channel to form NRX 1 dimensional yS,R：
yS,R＝haisre+jhajsim+nS,R (7)
(7) In the formula nS,RN of (A)RThe elements are the same as the element distribution of n in the formula (4), namely nk～CN(0,σR 2)
In the second stage, according to the reference [10]]The relay node R adopts an Amplification Forwarding (AF) transmission mode to transmit yS,RForm a vector AyS,R(A is the amplification factor of the relay node) and node D receives Ay transmitted through the wireless channelS,RFormed NDX 1 dimensional signal vector yR,DComprises the following steps:
yR,D＝G(AyS,R)+nR,D＝G(Ahisre+Ajhjsim)+GAnS,R+nR,D (8)
(8) amplification factor in formula
Figure BDA0001938673530000061
nR,DN in (1)DThe elements are also the same as the element distribution of n in the formula (4), nk to CN (0, sigma)D 2)
Similarly, assuming node D knows the channel matrices H and G, node D will depend on H and G and the received signal yR,DCan be detected according to the formula (6)
Figure BDA0001938673530000062
And recovering the bit stream
Figure BDA0001938673530000063
Figure BDA0001938673530000064
The second processing mode is QSM-DF-MIMO
The number of the antennas configured for the source node S and the relay node R is N respectivelyS、NRModulation symbol constellation is MS-QAM and MR-QAM and having:
Figure BDA0001938673530000065
in the first stage of each transmission time slot, the communication mode from the source node S to the relay node R is the same as that of the QSM-AF-MIMO system, and the relay node R receives yS,RThen, for yS,RDetecting bit stream c with recovery length b according to formula (6)R。
In the second phase of each transmission slot, the relay node R recovers the bit stream c of length bRThen forming a transmitting vector x according to an orthogonal space modulation modeR。xRVia N between the relay node R and the destination node DD×NRThe dimensional channel matrix G is transmitted to a destination node D, and the node D receives NDX 1 dimensional signal yR,DComprises the following steps:
Figure BDA0001938673530000066
(10) n in the formulaR,DThe same as in the formula (8).
yR,DAccording to the formula (6)
Figure BDA0001938673530000071
And restores the bit stream cD of b length:
Figure BDA0001938673530000072
compared with the prior art, the invention has the advantages that: when the antenna configuration of the wireless relay communication system is the same, the error code performance of the QSM-AF-MIMO and the QSM-DF-MIMO system is obviously improved compared with the relay MIMO system based on the traditional spatial modulation designed in the document [10 ]. Finally, the two transmission schemes are compared to find that the decoding forwarding protocol has better error code performance compared with the amplifying forwarding protocol along with the increase of the number of the relay node antennas.
Drawings
Fig. 1 is a block diagram of a multi-antenna wireless relay MIMO communication system according to embodiment 1 of the present invention;
FIG. 2 is a block diagram of an orthogonal spatial modulation system according to embodiment 1 of the present invention;
FIG. 3 is a QSM-AF-MIMO system error code curve diagram in embodiment 1 of the present invention;
FIG. 4 is a simulation graph of a QSM-DF-MIMO system in accordance with embodiment 1 of the present invention; -
FIG. 5 is a diagram of error code curves of QSM-AF-MIMO and QSM-DF-MIMO transmission schemes at different antennas of a relay node in the example 1 of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings by way of examples.
As shown in fig. 1, the multi-antenna wireless relay MIMO communication system includes: a source node S, a relay node R and a destination node D;
the source node S, the relay node R and the destination node D are respectively provided with NS、NRAnd NDN is formed between root antenna and node S, RR×NSDimension channel matrix H, N formed between nodes R, DD×NRThe channel matrix G is maintained.
H. G is respectively represented as:
Figure BDA0001938673530000081
Figure BDA0001938673530000082
(1) in the formula
Figure BDA0001938673530000083
hji、glkAll obey a complex gaussian distribution with a mean of 0 and a variance of 1.
In a transmission time slot of the system, the node S, R and the node R, D both use orthogonal space modulation transmission, and the whole communication process is divided into two stages: the first stage is that the source node S sends a signal to the relay node R; in the second stage, the relay node R processes the received signal in two ways (see the transmission scheme based on orthogonal spatial modulation in the multi-antenna relay MIMO system), and forwards the processed signal to the destination node D.
Quadrature Spatial Modulation (QSM)
As shown in FIG. 2, the quadrature spatial modulation system is provided with NtRoot transmitting antenna and NrThe root receives the antenna. In each transmission period, the source is generated to a length of
Figure BDA0001938673530000084
Is divided into a stream of binary information bits c of length b1＝log2(M)、b2＝log2(Nt) And b3＝log2(Nt) C ofb1、cb2And cb3Three parts
Figure BDA0001938673530000085
Length ofIs b is1Of the information bit stream cb1Constellation symbol set S ═ S in M-QAM modulation1,s2,...,sMMapping into modulation symbol s ═ s in }re+jsim(S ∈ S); length b2、b3Of the information bit stream cb2、cb3Respectively for use in NtSelecting the a-th transmitting antennaiRoot, ajRoot aerial emission sreAnd sim(ai,aj∈{1,2,...,Nt}). According to ai，ajIs mapped to form NtThe dimension transmit vector x has two cases:
③ai≠ajwhen the temperature of the water is higher than the set temperature,
Figure BDA0001938673530000091
④ai＝ajwhen the temperature of the water is higher than the set temperature,
Figure BDA0001938673530000092
sending vector x via Nr×NtThe dimensional channel matrix H reaches the receiving end, and the receiving end receives NrThe x 1-dimensional signal y is:
y＝Hx+n (4)
(4) in the formula
Figure BDA0001938673530000093
(4) The column vector by H in the formula can be written as:
Figure BDA0001938673530000094
assuming that the receiving end knows the channel matrix H, the maximum likelihood detection (ML) algorithm is adopted to detect the channel matrix H according to the H and the received vector y
Figure BDA0001938673530000095
And recovering a bit stream of length b
Figure BDA0001938673530000096
Figure BDA0001938673530000097
(6) In the formula | · | non-conducting phosphor2Is Frobenius norm.
Transmission scheme based on orthogonal spatial modulation in multi-antenna relay MIMO system
QSM-AF-MIMO
In a multiple-antenna relay network based on orthogonal spatial modulation amplify-and-forward transmission scheme (QSM-AF-MIMO) designed according to the block diagram of the multiple-antenna wireless relay MIMO system shown in FIG. 1, in the first stage of each transmission time slot, a transmission vector x generated by an information bit stream of a source node S according to the orthogonal spatial modulation transmission scheme arrives at a relay node R from a transmission channel to form NRX 1 dimensional yS,R：
Figure BDA0001938673530000101
(7) In the formula nS,RN of (A)RThe elements are the same as the distribution of n in the formula (4), namely nk to CN (0, sigma)R 2)
In the second stage, according to the reference [10]]The relay node R adopts an Amplification Forwarding (AF) transmission mode to transmit yS,RForm a vector AyS,R(A is the amplification factor of the relay node) and node D receives Ay transmitted through the wireless channelS,RFormed ND ×1Dimension signal vector yR,DComprises the following steps:
yR,D＝G(AyS,R)+nR,D＝G(Ahisre+Ajhjsim)+GAnS,R+nR,D (8)
(8) amplification factor in formula
Figure BDA0001938673530000102
nR,DN in (1)DEach element is also in phase with the element distribution of n in the formula (4)Same, nk to CN (0, sigma)D 2)
Similarly, assuming node D knows the channel matrices H and G, node D will depend on H and G and the received signal yR,DCan be detected according to the formula (6)
Figure BDA0001938673530000103
And recovering the bit stream
Figure BDA0001938673530000104
Figure BDA0001938673530000105
QSM-DF-MIMO
In a decoding forwarding transmission scheme (QSM-DF-MIMO) based on orthogonal spatial modulation in a multi-antenna relay network designed according to a block diagram of a multi-antenna wireless relay MIMO system shown in FIG. 1, the number of antennas configured for a source node S and a relay node R is N respectivelyS、NRModulation symbol constellation is MS-QAM and MR-QAM and having:
Figure BDA0001938673530000106
in the first stage of each transmission time slot, the communication mode from the source node S to the relay node R is the same as that of the QSM-AF-MIMO system, and the relay node R receives yS,RThen, for yS,RDetecting bit stream c with recovery length b according to formula (6)R。
In the second phase of each transmission slot, the relay node R recovers the bit stream c of length bRThen forming a transmitting vector x according to an orthogonal space modulation modeR。xRVia N between the relay node R and the destination node DD×NRThe dimensional channel matrix G is transmitted to a destination node D, and the node D receives NDX 1 dimensional signal yR,DComprises the following steps:
Figure BDA0001938673530000111
(10) n in the formulaR,DThe same as in the formula (8).
yR,DAccording to the formula (6)
Figure BDA0001938673530000112
And recovering a bit stream c of length bD：
Figure BDA0001938673530000113
Simulation experiment
The multi-antenna relay MIMO system based on orthogonal spatial modulation designed according to fig. 1 and fig. 2, here, experimental simulation was performed on the communication system under the amplify-and-forward protocol and the decode-and-forward protocol, respectively. The system is configured to: n is a radical ofS＝4,ND＝4, N R1,2, 4. Wherein, in the comparison experiment of QSM and SM, the transmission bit number is fixed, i.e.
Figure BDA0001938673530000114
Therefore, the SM-MIMO system needs to select proper M under the condition that the number of antennas is the same as that of the QSM-MIMO systemSMThe QAM modulation scheme satisfies the above condition.
QSM-AF-MIMO communication system
FIG. 3 is a graph showing a simulation of a QSM-AF-MIMO system. With relay node NRIncrease of (2), i.e. NREqual to 1,2 and 4, respectively, and BER equal to 10-3In time, the error code performance of the AF-MIMO system based on the orthogonal spatial modulation is about 1.5dB, 1.8dB and 2dB of gains compared with the AF-MIMO system based on the traditional spatial modulation.
QSM-DF-MIMO communication system
FIG. 4 is a graph showing a simulation of a QSM-DF-MIMO system. From the simulation curve, when BER is 10-3，NRWhen the error code performance of the QSM-DF-MIMO system is equal to 1,2 and 4 respectively, compared with a DF-MIMO system based on traditional spatial modulation, the QSM-DF-MIMO system has gains of about 0.7dB, 1.6dB and 3dB respectively.
As shown in FIG. 5, the QSM-AF-MIMO system and the QSM-DF-MIMO system have different antennas at the relay node RAnd (5) lowering an error code graph. From the simulation curve, when BER is 10-3，NRWhen the error code performance of the DF-MIMO system is 1, the error code performance of the AF-MIMO system is not greatly different; n is a radical ofRThe DF-MIMO system has about 2.1dB and 5.7dB gains in error performance compared to the AF-MIMO system, 2 and 4 respectively.
It will be appreciated by those of ordinary skill in the art that the examples described herein are intended to assist the reader in understanding the manner in which the invention is practiced, and it is to be understood that the scope of the invention is not limited to such specifically recited statements and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (1)

1. A multi-antenna wireless relay MIMO system, comprising: a source node S, a relay node R and a destination node D; both nodes S, R and R, D are transmitted using orthogonal spatial modulation systems;
the source node S, the relay node R and the destination node D are respectively provided with NS、NRAnd NDN is formed between root antenna and node S, RR×NSDimension channel matrix H, N formed between nodes R, DD×NRA dimensional channel matrix G;
H. g is respectively represented as:
Figure FDA0002811658660000011
Figure FDA0002811658660000012
(1) in the formula
Figure FDA0002811658660000013
hji、glkAll obey complex Gaussian distribution with mean value of 0 and variance of 1;
the quadrature spatial modulation system is provided with NtRoot transmitting antenna and NrA root receiving antenna; in each transmission period, the source is generated to a length of
Figure FDA0002811658660000014
Is divided into a stream of binary information bits c of length b1＝log2(M)、b2＝log2(Nt) And b3＝log2(Nt) Is/are as follows
Figure FDA0002811658660000015
And
Figure FDA0002811658660000016
in the three parts, the first part and the second part,
Figure FDA0002811658660000017
length b1Of the information bit stream
Figure FDA0002811658660000018
Constellation symbol set S ═ S in M-QAM modulation1,s2,...,sMMapping into modulation symbol s ═ s in }re+jsim(S ∈ S); length b2、b3Of the information bit stream
Figure FDA0002811658660000019
Respectively for use in NtSelecting the a-th transmitting antennaiRoot, ajRoot aerial emission sreAnd sim，ai,aj∈{1,2,...,Nt}; according to ai，ajIs mapped to form NtThe dimension transmit vector x has two cases:
①ai≠ajwhen the temperature of the water is higher than the set temperature,
Figure FDA00028116586600000110
②ai＝ajwhen the temperature of the water is higher than the set temperature,
Figure FDA00028116586600000111
sending vector x via Nr×NtThe dimensional channel matrix H reaches the receiving end, and the receiving end receives NrThe x 1-dimensional signal y is:
y＝Hx+n (4)
(4) in the formula
Figure FDA0002811658660000021
(k∈{1,2,...,Nr})，nk～CN(0,σ2)；
(4) The column vector by H in the formula can be written as:
Figure FDA0002811658660000022
assuming that the receiving end knows the channel matrix H, the maximum likelihood detection (ML) algorithm is adopted to detect the channel matrix H according to the H and the received vector y
Figure FDA0002811658660000023
And recovering a bit stream of length b
Figure FDA0002811658660000024
Figure FDA0002811658660000025
(6) In the formula | · | non-conducting phosphor2Is a Frobenius norm;
in a transmission time slot of the system, the node S, R and the node R, D both use orthogonal space modulation transmission, and the whole communication process is divided into two stages: the first stage is that the source node S sends a signal to the relay node R; in the second stage, the relay node R forwards the received signal to a destination node D according to a QSM-AF-MIMO processing mode; or in the second stage, the relay node R forwards the received signal to the destination node D according to the QSM-DF-MIMO processing mode;
QSM-AF-MIMO: in the first phase of each transmission time slot, the information bit stream of the source node S reaches the relay node R according to the transmission vector x generated by the orthogonal space modulation transmission scheme from the transmission channel to form NRX 1 dimensional yS,R：
yS,R＝haisre+jhajsim+nS,R (7)
(7) In the formula nS,RN of (A)RThe elements are the same as the element distribution of n in the formula (4), namely nk～CN(0,σR 2) In the second stage, the relay node R adopts an amplification forwarding transmission mode to transmit yS,RForm a vector AyS,RTransmitting, A is the amplification factor of the relay node, and D receives Ay transmitted by the wireless channelS,RFormed NDX 1 dimensional signal vector yR,DComprises the following steps:
yR,D＝G(AyS,R)+nR,D＝G(Ahisre+Ajhjsim)+GAnS,R+nR,D (8)
(8) amplification factor in formula
Figure FDA0002811658660000031
nR,DN in (1)DEach element is also distributed in the same manner as n in the formula (4), nk～CN(0,σD 2)
Similarly, assuming node D knows the channel matrices H and G, node D will depend on H and G and the received signal yR,DCan be detected according to the formula (6)
Figure FDA0002811658660000032
And recovering the bit stream
Figure FDA0002811658660000033
Figure FDA0002811658660000034
QSM-DF-MIMO: the number of the antennas configured for the source node S and the relay node R is N respectivelyS、NRModulation symbol constellation is MS-QAM and MR-QAM and having:
Figure FDA0002811658660000035
in the first stage of each transmission time slot, the communication mode from the source node S to the relay node R is the same as that of the QSM-AF-MIMO system, and the relay node R receives yS,RThen, for yS,RDetecting bit stream c with recovery length b according to formula (6)R；
In the second phase of each transmission slot, the relay node R recovers the bit stream c of length bRThen forming a transmitting vector x according to an orthogonal space modulation modeR；xRVia N between the relay node R and the destination node DD×NRThe dimensional channel matrix G is transmitted to a destination node D, and the node D receives NDX 1 dimensional signal yR,DComprises the following steps:
Figure FDA0002811658660000036
(10) n in the formulaR,DThe same as in formula (8);
yR,Daccording to the formula (6)
Figure FDA0002811658660000037
And recovering a bit stream c of length bD：
Figure FDA0002811658660000038
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