CN113194056A - Orthogonal space-frequency index modulation method adopting Givens precoding and diagonal code word structure - Google Patents

Orthogonal space-frequency index modulation method adopting Givens precoding and diagonal code word structure Download PDF

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CN113194056A
CN113194056A CN202110437262.4A CN202110437262A CN113194056A CN 113194056 A CN113194056 A CN 113194056A CN 202110437262 A CN202110437262 A CN 202110437262A CN 113194056 A CN113194056 A CN 113194056A
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王磊
薛奕蕾
邵彦彰
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Xian Jiaotong University
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    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
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    • 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
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
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Abstract

The invention discloses an orthogonal space-frequency index modulation method adopting Givens precoding and diagonal code word structure. For each resource block, two QAM constellation symbols are used to form a 2 x 1 vector, then two different Givens matrixes are used to precode the real part and the imaginary part of the vector respectively, then the real part and the imaginary part of the coded symbols are placed into a space frequency resource block in a diagonal or anti-diagonal mode to form a code word matrix, and finally the formed code word matrix is placed into a group of active antennas to form a Gi-SFIM sending signal. The invention combines the Givens pre-coding matrix and the diagonal design, so that the invention can obtain second-order transmit diversity; position selection is respectively carried out on the real part and the virtual part of the pre-coded signal, so that the spectrum efficiency is improved; the invention is suitable for any system with even number of antennas for transmitting; under different system configurations, the invention has better error code performance.

Description

Orthogonal space-frequency index modulation method adopting Givens precoding and diagonal code word structure
Technical Field
The invention belongs to the technical field of transmission diversity transmission in a multi-antenna wireless communication system, relates to a diversity transmission technology using a precoding matrix and a diagonal code word structure design in an MIMO-OFDM system, and particularly relates to an orthogonal space-frequency index modulation method adopting Givens precoding and a diagonal code word structure.
Background
The OFDM-IM (e.base, u.aygolu, e.panayirci, and h.v.poor, "Orthogonal frequency division multiplexing with index modulation," IEEE trans.signal process, vol.61, No.22, pp.5536-5549,2013 ") with index modulation is a technique that adds the selection of sub-carriers on the basis of the OFDM technique. The technique divides the OFDM signal into a plurality of sub-blocks, each of which contains the same number of sub-carriers. For each sub-block, the OFDM-IM scheme selects only a part of sub-carriers to activate, and the positions of the activated sub-carriers can be used to transmit a part of information bits, and another part of information bits is carried by modulation symbols transmitted by the activated sub-carriers. After the OFDM-IM proposal, many improvements have been introduced.
In the generalized orthogonal frequency division multiplexing with index modulation OFDM-GIM (r.fan, y.j.yu, and y.l.guan, "general understanding of orthogonal frequency division multiplexing with index modulation," IEEE trans.wireless communication ", vol.14, No.10, pp.5350-5359,2015.), the transmitted constellation symbols are divided into an isotropic component and an orthogonal component, in which the original OFDM-IM technique can be performed on the isotropic component and the orthogonal component simultaneously; in Multiple-mode MM-OFDM-IM (m.wen, e.base, q.li, b.zheng, and m.zhang, "Multiple-mode orthogonal frequency division multiplexing with index modulation," IEEE trans.command ", vol.65, No.9, pp.3892-3906,2017"), information bits are transmitted with different constellations and the order of arrangement of the constellations. Compared with OFDM-IM, the above two schemes can obtain higher spectrum efficiency. While the OFDM-ISIM (y.xiao, s.wang, l.dan, x.lei, p.yang, and w.xing, "OFDM with interleaved subcarrier-index modulation," IEEE commu.let., vol.18, No.8, pp.1447-1450,2014 ") scheme improves system performance by increasing the euclidean distance between modulation symbols, the CI-OFDM-IM (e.base," OFDM with interleaved subcarrier interleaving, "IEEE Wireless Communications Letters, vol.4, No.4, pp. 384,2015) scheme groups every two constellation symbols on the basis of OFDM-IM 381 and exchanges the real and imaginary parts of the two symbols to obtain second order transmit diversity, thereby improving system performance.
The above schemes all use only one transmitting antenna, and in a multi-antenna wireless communication system, MIMO-OFDM-IM (e.base, "Multiple-input Multiple-output OFDM with index modulation," IEEE Signal process.let, vol.22, No.12, pp.2259-2263,2015 ") schemes directly combine MIMO technology and OFDM-IM technology, and extend the OFDM-IM technology to a spatial domain. And the Generalized space-frequency index modulation (GSFIM) technology (t.datta, h.s.eshwaraiah, and a.chockalingam, "Generalized space-and-frequency index modulation," IEEE trans.veh.technol., vol.65, No.7, pp.4911-4924,2016.) divides the signal into orthogonal and homodromous components for transmission on the basis of MIMO-OFDM-IM, further improving the spectral efficiency. In addition, orthogonal space-frequency index modulation (QSF-IM) technology (r.mesleh, s.s.ikki, and h.m.agnoune, "Quadrature spatial modulation," IEEE trans.veh.technol., vol.64, No.6, pp.2738-2742,2015.) not only divides a signal into a co-directional component and a Quadrature component, but also puts the signal into a joint space-frequency unit for transmission, thereby improving system performance by obtaining higher spectral efficiency. But QSF-IM technology does not achieve transmit diversity.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides an orthogonal space-frequency index modulation method adopting Givens precoding and a diagonal code word structure.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
the orthogonal space-frequency index modulation method adopting the Givens precoding and the diagonal code word structure comprises the following steps:
step 1: according to bit p1Determining 2 QAM signals xg,1And xg,2(ii) a Defining a symbol vector:
Figure BDA0003033525920000031
wherein,
Figure BDA0003033525920000032
and
Figure BDA0003033525920000033
respectively represent xg、xg,1And xg,2The real part of (a) is,
Figure BDA0003033525920000034
and
Figure BDA0003033525920000035
respectively represent xg、xg,1And xg,2An imaginary part of (d); order to
Figure BDA0003033525920000036
Multiplying by precoding matrices, respectively
Figure BDA0003033525920000037
Obtaining:
Figure BDA0003033525920000038
Figure BDA0003033525920000039
wherein,
Figure BDA00030335259200000310
not being zero, i.e.
Figure BDA00030335259200000311
Elements cos (θ) in the simultaneous precoding matrix1)、sin(θ1)、cos(θ2)、sin(θ2) Is also not zero;
step 2: according to bit p2Determining precoded real part symbols
Figure BDA00030335259200000312
And
Figure BDA00030335259200000313
according to the bit p3Determining precoded imaginary symbols
Figure BDA00030335259200000314
And
Figure BDA00030335259200000315
the position of (a); i.e. according to bit p2Selecting a real part codeword matrix
Figure BDA00030335259200000316
According to bit p3Selecting an imaginary codeword matrix
Figure BDA00030335259200000317
And
Figure BDA00030335259200000318
is respectively from the set of real part code word matrixes
Figure BDA00030335259200000319
And imaginary codeword matrix set
Figure BDA00030335259200000320
Is selected from; obtaining the selected code word matrix Sg：
Figure BDA00030335259200000321
Wherein, ag,t(τ) represents the codeword matrix SgSymbol on the τ -th subcarrier of the t-th column, τ ═ 1., n, t ═ 1,2 };
and step 3: will NtThe two transmitting antennas are divided into one group in sequence
Figure BDA0003033525920000041
Group, again according to
Figure BDA0003033525920000042
Bit slave
Figure BDA0003033525920000043
Selecting a group of antennas to activate; then the code word matrix SgPut into the active antenna, the transmission symbols of the rest antennas which are not active are represented by 0, thereby generating a Gi-SFIM transmission signal T in the g RBg；
And 4, step 4: combining all the transmission signals of the G groups and then interleaving the combined transmission signals; the combined signal is represented as
Figure BDA0003033525920000044
Passing the combined signal T through a block interleaver n of G x nG×nTo obtain the OFDM signal T to be transmittedin。
The invention further improves the following steps:
2 QAM signals x in the step 1g,1And xg,2Respectively by QAM constellation omega1And Ω2And (4) preparing.
The step 2 is to select
Figure BDA0003033525920000045
And
Figure BDA0003033525920000046
the specific method comprises the following steps:
defining two sets of dispersion matrices χ1Hexix-2The first dispersion matrices of the two are respectively:
Figure BDA0003033525920000047
Figure BDA0003033525920000048
let E1And F1Are all multiplied by right shift matrix in turn
Figure BDA0003033525920000049
Obtaining:
Figure BDA00030335259200000410
Figure BDA00030335259200000411
let the scatter matrix set χ1All the matrices in
Figure BDA00030335259200000412
Let the scatter matrix set χ2All the matrices in
Figure BDA00030335259200000413
The obtained union set of all the matrixes forms a code word matrix set
Figure BDA00030335259200000414
There are 2n codeword matrices;
let the scatter matrix set χ1All the matrices in
Figure BDA00030335259200000415
Let the scatter matrix set χ2All the matrices in
Figure BDA00030335259200000416
The obtained union set of all the matrixes forms a code word matrix set
Figure BDA00030335259200000417
Set of codeword matrices
Figure BDA0003033525920000051
There are 2n codeword matrices.
Activated per codeword matrixThe position of the carrier can carry 2log of information2(2n) bits, the spatial dimension being portable
Figure BDA0003033525920000052
Bit, p log that a modulation symbol can carry2(M1)+log2(M2) Bit, spectral efficiency can be expressed as:
Figure BDA0003033525920000053
where G is the number of groups of subcarriers, N is the total number of subcarriers, LCPIs the length of the cyclic prefix.
Transmit diversity dtIs denoted by dt＝d/NrWherein, the d diversity order is defined as the minimum value of the rank of the error matrix among all different equivalent transmission code matrices.
Finding optimal angle by maximizing minimum coding gain distance
Figure BDA0003033525920000054
For two different code matrices CgAnd
Figure BDA0003033525920000055
the minimum coding gain distance is defined as:
Figure BDA0003033525920000056
wherein λ isiRepresentation matrix
Figure BDA0003033525920000057
I 1.., q, q ═ rank (a); optimum angle
Figure BDA0003033525920000058
According to the formula
Figure BDA0003033525920000059
Determining; when (M)1,M2) When the angle is (2,2), (2,4), (4,4), (4,8), the optimum angle is obtained
Figure BDA00030335259200000510
Are respectively as
Figure BDA00030335259200000511
(3.4,1.1), (1.8,4.5), (1.6,3) radians.
For the interleaved OFDM signal TinSwitching the time domain signal T to the time domain signal T through IFFT conversion to obtain a time domain signal Ttime(ii) a Let time-domain signal TtimeSatisfy the requirement of
Figure BDA00030335259200000512
Wherein E issIs the average energy of a single symbol; after adding length LCPAfter the cyclic prefix and the parallel-serial and analog-to-digital conversion are carried out, the signal is sent through a frequency selective Rayleigh fading channel with the multipath number of L; the total energy that each OFDM block can transmit is
Figure BDA00030335259200000513
The energy carried per bit is
Figure BDA00030335259200000514
The frequency domain signal received by the g-th RB after deinterleaving is represented as:
Figure BDA00030335259200000515
wherein,
Figure BDA00030335259200000516
is the equivalent channel matrix after the g-th RB deinterleaving,
Figure BDA00030335259200000517
is the g group equivalent noise vector obtained after the frequency domain noise vector w is de-interleaved; noise(s)The elements in the vector w have a mean of zero and a variance of N0Of complex Gaussian random variables, i.e.
Figure BDA0003033525920000061
At the same time, the normalized signal transmission vector cgExpressed as:
Figure BDA0003033525920000062
wherein,
Figure BDA0003033525920000063
representing the vector on the τ th subcarrier in the g th RB.
Equivalent channel matrix after g RB de-interleaving
Figure BDA00030335259200000617
Obtained by the following method:
step 1, order
Figure BDA0003033525920000064
A channel matrix representing the ith path in the time domain, wherein L is 0 and L-1, elements in the matrix are complex Gaussian random variables with the average value of 0 and the variance of 1; then the time domain channel matrix HTExpressed as:
Figure BDA0003033525920000065
where vec (·) represents the operation of stacking the matrices in columns;
step 2, setting time domain channel matrix HTAfter CP addition and FFT conversion, NxN is obtainedrNtDimensional frequency domain channel matrix HF(ii) a Let the frequency domain channel matrix HFThrough de-interleaver
Figure BDA0003033525920000066
Obtaining a frequency domain channel matrix after de-interleaving
Figure BDA0003033525920000067
Step 3, order
Figure BDA0003033525920000068
Denotes an equivalent channel vector on the t sub-carrier after deinterleaving in the g RB in the frequency domain, that is
Figure BDA00030335259200000618
Row σ ═ n + τ, τ ═ 1.., n; will be provided with
Figure BDA0003033525920000069
Conversion to Nr×NtMatrix of dimensions
Figure BDA00030335259200000610
Then, the equivalent channel matrix after the g-th RB deinterleaving is expressed as
Figure BDA00030335259200000611
ivec (-) denotes the inverse operation of vec (-).
The frequency domain signal received by the g-th RB after deinterleaving is represented as:
Figure BDA00030335259200000612
wherein,
Figure BDA00030335259200000613
is the equivalent channel vector after de-interleaving;
Figure BDA00030335259200000614
which represents a matrix of equivalent transmission codes,
Figure BDA00030335259200000615
at a receiving end, carrying out independent maximum likelihood detection on each RB; according to the formula
Figure BDA00030335259200000616
The detected signal is expressed as:
Figure BDA0003033525920000071
detecting a transmission signal
Figure BDA0003033525920000072
Then, p information bits transmitted in the g RB can be recovered accordingly.
Compared with the prior art, the invention has the following beneficial effects:
the present invention proposes to use Givens Matrix to perform precoding, and perform Diagonal Code Block Design on the coded symbols, so the scheme is called as orthogonal Space-Frequency Index Modulation scheme (Space-Frequency Index Modulation using Givens Matrix and digital Code Block Design, Gi-SFIM) using Givens precoding and Diagonal Code word structure. The antenna and the subcarrier are divided into a plurality of resource blocks, and the number of the space-frequency units in each resource block is the same. For each resource block, firstly two QAM constellation symbols form a 2 x 1 vector, then two different Givens matrixes are used for respectively pre-coding the real part and the imaginary part of the vector, then the real part and the imaginary part of the coded symbols are placed into a space frequency resource block in a diagonal or anti-diagonal mode to form a code word matrix, and the formed code word matrix is placed into a group of active antennas to form a Gi-SFIM sending signal. Simulation results show that: under different system configurations, the Gi-SFIM has better error code performance than other existing space-frequency index modulation schemes.
Furthermore, the invention supports flexible antenna number configuration, and the Gi-SFIM system supports arbitrary even number of transmitting antennas Nt。
Furthermore, analysis shows that in the Gi-SFIM scheme, because the Givens precoding matrix and the diagonal design are combined, the minimum rank of all equivalent error matrixes is 2, and the scheme can be ensured to obtain second-order transmit diversity.
Furthermore, because the invention adopts the orthogonal modulation to respectively select the position of the real part and the virtual part of the signal after precoding, the information which can be carried by the position of the subcarrier activated by each code matrix is 2log2(2n) bits, log being transmitted more than without quadrature modulation2(2n) bits, further improving spectral efficiency. Plus portable in spatial dimensions
Figure BDA0003033525920000073
P log that bits and modulation symbols can carry2(M1)+log2(M2) The spectral efficiency of a bit, Gi-SFIM scheme can be expressed as:
Figure BDA0003033525920000081
where G is the number of groups of subcarriers, N is the total number of subcarriers, LCPIs the length of the cyclic prefix.
Drawings
In order to more clearly explain the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention, and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a block diagram of a Gi-SFIM transmitter of the present invention;
FIG. 2 is a graph comparing the BER performance of Gi-SFIM of the present invention with other space-frequency indexing schemes;
FIG. 3 is a graph comparing the BER performance of Gi-SFIM and QSF-IM at a spectral efficiency of 2bits/s/Hz in accordance with the present invention;
FIG. 4 is a graph comparing the BER performance of Gi-SFIM with QSF-IM and SFC-IM for 4 or 8 antennas;
fig. 5 is a comparison of CCDF curves for Gi-SFIM of the present invention versus other space frequency index modulation schemes.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
In the description of the embodiments of the present invention, it should be noted that if the terms "upper", "lower", "horizontal", "inner", etc. are used for indicating the orientation or positional relationship based on the orientation or positional relationship shown in the drawings or the orientation or positional relationship which is usually arranged when the product of the present invention is used, the description is merely for convenience and simplicity, and the indication or suggestion that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and thus, cannot be understood as limiting the present invention. Furthermore, the terms "first," "second," and the like are used merely to distinguish one description from another, and are not to be construed as indicating or implying relative importance.
Furthermore, the term "horizontal", if present, does not mean that the component is required to be absolutely horizontal, but may be slightly inclined. For example, "horizontal" merely means that the direction is more horizontal than "vertical" and does not mean that the structure must be perfectly horizontal, but may be slightly inclined.
In the description of the embodiments of the present invention, it should be further noted that unless otherwise explicitly stated or limited, the terms "disposed," "mounted," "connected," and "connected" should be interpreted broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
The invention is described in further detail below with reference to the accompanying drawings:
referring to fig. 1, an embodiment of the present invention discloses an orthogonal space-frequency index modulation method using Givens precoding and diagonal codeword structures, wherein in a MIMO-OFDM system, N is assumed to be presenttRoot transmitting antenna, NrA root receive antenna and N subcarriers. The N subcarriers are divided into G groups of N subcarriers, where N is an integer power of 2. N of each grouptAll n subcarriers on the root antenna are called a Resource Block (RB), and then each RB has nNtAnd a space frequency unit. For the G-th RB, G11+p2+p3+p4Bit entry transmitter:
p1＝log2(M1)+log2(M2) (1)
p2＝log2(2n) (2)
p3＝log2(2n) (3)
Figure BDA0003033525920000101
wherein M is1、M2Respectively representing modulation orders of 1 st symbol and 2 nd symbol; symbol
Figure BDA0003033525920000102
Indicating a rounding down. Particularly, the method adopts Givens precoding and diagonal code word structureThe AC-spatial frequency index modulation method comprises the following steps:
step 1: according to p1Bit determination of 2 QAM signals xg,1、xg,2Respectively by QAM constellation omega1And Ω2Modulation is carried out to obtain; defining a symbol vector
Figure BDA0003033525920000103
Wherein
Figure BDA0003033525920000104
Respectively represent xg、xg,1、xg,2The real part of (a) is,
Figure BDA0003033525920000105
respectively represent xg、xg,1、xg,2An imaginary part of (d); let
Figure BDA0003033525920000106
Multiplying by precoding matrices, respectively
Figure BDA0003033525920000107
Obtaining:
Figure BDA0003033525920000108
Figure BDA0003033525920000109
it is noted that,
Figure BDA00030335259200001010
is not zero, that is,
Figure BDA00030335259200001011
elements cos (θ) in the simultaneous precoding matrix1)、sin(θ1)、cos(θ2)、sin(θ2) Nor is it zero.
Step 2: according to p2Bit determination step1 resulting precoded real part symbols
Figure BDA00030335259200001012
According to p, according to3Bit determining the pre-coded imaginary part symbol obtained in step 1
Figure BDA00030335259200001013
The position of (a). I.e. according to p2Bit selection real part code word matrix
Figure BDA0003033525920000111
According to p3Bit selection imaginary codeword matrix
Figure BDA0003033525920000112
While
Figure BDA0003033525920000113
And
Figure BDA0003033525920000114
is respectively from the set of real part code word matrixes
Figure BDA0003033525920000115
And imaginary codeword matrix set
Figure BDA0003033525920000116
Is selected from (1).
Figure BDA0003033525920000117
And
Figure BDA0003033525920000118
the specific forming process is as follows:
defining two sets of dispersion matrices χ1Hexix-2The first dispersion matrix of the two is respectively
Figure BDA0003033525920000119
And
Figure BDA00030335259200001110
then let E1And F1Are all multiplied by right shift matrix in turn
Figure BDA00030335259200001111
It is possible to obtain:
Figure BDA00030335259200001112
Figure BDA00030335259200001113
let chi1All the matrices in
Figure BDA00030335259200001114
Let chi2All the matrices in
Figure BDA00030335259200001115
The obtained union set of all the matrixes forms a code word matrix set
Figure BDA00030335259200001116
Figure BDA00030335259200001117
There are 2n codeword matrices;
let chi1All the matrices in
Figure BDA00030335259200001118
Let chi2All the matrices in
Figure BDA00030335259200001119
The obtained union set of all the matrixes forms a code word matrix set
Figure BDA00030335259200001120
Figure BDA00030335259200001121
There are 2n codeword matrices.
According to p2The bit can be selected from
Figure BDA00030335259200001122
To select a codeword matrix
Figure BDA00030335259200001123
According to p3The bit can be selected from
Figure BDA00030335259200001124
To select a codeword matrix
Figure BDA00030335259200001130
Then the selected codeword matrix
Figure BDA00030335259200001125
Wherein, ag,t(τ) represents the codeword matrix SgThe symbol on the τ -th subcarrier in the t-th column, τ ═ 1.
And step 3: will NtThe two transmitting antennas are divided into one group in sequence
Figure BDA00030335259200001126
Group, again according to
Figure BDA00030335259200001127
Bit slave
Figure BDA00030335259200001128
A group of antennas is selected for activation. Then the code word matrix S selected in the second stepgPut into the active antenna, the transmission symbols of the rest antennas which are not active are represented by 0, thereby generating a Gi-SFIM transmission signal T in the g RBg。
And 4, step 4: and combining the transmission signals of all the G groups and then interleaving the combined transmission signals. The combined signal can be represented as
Figure BDA00030335259200001129
According to the method in "OFDM with interleaved subcarrier-index modulation" (Y.Xiao, S.Wang, L.Dan, X.Lei, P.Yang, and W.Xiang, "OFDM with interleaved subcarrier-index modulation," IEEE Commun.Lett., vol.18, No.8, pp.1447-1450,2014 "), the combined signal T is passed through a G × n block interleaverG×nThe OFDM signal T to be transmitted can be obtainedin。
For the above steps, when the system parameter is Nt＝4，n＝4，M1＝M2When 2, the transmission signal T of Gi-SFIM in the g-th RBgThe generation process of (2) is exemplified.
Under the condition of the parameters of the system,
Figure BDA0003033525920000121
bit, wherein p12bits for determining the first and second modulation symbols xg,1And xg,2Obtaining s after precodingg,1And sg,2。p2＝log2(2n) 3 bits and p3＝log2The (2n) -3 bits are used to select real part code matrix
Figure BDA0003033525920000122
And imaginary codeword matrix
Figure BDA0003033525920000123
p 41 bit is used to select the active antenna.
Example (b): assume that the input information bit is "011010000".
Step 1: according to p1Determining a first and a second modulation symbol x for 2bitsg,1And xg,2Each of which consists of a QAM constellation omega1And Ω2Modulation is carried out to obtain; next, a symbol vector is defined
Figure BDA0003033525920000124
Wherein
Figure BDA0003033525920000125
Respectively represent xg、xg,1、xg,2The real part of (a) is,
Figure BDA0003033525920000126
respectively represent xg、xg,1、xg,2An imaginary part of (d); let
Figure BDA0003033525920000127
Multiplying by precoding matrices, respectively
Figure BDA0003033525920000128
Obtaining:
Figure BDA0003033525920000129
Figure BDA00030335259200001210
step 2: according to p2Set of bits from real part codeword matrix
Figure BDA00030335259200001211
In selecting a real part codeword matrix
Figure BDA00030335259200001212
According to p3Bit from imaginary part code word matrix set
Figure BDA00030335259200001213
To select an imaginary codeword matrix
Figure BDA00030335259200001214
Figure BDA00030335259200001215
And
Figure BDA00030335259200001216
the specific forming process is as follows:
defining two sets of dispersion matrices χ1Hexix-2Since n is 4, their first dispersion matrices are respectively
Figure BDA0003033525920000131
Then according to the formula
Figure BDA0003033525920000132
Let E1And F1Are all multiplied by right shift matrix in turn
Figure BDA0003033525920000133
The obtained χ1Hexix-2Can be expressed as:
Figure BDA0003033525920000134
Figure BDA0003033525920000135
let χ for the codeword matrix of the real part1All the matrices in
Figure BDA0003033525920000136
Obtaining:
Figure BDA0003033525920000137
let chi2All the matrices in
Figure BDA0003033525920000138
Obtaining:
Figure BDA0003033525920000139
then the set of real part codeword matrices formed
Figure BDA00030335259200001310
Can be expressed as:
Figure BDA00030335259200001311
let χ be, for the imaginary codeword matrix1All the matrices in
Figure BDA00030335259200001312
Let chi2All the matrices in
Figure BDA00030335259200001313
Then the set of imaginary codeword matrices formed
Figure BDA00030335259200001314
Can be expressed as:
Figure BDA00030335259200001315
as can be seen from Table 1, p2Bit "101" slave
Figure BDA00030335259200001316
The selected code word matrix is
Figure BDA00030335259200001317
p3Bit "000" slave
Figure BDA0003033525920000141
The selected code word matrix is
Figure BDA0003033525920000142
According to selection
Figure BDA0003033525920000143
And
Figure BDA0003033525920000144
the final formed codeword matrix is:
Figure BDA0003033525920000145
table 1.p2Or p3And
Figure BDA0003033525920000146
mapping relation of (W ═ { R, I })
Figure BDA0003033525920000147
And step 3: will NtThe 4 transmitting antennas are divided into one group of two transmitting antennas in sequence, and the two transmitting antennas have 2 groups. Then according to p4Bit "0", select group 1 active from group 2 antennas. The code word matrix S selected in the second stepgAfter the activated antenna is placed, the generated transmission signal of Gi-SFIM in the g-th RB can be expressed as:
Figure BDA0003033525920000148
and 4, step 4: and combining the transmission signals of all the G groups and then interleaving the combined transmission signals. The combined signal can be expressed as:
Figure BDA0003033525920000149
according to the method in the document "OFDM with interleaved subcarrier-index modulation", the combined signal T is passed through a block interleaver n of G × nG×nThe OFDM signal T to be transmitted can be obtainedin。
2. Spectral efficiency of Gi-SFIM
In the Gi-SFIM scheme, the position of the activated subcarrier of each codeword matrix can carry 2log of information due to the orthogonal modulation2(2n) bits, log being transmitted more than without quadrature modulation2(2n) bits. Plus portable in spatial dimensions
Figure BDA0003033525920000151
P log that bits and modulation symbols can carry2(M1)+log2(M2) The spectral efficiency of a bit, Gi-SFIM scheme can be expressed as:
Figure BDA0003033525920000152
where G is the number of groups of subcarriers, N is the total number of subcarriers, LCPIs the length of the cyclic prefix.
3. Transmit diversity for Gi-SFIM
The diversity order d may be defined as the minimum of the rank of the error matrix among all different equivalent transmission code matrices. Transmit diversity d according to the property "rank of tensor product of two matrices equals product of ranks of two matricestCan be expressed as dt＝d/Nr. First, the transmitting antenna N will be discussedtTransmit diversity at 2.
Transmitting antenna NtWhen 2, the transmission signal T of Gi-SFIM in the g-th RBg＝Sg. To calculate dtConsider two different codeword matrices SgAnd
Figure BDA0003033525920000153
then the error matrix asgCan be expressed as
Figure BDA0003033525920000154
Error matrix deltaSgRespectively using z for the first and second rows ofg,1And zg,2And (4) showing. Let B be [ diag (z) ]g,1),diag(zg,2)]Then transmit diversity dtCan be expressed as dt＝min{rank(BHB) And (4) dividing. In addition, the diversity order d may also be expressed as d min { rank (a) }, where C isgAnd
Figure BDA0003033525920000155
are two different matrices of the transmission code,
Figure BDA0003033525920000156
rank (B) is discussed next in terms of both real and imaginary componentsHB)。
Real part of
Considering two different real part code word matrixes
Figure BDA0003033525920000157
And
Figure BDA0003033525920000158
wherein
Figure BDA0003033525920000159
Respectively represent
Figure BDA00030335259200001510
And
Figure BDA00030335259200001511
and the first and second elements of
Figure BDA00030335259200001512
And
Figure BDA00030335259200001513
respectively in the real part of the code word matrix
Figure BDA00030335259200001514
And
Figure BDA00030335259200001515
two precoded vectors, V and
Figure BDA00030335259200001516
respectively representing real part code word matrix
Figure BDA00030335259200001517
And
Figure BDA00030335259200001518
two dispersion matrices used in (1). Is defined herein
Figure BDA00030335259200001519
To ensure that:
(a) when in use
Figure BDA00030335259200001520
When the temperature of the water is higher than the set temperature,
Figure BDA00030335259200001521
(b)
Figure BDA0003033525920000161
and
Figure BDA0003033525920000162
next, the following two cases will be discussed
Figure BDA0003033525920000163
The first condition is as follows:
Figure BDA0003033525920000164
and
Figure BDA0003033525920000165
two dispersion matrices used in the same
Under these conditions, it is easy to know
Figure BDA0003033525920000166
Figure BDA0003033525920000167
Then for the error matrix deltasgFrom
Figure BDA0003033525920000168
And
Figure BDA0003033525920000169
the sub-matrix formed by the located rows must be a diagonal matrix or an anti-diagonal matrix, so the rank of the sub-matrix is determined to be 2. In this case, therefore, there are
Figure BDA00030335259200001610
Case two:
Figure BDA00030335259200001611
and
Figure BDA00030335259200001612
the two dispersion matrices used in are different
In this case, it can be seen that
Figure BDA00030335259200001613
For convenience, the non-zero rows of the first and second columns in V are denoted by rs1And rs2It is shown that,
Figure BDA00030335259200001614
for non-zero rows of the first and second columns, respectively
Figure BDA00030335259200001615
And
Figure BDA00030335259200001616
and (4) showing. This is discussed in three sections next.
Figure BDA00030335259200001617
At this time, for the error matrix Δ SgFrom rs1And rs2The sub-matrix formed by the located rows can be expressed as
Figure BDA00030335259200001618
Or
Figure BDA00030335259200001619
From these two sub-matrices, rank (B) is knownR) 2, and therefore,
Figure BDA00030335259200001620
2){rs1,rs2and
Figure BDA00030335259200001621
wherein one element is different and the other element is the same
2.1)
Figure BDA00030335259200001622
Or
Figure BDA00030335259200001623
At this time, for the error matrix Δ SgFrom rs1，rs2And
Figure BDA00030335259200001624
(or r)s1，rs2And
Figure BDA00030335259200001625
) The sub-matrix formed by the located rows can be expressed as
Figure BDA00030335259200001626
(or
Figure BDA00030335259200001627
) For both cases, there is rank (B)R) As a result of 3, the number of pixels,
Figure BDA00030335259200001628
2.2)
Figure BDA00030335259200001629
or
Figure BDA00030335259200001630
At this time, for the error matrix Δ SgFrom rs1，rs2And
Figure BDA00030335259200001631
(or r)s1，rs2And
Figure BDA00030335259200001632
) The sub-matrix formed by the located rows can be expressed as
Figure BDA00030335259200001633
(or
Figure BDA00030335259200001634
) For both cases, there is rank (B)R) As a result of 3, the number of pixels,
Figure BDA0003033525920000171
Figure BDA0003033525920000172
error matrix Δ S at this timegEach row of (A) has a non-zero element, and therefore must have
Figure BDA0003033525920000173
To sum up, there are
Figure BDA0003033525920000174
Imaginary part
Similarly, for the imaginary part B of BIIs provided with
Figure BDA0003033525920000175
Combining the real and imaginary parts of B to obtain the N antennatWhen 2, transmit diversity dt＝min{rank(BHB)}＝2。
When N is transmittedtIn the g-th RB, the transmission signal T for two different Gi-SFIMs is greater than 2gAnd
Figure BDA0003033525920000176
if TgAnd
Figure BDA0003033525920000177
is a codeword matrix SgAnd
Figure BDA0003033525920000178
the selected active antenna is the same, then N is the same as abovetSimilar to the discussion at 2, second order transmit diversity can also be achieved. If TgAnd
Figure BDA0003033525920000179
is a codeword matrix SgAnd
Figure BDA00030335259200001710
the active antennas selected are different, the subtracted error matrix
Figure BDA00030335259200001711
In this case, at least one of the sub-matrices is a diagonal matrix with a rank of 2, and thus second-order transmit diversity is also obtained.
4. Optimal angle selection for Gi-SFIM scheme
For two angles theta used in the Givens matrix1And theta2Finding the optimal angle by maximizing the minimum Coding Gain Distance (CGD)
Figure BDA00030335259200001712
For two different code matrices CgAnd
Figure BDA00030335259200001713
the minimum coding gain distance is defined as
Figure BDA00030335259200001714
Wherein λi(i ═ 1.. times, q) denotes a matrix
Figure BDA00030335259200001715
Q ═ rank (a). Then the optimum angle
Figure BDA00030335259200001716
Can be according to the formula
Figure BDA00030335259200001717
And (4) determining. Due to the fact that
Figure BDA00030335259200001718
The closed-form solution is difficult to obtain, and the optimal angle is obtained through computer traversal. In particular, when (M)1,M2) When the angle is (2,2), (2,4), (4,4), (4,8), the optimum angle is obtained
Figure BDA00030335259200001719
Are respectively as
Figure BDA00030335259200001720
(3.4,1.1), (1.8,4.5), (1.6,3) radians.
5. Transmission and detection of Gi-SFIM scheme
For the interleaved OFDM signal TinFirstly, it is switched to time domain by IFFT conversion to obtain time domain signal Ttime. Let time-domain signal TtimeSatisfy the requirement of
Figure BDA0003033525920000181
Wherein EsIs the average energy of a single symbol. After adding length LCPAfter parallel-serial and analog-to-digital conversion, the signal is transmitted through a frequency selective rayleigh fading channel with a multipath number L. In addition, each OFDM block may transmit a total energy of
Figure BDA0003033525920000182
Each bit carrierThe energy of the belt is
Figure BDA0003033525920000183
According to the documents "Multiple-input Multiple-output OFDM with index modulation" (e.g. base, "Multiple-input Multiple-output OFDM with index modulation," IEEE Signal process.let., vol.22, No.12, pp.2259-2263,2015 ") and" Quadrature spectral response index modulation for energy-efficiency 5G wireless communication systems "(p.paternampanepakon, c.wang, y.fu, e.m.ag., m.al.always, x.tao, and x.ge," Quadrature spectral response index modulation for energy-efficiency 5G wireless communication systems ", the" frequency domain modulation for energy-efficiency 5G wireless communication "may be received as frequency domain communication signals, pp.30584, after receiving" frequency domain communication signals ":
Figure BDA0003033525920000184
wherein,
Figure BDA0003033525920000185
is the g-th group of equivalent noise vectors obtained after the frequency domain noise vectors w are de-interleaved. The elements in the noise vector w are zero mean and N variance0Of complex Gaussian random variables, i.e.
Figure BDA0003033525920000186
At the same time, the normalized signal transmission vector cgCan be expressed as:
Figure BDA0003033525920000187
wherein,
Figure BDA0003033525920000188
representing the vector on the τ th subcarrier in the g th RB. In addition, the method can be used for producing a composite material
Figure BDA0003033525920000189
The method comprises the following three steps:
the method comprises the following steps: order to
Figure BDA00030335259200001810
A channel matrix representing the L-th path (L ═ 0., L-1) in the time domain, the elements in the matrix being complex gaussian random variables with a mean value of 0 and a variance of 1. Then the time domain channel matrix HTCan be expressed as:
Figure BDA0003033525920000191
where vec (·) represents the operation of stacking the matrices in columns;
step two: for time domain channel matrix HTAfter CP addition and FFT conversion, N × N can be obtainedrNtDimensional frequency domain channel matrix HF. Let the frequency domain channel matrix H follow the method in the document "Multiple-input Multiple-output OFDM with index modulationFThrough de-interleaver
Figure BDA0003033525920000192
The frequency domain channel matrix after de-interleaving can be obtained
Figure BDA0003033525920000193
Step three: order to
Figure BDA0003033525920000194
Denotes an equivalent channel vector on the t (τ ═ 1.. multidata., n) th sub-carrier after deinterleaving in the g (th) RB in the frequency domain, that is, an equivalent channel vector
Figure BDA0003033525920000195
Row (g-1) n + τ. Will be provided with
Figure BDA0003033525920000196
Conversion to Nr×NtMatrix of dimensions
Figure BDA0003033525920000197
Thereafter, the equivalent channel matrix after the g-th RB deinterleaving can be expressed as
Figure BDA0003033525920000198
ivec (-) denotes the inverse operation of vec (-).
On the other hand, the frequency domain signal received by the g-th RB after deinterleaving can also be represented as:
Figure BDA0003033525920000199
wherein
Figure BDA00030335259200001910
Is the equivalent channel vector after deinterleaving.
Figure BDA00030335259200001911
Which represents a matrix of equivalent transmission codes,
Figure BDA00030335259200001912
at the receiving end, independent maximum likelihood detection can be performed for each RB. According to equation (5), the detected signal can be expressed as:
Figure BDA00030335259200001913
detecting a transmission signal
Figure BDA00030335259200001914
Thereafter, the p information bits transmitted in the g RB can be recovered accordingly.
6. Simulation experiment
The bit error performance of the proposed Gi-SFIM algorithm is subjected to Monte Carlo simulation and compared with the existing CI-OFDM-IM, QSF-IM, SFC-IM and MIMO-OFDM schemes. The horizontal axis in the simulation plots represents the bit signal-to-noise ratio (E) at each receive antennab/N0) And the vertical axis represents the average bit error rate. Without further declaration, the parameter configuration of the MIMO-OFDM system is as follows: n is a radical oft＝2，Nr＝2，n＝4，L＝10，LCPSetting the modulation order of two modulation symbols in the Gi-SFIM to M at 1.778bits/s/Hz1＝2，M 22, the modulation order at 2bits/s/Hz is set to M1＝2，M 24. The signal-to-noise ratio is defined as
Figure BDA0003033525920000201
Figure BDA0003033525920000202
Furthermore, for the Gi-SFIM scheme, when M is1＝M2When 2, to avoid codeword repetition, the QAM constellation Ω is required2Rotate by pi/2.
Fig. 2 shows the comparison results of the Gi-SFIM scheme and the CI-OFDM-IM, QSF-IM and SFC-IM schemes when signals pass through independent and identically distributed rayleigh fading channels. It can be seen that under the same spectral efficiency, the Gi-SFIM scheme can obtain very significant performance improvement compared to the three comparison schemes. In particular, when BER is 10-5When the spectral efficiency is 1.778bits/s/Hz, the Gi-SFIM scheme can obtain performance gains of about 2dB and 7dB without interleaving and with interleaving, respectively, compared with the QSF-IM scheme. This is because the Gi-SFIM can obtain second-order transmit diversity compared to the QSF-IM scheme, and the addition of interleaving can further increase the euclidean distance between codewords. In addition, fig. 2 also shows a theoretical error rate curve of the Gi-SFIM scheme, and it can be seen that, at a high signal-to-noise ratio, the theoretical error rate curve can be well matched with the simulation curve, which further proves the correctness of theoretical analysis.
Fig. 3 shows the performance comparison between the Gi-SFIM scheme and the QSF-IM scheme when the signals pass through independent and distributed rayleigh fading channels. It can be seen that the performance of the Gi-SFIM scheme is much better than the QSF-IM scheme at a spectral efficiency of 2 bits/s/Hz. At BER of 10-4When compared to the QSF-IM scheme, the Gi-SFIM scheme uses no interleaving and uses interleavingIn this case, performance gains of about 4dB and 7dB, respectively, can be obtained.
FIG. 4 shows the Gi-SFIM and QSF-IM and SFC-IM schemes at NtBER performance at 4 and 8 was compared. It can be seen that when the number of transmit antennas is greater than 2, the Gi-SFIM scheme can still obtain better BER performance than the QSF-IM and SFC-IM schemes at the same spectral efficiency. In particular, when BER is 10-5When the frequency spectrum efficiency of the Gi-SFIM is 2.222bits/s/Hz, compared with a QSF-IM scheme, the Gi-SFIM scheme can obtain about 6.5dB performance gain; at a spectral efficiency of 2.667bits/s/Hz, a performance gain of about 7dB may be achieved for the Gi-SFIM scheme as compared to the QSF-IM scheme. While still achieving a performance gain of about 1.5dB compared to the SFC-IM scheme, which can achieve second order transmit diversity.
FIG. 5 shows Complementary Cumulative Distribution Function (CCDF) curves for the Gi-SFIM scheme and other existing OFDM-IM techniques. The abscissa of this curve represents a particular peak-to-average ratio and the ordinate represents the probability that the peak-to-average ratio is greater than the value corresponding to the abscissa. It can be seen that there is no significant difference between different space-frequency index modulation schemes at the same spectral efficiency. In addition, under the same spectrum efficiency, the PAPR performance of the Gi-SFIM is better as the number of transmitting antennas increases, because the proportion of non-zero elements is smaller.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. The orthogonal space-frequency index modulation method adopting Givens precoding and diagonal code word structure is characterized by comprising the following steps:
step 1: according to bit p1Determining 2 QAM signals xg,1And xg,2(ii) a Defining a symbol vector:
Figure FDA0003033525910000011
wherein,
Figure FDA0003033525910000012
and
Figure FDA0003033525910000013
respectively represent xg、xg,1And xg,2The real part of (a) is,
Figure FDA0003033525910000014
and
Figure FDA0003033525910000015
respectively represent xg、xg,1And xg,2An imaginary part of (d); order to
Figure FDA0003033525910000016
Multiplying by precoding matrices, respectively
Figure FDA0003033525910000017
And
Figure FDA0003033525910000018
obtaining:
Figure FDA0003033525910000019
Figure FDA00030335259100000110
wherein,
Figure FDA00030335259100000111
not being zero, i.e.
Figure FDA00030335259100000112
Elements cos (θ) in the simultaneous precoding matrix1)、sin(θ1)、cos(θ2)、sin(θ2) Is also not zero;
step 2: according to bit p2Determining precoded real part symbols
Figure FDA00030335259100000113
And
Figure FDA00030335259100000114
according to the bit p3Determining precoded imaginary symbols
Figure FDA00030335259100000115
And
Figure FDA00030335259100000116
the position of (a); i.e. according to bit p2Selecting a real part codeword matrix
Figure FDA00030335259100000117
According to bit p3Selecting an imaginary codeword matrix
Figure FDA00030335259100000118
And
Figure FDA00030335259100000119
is respectively from the set of real part code word matrixes
Figure FDA00030335259100000120
And imaginary codeword matrix set
Figure FDA00030335259100000121
Is selected from; obtaining the selected code word matrix Sg：
Figure FDA00030335259100000122
Wherein, ag,t(τ) represents the codeword matrix SgSymbol on the τ -th subcarrier of the t-th column, τ ═ 1., n, t ═ 1,2 };
and step 3: will NtThe two transmitting antennas are divided into one group in sequence
Figure FDA00030335259100000123
Group, again according to
Figure FDA00030335259100000124
Bit slave
Figure FDA00030335259100000125
Selecting a group of antennas to activate; then the code word matrix SgPut into the active antenna, the transmission symbols of the rest antennas which are not active are represented by 0, thereby generating a Gi-SFIM transmission signal T in the g RBg；
And 4, step 4: combining all the transmission signals of the G groups and then interleaving the combined transmission signals; the combined signal is represented as
Figure FDA0003033525910000021
Passing the combined signal T through a block interleaver n of G x nG×nTo obtain the OFDM signal T to be transmittedin。
2. The method of claim 1, wherein the 2 QAM signals x in step 1 are orthogonal space-frequency index modulated by Givens precoding and diagonal codeword structuresg,1And xg,2Respectively by QAM constellation omega1And Ω2And (4) preparing.
3. The method of claim 1, wherein the step 2 selects orthogonal space-frequency index modulation using Givens precoding and diagonal codeword structure
Figure FDA0003033525910000022
And
Figure FDA0003033525910000023
the specific method comprises the following steps:
defining two sets of dispersion matrices χ1Hexix-2The first dispersion matrices of the two are respectively:
Figure FDA0003033525910000024
Figure FDA0003033525910000025
let E1And F1Are all multiplied by right shift matrix in turn
Figure FDA0003033525910000026
Obtaining:
Figure FDA0003033525910000027
Figure FDA0003033525910000028
let the scatter matrix set χ1All the matrices in
Figure FDA0003033525910000029
Let the scatter matrix set χ2All the matrices in
Figure FDA00030335259100000210
The obtained union set of all the matrixes forms a code word matrix set
Figure FDA00030335259100000211
There are 2n codeword matrices;
let the scatter matrix set χ1All the matrices in
Figure FDA00030335259100000212
Let the scatter matrix set χ2All the matrices in
Figure FDA00030335259100000213
The obtained union set of all the matrixes forms a code word matrix set
Figure FDA00030335259100000214
Set of codeword matrices
Figure FDA00030335259100000215
There are 2n codeword matrices.
4. The method of claim 1, wherein the information that can be carried by the position of the subcarrier activated by each codeword matrix is 2log2(2n) bits, the spatial dimension being portable
Figure FDA0003033525910000031
Bit, p log that a modulation symbol can carry2(M1)+log2(M2) Bit, spectral efficiency is expressed as:
Figure FDA0003033525910000032
where G is the number of groups of subcarriers, N is the total number of subcarriers, LCPIs the length of the cyclic prefix.
5. According to claim1 the orthogonal space-frequency index modulation method using Givens precoding and diagonal codeword structure is characterized in that the transmit diversity dtIs denoted by dt＝d/NrWherein, the d diversity order is defined as the minimum value of the rank of the error matrix among all different equivalent transmission code matrices.
6. The method of claim 1, wherein the optimal angle is found by maximizing the minimum coding gain distance
Figure FDA00030335259100000313
For two different code matrices CgAnd
Figure FDA0003033525910000033
the minimum coding gain distance is defined as:
Figure FDA0003033525910000034
wherein λ isiRepresentation matrix
Figure FDA0003033525910000035
I 1.., q, q ═ rank (a); optimum angle
Figure FDA0003033525910000036
According to the formula
Figure FDA0003033525910000037
Determining; when (M)1,M2) When the angle is (2,2), (2,4), (4,4), (4,8), the optimum angle is obtained
Figure FDA0003033525910000038
Are respectively as
Figure FDA0003033525910000039
And (4) radian.
7. The method of claim 1, wherein for the interleaved OFDM signal T, the orthogonal space-frequency index modulation method using Givens precoding and diagonal codeword structuresinSwitching the time domain signal T to the time domain signal T through IFFT conversion to obtain a time domain signal Ttime(ii) a Let time-domain signal TtimeSatisfy the requirement of
Figure FDA00030335259100000310
Wherein E issIs the average energy of a single symbol; after adding length LCPAfter the cyclic prefix and the parallel-serial and analog-to-digital conversion are carried out, the signal is sent through a frequency selective Rayleigh fading channel with the multipath number of L; the total energy that each OFDM block can transmit is
Figure FDA00030335259100000311
The energy carried per bit is
Figure FDA00030335259100000312
8. The method of claim 7, wherein the frequency domain signal received by the g-th RB after de-interleaving is represented as:
Figure FDA0003033525910000041
wherein,
Figure FDA0003033525910000042
is the equivalent channel matrix after the g-th RB deinterleaving,
Figure FDA0003033525910000043
is the frequency domain noise vector w is deinterleavedThe equivalent noise vector of the g group is obtained; the elements in the noise vector w are zero mean and N variance0Of complex Gaussian random variables, i.e.
Figure FDA0003033525910000044
At the same time, the normalized signal transmission vector cgExpressed as:
Figure FDA0003033525910000045
wherein,
Figure FDA0003033525910000046
representing the vector on the τ th subcarrier in the g th RB.
9. The method of claim 8, wherein the equivalent channel matrix after the g-th RB deinterleaving is an orthogonal space-frequency index modulation method using Givens precoding and diagonal codeword structure
Figure FDA0003033525910000047
Obtained by the following method:
step 1, order
Figure FDA0003033525910000048
A channel matrix representing the ith path in the time domain, wherein L is 0., L-1, and elements in the matrix are complex gaussian random variables with a mean value of 0 and a variance of 1; then the time domain channel matrix HTExpressed as:
Figure FDA0003033525910000049
where vec (·) represents the operation of stacking the matrices in columns;
step 2, setting time domain channel matrix HTAfter CP addition and FFT conversion, NxN is obtainedrNtDimensional frequency domain channel matrix HF(ii) a Let the frequency domain channel matrix HFThrough de-interleaver
Figure FDA00030335259100000410
Obtaining a frequency domain channel matrix after de-interleaving
Figure FDA00030335259100000411
Step 3, order
Figure FDA00030335259100000412
Denotes an equivalent channel vector on the t sub-carrier after deinterleaving in the g RB in the frequency domain, that is
Figure FDA00030335259100000413
Row σ ═ n + τ, τ ═ 1.., n; will be provided with
Figure FDA00030335259100000414
Conversion to Nr×NtMatrix of dimensions
Figure FDA00030335259100000415
After that, the firstgThe equivalent channel matrix after one RB deinterleave is expressed as
Figure FDA00030335259100000416
ivec (-) denotes the inverse operation of vec (-).
10. The method of claim 7, wherein the frequency domain signal received by the g-th RB after de-interleaving is represented as:
Figure FDA0003033525910000051
wherein,
Figure FDA0003033525910000052
is the equivalent channel vector after de-interleaving;
Figure FDA0003033525910000053
which represents a matrix of equivalent transmission codes,
Figure FDA0003033525910000054
at a receiving end, carrying out independent maximum likelihood detection on each RB; according to the formula
Figure FDA0003033525910000055
The detected signal is expressed as:
Figure FDA0003033525910000056
detecting a transmission signal
Figure FDA0003033525910000057
Then, p information bits transmitted in the g RB can be recovered accordingly.
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