CN113794492A - Space-time shift keying method based on code index modulation - Google Patents

Space-time shift keying method based on code index modulation Download PDF

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CN113794492A
CN113794492A CN202111182200.XA CN202111182200A CN113794492A CN 113794492 A CN113794492 A CN 113794492A CN 202111182200 A CN202111182200 A CN 202111182200A CN 113794492 A CN113794492 A CN 113794492A
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stsk
cim
index
code
modulation symbol
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金小萍
卞李娜
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China Jiliang University
China Jiliang University Shangyu Advanced Research Institute Co Ltd
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China Jiliang University Shangyu Advanced Research Institute Co Ltd
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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
    • H04L1/02—Arrangements for detecting or preventing errors in the information received by diversity reception
    • H04L1/06—Arrangements for detecting or preventing errors in the information received by diversity reception using space diversity
    • H04L1/0618—Space-time coding
    • 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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a space-time shift keying (STSK) method based on Code Index Modulation (CIM), which divides a bit stream into three parts: selection of a dispersion matrix, selection of a modulation symbol, and selection of a spreading code. Therefore, besides transmitting the traditional constellation symbols, the information bits are mapped to Hadamard codes and dispersion matrix indexes, and the transmission efficiency of the scheme is improved. The invention also deduces the mathematical expression of the error rate of the CIM-STSK system in detail and analyzes the error code performance of the scheme. Simulation results show that compared with CIM-SS, STSK and CIM-SM schemes, the CIM-STSK scheme of the invention can realize better error code performance and higher transmission efficiency. Meanwhile, simulation of the CIM-STSK scheme is identical with a theoretical graph.

Description

Space-time shift keying method based on code index modulation
Technical Field
The invention relates to the technical field of communication, in particular to an index modulation method of a wireless communication system, and specifically relates to a Code Index Modulation (CIM) -based space-time shift keying (STSK) method.
Background
Recently, 6G wireless communication is expected to bring higher spectral efficiency and energy efficiency, and various emerging technologies have been proposed for this purpose. Index modulation is one of the key technologies, and uses the index of the resource to transmit extra information bits, which can achieve higher Spectral Efficiency (SE) and energy efficiency (EE, which has attracted great attention by researchers Systems such as Spatial Modulation (SM) and Quadrature Spatial Modulation (QSM) combine to achieve higher throughput.
The code index modulation-spatial modulation (CIM-SM) series technology not only can transmit traditional modulation symbols, but also carries more information bits by introducing a mode of activating an antenna and spreading code indexes, and improves the spectrum efficiency. And energy consumption and system complexity are greatly reduced by only activating a single antenna in each time slot. Therefore, the CIM-SM system can realize high-speed transmission under the conditions of low power consumption and low complexity, and meets the requirements of a 6G communication system. However, in the CIM-SM system, since the SM activates only one antenna per transmission, this scheme does not have a transmit diversity gain, and the error rate performance of the system is to be improved. The CIM-SM system has a problem of consuming a large amount of antenna resources, and at the same time, the transmission rate and the energy consumption of the system need to be further improved.
Disclosure of Invention
In view of the above-mentioned drawbacks in the prior art, the present invention provides a space-time shift keying method based on code index modulation. The method can realize the advantages of low power consumption, low complexity and high performance.
The invention is realized by adopting the following technical scheme:
a space-time shift keying method based on code index modulation constructs a code with NtRoot transmitting antenna, NrRoot receiving antenna, Q dispersion matrixes, M-QAM modulation symbols and log2(L) CIM-STSK system of spread spectrum code, L is the number of selectable spread spectrum codes; the receiving end of the system utilizes the autocorrelation property of the spread spectrum code to detect the dispersion matrix and the modulation symbol after despreading.
In the above technical solution, further, the working method of the CIM-STSK system is as follows:
1.1) the binary information vector to be sent by the transmitting end of the CIM-STSK system is a vector b with dimension b x 1; the vector b is subdivided into three blocks b1 log2(Q) bit, b2 ═ log2(M) bit and b3 ═ 2log2(L) bits, b ═ b1+ b2+ b 3; where b1 bits are used to derive a set of dispersion matrices
Figure BDA0003297748330000021
q 1.. that N is selected one dispersion matrix a, each dispersion matrix a should satisfy a power constraint tr [ aq·(Aq)H]＝TB(ii) a Wherein T isBSatisfy TB＝Ts，TsRepresents the duration of each STSK codeword; b2 bits for selecting one M-QAM modulation symbol x, b3 bits for each log2(L) bits to select spreading codes required for in-phase and quadrature of M-QAM modulated symbols
Figure BDA0003297748330000022
And
Figure BDA0003297748330000023
the spread spectrum code can adopt a Hadamard code, an m sequence and a gold sequence, and the length of the spread spectrum code is Len;
the M-QAM modulation symbol is in the form of
Figure BDA0003297748330000024
Is the real part of the modulation symbol x,
Figure BDA0003297748330000025
is the imaginary part of the M-QAM modulation symbol x; then, the user can use the device to perform the operation,
Figure BDA0003297748330000026
and selected spreading codes
Figure BDA0003297748330000027
Multiplication is as follows
Figure BDA0003297748330000028
And selected spreading codes
Figure BDA0003297748330000029
Multiplication is as follows
Figure BDA00032977483300000210
Realizing the respective spread spectrum of the real part and the imaginary part of the modulation symbol; after spreading
Figure BDA00032977483300000211
And
Figure BDA00032977483300000212
adding, and multiplying the added result by the selected dispersion matrix A to obtain a final transmitting signal;
1.2) transmitting the signal through a Rayleigh fading channel matrix H
Figure BDA00032977483300000213
Obedience mean 0, variance
Figure BDA00032977483300000214
Is subjected to additive white Gaussian noise AWGN, noise
Figure BDA00032977483300000215
Obedience mean 0, variance
Figure BDA00032977483300000216
Complex gaussian distribution of (a); finally, the output received baseband signal is given by
Figure BDA00032977483300000217
Wherein the dispersion matrix
Figure BDA00032977483300000218
Receiving baseband signals
Figure BDA00032977483300000219
1.3) the components of the M-QAM modulation symbol in-phase and quadrature are
YI＝[YI,1,...YI,j...,YI,Len] (2)
YQ＝[YQ,1,...YQ,j...,YQ,Len] (3)
Wherein
Figure BDA0003297748330000031
Figure BDA0003297748330000032
In-phase partial noise matrix
Figure BDA0003297748330000033
Orthogonal partial noise matrix
Figure BDA0003297748330000034
1.4) to implement single-stream maximum likelihood detection at the receiving end, the above formula is converted into
Figure BDA0003297748330000035
Figure BDA0003297748330000036
Wherein
Figure BDA0003297748330000037
Figure BDA0003297748330000038
Figure BDA0003297748330000039
Figure BDA00032977483300000310
Figure BDA00032977483300000311
Figure BDA00032977483300000312
Will be provided with
Figure BDA00032977483300000313
Is marked as
Figure BDA00032977483300000314
Figure BDA00032977483300000315
Wherein, M-QAM modulation symbol x is located at the qth element, q corresponds to the index of the dispersion matrix in STSK;
Figure BDA00032977483300000316
the total number of (A) is Q.M;
1.5) at the receiving end of CIM-STSK system, firstly, carrying out de-spreading operation, and obtaining the spreading code index used by the in-phase and quadrature parts of M-QAM modulation symbol according to each branch
Figure BDA00032977483300000317
And
Figure BDA00032977483300000318
dispersion matrix indexing
Figure BDA00032977483300000319
And modulation symbol index
Figure BDA00032977483300000320
The spreading code index is estimated by using a correlator; matrix array
Figure BDA00032977483300000321
And
Figure BDA00032977483300000322
multiplying by the corresponding spreading code c in each branchiAnd summing, i 1.... L; the despread output of the ith correlator for the M-QAM modulated symbol in-phase and quadrature components is represented as:
Figure BDA00032977483300000323
Figure BDA0003297748330000041
for the
Figure BDA0003297748330000042
And
Figure BDA0003297748330000043
respectively expressed as
Figure BDA0003297748330000044
Figure BDA0003297748330000045
Figure BDA0003297748330000046
For the energy transmitted for each spreading code,
Figure BDA0003297748330000047
is that
Figure BDA0003297748330000048
The r-th row vector of (2),
Figure BDA0003297748330000049
and
Figure BDA00032977483300000410
are respectively
Figure BDA00032977483300000411
And
Figure BDA00032977483300000412
the r-th row vector of (2),
Figure BDA00032977483300000413
and
Figure BDA00032977483300000414
multiplying the associated AWGN term by a spreading code, r 1rTB；
1.6) receiving baseband signal, despreading M-QAM modulation symbol in-phase and quadrature components by all despreaders, converting (16) and (17) into vectors according to the vector set obtained at the receiving end
Figure BDA00032977483300000415
Figure BDA00032977483300000416
1.7) despreading index for inphase and quadrature components of M-QAM modulated symbols
Figure BDA00032977483300000417
The maximum value can be found out according to the autocorrelation property of the spread spectrum code to obtain the corresponding index value, and the formula is expressed as
Figure BDA00032977483300000418
Figure BDA00032977483300000419
1.8) preparation of
Figure BDA00032977483300000420
The index is fed back into the set of despread vectors, which will only be AND
Figure BDA00032977483300000421
Indexing a set of associated despreading vectors
Figure BDA00032977483300000422
Applied to the input of the STSK detector; the detector of STSK uses ML detection algorithm, and is expressed by formula
Figure BDA00032977483300000423
Figure BDA0003297748330000051
1.9) then, the detector of STSK demodulates
Figure BDA0003297748330000052
Indexing; will obtain
Figure BDA0003297748330000053
Index and
Figure BDA0003297748330000054
index merging to obtain
Figure BDA0003297748330000055
All index values; finally, the index value
Figure BDA0003297748330000056
At the receiving end by means of a demapper
Figure BDA0003297748330000057
Furthermore, the spreading code uses a Hadamard code, and the inner elements consist of +/-1.
In the CIM-STSK scheme provided by the invention, the receiving end of the scheme utilizes the autocorrelation property of the spreading code to detect the dispersion matrix and the modulation symbol after despreading. Therefore, the performance analysis of the CIM-STSK scheme is solved by the invention in two parts. And deducing the performance analysis of the spread spectrum code by using an upper bound numerical integration formula. In addition, the invention also utilizes the half-analysis probability to deduce the performance analysis of the STSK scheme.
The performance analysis of the CIM-STSK scheme specifically comprises the following steps:
2.1) the operations taken by the receiving part of the CIM-STSK system are: despreading, single stream ML detection of STSK. Therefore, the total error rate of the receiving end can be expressed as a spreading code index mapping bit (P)code) Is/are as followsBit error rate (BEP), dispersion matrix mapping bits and modulation symbol bits (P)stsk) The sum of the BEPs of (a). Therefore, the average bit error rate of the CIM-STSK scheme can be defined as:
Figure BDA0003297748330000058
PCIM-STSKis the average bit error rate, P, of the CIM-STSK systemcodeIs the bit error rate, P, of the spreading codestskThe dispersion matrix index and the bit error rate of the modulation bits. b is the total number of bits transmitted by the transmitting end, b1Number of bits selected for the dispersion matrix, b2Number of bits selected for M-QAM modulation, b3The number of bits selected for the in-phase and quadrature spreading codes.
If the spreading code index
Figure BDA0003297748330000059
Estimation errors also cause the bits of the original spreading code mapping to be estimated incorrectly. The bit error rate expression for the spreading code index map bit can be defined by the following two values, PcAnd L. Thus, the bit error rate P of the spreading code indexcodeCan be expressed as:
Figure BDA00032977483300000510
Figure BDA0003297748330000061
Pcis the average probability of an erroneous spreading code index,
Figure BDA0003297748330000062
and
Figure BDA0003297748330000063
average probability of error spreading code indices in-phase and quadrature, respectively. In CIM-STSK systems, the dispersion matrix maps bits and modulation symbol bits (P)stsk) BEP solving of (A) can be divided into two scenariosThe method is described. The first case is that the spreading code index is correctly estimated, but the dispersion matrix and modulation bit index are erroneously detected according to the correct spreading code index; the second case is where the spreading code index is estimated incorrectly, and the probability of STSK detecting an error is based on the incorrectly estimated spreading code index
Figure BDA0003297748330000064
Thus, PstskThe concrete formula is as follows
Figure BDA0003297748330000065
Wherein, PsIs the BEP for STSK detection. As can be seen from (27) and (28), P is obtainedcodeAnd PstskFirst, P should be determinedcAnd Ps。
2.2) average probability P of wrong spreading code index detectionc
Average probability P of error spread spectrum code index detection of this partcCarry out the solution from
Figure BDA0003297748330000066
In can know that PcIs solved depending on
Figure BDA0003297748330000067
And
Figure BDA0003297748330000068
and (4) solving. As can be seen from the autocorrelation property of the spreading codes, the autocorrelation multiplication of the spreading codes will obtain a maximum value. Thus, error probability
Figure BDA0003297748330000069
And
Figure BDA00032977483300000610
can be converted to a solution with the greatest norm value smaller than
Figure BDA00032977483300000611
And
Figure BDA00032977483300000612
the minimum standard value of the standard value is,
Figure BDA00032977483300000613
therefore, under the premise of equal probability transmission of the spread spectrum codes, the spread spectrum codes and the channel coefficients are taken as conditions,
Figure BDA00032977483300000614
and
Figure BDA00032977483300000615
can be expressed as
Figure BDA00032977483300000616
Figure BDA00032977483300000617
Wherein the content of the first and second substances,
Figure BDA00032977483300000618
from the above formula, it can be seen that
Figure BDA00032977483300000619
The solution of both the in-line and quadrature components can be simplified to only the in-line component. Since each noise sample at the receiving end of the system is multiplied by a different spreading code, the norm squared random variable is independent. And is in
Figure BDA00032977483300000620
Following a non-centric chi-square distribution in
Figure BDA00032977483300000621
Following a central chi-square distribution.
To obtain P of CIM-STSK SystemcAccording toThe order statistics theory can deduce the index probability of the same-direction and orthogonal spread spectrum codes. First, two random variables, λ and ν, are defined as follows:
Figure BDA0003297748330000071
Figure BDA0003297748330000072
it can be seen that two random variables λiAnd ν obeys central chi-square and non-central chi-square distributions, respectively. Random variable lambdaiWith degree of freedom NrThe cumulative distribution function, probability density function, and probability density function of the random variable ν of 2n are shown below
Figure BDA0003297748330000073
Figure BDA0003297748330000074
Figure BDA0003297748330000075
Wherein the content of the first and second substances,
Figure BDA0003297748330000076
a modified bessel function of order alpha of the first kind,
Figure BDA0003297748330000077
is a gamma function.
Figure BDA0003297748330000078
And
Figure BDA0003297748330000079
respectively has a variance of
Figure BDA00032977483300000710
Known as λiAnd v has a variance of
Figure BDA00032977483300000711
Figure BDA00032977483300000712
Thus, the probability of v < λ can be expressed as
Figure BDA00032977483300000713
From (33), (34), (35) and (36)
Figure BDA00032977483300000714
As can be seen from (37), in the above-mentioned publication,
Figure BDA0003297748330000081
is solved depending on λiAnd
Figure BDA0003297748330000082
two random variables. Therefore, it is desired to obtain
Figure BDA0003297748330000083
Must be known
Figure BDA0003297748330000084
Is determined. While
Figure BDA0003297748330000085
The mean is 0 and the variance is
Figure BDA0003297748330000086
Obeying a generalized rayleigh distribution. The corresponding probability density function is as follows:
Figure BDA0003297748330000087
from (37), (38) and (39), P is knowncIs shown below
Figure BDA0003297748330000088
Finally, the average probability P of error spread spectrum code index is obtainedcCan be expressed as
Figure BDA0003297748330000089
2.3) BEP for STSK detection
P of this section for STSK detectionsTheoretical analysis was performed, PsIs defined as shown in the following
Figure BDA00032977483300000810
Wherein the content of the first and second substances,
Figure BDA00032977483300000811
is the pair-wise error probability (CPEP) under known conditions of the channel.
Figure BDA00032977483300000812
Figure BDA00032977483300000813
In order to modulate the symbols, the symbols are modulated,
Figure BDA00032977483300000814
is a dispersion matrix.
Figure BDA00032977483300000815
For corresponding PEP (unconditional pairwise error probability i.e.
Figure BDA00032977483300000816
) Thing (2)The number of erroneous bits of the element. In addition, based on PEP (CPEP) under the condition of channel matrix H
Figure BDA00032977483300000817
Can be expressed using a Q function, as shown below
Figure BDA00032977483300000818
Wherein the content of the first and second substances,
Figure BDA0003297748330000091
variance σ of noisez＝N0，INrIs dimension Nr×NrThe identity matrix of (2).
Since the Q function is expressed as
Figure BDA0003297748330000092
Thus, the CPEP corresponding to equation (42) can be written as
Figure BDA0003297748330000093
Then, the Moment Generating Function (MGF) is called to average the matrix H. PEP results were obtained as follows
Figure BDA0003297748330000094
Wherein the content of the first and second substances,
Figure BDA0003297748330000095
in the formula (45), the first and second groups,
Figure BDA0003297748330000096
m＝vec(CH)。
Figure BDA0003297748330000097
and CmI is gaussian vector m ═ vec (C) respectivelyH) The corresponding mean vector and covariance matrix. Wherein
Figure BDA0003297748330000098
ε is the all 1 column vector and I is the identity matrix. Thus, CPEP of the STSK system is
Figure BDA0003297748330000099
Software for performing numerical integration on P by utilizing Mathemica, Matlab and the likecIntegral of upper bound value in and PsIs solved for the paired error probabilities.
The invention has the beneficial effects that:
according to the space-time shift keying method based on code index modulation, the constructed CIM-STSK system can transmit traditional constellation symbols, and information bits are mapped to Hadamard codes and dispersion matrix indexes, so that the transmission efficiency of the system is improved; because the spread spectrum code index is used as an additional parameter to transmit information, compared with the traditional STSK system, the radio frequency number of the transmitting antenna can be reduced under the condition of the same transmission rate, thereby achieving the effect of energy saving; and because the STSK system transmits information after multiplying a single space-time two-dimensional dispersion matrix and a single modulation symbol, the mode brings transmission diversity gain to the system, thereby realizing better error rate performance. In addition, the CIM-STSK system does not change the large structure of the STSK system, so that the excellent characteristics of the STSK system can be continuously maintained at the receiving end. Similarly, the receiving end of the CIM-STSK system can use single-stream ML detection, and on the basis of ensuring the error rate performance of the system, the detection complexity is greatly reduced
The invention also deduces the average pairwise error probability of the CIM-STSK system, and performs performance analysis on the CIM-STSK scheme provided by the invention, and experimental results show that the simulation result of the CIM-STSK system provided by the invention is consistent with the theoretical performance analysis, and better error rate performance can be realized compared with CIM-SS, STSK and CIM-SM under the condition of the same transmission rate.
Drawings
FIG. 1 is a schematic representation of a CIM-STSK protocol model;
FIG. 2 shows a comparison of the performance of CIM-STSK with that of STSK, CIM-SS, and CIM-SM.
Detailed Description
Specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
FIG. 1 is a schematic diagram of the model of CIM-STSK scheme of the present invention.
A space-time shift keying method based on code index modulation constructs a code with NtRoot transmitting antenna, NrRoot receiving antenna, Q dispersion matrixes, M-QAM modulation symbols and log2(L) CIM-STSK system of spread spectrum code, L is the number of selectable spread spectrum codes; the receiving end of the system utilizes the autocorrelation property of the spread spectrum code to detect the dispersion matrix and the modulation symbol after despreading.
The working method of the CIM-STSK system comprises the following steps:
1.1) the binary information vector to be sent by the transmitting end of the CIM-STSK system is a vector b with dimension b x 1; the vector b is subdivided into three blocks b1 log2(Q) bit, b2 ═ log2(M) bit and b3 ═ 2log2(L) bits, b ═ b1+ b2+ b 3; where b1 bits are used to derive a set of dispersion matrices
Figure BDA0003297748330000101
One dispersion matrix A is selected, and each dispersion matrix A should satisfy a power constraint tr [ Aq·(Aq)H]＝TB(ii) a Wherein T isBSatisfy TB＝Ts，TsRepresents the duration of each STSK codeword; b2 bits for selecting one M-QAM modulation symbol x, b3 bits for each log2(L) bits to select spreading codes required for in-phase and quadrature of M-QAM modulated symbols
Figure BDA0003297748330000111
And
Figure BDA0003297748330000112
the spread spectrum code can adopt a Hadamard code, an m sequence and a gold sequence, and the length of the spread spectrum code is Len;
the M-QAM modulation symbol is in the form of
Figure BDA0003297748330000113
Is the real part of the modulation symbol x,
Figure BDA0003297748330000114
is the imaginary part of the M-QAM modulation symbol x; then, the user can use the device to perform the operation,
Figure BDA0003297748330000115
and selected spreading codes
Figure BDA0003297748330000116
Multiplication is as follows
Figure BDA0003297748330000117
And selected spreading codes
Figure BDA0003297748330000118
Multiplication is as follows
Figure BDA0003297748330000119
Realizing the respective spread spectrum of the real part and the imaginary part of the modulation symbol; after spreading
Figure BDA00032977483300001110
And
Figure BDA00032977483300001111
adding, and multiplying the added result by the selected dispersion matrix A to obtain a final transmitting signal;
1.2) transmitting the signal through a Rayleigh fading channel matrix H
Figure BDA00032977483300001112
Obedience mean 0, variance
Figure BDA00032977483300001113
Complex gaussian distribution ofAnd is subjected to additive white Gaussian noise AWGN
Figure BDA00032977483300001114
Obedience mean 0, variance
Figure BDA00032977483300001115
Complex gaussian distribution of (a); finally, the output received baseband signal is given by
Figure BDA00032977483300001116
Wherein the dispersion matrix
Figure BDA00032977483300001117
Receiving baseband signals
Figure BDA00032977483300001118
1.3) the components of the M-QAM modulation symbol in-phase and quadrature are
YI＝[YI,1,...YI,j...,YI,Len] (2)
YQ＝[YQ,1,...YQ,j...,YQ,Len] (3)
Wherein
Figure BDA00032977483300001119
Figure BDA00032977483300001120
In-phase partial noise matrix
Figure BDA00032977483300001121
Orthogonal partial noise matrix
Figure BDA00032977483300001122
1.4) to implement single-stream maximum likelihood detection at the receiving end, the above formula is converted into
Figure BDA00032977483300001123
Figure BDA00032977483300001124
Wherein
Figure BDA00032977483300001125
Figure BDA0003297748330000121
Figure BDA0003297748330000122
Figure BDA0003297748330000123
Figure BDA0003297748330000124
Figure BDA0003297748330000125
Will be provided with
Figure BDA0003297748330000126
Is marked as
Figure BDA0003297748330000127
Figure BDA0003297748330000128
Wherein, M-QAM modulation symbol x is located at the qth element, q corresponds to the index of the dispersion matrix in STSK;
Figure BDA0003297748330000129
the total number of (A) is Q.M;
1.5) at the receiving end of CIM-STSK system, firstly, carrying out de-spreading operation, and obtaining the spreading code index used by the in-phase and quadrature parts of M-QAM modulation symbol according to each branch
Figure BDA00032977483300001210
And
Figure BDA00032977483300001211
dispersion matrix indexing
Figure BDA00032977483300001220
And modulation symbol index
Figure BDA00032977483300001212
The spreading code index is estimated by using a correlator; matrix array
Figure BDA00032977483300001213
And
Figure BDA00032977483300001214
multiplying by the corresponding spreading code c in each branchiAnd summing, i 1.... L; the despread output of the ith correlator for the M-QAM modulated symbol in-phase and quadrature components is represented as:
Figure BDA00032977483300001215
Figure BDA00032977483300001216
for the
Figure BDA00032977483300001217
And
Figure BDA00032977483300001218
respectively expressed as
Figure BDA00032977483300001219
Figure BDA0003297748330000131
Figure BDA0003297748330000132
For the energy transmitted for each spreading code,
Figure BDA0003297748330000133
is that
Figure BDA0003297748330000134
The r-th row vector of (2),
Figure BDA0003297748330000135
and
Figure BDA0003297748330000136
are respectively
Figure BDA0003297748330000137
And
Figure BDA0003297748330000138
the r-th row vector of (2),
Figure BDA0003297748330000139
and
Figure BDA00032977483300001310
multiplying the associated AWGN term by a spreading code, r 1rTB；
1.6) receiving baseband signal, despreading M-QAM modulation symbol in-phase and quadrature components by all despreaders, converting (16) and (17) into vectors according to the vector set obtained at the receiving end
Figure BDA00032977483300001311
Figure BDA00032977483300001312
1.7) despreading index for inphase and quadrature components of M-QAM modulated symbols
Figure BDA00032977483300001313
The maximum value can be found out according to the autocorrelation property of the spread spectrum code to obtain the corresponding index value, and the formula is expressed as
Figure BDA00032977483300001314
Figure BDA00032977483300001315
1.8) preparation of
Figure BDA00032977483300001316
The index is fed back into the set of despread vectors, which will only be AND
Figure BDA00032977483300001317
Indexing a set of associated despreading vectors
Figure BDA00032977483300001318
Applied to the input of the STSK detector;the detector of STSK uses ML detection algorithm, and is expressed by formula
Figure BDA00032977483300001319
Figure BDA00032977483300001320
1.9) then, the detector of STSK demodulates
Figure BDA00032977483300001321
Indexing; will obtain
Figure BDA00032977483300001322
Index and
Figure BDA00032977483300001323
index merging to obtain
Figure BDA00032977483300001324
All index values; finally, the index value
Figure BDA00032977483300001325
At the receiving end by means of a demapper
Figure BDA00032977483300001326
The spread spectrum code uses Hadamard code, and the inner elements consist of +/-1.
In the CIM-STSK scheme provided by the invention, the performance analysis of the CIM-STSK scheme is divided into two parts for solving because the receiving end utilizes the autocorrelation property of the spreading code to detect the dispersion matrix and the modulation symbol after despreading. And deducing the performance analysis of the spread spectrum code by using an upper bound numerical integration formula. In addition, the invention also utilizes the half-analysis probability to deduce the performance analysis of the STSK scheme. Finally, the proposed performance analysis of the CIM-STSK protocol is obtained.
The performance analysis of the CIM-STSK scheme specifically comprises the following steps:
2.1) the operations taken by the receiving part of the CIM-STSK system are: despreading, single stream ML detection of STSK. Therefore, the total error rate of the receiving end can be expressed as a spreading code index mapping bit (P)code) Bit error rate BEP, dispersion matrix mapping bits and modulation symbol bits (P)stsk) The sum of the BEPs of (a). Therefore, the average bit error rate of the CIM-STSK scheme can be defined as:
Figure BDA0003297748330000141
PCIM-STSKis the average bit error rate, P, of the CIM-STSK systemcodeIs the bit error rate, P, of the spreading codestskThe dispersion matrix index and the bit error rate of the modulation bits. b is the total number of bits transmitted by the transmitting end, b1Number of bits selected for the dispersion matrix, b2Number of bits selected for M-QAM modulation, b3The number of bits selected for the in-phase and quadrature spreading codes.
If the spreading code index
Figure BDA0003297748330000142
Estimation errors also cause the bits of the original spreading code mapping to be estimated incorrectly. The bit error rate expression for the spreading code index map bit can be defined by the following two values, PcAnd L. Thus, the bit error rate P of the spreading code indexcodeCan be expressed as:
Figure BDA0003297748330000143
Figure BDA0003297748330000144
Pcis the average probability of an erroneous spreading code index,
Figure BDA0003297748330000145
and
Figure BDA0003297748330000146
average probability of error spreading code indices in-phase and quadrature, respectively. In CIM-STSK systems, the dispersion matrix maps bits and modulation symbol bits (P)stsk) The BEP solution of (a) can be divided into two cases. The first case is that the spreading code index is correctly estimated, but the dispersion matrix and modulation bit index are erroneously detected according to the correct spreading code index; the second case is where the spreading code index is estimated incorrectly, and the probability of STSK detecting an error is based on the incorrectly estimated spreading code index
Figure BDA0003297748330000147
Thus, PstskThe concrete formula is as follows
Figure BDA0003297748330000148
Wherein, PsIs the BEP for STSK detection. As can be seen from (27) and (28), P is obtainedcodeAnd PstskFirst, P should be determinedcAnd Ps。
2.2) average probability P of wrong spreading code index detectionc
Average probability P of error spread spectrum code index detection of this partcCarry out the solution from
Figure BDA0003297748330000151
In can know that PcIs solved depending on
Figure BDA0003297748330000152
And
Figure BDA0003297748330000153
and (4) solving. As can be seen from the autocorrelation property of the spreading codes, the autocorrelation multiplication of the spreading codes will obtain a maximum value. Thus, error probability
Figure BDA0003297748330000154
And
Figure BDA0003297748330000155
can be converted to a solution with the greatest norm value smaller than
Figure BDA0003297748330000156
And
Figure BDA0003297748330000157
the minimum standard value of the standard value is,
Figure BDA0003297748330000158
therefore, under the premise of equal probability transmission of the spread spectrum codes, the spread spectrum codes and the channel coefficients are taken as conditions,
Figure BDA0003297748330000159
and
Figure BDA00032977483300001510
can be expressed as
Figure BDA00032977483300001511
Figure BDA00032977483300001512
Wherein the content of the first and second substances,
Figure BDA00032977483300001513
from the above formula, it can be seen that
Figure BDA00032977483300001514
The solution of both the in-line and quadrature components can be simplified to only the in-line component. Since each noise sample at the receiving end of the system is multiplied by a different spreading code, the norm squared random variable is independent. And is in
Figure BDA00032977483300001515
Following a non-central chi-squareIs distributed at
Figure BDA00032977483300001516
Following a central chi-square distribution.
To obtain P of CIM-STSK SystemcAccording to the order statistical theory, the index probability of the same-direction and orthogonal spread spectrum codes can be deduced. First, two random variables, λ and ν, are defined as follows:
Figure BDA00032977483300001517
Figure BDA00032977483300001518
it can be seen that two random variables λiAnd ν obeys central chi-square and non-central chi-square distributions, respectively. Random variable lambdaiWith degree of freedom NrThe cumulative distribution function, probability density function, and probability density function of the random variable ν of 2n are shown below
Figure BDA0003297748330000161
Figure BDA0003297748330000162
Figure BDA0003297748330000163
Wherein the content of the first and second substances,
Figure BDA0003297748330000164
a modified bessel function of order alpha of the first kind,
Figure BDA0003297748330000165
is a gamma function.
Figure BDA0003297748330000166
And
Figure BDA0003297748330000167
respectively has a variance of
Figure BDA0003297748330000168
Known as λiAnd v has a variance of
Figure BDA0003297748330000169
Figure BDA00032977483300001610
Thus, the probability of v < λ can be expressed as
Figure BDA00032977483300001611
From (33), (34), (35) and (36)
Figure BDA00032977483300001612
As can be seen from (37), in the above-mentioned publication,
Figure BDA00032977483300001613
is solved depending on λiAnd
Figure BDA00032977483300001614
two random variables. Therefore, it is desired to obtain
Figure BDA00032977483300001615
Must be known
Figure BDA00032977483300001616
Is determined. While
Figure BDA00032977483300001617
The mean is 0 and the variance is
Figure BDA00032977483300001618
Obeying a generalized rayleigh distribution. The corresponding probability density function is as follows:
Figure BDA00032977483300001619
from (37), (38) and (39), P is knowncIs shown below
Figure BDA0003297748330000171
Finally, the average probability P of error spread spectrum code index is obtainedcCan be expressed as
Figure BDA0003297748330000172
2.3) BEP for STSK detection
P of this section for STSK detectionsTheoretical analysis was performed, PsIs defined as shown in the following
Figure BDA0003297748330000173
Wherein the content of the first and second substances,
Figure BDA0003297748330000174
is the pair-wise error probability (CPEP) under known conditions of the channel.
Figure BDA0003297748330000175
Figure BDA0003297748330000176
In order to modulate the symbols, the symbols are modulated,
Figure BDA0003297748330000177
is a dispersion matrix.
Figure BDA0003297748330000178
For corresponding PEP (unconditional pairwise error probability i.e.
Figure BDA0003297748330000179
) The number of erroneous bits of the event. In addition, based on PEP (CPEP) under the condition of channel matrix H
Figure BDA00032977483300001710
Can be expressed using a Q function, as shown below
Figure BDA00032977483300001711
Wherein the content of the first and second substances,
Figure BDA00032977483300001712
variance σ of noisez＝N0，INrIs dimension Nr×NrThe identity matrix of (2).
Since the Q function is expressed as
Figure BDA00032977483300001713
Thus, the CPEP corresponding to equation (42) can be written as
Figure BDA00032977483300001714
Then, the Moment Generating Function (MGF) is called to average the matrix H. PEP results were obtained as follows
Figure BDA0003297748330000181
Wherein the content of the first and second substances,
Figure BDA0003297748330000182
in the formula (45), the first and second groups,
Figure BDA0003297748330000183
m＝vec(CH)。
Figure BDA0003297748330000184
and CmI is gaussian vector m ═ vec (C) respectivelyH) The corresponding mean vector and covariance matrix. Wherein
Figure BDA0003297748330000185
ε is the all 1 column vector and I is the identity matrix. Thus, CPEP of the STSK system is
Figure BDA0003297748330000186
Software for performing numerical integration on P by utilizing Mathemica, Matlab and the likecIntegral of upper bound value in and PsIs solved for the paired error probabilities.
FIG. 2 shows that b is 8bit, Nt＝4、NrAnd (3) comparing the performance of the CIM-STSK with that of the STSK, CIM-SS and CIM-SM under the condition of 2. As can be seen from the figure, the error code performance of CIM-SS is better than that of CIM-STSK, CIM-SM and STSK in the low SNR range, however, the error code performance of CIM-STSK is only inferior to that of CIM-SS. Meanwhile, when the bit error rate is-5 dB, the code error performance of the CIM-STSK is consistent with that of the CIM-SS. In the range of signal-to-noise ratio, the error code performance of CIM-STSK is superior to that of CIM-SS, CIM-SM and STSK. Meanwhile, the CIM-STSK has the advantages of transmit diversity gain and spread spectrum code, so that the contrast difference of the performance of the four systems is large. As can be seen from the bit error rate results shown in fig. 2, the BER is 10-5In this case, the differences between the signal-to-noise ratios of the CIM-STSK system and the STSK, CIM-SS, and CIM-SM systems are 15.5dB, 23.5dB, and 10dB, respectively.
While the present invention has been described in detail with reference to the specific embodiments thereof, the present invention is not limited to the above-described embodiments, and various modifications or alterations can be made by those skilled in the art without departing from the spirit and scope of the claims of the present application.

Claims (3)

1. A space-time shift keying (STSK) method based on Code Index Modulation (CIM) is characterized in that a Code Index Modulation (CIM) is constructed with NtRoot transmitting antenna, NrRoot receiving antenna, Q dispersion matrixes, M-QAM modulation symbols and log2(L) CIM-STSK system of spread spectrum code, L is the number of selectable spread spectrum codes; the receiving end of the system utilizes the autocorrelation property of the spread spectrum code to detect the dispersion matrix and the modulation symbol after despreading.
2. A method for space-time shift keying based on code index modulation according to claim 1, characterized in that: the working method of the CIM-STSK system comprises the following steps:
1.1) the binary information vector to be sent by the transmitting end of the CIM-STSK system is a vector b with dimension b x 1; the vector b is subdivided into three blocks b1 log2(Q) bit, b2 ═ log2(M) bit and b3 ═ 2log2(L) bits, b ═ b1+ b2+ b 3; where b1 bits are used to derive a set of dispersion matrices
Figure FDA0003297748320000011
One dispersion matrix A is selected, and each dispersion matrix A should satisfy a power constraint tr [ Aq·(Aq)H]＝TB(ii) a Wherein T isBSatisfy TB＝Ts，TsRepresents the duration of each STSK codeword; b2 bits for selecting one M-QAM modulation symbol x, b3 bits for each log2(L) bits to select spreading codes required for in-phase and quadrature of M-QAM modulated symbols
Figure FDA0003297748320000012
And
Figure FDA0003297748320000013
the spread spectrum code adopts a Hadamard code, an m sequence or a gold sequence, and the length is Len;
the M-QAM modulation symbol is in the form of
Figure FDA0003297748320000014
Figure FDA0003297748320000015
Is the real part of the modulation symbol x,
Figure FDA0003297748320000016
is the imaginary part of the M-QAM modulation symbol x; then, the user can use the device to perform the operation,
Figure FDA0003297748320000017
and selected spreading codes
Figure FDA0003297748320000018
Multiplication is as follows
Figure FDA0003297748320000019
Figure FDA00032977483200000110
And selected spreading codes
Figure FDA00032977483200000111
Multiplication is as follows
Figure FDA00032977483200000112
Realizing the respective spread spectrum of the real part and the imaginary part of the modulation symbol; after spreading
Figure FDA00032977483200000113
And
Figure FDA00032977483200000114
adding, and multiplying the added result by the selected dispersion matrix A to obtain a final transmitting signal;
1.2) transmitting the signal through a Rayleigh fading channel matrix H
Figure FDA00032977483200000115
Obedience mean 0, variance
Figure FDA00032977483200000116
Is subjected to additive white Gaussian noise AWGN, noise
Figure FDA00032977483200000117
Obedience mean 0, variance
Figure FDA00032977483200000118
Complex gaussian distribution of (a); finally, the output received baseband signal is given by
Figure FDA0003297748320000021
Wherein the dispersion matrix
Figure FDA0003297748320000022
Receiving baseband signals
Figure FDA0003297748320000023
1.3) the components of the M-QAM modulation symbol in-phase and quadrature are
YI＝[YI,1,...YI,j...,YI,Len] (2)
YQ＝[YQ,1,...YQ,j...,YQ,Len] (3)
Wherein
Figure FDA0003297748320000024
Figure FDA0003297748320000025
In-phase partial noise matrix
Figure FDA0003297748320000026
Orthogonal partial noise matrix
Figure FDA0003297748320000027
1.4) to implement single-stream maximum likelihood detection at the receiving end, the above formula is converted into
Figure FDA0003297748320000028
Figure FDA0003297748320000029
Wherein
Figure FDA00032977483200000210
Figure FDA00032977483200000211
Figure FDA00032977483200000212
Figure FDA00032977483200000213
Figure FDA00032977483200000214
Figure FDA00032977483200000215
Will be provided with
Figure FDA00032977483200000216
Is marked as
Figure FDA00032977483200000217
Figure FDA00032977483200000218
Wherein, M-QAM modulation symbol x is located at the qth element, q corresponds to the index of the dispersion matrix in STSK;
Figure FDA00032977483200000219
the total number of (A) is Q.M;
1.5) at the receiving end of CIM-STSK system, firstly, carrying out de-spreading operation, and obtaining the spreading code index used by the in-phase and quadrature parts of M-QAM modulation symbol according to each branch
Figure FDA0003297748320000031
And
Figure FDA0003297748320000032
dispersion matrix indexing
Figure FDA0003297748320000033
And modulation symbol index
Figure FDA0003297748320000034
The spreading code index is estimated by using a correlator; matrix array
Figure FDA0003297748320000035
And
Figure FDA0003297748320000036
multiplying by the corresponding spreading code c in each branchiAnd summing, i 1.... L; the despread output of the ith correlator for the M-QAM modulated symbol in-phase and quadrature components is represented as:
Figure FDA0003297748320000037
Figure FDA0003297748320000038
for the
Figure FDA0003297748320000039
And
Figure FDA00032977483200000310
respectively expressed as
Figure FDA00032977483200000311
Figure FDA00032977483200000312
Figure FDA00032977483200000313
For the energy transmitted for each spreading code,
Figure FDA00032977483200000314
is that
Figure FDA00032977483200000315
R row vector of，
Figure FDA00032977483200000316
And
Figure FDA00032977483200000317
are respectively
Figure FDA00032977483200000318
And
Figure FDA00032977483200000319
the r-th row vector of (2),
Figure FDA00032977483200000320
and
Figure FDA00032977483200000321
multiplying the associated AWGN term by a spreading code, r 1rTB；
1.6) receiving baseband signal, despreading M-QAM modulation symbol in-phase and quadrature components by all despreaders, converting (16) and (17) into vectors according to the vector set obtained at the receiving end
Figure FDA00032977483200000322
Figure FDA00032977483200000323
1.7) despreading index for inphase and quadrature components of M-QAM modulated symbols
Figure FDA00032977483200000324
The maximum value can be found out according to the autocorrelation property of the spread spectrum code to obtain the corresponding index value, and the formula is expressed as
Figure FDA00032977483200000325
Figure FDA00032977483200000326
1.8) preparation of
Figure FDA0003297748320000041
The index is fed back into the set of despread vectors, which will only be AND
Figure FDA0003297748320000042
Indexing a set of associated despreading vectors
Figure FDA0003297748320000043
Applied to the input of the STSK detector; the detector of STSK uses ML detection algorithm, and is expressed by formula
Figure FDA0003297748320000044
Figure FDA0003297748320000045
1.9) then, the detector of STSK demodulates
Figure FDA0003297748320000046
Indexing; will obtain
Figure FDA0003297748320000047
Index and
Figure FDA0003297748320000048
index merging to obtain
Figure FDA0003297748320000049
All index values; finally, the index value
Figure FDA00032977483200000410
At the receiving end by means of a demapper
Figure FDA00032977483200000411
3. A space-time shift keying method based on code index modulation according to claim 2, characterized in that: the spread spectrum code uses Hadamard code, and the inner elements consist of +/-1.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114629524A (en) * 2022-03-11 2022-06-14 中国计量大学上虞高等研究院有限公司 Generalized code index modulation based method
CN114629525A (en) * 2022-03-11 2022-06-14 中国计量大学上虞高等研究院有限公司 Method for modulating based on generalized orthogonal code index
CN114629525B (en) * 2022-03-11 2024-06-07 中国计量大学上虞高等研究院有限公司 Method for modulating index based on generalized orthogonal code

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114629524A (en) * 2022-03-11 2022-06-14 中国计量大学上虞高等研究院有限公司 Generalized code index modulation based method
CN114629525A (en) * 2022-03-11 2022-06-14 中国计量大学上虞高等研究院有限公司 Method for modulating based on generalized orthogonal code index
CN114629525B (en) * 2022-03-11 2024-06-07 中国计量大学上虞高等研究院有限公司 Method for modulating index based on generalized orthogonal code

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