CN111525970A - Large-scale MIMO system performance analysis method based on spatial modulation - Google Patents

Large-scale MIMO system performance analysis method based on spatial modulation Download PDF

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CN111525970A
CN111525970A CN201911154224.7A CN201911154224A CN111525970A CN 111525970 A CN111525970 A CN 111525970A CN 201911154224 A CN201911154224 A CN 201911154224A CN 111525970 A CN111525970 A CN 111525970A
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CN111525970B (en
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李祺亦舒
虞湘宾
胡亚平
谢明峰
党小宇
胡文
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Nanjing University Of Aeronautics And Astronautics Wuxi Research Institute
Nanjing University of Aeronautics and Astronautics
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Nanjing University Of Aeronautics And Astronautics Wuxi Research Institute
Nanjing University of Aeronautics and Astronautics
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
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Abstract

The invention discloses a performance analysis method of a large-scale MIMO system based on spatial modulation, aiming at the large-scale MIMO system based on the spatial modulation, a system model of the system under a relevant Rayleigh channel is established, an effective signal-to-noise ratio is calculated, and an upper bound approximate expression of a system bit error rate and a progressive expression under a high signal-to-noise ratio condition are given by utilizing a probability density function of the effective signal-to-noise ratio; in addition, according to the progressive expression, the diversity degree of the system is derived. Through simulation verification, the performance analysis method provided by the invention can effectively evaluate the performance of the system.

Description

Large-scale MIMO system performance analysis method based on spatial modulation
Technical Field
The invention belongs to the field of mobile communication, relates to a performance analysis method of a mobile communication system, and particularly relates to a bit error performance analysis method based on a spatial modulation system in a large-scale MIMO uplink under a relevant channel.
Background
The large-scale MIMO technology, as a key technology of the fifth-generation mobile communication, can provide a greater degree of freedom compared with the conventional MIMO, has the characteristics of low power consumption, high energy efficiency, less incoherent interference and higher spatial resolution, and has been widely researched and applied. The spatial modulation technology only activates one antenna in each time slot for transmitting signals, so that the interference between channels can be effectively overcome, besides the constellation symbols transmitted by the antennas, the serial numbers of the activated antennas can also transmit information invisibly, and the spatial modulation has the characteristics of high transmission rate and large channel capacity.
When system performance analysis is performed, it is generally assumed that a channel in a large-scale MIMO system is composed of large-scale fading and small-scale fading, and the large-scale fading follows lognormal distribution, but since the lognormal distribution is relatively complex and difficult to analyze, the large-scale fading is regarded as a fixed value and then analyzed in theoretical research so far, which is obviously insufficient to accurately describe channel characteristics. In addition, in the uplink of a massive MIMO system, a user may send information to a base station, and since there is almost no space constraint in arranging the base station, a sufficient distance may be left between antennas of the base station to eliminate correlation, and the user equipment is limited by physical size, which often cannot avoid occurrence of spatial correlation. Therefore, the correlation of the transmitting end is an important factor influencing the system performance, however, the problem of what probability distribution the effective snr obeys in a massive MIMO system based on spatial modulation under the transmission of a correlation channel is not solved in the existing research, and a performance analysis scheme related to the system is not proposed.
In summary, in the existing research, a more rigorous channel model is not established for the massive MIMO system, and a performance analysis method of the massive MIMO system based on spatial modulation under a relevant channel is not proposed.
Disclosure of Invention
In order to analyze the performance of a large-scale MIMO uplink system based on spatial modulation more accurately, the invention perfects a channel model, calculates the probability density function of the effective signal-to-noise ratio when relevant transmission is carried out, and provides an approximate expression and an asymptotic expression for deducing the bit error rate of the system and an effective method for calculating the diversity order of the system.
In order to achieve the purpose, the invention adopts the following technical scheme:
a large-scale MIMO system performance analysis method based on spatial modulation comprises the following steps:
s1, establishing a large-scale MIMO system uplink transmission model based on space modulation, wherein the system comprises a base station and K users, and the number of antennas equipped for the base station and the users is N respectivelyrAnd Nt(ii) a At each transmission time slot, the user sends log to the base station using spatial modulation2(MNt) A signal of bits, wherein log2NtThe bits are used to determine the activated transmit antenna sequence number, log2M bits are used for selecting constellation symbols of M-QAM; transmitting the signal under the Rayleigh channel related to the sending;
s2, assuming that the base station can obtain complete channel information, detecting the signal of user k by a zero forcing detection method after receiving the signal sent by each user, and judging the information sent by the user based on the maximum likelihood criterion;
s3, according to the property of space-related Rayleigh fading channel, respectively obtaining Probability Density Function (PDF) of effective signal-to-noise ratio when detecting antenna serial number and constellation symbol, thereby obtaining probability P of antenna serial number erroraProbability of error with constellation symbol PdAnd a bit error rate PeAn approximate expression of (c);
s4, according to PaAnd PdThe expression P is obtained as a progressive expression P of the antenna sequence number judgment error probability and the constellation symbol judgment error probability under the high signal-to-noise ratioa_asyAnd Pd_asyAnd obtaining a system bit error rate progressive expression P by the calculation formula in S3e_asyAnd calculating the diversity gain G of the system using a progressive expressiond。
Further, S1 includes the following sub-steps:
s11, transmitting the correlated Rayleigh fading channel matrix in the massive MIMO system based on the space modulation as
Figure BDA0002284376460000031
Wherein
Figure BDA0002284376460000032
Represents small scale fading, the elements in the matrix obey CN (0); diagonal matrix
Figure 100002_DEST_PATH_GDA0002566030000000033
Its element βk(K1, 2.. K.) is the large scale fading coefficient, βk＝zk/(d/d0)vShadow fading zkIs modeled as a gamma distribution, zkTo (a, b), and (d/d)0)vTo characterize path loss; block diagonal matrix Rt＝diag{Σt1,...,ΣtKElement of [ sigma ] }tk]i,j＝ρt |i-j|，ρtRepresenting the correlation coefficient of the transmitting end;
s12, the user sends a signal to the base station using spatial modulation, and the received signal at the base station is expressed as:
Figure BDA0002284376460000034
where P denotes the transmission power and s is the signal transmitted by all users
Figure BDA0002284376460000035
xk，
Figure BDA0002284376460000036
Respectively representing constellation symbols sent by a user k and sequence number vectors of activated antennas, and n is noise subject to complex gaussian distribution.
Further, S2 includes the following sub-steps:
s21, assuming that the base station knows the complete channel state, and performs zero forcing detection on the received signal:
Figure BDA0002284376460000037
wherein:
Figure BDA0002284376460000041
s22, from the received signal in S12, the signal of the user k to be detected is represented as:
Figure BDA0002284376460000042
s23, determining the antenna signal information transmitted by the user by using the maximum likelihood criterion, that is:
Figure BDA0002284376460000043
wherein: n iskIndicating the number of antennas selected by user k, at ekIn addition to the n-thkEach element, and any other element is zero.
Further, S3 includes the following sub-steps:
s31, assuming that the transmission constellation symbol and the channel information are known, the probability of the antenna signal being erroneously determined is:
Figure BDA0002284376460000044
in the above formula, the first and second carbon atoms are,
Figure BDA0002284376460000045
indicating an estimate of the antenna sequence number,
Figure BDA0002284376460000046
and is
Figure BDA0002284376460000047
And due to the effective snr γ with known shadow fadingakObeying chi-square distribution, while shadow fading zkObey the gamma distribution, the probability densities of the effective snr and the shadowing fading coefficients are expressed as:
Figure BDA0002284376460000048
Figure BDA0002284376460000049
obtaining the average error probability of antenna detection according to a conditional probability density formula:
Figure BDA0002284376460000051
then, by using the upper bound formula, the probability that the antenna serial number is judged to be wrong is expressed as:
Figure BDA0002284376460000052
s32, assuming that the serial number of the active antenna and the channel information are known, the effective snr is as follows:
Figure BDA0002284376460000053
and since the effective snr obeys the chi-squared distribution:
Figure BDA0002284376460000054
under the gaussian channel, the symbol error probability expression is:
Figure BDA0002284376460000055
wherein erfc (·) is an error function, systemA number n, mun,vnAll are related to modulation mode, and the probability of symbol decision error obtained according to equations (8) to (10) is:
Figure BDA0002284376460000056
s33, according to PaAnd PdThe upper bound approximation formula of the bit error rate of the system can be calculated according to the following formula, namely: pe≈Pa+Pd-PaPd。
Further, S4 includes the following sub-steps:
s41, using numerical integration, PaThe approximate expression of (a) is expressed as:
Figure BDA0002284376460000061
wherein phiu＝cos((2u-1)π/2Np)，NpFor Chebyshev coefficients, U (-) represents the confluent hyper-geometric function; at high signal-to-noise ratio, the U (-) function is approximately expanded to:
Figure BDA0002284376460000062
substituting the above formula into PaThe approximate expression then obtains an asymptotic expression of the error probability of the antenna sequence number under high signal-to-noise ratio:
Figure BDA0002284376460000063
s42, and calculating PaThe progressive expressions are similar in method, PdThe approximate expression of (c) is:
Figure BDA0002284376460000064
under high signal-to-noise ratio conditions, the U (-) function is approximated as:
Figure BDA0002284376460000065
thus obtaining PdAsymptotic expression of (a):
Figure BDA0002284376460000066
s43, when the signal-to-noise ratio is large, Pe_asyIs further approximated by Pe_asy≈Pa_asy+Pd_asy；
S44, from Pe_asyCalculating the diversity gain of the system, namely:
Figure BDA0002284376460000071
has the advantages that:
the randomness of large-scale fading of the channel in a large-scale MIMO system is considered during channel modeling, so that a channel model is more perfect, and the obtained analysis result is more accurate; calculating the probability density function of the effective signal-to-noise ratio of the system under the relevant sending condition, and providing necessary conditions for the performance evaluation of the system; in addition, a closed expression of the system error ratio characteristic can be deduced according to the analysis method provided by the invention, and a convenient and effective way is provided for the performance evaluation of the same type of system.
Drawings
FIG. 1 is a diagram of a model of a system in an embodiment of the invention;
FIG. 2 is a graph of theoretical values and simulated values of the error probability of the serial number determination of the system antenna when the number of the transmitting antenna and the receiving antenna changes according to the embodiment of the present invention;
FIG. 3 is a graph of theoretical values and simulated values of the system constellation symbol determination error probability when the number of transmitting antennas and receiving antennas changes in the embodiment of the present invention;
fig. 4 is a graph of theoretical values and simulated values of the average bit error rate of the system when the number of the transmitting antennas and the receiving antennas varies according to the embodiment of the present invention;
FIG. 5 is a graph of a theoretical value and a simulated value of an average bit error rate of a system when a correlation coefficient changes according to an embodiment of the present invention;
fig. 6 is a graph of a theoretical value of an average bit error rate of a system and an asymptote line when the number of transmitting antennas and the number of receiving antennas vary according to an embodiment of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
First, system model
The model of the large-scale MIMO uplink system based on space modulation under the transmission of the related channels is shown in figure 1. in a multi-user cell, a base station simultaneously serves K users, and the number of antennas allocated to the base station is NrThe number of antennas of each user equipment is Nt. At each transmission time slot, the user sends log to the base station using spatial modulation2(MNt) A signal of bits, wherein log2NtThe bits are used to determine the activated transmit antenna sequence number, log2The M bits are used to select constellation symbols for M-QAM. The signal is transmitted under a rayleigh channel with transmit correlation, and the channel matrix can be represented as:
Figure BDA0002284376460000081
wherein
Figure BDA0002284376460000082
Representing small-scale fading, and elements in the matrix obey complex Gaussian distribution with the mean value of zero and the variance of 1, and are marked as H-CN (0, 1); diagonal matrix
Figure BDA0002284376460000083
Its element βk(K1, 2.. K.) is a large scale fading coefficient satisfying βk＝zk/(d/d0)v，zkFor representing shadow fading, and (d/d)0)vFor characterizing path loss, d0And d denotes a given reference distance and the actual distance between the user and the base station, respectivelyV is the fading coefficient. Shadow fading z in the analysiskApproximated as a random variable z subject to a gamma distributionk- (a, b); block diagonal matrix Rt＝diag{Σt1,...,ΣtKElement of [ sigma ] }tk]i,j＝ρt |i-j|，ρtIndicating the correlation coefficient of the transmitting end.
When the system performs uplink transmission, K users simultaneously transmit signals to the base station by using spatial modulation, and the signals received by the base station at this time may be represented as:
Figure BDA0002284376460000084
where P represents transmit power, n is additive noise n-CN (0,1),
Figure BDA0002284376460000091
is a signal transmitted by all users, satisfies
Figure BDA0002284376460000092
xkAnd
Figure BDA0002284376460000093
respectively representing constellation symbols sent by user k and sequence number vectors of activated antennas, if activating the nthk(nk＝1,2,...,Nt) A root antenna, then
Figure BDA0002284376460000094
Assuming that the base station knows the full channel state and performs zero forcing detection on the received signal:
Figure BDA0002284376460000095
wherein the content of the first and second substances,
Figure BDA0002284376460000096
if the signal transmitted by user k is to be detected, the signal of user k can be obtained from the above equation
Figure BDA0002284376460000097
Second, calculating method of approximate upper bound expression of average bit error rate of system
1. Approximate expression P of error probability of antenna sequence numbera
Using maximum likelihood criterion for making decisions on antenna signal information transmitted by the user, i.e.
Figure BDA0002284376460000098
In the case that the channel and the transmission symbol are known, the probability that the antenna sequence number is judged incorrectly can be expressed as:
Figure BDA0002284376460000099
in the above formula, γakIs the effective snr at the time of antenna detection,
Figure BDA00022843764600000910
indicating an estimate of the antenna sequence number,
Figure BDA00022843764600000911
and is
Figure BDA0002284376460000101
And because gamma is known in the case of shadow fadingakObeying chi-square distribution, while shadow fading zkSubject to the gamma distribution, the probability densities of the effective snr and the shadowing fading coefficients can be expressed as:
Figure BDA0002284376460000102
Figure BDA0002284376460000103
the average error probability of the antenna detection can be obtained according to a conditional probability density formula:
Figure BDA0002284376460000104
in the formula
Figure BDA0002284376460000105
Expressing the MeijerG function, and then utilizing an upper bound formula, wherein the expression of the error probability of the antenna serial number judged is as follows:
Figure BDA0002284376460000106
now, suppose that the number K of users in the cell is 3, the reference distance between the user and the base station is 100m, the distances between the three users and the base station are 100m, 300m and 500m, respectively, and the fading coefficient v is 3.8. Shadow fading zkAnd (a, b), wherein a is 3.3 and b is 1/a. Correlation coefficient rho between user equipment transmitting antennastWhen the antenna number is 0.3, the base station performs antenna number detection for user 2. When the number of the transmitting antennas and the number of the receiving antennas are changed, the error probability of antenna serial number detection is shown in fig. 2, and it can be seen from the figure that under different conditions, theoretical values and simulation results almost coincide, which verifies the correctness of the method for calculating the error probability of the antenna serial number in the invention.
2. Approximate expression P of constellation symbol error probabilityd
Assuming that the serial number of the active antenna and the channel information are known, the effective SNR γ at this time is obtained from equation (5)dkThe following expression is given:
Figure BDA0002284376460000111
the effective snr obeys a chi-squared distribution with a probability density function of:
Figure BDA0002284376460000112
and because under the Gaussian channel, the symbol error probability is expressed as
Figure BDA0002284376460000113
Where erfc (·) is an error function, coefficient n, μn,vnAll related to modulation mode, the probability of symbol being judged incorrectly is obtained according to equations (12) to (14):
Figure BDA0002284376460000114
under the same conditions as the simulation parameters of fig. 2, the probability of constellation symbol error when the system changes the transmitting antenna and the receiving antenna is shown in fig. 3, and similarly, it can be seen from the figure that even if the number of antennas changes, the derived theoretical value and the simulation result are completely consistent, which proves the accuracy of the system constellation symbol error probability calculation method provided by the invention.
3. Approximate expression P of system average bit error ratee
According to PaAnd PdApproximate expressions (12) and (15), the upper bound approximation formula of the bit error rate of the system is:
Pe≈Pa+Pd-PaPd(16)
under the same conditions as the simulation parameters in fig. 2, the average bit error rate of the system is shown in fig. 4, and it can be observed that the theoretical curves are slightly higher than the simulation value when the number of transmit antennas N is equal totWhen the bit error rate is increased, the compactness of the simulation curve is deteriorated, and the bit error performance of the system can be better evaluated, which shows that the approximate upper bound formula of the bit error rate of the system provided by the invention is correct and effective.
FIG. 5 illustrates a system under different transmit correlation coefficientsBit error performance of, assuming transmit antenna N t2, receiving antenna NrTaking rho as the correlation coefficient, 16 respectivelyt0,0.3,0.5, 0.7. From simulation results, the theoretical upper bound compactness degree is deteriorated with the increase of the correlation coefficient, and the system performance can be evaluated more accurately.
Third, calculating method of gradual approximate expression of average bit error rate of system
1. Progressive approximation expression P of error probability of antenna sequence number under high signal-to-noise ratioa_asy
By numerical integration, PaThe approximate expression of (c) can also be expressed as:
Figure BDA0002284376460000121
wherein phiu＝cos((2u-1)π/2Np)，NpFor the Chebyshev coefficient, U (-) represents the confluent hypergeometric function. At high signal-to-noise ratios, the U (-) function can be approximately expanded to:
Figure BDA0002284376460000122
substituting the above formula into PaThe approximate expression can then obtain an asymptotic expression of the error probability of the antenna sequence number under high signal-to-noise ratio:
Figure BDA0002284376460000131
2. progressive approximation expression P of constellation symbol error probability under high signal-to-noise ratiod_asy
And calculating PaThe progressive expression method is similar, and P is obtained after numerical integrationdThe approximate expression of (c) is:
Figure BDA0002284376460000132
under high signal-to-noise ratio conditions, the U (-) function is approximated as:
Figure BDA0002284376460000133
so as to obtain PdAsymptotic expression of (a):
Figure BDA0002284376460000134
3. progressive approximation expression P of average bit error rate under high signal-to-noise ratioe_asy
At higher signal-to-noise ratio, Pe_asyThe expression of (c) can be further approximated as:
Pe_asy≈Pa_asy+Pd_asy(23)
fourth, system diversity
From Pe_asyThe diversity gain of the system can be calculated, namely:
Figure BDA0002284376460000135
under the same condition as the parameter setting of fig. 2, fig. 6 shows the theoretical value of the average bit error rate and the asymptotic approximation value of the system at different antenna number settings, and it can be seen that under the condition of high signal-to-noise ratio, the asymptotic line and the theoretical value are completely coincident, and the asymptotic expression is more concise than the theoretical expression.
The limitation of the protection scope of the present invention is understood by those skilled in the art, and various modifications or changes which can be made by those skilled in the art without inventive efforts based on the technical solution of the present invention are still within the protection scope of the present invention.

Claims (5)

1. A large-scale MIMO system performance analysis method based on spatial modulation is characterized by comprising the following steps:
s1, establishing a large-scale MIMO system uplink transmission model based on space modulation, wherein the system comprises a base station and K users, and the number of antennas allocated to the base station and the users is respectivelyNrAnd Nt(ii) a At each transmission time slot, the user sends log to the base station using spatial modulation2(MNt) A signal of bits, wherein log2NtThe bits are used to determine the activated transmit antenna sequence number, log2M bits are used for selecting constellation symbols of M-QAM; transmitting the signal under the Rayleigh channel related to the sending;
s2, assuming that the base station can obtain complete channel information, detecting the signal of user k by a zero forcing detection method after receiving the signal sent by each user, and judging the information sent by the user based on the maximum likelihood criterion;
s3, according to the property of space-related Rayleigh fading channel, respectively obtaining Probability Density Function (PDF) of effective signal-to-noise ratio when detecting antenna serial number and constellation symbol, thereby obtaining probability P of antenna serial number erroraProbability of error with constellation symbol PdAnd a bit error rate PeAn approximate expression of (c);
s4, according to PaAnd PdThe expression P is obtained as a progressive expression P of the antenna sequence number judgment error probability and the constellation symbol judgment error probability under the high signal-to-noise ratioa_asyAnd Pd_asyAnd obtaining a system bit error rate progressive expression P by the calculation formula in S3e_asyAnd calculating the diversity gain G of the system using a progressive expressiond。
2. The method for massive MIMO system performance analysis based on spatial modulation according to claim 1, wherein the S1 comprises the following sub-steps:
s11, transmitting the correlated Rayleigh fading channel matrix in the massive MIMO system based on the space modulation as
Figure FDA0002284376450000021
Wherein
Figure FDA0002284376450000022
Represents small scale fading, the elements in the matrix obey CN (0); diagonal matrix
Figure DEST_PATH_GDA0002566030000000033
Its element βk(K1, 2.. K.) is the large scale fading coefficient, βk＝zk/(d/d0)vShadow fading zkIs modeled as a gamma distribution, zkTo (a, b), and (d/d)0)vTo characterize path loss; block diagonal matrix Rt＝diag{Σt1,...,ΣtKElement of [ sigma ] }tk]i,j＝ρt |i-j|，ρtRepresenting the correlation coefficient of the transmitting end;
s12, the user sends a signal to the base station using spatial modulation, and the received signal at the base station is expressed as:
Figure FDA0002284376450000024
where P denotes the transmission power and s is the signal transmitted by all users
Figure FDA0002284376450000025
xk，
Figure FDA0002284376450000026
Respectively representing constellation symbols sent by a user k and sequence number vectors of activated antennas, and n is noise subject to complex gaussian distribution.
3. The method for massive MIMO system performance analysis based on spatial modulation according to claim 1, wherein the S2 comprises the following sub-steps:
s21, assuming that the base station knows the complete channel state, and performs zero forcing detection on the received signal:
Figure FDA0002284376450000027
wherein:
Figure FDA0002284376450000028
s22, according to the reception in S12Signal, the signal of user k to be detected is represented as:
Figure FDA0002284376450000029
s23, determining the antenna signal information transmitted by the user by using the maximum likelihood criterion, that is:
Figure FDA00022843764500000210
wherein: n iskIndicating the number of antennas selected by user k, at ekIn addition to the n-thkEach element, and any other element is zero.
4. The method for massive MIMO system performance analysis based on spatial modulation according to claim 1, wherein the S3 comprises the following sub-steps:
s31, assuming that the transmission constellation symbol and the channel information are known, the probability of the antenna signal being erroneously determined is:
Figure FDA0002284376450000031
in the above formula, the first and second carbon atoms are,
Figure FDA0002284376450000032
indicating an estimate of the antenna sequence number,
Figure FDA0002284376450000033
and is
Figure FDA0002284376450000034
And due to the effective snr γ with known shadow fadingakObeying chi-square distribution, while shadow fading zkObey the gamma distribution, the probability densities of the effective snr and the shadowing fading coefficients are expressed as:
Figure FDA0002284376450000035
Figure FDA0002284376450000036
obtaining the average error probability of antenna detection according to a conditional probability density formula:
Figure FDA0002284376450000037
then, by using the upper bound formula, the probability that the antenna serial number is judged to be wrong is expressed as:
Figure FDA0002284376450000038
s32, assuming that the serial number of the active antenna and the channel information are known, the effective snr is as follows:
Figure FDA0002284376450000041
and since the effective snr obeys the chi-squared distribution:
Figure FDA0002284376450000042
under the gaussian channel, the symbol error probability expression is:
Figure FDA0002284376450000043
where erfc (·) is an error function, coefficient n, μn,vnAll are related to modulation mode, and the probability of symbol decision error obtained according to equations (8) to (10) is:
Figure FDA0002284376450000044
s33, according to PaAnd PdThe upper bound approximation formula of the bit error rate of the system can be calculated according to the following formula, namely: pe≈Pa+Pd-PaPd。
5. The method for massive MIMO system performance analysis based on spatial modulation according to claim 1, wherein the S4 comprises the following sub-steps:
s41, using numerical integration, PaThe approximate expression of (a) is expressed as:
Figure FDA0002284376450000045
wherein phiu＝cos((2u-1)π/2Np)，NpFor Chebyshev coefficients, U (-) represents the confluent hyper-geometric function; at high signal-to-noise ratio, the U (-) function is approximately expanded to:
Figure FDA0002284376450000051
substituting the above formula into PaThe approximate expression then obtains an asymptotic expression of the error probability of the antenna sequence number under high signal-to-noise ratio:
Figure FDA0002284376450000052
s42, and calculating PaThe progressive expressions are similar in method, PdThe approximate expression of (c) is:
Figure FDA0002284376450000053
under high signal-to-noise ratio conditions, the U (-) function is approximated as:
Figure FDA0002284376450000054
thus obtaining PdAsymptotic expression of (a):
Figure FDA0002284376450000055
s43, when the signal-to-noise ratio is large, Pe_asyIs further approximated by Pe_asy≈Pa_asy+Pd_asy；
S44, from Pe_asyCalculating the diversity gain of the system, namely:
Figure FDA0002284376450000061
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