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CN109547139B - Uplink model construction and performance analysis method based on Rician channel - Google Patents

Uplink model construction and performance analysis method based on Rician channel Download PDF

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CN109547139B
CN109547139B CN201811632355.7A CN201811632355A CN109547139B CN 109547139 B CN109547139 B CN 109547139B CN 201811632355 A CN201811632355 A CN 201811632355A CN 109547139 B CN109547139 B CN 109547139B
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CN109547139A (en
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于舒娟
曹健
李冰蕊
杨杰
张昀
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Nanjing University Of Posts And Telecommunications Institute At Nantong Co ltd
Nanjing University of Posts and Telecommunications
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Abstract

本发明考虑用户到BR和BR到目的地BD存在LOS路径的情况，构建了基于Rician信道的Massive MIMO中继系统的上行链路模型，并对基于Rician信道的Massive MIMO中继系统的上行链路模型推导出其可实现速率的近似闭合表达式，并基于该推导的表达式导出了另外三种情况下实现速率的近似表达式。本发明推导出的基于Rician信道的Massive MIMO中继系统上行链路可实现速率的闭合表达式与传统的瑞利衰减信道下推导出上行链路可实现速率的闭合表达式相比具有明显的优势，这是因为在用户到BR和BR到目的地BD的信道都考虑了LOS路径的存在，使所得速率更接近实际通信过程中的速率。

Figure 201811632355

The present invention considers the existence of LOS paths from the user to the BR and from the BR to the destination BD, constructs the uplink model of the Massive MIMO relay system based on the Rician channel, and analyzes the uplink model of the Massive MIMO relay system based on the Rician channel. The model derives an approximate closed expression for its achievable rate, and based on the derived expression, an approximate expression for the achievable rate in three other cases is derived. Compared with the closed expression of the achievable rate of the uplink of the Massive MIMO relay system based on the Rician channel derived by the present invention, it has obvious advantages compared with the closed expression of the achievable rate of the uplink derived under the traditional Rayleigh fading channel. , this is because the existence of the LOS path is considered in the channels from the user to the BR and from the BR to the destination BD, so that the resulting rate is closer to the rate in the actual communication process.

Figure 201811632355

Description

Uplink model construction and performance analysis method based on Rician channel
Technical Field
The invention relates to the technical field of wireless communication signal processing, in particular to a method for constructing and analyzing performance of an uplink model of a Massive MIMO relay system based on a Rician channel.
Background
In recent years, with the widespread use of various handheld devices (such as smartphones and tablet computers), the traffic of mobile data is expected to increase by about 1000 times than before, which puts higher demands on future spectral efficiency. 5G wireless networks have been developed to meet this dramatic traffic increase and quality of service improvement.
The 5G wireless network shows many excellent performances in Massive MIMO, such as greatly improving the throughput and communication security of the system. For example, in a massive MIMO system, as the number of base station antennas tends to infinity, the effect between uncorrelated additive white gaussian noise and intra-cell user interference will gradually disappear, and it can improve the spectrum and energy efficiency by several orders of magnitude compared to conventional MIMO techniques. Furthermore, optimal receiver performance can be achieved using simple linear processing, which makes it possible to apply Massive MIMO techniques in 5G networks. Therefore, it is important to evaluate the spectrum efficiency of the Massive MIMO system under different transmission/reception schemes and different channels.
The spectral efficiency of uncorrelated channels is discussed in the literature [ Ngo, H.Q., Larsson, E.G., Marzetta, T.L.: Energy and spectral efficiency of top large multiuser MIMO systems', IEEE trans.Commun.,2013,61, (4), pp.1436-1449 ]. In the literature [ Hoydis, J., ten Brink, S., Debbah, M.: Mass MIMO in the UL/DL of cellular networks: How do Home many antennas connected? Antenna correlation is taken into account in IEEE j.sel.areas commun.,2013,31, (2), pp.160-171 to derive an asymptotic approximate closed expression of achievable rates for uncooperative multi-cellular systems. The advantages and challenges of massive MIMO are then fully summarized in the literature [ Rusek, f., Persson, d., Lau, b.k., et al.: Scaling up MIMO: opportunities and exchange with very large arrays', IEEE Signal process. mag.,2013,30, (1), pp.40-46 ].
Meanwhile, various relay technologies such as amplify-and-forward (AF) are receiving great attention due to their ability to provide extended coverage and improve quality of service and link reliability for cell edge users. Many combinations of relay technology with massive MIMO have emerged since this combination takes advantage of both, see literature [ Ngo, h.q., Larsson, e.g.: Spectral efficiency of the multiproir two-way relay channel with massive array'. proc.aid, Pacific group, CA, USA, November 2013, pp.275-279 ]. In the documents of [ h.q.ngo, h.a.suraweera, m.matthaiou, and e.g.larsson, "Multi-pair full-duplex relay with a massive array and linear processing," IEEE j.sei.areas command, vol.32, No.9, pp.1721-1737, sep.2014 ], a large-scale MIMO relay is studied using full duplex Decoding and Forwarding (DF), and a received signal is obtained at the Relay (RS), and a closed expression for realizing the rate is obtained by performing simple signal processing using a maximum ratio transmission/maximum ratio combination (MRT/MRC) and a Zero Forcing (ZF) receiver. In view of simpler relay protocols, the literature [ h.a.suraweera, h.q.ngo, t.q.duong, c.yuen, and e.g.larsson, "Multi-pair amplification-and-forward relay with large antenna array," in proc.ieee int.conf.comm., Budapest, Hungary, jun.2013, pp.4635-4640 ] studies many pairs of massive MIMO unidirectional Amplification and Forwarding (AF) relay networks. The MRT/MRC and ZF processing used in the RS yields a closed expression that approximately achieves the total rate. In order to further improve the spectral efficiency, the documents [ h.cui, l.song, and b.jiao, "Multi-pair two-way amplification-and-forward with change large number of relay antennas," IEEE trans.wirelesscommu., vol.13, No.5, pp.2636-2645, May 2014 ] intensively study a plurality of pairs of large-scale MIMO bidirectional AF relay networks. The analysis results of this document show that a large antenna array in the system can average small-scale fading, eliminate intersymbol interference, and reduce the total power consumption.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a Rician channel based Massive MIMO relay system uplink model construction method, and considers the LOS between a user and a BR and between the BR and a destination BD.
In order to solve the technical problem, the invention provides a Rician channel based Massive MIMO relay system uplink model construction method, which comprises the following steps:
s1, modeling user-to-BR and BR-to-BD channels as Rician channels considering the existence of LOS path;
and S2, calculating and obtaining channel coefficient matrixes from the user to the BR and the BR to the BD according to the fast fading matrixes from the user to the BR and the BR to the BD and the large-scale fading matrixes.
Further, the rapid decay matrix HSRAnd HRDCan be expressed as follows:
Figure BDA0001929233260000031
Figure BDA0001929233260000032
here omegaSRAnd ΩRDThe Rician-factor diagonal matrix of K multiplied by K can be expressed, and the Rician-factor of the K user can respectively express [ omega ]SR]kk＝μkAnd [ omega ]RD]kk＝εk，
Figure BDA0001929233260000033
And
Figure BDA0001929233260000034
which represents the random component of the channel and,
Figure BDA0001929233260000035
and
Figure BDA0001929233260000036
representing a deterministic component of the channel, IKRepresenting a K × K identity matrix.
Further, the channel coefficient matrix is written as follows:
Figure BDA0001929233260000037
Figure BDA0001929233260000038
here, the
Figure BDA0001929233260000041
And
Figure BDA0001929233260000042
representing channel matrices containing fast fading and large-scale fading between user-to-BR and BR-to-BD respectively,
Figure BDA0001929233260000043
and
Figure BDA0001929233260000044
representing the fast fading matrix, N, of users to BR and BR to BDrAnd NdRespectively representing the number of antennas of BR and BD, and K is the number of users.
The invention also provides a performance analysis method of the uplink model of the Massive MIMO relay system based on the Rician channel, and an expression of the model rate is obtained so as to analyze the performance of the model.
Correspondingly, the invention also provides a performance analysis method of the uplink model of the Massive MIMO relay system based on the Rician channel, which comprises the following processes:
s1, calculating and obtaining channel coefficient matrixes from users to BR and BR to BD according to the method;
s2, calculating and obtaining a receiving signal expression at the BD according to the channel coefficient matrixes from the user to the BR and from the BR to the BD;
s3, calculating to obtain a real total rate expression according to the received signal expression;
and S4, expressing the real total rate expression by using the channel high-order statistics, and obtaining a closed expression for analyzing the total rate so as to analyze the performance.
Further, the process of calculating and obtaining the received signal expression at the BD is as follows:
in the first time slot, K users send signals to the BR;
suppose that
Figure BDA0001929233260000045
Is a transmission signal vector of K users, and xsPower satisfies normalized E { xsxs H}＝IK，GSRIs that fast fading and large scale fading N are involved between the user and the BRrxK, the received signal at BR is:
Figure BDA0001929233260000046
where the transmit power per user is pu，nRRepresents complex white Gaussian noise independently and equally distributed and
Figure BDA0001929233260000047
obtaining a received signal y at BRRThe received signal is then processed by the maximal ratio receiver, which can be made dependent on
Figure BDA0001929233260000051
Of the receiving matrix
Figure BDA0001929233260000052
Then receiving signal yRAnd depend on
Figure BDA0001929233260000053
Receiver matrix of
Figure BDA0001929233260000054
By multiplication, the simply processed received signal can be expressed as:
Figure BDA0001929233260000055
subsequently, a signal x is receivedRIs power amplified at BR, and the power amplified signal can be expressed as:
Figure BDA0001929233260000056
here power amplified signal
Figure BDA0001929233260000057
Satisfy the requirement of
Figure BDA0001929233260000058
PRRepresenting power amplified signals
Figure BDA0001929233260000059
Is an amplification factor that satisfies the total transmit power constraint at BR,
the overall transmit power constraint of the BR has an amplification factor γ of:
Figure BDA00019292332600000510
in the second time slot, the BR arbitrarily selects K antennas for forwarding
Figure BDA00019292332600000511
The received signal arriving at the destination BD is:
Figure BDA00019292332600000512
where G isRDIs that fast fading and large scale fading N are contained between BR and destination BDdChannel matrix of xK, nDIs complex additive white gaussian noise at the destination BD and
Figure BDA00019292332600000513
MRC reception is also employed at the destination BD, where the reception matrix
Figure BDA00019292332600000514
Depend on
Figure BDA00019292332600000515
After being processed at the destination BD, the received signal of the Massive MIMO relay system based on the Rician channel can be obtained as follows:
Figure BDA00019292332600000516
further, according to the received signal expression, the specific process of calculating and obtaining the real total rate expression is as follows:
assuming that users to BR and BR to destination BD have perfect channel state information, without performing channel estimation, the acceptance signal of the kth user at destination BD can be written as follows according to the above equation:
Figure BDA0001929233260000061
suppose that the user interference is gaussian distributed and follows the transmitted signal x of the kth users,kIndependently, the SNR of the k-th user can be obtainedkFurther, the achievement rate R can be obtainedkComprises the following steps:
Figure BDA0001929233260000062
Figure BDA0001929233260000063
the above equation can be approximated as:
Figure BDA0001929233260000064
the actual total rate achieved by the above equation is:
Figure BDA0001929233260000065
further, the process of calculating and analyzing the total rate is as follows:
the total analysis rate of the Massive MIMO relay system under a Rician channel is as follows:
Figure BDA0001929233260000066
is provided with
Figure BDA0001929233260000067
Figure BDA0001929233260000068
A in the above formulakRepresents the power of the k-th user's desired signal, BkIndicating the power of the kth user interfered by other users, CkAnd DkRepresenting noise power, using ΔSR,k、Qki、Φki、ΔRD,k、Rki、φkiTo express Ak～DkWhich can be respectively expressed as:
Figure BDA0001929233260000071
Figure BDA0001929233260000072
Figure BDA0001929233260000073
Dk＝σD 2βkNd。
further, the rate expression is analyzed in three other cases derived from analyzing the total power expression:
the first method comprises the following steps: when only a LOS path exists between the user to the BR, the Ricean-factor between the BR and the destination BD is ∞ dB, i.e.,. epsilon. + -i0(i is 0, 1.., K), at which time the channel between BR and the destination BD degenerates to a rayleigh fading channel, and ΔRD,k＝1，Rki1, in Massive MIMO available at this timeThe closed expression for the total rate achieved by the relay system in the case where only LOS paths exist between the users to the BRs is as follows:
Figure BDA0001929233260000074
will be deltaRD,k＝1，RkiSubstituting 1 into a in step fourk、Bk、Ck、DkObtained of (A)case1,k、Bcase1,k、Ccase1,k、Dcase1,kThe following were used:
Figure BDA0001929233260000075
Figure BDA0001929233260000076
Figure BDA0001929233260000077
Dcase1,k＝σD 2βkNd
second (case 2): in the case where only a LOS path exists between the BR to the destination BD, the Ricean-factor between the user and the BR is-infinity dB, i.e., μi0(i 0, 1.., K), when the channel between the user and the BR degenerates to a rayleigh fading channel, and ΔSR,k＝1，QkiAt this time, the closed expression of the Massive MIMO relay system for achieving the total rate in the case where only a LOS path exists between the BR and the destination BD is as follows:
Figure BDA0001929233260000081
will be deltaSR,k＝1，QkiSubstituting 1 into a in step fourk、Bk、Ck、DkObtained of (A)case2,k、Bcase2,k、Ccase2,k、Dcase2,kThe following were used:
Figure BDA0001929233260000082
Figure BDA0001929233260000083
Figure BDA0001929233260000084
Dcase2,k＝σD 2βkNd
third (case 3): in the case where there is no LOS path between the user to both the BR and BR to the destination BD, the Ricean-factors between the user to both the BR and BR to the destination BD are ∞ dB, i.e., μi＝0，εi0(i 0, 1.., K), the model degenerates to a pure rayleigh channel attenuation model, in which case, Δ isSR,k＝1，Qki＝1，ΔRD,k＝1，Rki1 is ═ 1; the closed expression for the masive MIMO relay system to achieve the total rate when there is no LOS path between the user to the BR and the BR to the destination BD at this time is as follows:
Figure BDA0001929233260000091
will be deltaSR,k＝1，Qki＝1，ΔRD,k＝1，RkiSubstituting 1 into a in step fourk、Bk、Ck、DkObtained of (A)case3,k、Bcase3,k、Ccase3,k、Dcase3,kThe following were used:
Figure BDA0001929233260000092
Figure BDA0001929233260000093
Figure BDA0001929233260000094
Dcase3,k＝σD 2βkNd。
compared with the prior art, the invention has the following beneficial effects: the method and the device provided by the invention have the advantages that the condition that LOS paths exist between a user and a BR and a destination BD is considered, an uplink model of a Rician channel-based Massive MIMO relay system is constructed, the uplink performance of the Rician channel-based Massive MIMO relay system is analyzed, and an approximate closed expression of the uplink achievable rate is deduced. Compared with the traditional closed expression for deducing the uplink achievable rate by the push-down of the Rayleigh fading channel, the closed expression for deducing the uplink achievable rate of the Massive MIMO relay system based on the Rician channel has obvious advantages, because the LOS paths exist between the user and the BR and between the user and the destination BD, and the practical communication is better met. And the approximate closed-form expression for the rate achieved under a conventional rayleigh fading channel can be seen as a special case when Rician-factor is- ∞ dB in the model. And the expressions of the achievable rates in the other three cases are derived through the derived closed expression of the rate achievable by the uplink of the Massive MIMO relay system based on the Rician channel.
Drawings
FIG. 1 is a block diagram of a model of the present invention;
FIG. 2 is a graph of total rate as a function of number of relay (BR) antennas;
FIG. 3 is a graph of total rate versus Ricain-factor;
fig. 4 is a graph of average rate versus number of users.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The invention relates to a model construction method of a Massive MIMO relay system based on a Rician channel, which comprises the following processes:
s1, modeling user-to-BR and BR-to-BD channels as Rician channels considering the existence of LOS path;
and S2, calculating and obtaining channel coefficient matrixes from the user to the BR and the BR to the BD according to the fast fading matrixes from the user to the BR and the BR to the BD and the large-scale fading matrixes.
Correspondingly, the invention discloses a Rician channel-based Massive MIMO relay system performance analysis method, which comprises the following steps:
s1, establishing a Rician channel-based Massive MIMO relay system model according to the method, and calculating to obtain channel coefficient matrixes from users to BR and BR to BD;
s2, calculating and obtaining a receiving signal expression at the BD according to the channel coefficient matrixes from the user to the BR and from the BR to the BD;
s3, calculating to obtain a real total rate realization expression according to the received signal expression;
and S4, expressing the total rate realization expression by using the channel high-order statistics to obtain a closed expression for analyzing the total rate so as to analyze the performance of the model.
Examples
In the uplink process of the Massive MIMO relay system, as shown in fig. 1, a user does not have a direct link to a destination base station (BD) due to severe shadowing and path LOSs, a signal transmitted by the user needs to be relayed by a relay (BR) to reach the destination BD, LOS (line-of-sight) paths exist between the user and the BR and between the user and the destination BD, and the BR and the destination BD are equipped with a large number of antenna arrays, wherein the number of antennas is N respectivelyrAnd Nd(assume N)d≥NrK > K, the number of users).
The embodiment of the invention relates to a model construction and performance analysis method of a Massive MIMO relay system based on a Rician channel, which comprises the following steps:
the first step is as follows: the channel model is modeled to obtain a Rician channel.
The user-to-relay (BR) and BR-to-destination base station (BD) channel coefficients may be expressed as:
Figure BDA0001929233260000111
Figure BDA0001929233260000112
wherein, gSR,mkIs the channel coefficient from the kth user to the mth antenna of BR, hSR,mkIs the fast fading element, g, from the k-th user to the m-th antenna of the BRRD,mkIs the channel coefficient between the optional kth transmitting antenna of the BR and the antenna of the mth destination BD, hRD,mkIs a fast fading element between the optional kth transmitting antenna of the BR and the antenna of the mth destination BD, and αkAnd betakIs a large scale fading coefficient used to model geometric attenuation and shadow fading.
The channel coefficients can be written as follows:
Figure BDA0001929233260000113
Figure BDA0001929233260000114
here, the
Figure BDA0001929233260000121
And
Figure BDA0001929233260000122
representing channel matrices containing fast fading and large-scale fading between user-to-BR and BR-to-BD respectively,
Figure BDA0001929233260000123
and
Figure BDA0001929233260000124
representing the fast fading matrix, N, of users to BR and BR to BDrAnd NdRespectively representing the number of antennas of BR and BD, K being the number of users, and [ HSR]mk＝hSR,mk，[HRD]mk＝hRD,mk。DSRAnd DRDRepresents a large scale fading diagonal matrix of K x K, and [ DSR]kk＝αk，[DRD]kk＝βk。
Fast fading matrix H in the above two formulasSRAnd HRDCan be expressed as follows:
Figure BDA0001929233260000125
Figure BDA0001929233260000126
here omegaSRAnd ΩRDA Rician-factor diagonal matrix (a matrix composed of Rician-factors) representing K × K, and Rician-factor representing the ratio of the power of a deterministic component to the power of a dispersive component, which is a number with which the matrix Ω is constructedSRAnd ΩRD. The Rician-factor of the kth user can respectively represent [ omegaSR]kk＝μkAnd [ omega ]RD]kk＝εk。
Figure BDA0001929233260000127
And
Figure BDA0001929233260000128
representing the random component of the channel, HSR,wAnd HRD,wEach column of (a) has a zero mean, and the real and imaginary parts are independent of each other, the variance is 1/2, and are independent identically distributed (iid) complex gaussian random variables (each of the two H columns is phase-wise)Independent of each other and the probability distributions are all the same),
Figure BDA0001929233260000129
and
Figure BDA00019292332600001210
representing a deterministic component of the channel, IKRepresenting a K × K identity matrix.
In the above two equations
Figure BDA00019292332600001211
And
Figure BDA00019292332600001212
a deterministic component representing the channel, wherein
Figure BDA00019292332600001213
And
Figure BDA00019292332600001214
element of m row and k column in matrix
Figure BDA00019292332600001215
And
Figure BDA00019292332600001216
can be expressed as:
Figure BDA00019292332600001217
Figure BDA00019292332600001218
wherein d isSRAnd dRDIs the spatial distance of the antenna array, λ is the wavelength of the light, θSR,kAnd thetaRD,kIs the angle of arrival of the kth user.
The second step is that: the signal in the whole uplink process is processed to obtain the received signal at the destination base station BD.
In the first slot, K users transmit signals to the BR.
Suppose that
Figure BDA0001929233260000131
Is a transmission signal vector of K users, and xsPower satisfies normalized E { xsxs H}＝IK，GSRIs that fast fading and large scale fading N are involved between the user and the BRrxK channel matrix. The acceptance signal at the BR is:
Figure BDA0001929233260000132
where the transmit power per user is pu，nRRepresents complex white Gaussian noise independently and equally distributed and
Figure BDA0001929233260000133
(this is a mathematical expression of a complex Gaussian distribution, cn represents complex Gaussian, 0 represents mean, and the following represents variance).
Obtaining a received signal y at BRRThen, the received signal is simply processed by a maximum ratio receiver (MRC), which is referred to in documents p.dong, h.zhang, w.xu, and x.you, "Efficient low-resolution ADC reproducing for multi-user massive MIMO system," IEEE trans.ve.techonol., vol.66, No.12, pp.11039-11056, and dec.2017.]Can be obtained to rely on
Figure BDA0001929233260000134
Of the receiving matrix
Figure BDA0001929233260000135
Then receiving signal yRAnd depend on
Figure BDA0001929233260000136
Receiver matrix of
Figure BDA0001929233260000137
Multiplication. The simply processed received signal can be expressed as:
Figure BDA0001929233260000138
subsequently, a signal x is receivedRIs power amplified at BR, and the power amplified signal can be expressed as:
Figure BDA0001929233260000139
here power amplified signal
Figure BDA00019292332600001310
Satisfy the requirement of
Figure BDA00019292332600001311
PRRepresenting power amplified signals
Figure BDA00019292332600001312
Is an amplification factor that satisfies the total transmit power constraint at BR. The overall transmit power constraint of the BR has an amplification factor γ of:
Figure BDA0001929233260000141
in the second time slot, the BR arbitrarily selects K antennas for forwarding
Figure BDA0001929233260000142
The received signal arriving at the destination BD is:
Figure BDA0001929233260000143
where G isRDIs that fast fading and large scale fading N are contained between BR and destination BDdChannel matrix of xK, nDIs complex additive white gaussian noise at the destination BD and
Figure BDA0001929233260000144
MRC reception is also employed at the destination BD, where the reception matrix
Figure BDA0001929233260000145
Depend on
Figure BDA0001929233260000146
After simple processing at the destination BD, the received signal of the Massive MIMO relay system based on Rician channel can be obtained as follows:
Figure BDA0001929233260000147
the third step: calculating the real realization total rate of the model, and analyzing the performance of the model by simulation:
in this section, assuming that users to BR and BR to destination BD have perfect channel state information, without performing channel estimation, the received signal of the kth user at destination BD can be written as follows according to the above equation:
Figure BDA0001929233260000148
suppose that the user interference is gaussian distributed and follows the transmitted signal x of the kth users,kIndependently, the SNR of the k-th user can be obtainedkFurther, the achievement rate R can be obtainedkComprises the following steps:
Figure BDA0001929233260000149
Figure BDA00019292332600001410
the above equation can be approximated as:
Figure BDA00019292332600001411
the actual total rate achieved by the above equation is:
Figure BDA0001929233260000151
the fourth step: the model analysis total rate is calculated for later performance analysis by simulation:
the total analysis rate of the Massive MIMO relay system under a Rician channel is as follows:
Figure BDA0001929233260000152
is provided with
Figure BDA0001929233260000153
Figure BDA0001929233260000154
A in the above formulakRepresents the power of the k-th user's desired signal, BkIndicating the power of the kth user interfered by other users, CkAnd DkRepresenting noise power, using ΔSR,k、Qki、Φki、ΔRD,k、Rki、φkiTo express Ak～DkWhich can be respectively expressed as:
Figure BDA0001929233260000155
Figure BDA0001929233260000156
Figure BDA0001929233260000157
Dk＝σD 2βkNd
above Ak、Bk、Ck、DkThe following were demonstrated: reference [ Q.Zhang, S.jin, K. -K.Wong, H.Zhu, and M.Matthaiou, "Power scaling of uplink massive MIMO systems with overhead-channel networks," IEEE J.Sel.Topics Signal Process, vol.8, No.5, pp.966-981, Oct.2014.]The following high order statistics can be obtained:
Figure BDA0001929233260000161
Figure BDA0001929233260000162
Figure BDA0001929233260000163
Figure BDA0001929233260000164
the formula of the calculation of the real total rate in the third step can be defined as
Figure BDA0001929233260000165
Figure BDA0001929233260000166
Gamma is expressed by the above high-order statistic, the total analysis rate in the fourth step can be obtained, so that A in the expressionkThe method comprises the following steps:
Figure BDA0001929233260000167
in the above formula
Figure BDA0001929233260000168
The following calculation can be made:
Figure BDA0001929233260000169
using the above calculation
Figure BDA00019292332600001610
As a result, the power A of the desired signal can be calculatedkComprises the following steps:
Figure BDA00019292332600001611
similar available user interference power BkComprises the following steps:
Figure BDA00019292332600001612
in the above formula
Figure BDA0001929233260000171
Can be calculated as follows:
Figure BDA0001929233260000172
power of user interference BkCan be expressed in the following form:
Figure BDA0001929233260000173
same noise power CkThe method comprises the following steps:
Figure BDA0001929233260000174
in the above formula
Figure BDA0001929233260000175
Is calculated as follows:
Figure BDA0001929233260000176
because at GSRAnd GRDAre independently and identically distributed, so GSRAnd GRDThe inner product of any two different columns is 0, so that the above formula is not zero only when i ═ k, i.e.
Figure BDA0001929233260000177
The noise power is:
Figure BDA0001929233260000181
Figure BDA0001929233260000182
using Δ for γ in all equations aboveSR,k、Qki、Φki、ΔRD,k、Rki、φkiCan be expressed as follows:
Figure BDA0001929233260000183
the demonstration of γ is as follows:
through the second step, the following steps are known:
Figure BDA0001929233260000184
in the above formulaIn the expression
Figure BDA0001929233260000185
The expectation of the first element is calculated as follows:
Figure BDA0001929233260000186
can obtain
Figure BDA0001929233260000187
Figure BDA0001929233260000188
The following are also readily available:
Figure BDA0001929233260000189
the fifth step: implementation of rate R using the derivation in step foursumThe rate expression is analyzed in three other cases derived from the expression of (c).
First (case 1): when only a LOS path exists between the user to the BR, the Ricean-factor between the BR and the destination BD is ∞ dB, i.e.,. epsilon. + -i＝0(i＝0,1,..,K) At this time, the channel between BR and the destination BD is degenerated to a Rayleigh fading channel, and ΔRD,k＝1，RkiAt this time, the closed expression of the Massive MIMO relay system for achieving the total rate under the condition that only LOS paths exist between users and BRs is as follows:
Figure BDA0001929233260000191
will be deltaRD,k＝1，RkiSubstituting 1 into a in step fourk、Bk、Ck、DkObtained of (A)case1,k、Bcase1,k、Ccase1,k、Dcase1,kThe following were used:
Figure BDA0001929233260000192
Figure BDA0001929233260000193
Figure BDA0001929233260000194
Dcase1,k＝σD 2βkNd
second (case 2): in the case where only a LOS path exists between the BR to the destination BD, the Ricean-factor between the user and the BR is-infinity dB, i.e., μi0(i 0, 1.., K), when the channel between the user and the BR degenerates to a rayleigh fading channel, and ΔSR,k＝1，QkiAt this time, the closed expression of the Massive MIMO relay system for achieving the total rate in the case where only a LOS path exists between the BR and the destination BD is as follows:
Figure BDA0001929233260000195
will be deltaSR,k＝1，QkiSubstituting 1 into a in step fourk、Bk、Ck、DkObtained of (A)case2,k、Bcase2,k、Ccase2,k、Dcase2,kThe following were used:
Figure BDA0001929233260000201
Figure BDA0001929233260000202
Figure BDA0001929233260000203
Dcase2,k＝σD 2βkNd
third (case 3): in the case where there is no LOS path between the user to both the BR and BR to the destination BD, the Ricean-factors between the user to both the BR and BR to the destination BD are ∞ dB, i.e., μi＝0，εi0(i 0, 1.., K), the model degenerates to a pure rayleigh channel attenuation model, in which case, Δ isSR,k＝1，Qki＝1，ΔRD,k＝1，Rki1. The closed expression for the masive MIMO relay system to achieve the total rate when there is no LOS path between the user to the BR and the BR to the destination BD at this time is as follows:
Figure BDA0001929233260000204
will be deltaSR,k＝1，Qki＝1，ΔRD,k＝1，RkiSubstituting 1 into a in step fourk、Bk、Ck、DkObtained of (A)case3,k、Bcase3,k、Ccase3,k、Dcase3,kThe following were used:
Figure BDA0001929233260000205
Figure BDA0001929233260000211
Figure BDA0001929233260000212
Dcase3,k＝σD 2βkNd
in summary, in the uplink process, based on the Rician channel Massive MIMO model, the LOS path condition is considered in the channels from the user to the BR and from the BR to the destination BD, so that the model better conforms to the actual communication compared with the traditional rayleigh fading model. The model has the advantages that closed expressions of the achievable rates of the Massive MIMO relay system under three different practical scenes can be deduced according to the value of the special Rician-factor, namely when the Ricin-factor of a channel between a user and a BR is infinity dB, the delta-factor is delta-infinity dBSR,k＝1，Qki1, the model only has Rician fading channel from BR to destination BD, and in channel where user to BR degrades to Rayleigh fading, will be ΔSR,k、QkiSubstituting the expression of the analysis rate to obtain a closed expression of the realization rate of the LOS path only from the BR to the BD of the destination in the uplink; second, when the Ricin-factor of the channel between BR to the destination BD is- ∞ dB, Δ aboveRD,k＝1，Rki1, the model only exists Rician fading channel from user to BR, and the delta is degraded to Rayleigh fading channel from BR to destination BDRD,k、RkiSubstituting the expression of the analysis rate to obtain a closed expression of the realization rate of the LOS path from the user to the BR in the uplink; finally, Δ above when the Ricain-factor of the channel between user to BR and BR to destination BD is both- ∞ dBSR,k＝1，Qki＝1，ΔRD,k＝1，Rki1, the model degenerates to a pure Rayleigh decay model, and Δ is calculatedSR,k、Qki、ΔRD,k、RkiAnd substituting the expression of the analysis rate to obtain a closed expression of the realization rate of the pure Rayleigh attenuation model in the uplink.
The present invention obtains an expression of the model rate in order to analyze the performance of the model.
Fig. 2 shows the transmission power p for the number K of users being 10 under perfect channel state informationuAnd when the Rician-factor takes 0dB and 10dB, the simulation result of the total rate along with the number of BR antennas is realized based on the Rician channel Massive MIMO relay system. Wherein the small square and the small circle are formed by taking 1000 MongoliaTrue rates from the tecarol experiment, while the point in the middle of the small square and circle is the simulation result from the analysis. As can be seen from fig. 2, the curves obtained by the analysis almost coincide with the true curves of the 1000 monte carlo simulations, which confirms the correctness of the analysis results.
Fig. 3 shows that for the number of users K equal to 10, the number of BR antennas Nr is 100 and 200, respectively, and the transmission power puThe total rate of the third and fourth steps is plotted against Rician-factor at 5,10, 15. It can be seen from fig. 3 that the total achievable rate increases with increasing Rician-factor, transmit power, and number of antennas. It can also be seen from fig. 3 that when Rician-factor is reduced to a relatively small value, when the channel degrades to a rayleigh fading channel, the total rate no longer changes with Rician-factor, and when Rician-factor reaches 25dB, the total rate no longer increases to saturation with increasing Rician-factor.
FIG. 4 shows the transmission power p for a BR antenna number Nr of 50, 100, 150 and 200, respectivelyu10 and Rician-factor mui＝εiThe average rate per user is plotted against the number of users K, 10 dB. As can be seen from the graph, the average per-user rate is in a logarithmic monotonically decreasing trend as the number of users increases. Meanwhile, the average frequency spectrum efficiency of each user is improved by increasing the number of relay antennas, so that the service quality of the system is improved.
The invention considers the condition that LOS paths exist between a user and a BR and between the BR and a destination BD in the uplink process of the Massive MIMO relay system, so that the model is more consistent with actual communication. Simulation verification is carried out under different transmitting powers, different Rician-factors and different user numbers: the simulation results show that the total rate curve obtained by Monte-Carlo simulation almost completely coincides with the total rate curve obtained by analysis.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (6)

1. A Rician channel based Massive MIMO relay system uplink model construction method is characterized by comprising the following steps:
s1, modeling user-to-BR and BR-to-BD channels as Rician channels considering the existence of LOS path;
s2, calculating and obtaining channel coefficient matrixes from the user to the BR and the BR to the BD according to the fast fading matrix and the large-scale fading matrix from the user to the BR and the BR to the BD;
the user-to-relay (BR) and BR-to-destination base station (BD) channel coefficients may be expressed as:
Figure FDA0002823562570000011
Figure FDA0002823562570000012
wherein, gSR，mkIs the channel coefficient from the kth user to the mth antenna of BR, hSR，mkIs the fast fading element, g, from the k-th user to the m-th antenna of the BRRD，mkIs the channel coefficient between the optional kth transmitting antenna of the BR and the antenna of the mth destination BD, hRD，mkIs a fast fading element between the optional kth transmitting antenna of the BR and the antenna of the mth destination BD, and αkAnd betakIs a large-scale fading coefficient used for simulating geometric attenuation and shadow fading;
the channel coefficients are written as follows:
Figure FDA0002823562570000013
Figure FDA0002823562570000014
here, the
Figure FDA0002823562570000015
And
Figure FDA0002823562570000016
representing channel matrices containing fast fading and large-scale fading between user-to-BR and BR-to-BD respectively,
Figure FDA0002823562570000017
and
Figure FDA0002823562570000018
representing the fast fading matrix, N, of users to BR and BR to BDrAnd NdRespectively representing the number of antennas of BR and BD, K being the number of users, and [ HSR]mk＝hSR，mk，
Figure FDA0002823562570000019
And DRDRepresents a large scale fading diagonal matrix of K x K, and [ DSR]kk＝αk，[DRD]kk＝βk；
Fast fading matrix H in the above two formulasSRAnd HRDCan be expressed as follows:
Figure FDA0002823562570000021
Figure FDA0002823562570000022
here omegaSRAnd ΩRDRepresents a K x K Rician-factor diagonal matrix, and Rician-factor represents the ratio of the power of a deterministic component to the power of a dispersive component, which is a number from which the matrix omega is constructedSRAnd ΩRD(ii) a Rician-fa for kth userThe vectors can respectively represent [ omega ]SR]kk＝μkAnd [ omega ]RD]kk＝εk，
Figure FDA0002823562570000023
And
Figure FDA0002823562570000024
representing the random component of the channel, HSR，wAnd HRD，wEach column of (a) has a zero mean value, and the real part and the imaginary part are independent of each other, the variance is 1/2, and the columns are independent and identically distributed complex Gaussian random variables,
Figure FDA0002823562570000025
and
Figure FDA0002823562570000026
representing a deterministic component of the channel, IKRepresenting a K × K identity matrix.
2. A performance analysis method for an uplink model of a Massive MIMO relay system based on a Rician channel is characterized by comprising the following steps:
s1, calculating and obtaining channel coefficient matrixes from user to BR and BR to BD according to the method of claim 1;
s2, calculating and obtaining a receiving signal expression at the BD according to the channel coefficient matrixes from the user to the BR and from the BR to the BD;
s3, calculating to obtain a real total rate expression according to the received signal expression;
and S4, expressing the real total rate expression by using the channel high-order statistics, and obtaining a closed expression for analyzing the total rate to analyze the performance.
3. The method according to claim 2, wherein the process of calculating the received signal expression at BD is as follows:
in the first time slot, K users send signals to the BR;
suppose that
Figure FDA0002823562570000031
Is a transmission signal vector of K users, and xsPower satisfies normalized E { xsxs H}＝IK，GSRIs a channel coefficient matrix from user to BR, and the received signal at BR is:
Figure FDA0002823562570000032
wherein the transmission power of each user is pu，nRRepresents complex white Gaussian noise independently and equally distributed and
Figure FDA0002823562570000033
obtaining a received signal y at BRRThe received signal is then processed by the maximal ratio receiver, which can be made dependent on
Figure FDA0002823562570000034
Of the receiving matrix
Figure FDA0002823562570000035
Then receiving signal yRAnd depend on
Figure FDA0002823562570000036
Receiver matrix of
Figure FDA0002823562570000037
By multiplication, the simply processed received signal can be expressed as:
Figure FDA0002823562570000038
then receives the signal xRIs power amplified at BR, and the power amplified signal can be expressed as:
Figure FDA0002823562570000039
here power amplified signal
Figure FDA00028235625700000310
Satisfy the requirement of
Figure FDA00028235625700000311
PRRepresenting power amplified signals
Figure FDA00028235625700000312
Is an amplification factor that satisfies the total transmit power constraint at BR,
the overall transmit power constraint of the BR has an amplification factor γ of:
Figure FDA00028235625700000313
in the second time slot, the BR arbitrarily selects K antennas for forwarding
Figure FDA00028235625700000314
The received signal arriving at the destination BD is:
Figure FDA00028235625700000315
where G isRDIs that fast fading and large scale fading N are contained between BR and destination BDdChannel matrix of xK, nDIs complex additive white gaussian noise at the destination BD and
Figure FDA00028235625700000316
MRC reception is also employed at the destination BD, where the reception matrix
Figure FDA00028235625700000317
Depend on
Figure FDA00028235625700000318
After being processed at the destination BD, the received signal expression of the Rician channel Massive MIMO relay system can be obtained as follows:
Figure FDA0002823562570000041
4. the method for analyzing performance of the uplink model of the Massive MIMO relay system based on the Rician channel as claimed in claim 2, wherein the specific process of calculating and obtaining the expression of the real total rate according to the expression of the received signal is as follows:
assuming that users to BR and BR to destination BD have perfect channel state information, without performing channel estimation, the acceptance signal of the kth user at destination BD can be written as follows according to the above equation:
Figure FDA0002823562570000042
suppose that the user interference is gaussian distributed and follows the transmitted signal x of the kth users，kIndependently, the SNR of the k-th user can be obtainedkFurther, the achievement rate R can be obtainedkComprises the following steps:
Figure FDA0002823562570000043
Figure FDA0002823562570000044
the above equation can be approximated as:
Figure FDA0002823562570000045
the actual total rate achieved by the above equation is:
Figure FDA0002823562570000046
5. the method for analyzing performance of the uplink model of the Massive MIMO relay system based on the Rician channel as claimed in claim 2, wherein the process of calculating and analyzing the total rate comprises:
the total analysis rate of the Massive MIMO relay system under a Rician channel is as follows:
Figure FDA0002823562570000051
is provided with
Figure FDA0002823562570000052
Figure FDA0002823562570000053
A in the above formulakRepresents the power of the k-th user's desired signal, BkIndicating the power of the kth user interfered by other users, CkAnd DkRepresenting noise power, using ΔSR，k、Qki、Φki、ΔRD，k、Rki、φkiTo express Ak～DkWhich can be respectively expressed as:
Figure FDA0002823562570000054
Figure FDA0002823562570000055
Figure FDA0002823562570000056
Dk＝σD 2βkNd。
6. the method as claimed in claim 5, wherein the analysis rate expression is derived from the analysis total power expression under three other conditions:
the first method comprises the following steps: when only a LOS path exists between the user to the BR, the Ricean-factor between the BR and the destination BD is ∞ dB, i.e.,. epsilon. + -iAt this time, the channel between BR and destination BD degenerates to a rayleigh fading channel, and ΔRD，k＝1，RkiAt this time, the closed expression of the Massive MIMO relay system for achieving the total rate under the condition that only LOS paths exist between users and BRs is as follows:
Figure FDA0002823562570000061
will be deltaRD，k＝1，RkiSubstitution with 1 gives acase1，k、Bcase1，k、Ccase1，k、Dcase1，kThe expression is as follows:
Figure FDA0002823562570000062
Figure FDA0002823562570000063
Figure FDA0002823562570000064
Dcase1，k＝σD 2βkNd
and the second method comprises the following steps: in the case where only a LOS path exists between the BR to the destination BD, the Ricean-factor between the user and the BR is-infinity dB, i.e., μiAt 0, the channel between user and BR degenerates to rayleigh fading channel, and ΔSR，k＝1，QkiAt this time, the closed expression of the Massive MIMO relay system for achieving the total rate in the case where only a LOS path exists between the BR and the destination BD is as follows:
Figure FDA0002823562570000065
will be deltaSR，k＝1，QkiSubstitution with 1 gives acase2，k、Bcase2，k、Ccase2，k、Dcase2，kThe expression is as follows:
Figure FDA0002823562570000066
Figure FDA0002823562570000067
Figure FDA0002823562570000071
Dcase2，k＝σD 2βkNd
and the third is that: when no LOS path exists between the user to the BR and the BR to the destination BDIn the case, the Ricean-factors between user to BR and BR to destination BD are both- ∞ dB, i.e., μi＝0，εiAt 0, the model degenerates to a pure Rayleigh channel attenuation model, at which time ΔSR，k＝1，Qki＝1，ΔRD，k＝1，Rki1 is ═ 1; the closed expression for the masive MIMO relay system to achieve the total rate when there is no LOS path between the user to the BR and the BR to the destination BD at this time is as follows:
Figure FDA0002823562570000072
will be deltaSR，k＝1，Qki＝1，ΔRD，k＝1，RkiSubstitution with 1 gives acase3，k、Bcase3，k、Ccase3，k、Dcase3，kThe expression is as follows:
Figure FDA0002823562570000073
Figure FDA0002823562570000074
Figure FDA0002823562570000075
Dcase3，k＝σD 2βkNd。
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