CN112910517B - Massive MIMO relay system downlink model construction method based on low-precision quantization - Google Patents

Massive MIMO relay system downlink model construction method based on low-precision quantization Download PDF

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CN112910517B
CN112910517B CN202110067128.XA CN202110067128A CN112910517B CN 112910517 B CN112910517 B CN 112910517B CN 202110067128 A CN202110067128 A CN 202110067128A CN 112910517 B CN112910517 B CN 112910517B
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base station
model
user
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CN112910517A (en
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张昀
李双
徐钦晨
于舒娟
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Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • 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
    • H04B17/391—Modelling the propagation channel
    • H04B17/3911—Fading models or fading generators
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • H04B17/3912—Simulation models, e.g. distribution of spectral power density or received signal strength indicator [RSSI] for a given geographic region
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting

Abstract

The invention discloses a MassiveMIMO relay system downlink model construction method based on low precision quantization, firstly, modeling a channel coefficient from a base station to a relay and a channel from the relay to a target user into a Leise fading model; then, dividing signals of a Rice fading model downlink into two time slots for processing in sequence, wherein the first time slot is a signal processing process from a base station to a relay, and the second time slot is a signal processing process from the relay to a target user; secondly, deducing a real reachable total rate according to a received signal expression of a user and a Shannon formula; and finally, deriving a closed expression of the total rate by using the high-order statistic. The invention considers the condition that LOS paths exist between a base station to a relay and between the relay and a target user in the downlink process of the MassiveMIMO relay system, so that the model is more consistent with the actual communication condition, and the problem of high power consumption caused by multiple antennas is solved.

Description

Massive MIMO relay system downlink model construction method based on low-precision quantization
Technical Field
The invention belongs to the technical field of wireless communication signal processing, and particularly relates to a Massive MIMO relay system downlink model construction method based on low-precision quantization.
Background
In order to meet the technical indexes of the fifth generation mobile communication system in the aspects of thousand times of data volume, ultra-low delay, 10Gbit/s transmission rate, supporting diversified applications and the like and meet the requirements of high spectral efficiency, high energy efficiency and high cost efficiency, large-scale MIMO technology is provided in both academic circles and industrial circles.
The main idea of MIMO is to install hundreds of antennas at the base station and serve tens of users on the same time-frequency resource block. The large-scale MIMO system greatly improves the antenna array gain and spatial degree of freedom at the base station end, so that the interference influence between users can be reduced or even eliminated only by adopting a simple linear signal processing method, such as Maximum Ratio Combining (MRC) and Zero-Forcing (ZF), at the base station end, thereby effectively improving the system capacity and the spectral efficiency. Therefore, the research on the system capacity of the Massive MIMO system becomes more important under different transmission and reception schemes and different channels.
In addition, in order to increase the transmission rate of mobile communication, improve the small cell coverage radius and overcome the disadvantage that the mobile terminal is not properly configured with multiple antennas, a relay transmission technology is proposed and becomes one of the important technologies to solve the above problems. The relay technology can significantly improve the transmission reliability, multiplexing gain and coverage. For multi-user multiple-input multiple-output (MU-MIMO) networks, relay stations are widely deployed to enhance the quality of communication between base stations and users.
To benefit from the advantages of massive MIMO and relay technologies, some excellent domestic and foreign researchers have studied massive MIMO relay networks. Some MRT/MRC and ZF processing used in the relay is utilized to obtain an asymptotic sum rate, and the sum rate performance between the MRT/MRC and ZF under different powers is compared. There are several pairs of massive MIMO uplinks with AF relays where both the base station and the relay are equipped with massive antennas. Existing research is based on arranging a large number of antennas at the relay to improve spatial multiplexing, and does not consider using large-scale antennas at the base station.
However, the large number of antennas greatly complicates the hardware design implementation of massive MIMO systems. Especially, each receiving antenna in the system needs to be configured with an analog-to-digital converter (ADC) unit, and the use of a large number of antennas means that a large number of ADC units are required. The exponential increase in overhead and power consumption has caused high-bit analog-to-digital converters to become a major bottleneck in implementing massive MIMO systems.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a method for constructing a Massive MIMO relay system downlink model based on low-precision quantization, which constructs a wireless communication model and analyzes the wireless communication model, so that the model is more in line with the actual communication situation, and the problem of high power consumption caused by multiple antennas is solved.
The invention content is as follows: the invention provides a Massive MIMO relay system downlink model construction method based on low-precision quantization, which specifically comprises the following steps:
(1) constructing a channel model: modeling a channel coefficient from a base station to a relay and a channel from the relay to a target user into a Leise fading model;
(2) processing the signal transmission process of the Rice fading model downlink: the method comprises the following steps that the two time slots are sequentially processed, wherein the first time slot is a signal processing process from a base station to a relay, and the second time slot is a signal processing process from the relay to a target user;
(3) calculating the true achievable total rate of the Rice fading model: deducing a real reachable total rate according to a received signal expression of a user and a Shannon formula;
(4) calculating the theoretical total rate of the Rice fading model: deducing a closed expression of the total rate by using the high-order statistic;
(5) the system capacity is obtained by analyzing a closed expression of the achievable total rate.
Further, the channel coefficients in step (1) are written in the form of a matrix as follows:
Figure GDA0003406413690000021
Figure GDA0003406413690000022
wherein the content of the first and second substances,
Figure GDA0003406413690000023
and
Figure GDA0003406413690000024
fast fading matrix, M, for modeling base station to relay and relay to destination user1And M2Respectively representing the number of antennas of the base station and the relay, K being the number of users, and [ Hi]km＝hi,km,i＝1,2；D1And D2Represents a large scale fading diagonal matrix of K x K, and [ D1]kk＝αk,[D2]kk＝βk；
Fast fading channel matrix H1And H2Can be expressed as follows:
Figure GDA0003406413690000025
Figure GDA0003406413690000026
wherein the content of the first and second substances,
Figure GDA0003406413690000031
and
Figure GDA0003406413690000032
which represents the random component of the channel and,
Figure GDA0003406413690000033
and
Figure GDA0003406413690000034
representing the deterministic component of the channel, omega1And Ω2The Rician-factor diagonal matrix of K multiplied by K can be expressed, and the Rician-factor of the K user can respectively express [ omega ]1]kk＝μkAnd [ omega ]2]kk＝εk。
Further, the step (2) comprises the steps of:
(21) dividing the transmission signal of the whole downlink process into two time slots for processing;
(22) in the first time slot, the base station transmits the source signal to the relay after the maximum ratio transmission precoding processing, and the received signal of the relay end is as follows:
Figure GDA0003406413690000035
Figure GDA0003406413690000036
wherein the source signal is
Figure GDA0003406413690000037
And x satisfies the normalization E { x · x [ ] xH}＝IK，G1Is K M between base station and relay1The channel matrix comprises a fast fading part and a large-scale fading part; since MRT is used at the base station to process the signals, the precoding matrix is
Figure GDA0003406413690000038
Depend on
Figure GDA0003406413690000039
Is G1Conjugate transpose matrix of G1Is K M between base station and relay1The matrix of the channels is then used,
Figure GDA00034064136900000310
as a precoding matrix, yBSFor signals to be transmitted at the base station, puFor each user's transmit power, nRSRepresents complex white Gaussian noise independently and equally distributed and
Figure GDA00034064136900000311
(23) ADCs are configured at the relay terminal, and an additive quantization noise model is adopted to carry out on the received signal yRSAnd (3) quantification:
Figure GDA00034064136900000312
where ξ ═ 1- ρ is the linear quantization gain, nqIs quantization noise, and yRSNot related; ρ is the ratio of the quantizer error variance and the input variance; receiving signal yRS,qAnd performing power amplification at the relay, wherein the signals after power amplification are as follows:
yAF＝a·yRS,q
wherein, yAFSatisfies E { yAF·yAF H}＝pRA is an amplification factor satisfying the total transmit power constraint at the relay end; the amplification factor a that satisfies the total transmit power constraint at the relay, which can be obtained from the power constraint condition, is:
Figure GDA00034064136900000313
will yAFProcessing the signals by MRT to obtain signals
Figure GDA00034064136900000314
Comprises the following steps:
Figure GDA00034064136900000315
(24) in the second time slot, the relay will
Figure GDA0003406413690000041
And forwarding to the destination user, wherein the received signals reaching the destination user are as follows:
Figure GDA0003406413690000042
wherein G is2Is that fast fading and large-scale fading are contained between the relay and the target user2Of the channel matrix nUIs complex additive white gaussian noise at the destination user and
Figure GDA0003406413690000043
the user receiving signal based on Rician channel Massive MIMO relay system is:
Figure GDA0003406413690000044
further, the step (3) is realized as follows:
the received signal of the kth destination user is as follows:
Figure GDA0003406413690000045
signal to interference plus noise ratio SINR:
Figure GDA0003406413690000046
the achievable rate for the kth user is:
Figure GDA0003406413690000047
wherein:
Figure GDA0003406413690000048
further, the step (4) is realized as follows:
the achievable total rate of the Massive MIMO relay system under the Rician channel is as follows:
Figure GDA0003406413690000049
for ease of calculation, the following variables are defined:
Figure GDA00034064136900000410
Figure GDA0003406413690000051
using delta1,k,Δ2,k,Φ1,ik,φ2,ik,γ1,ki,γ2,kiIs S in the above formulak,Ik,N1,k,N2,kCan be expressed as:
Figure GDA0003406413690000052
Figure GDA0003406413690000053
Figure GDA0003406413690000054
Figure GDA0003406413690000055
has the advantages that: compared with the prior art, the invention has the beneficial effects that: the invention considers the condition that LOS paths exist between a base station to a relay and between the relay and a target user in the downlink process of the Massive MIMO relay system, so that the model is more consistent with the actual communication condition; and in order to solve the high power consumption problem brought by many aerials; configuring low-precision ADCs for the antenna at the relay to perform quantization processing; through the simulation result, the total rate curve obtained through Monte-Carlo simulation almost completely coincides with the total rate curve obtained through analysis; analyzing the downlink performance of a Massive MIMO relay system under a Rician fading channel based on low-precision quantization, and deriving an approximate closed expression of the downlink reachable rate of the Massive MIMO relay system; the large-scale MIMO system with low-precision quantization can obtain satisfactory throughput performance and spectral efficiency under a Rician channel.
Drawings
FIG. 1 is a diagram of a structural implementation of a Rician channel Massive MIMO relay system downlink model based on low-precision quantization;
FIG. 2 is a graph of total rate as a function of the number of relay antennas that can be achieved by the present invention;
FIG. 3 is a graph of the total rate achievable with the present invention as a function of Rician-factor;
fig. 4 is a graph of achievable rate as a function of the number of quantization bits.
Detailed Description
The technical scheme of the invention is clearly and completely described below with reference to the accompanying drawings.
In an actual communication system, due to the existence of severe shadowing and path LOSs between a base station and a destination user, a direct link is not available, signals transmitted by the base station need to be relayed to be received by the user, and LOS (line-of-sight) exists between the base station and the relay and the user.
The invention provides a method for constructing a Massive MIMO relay system downlink model based on low-precision quantization, which comprises the steps of carrying out corresponding processing on signals in a communication process to obtain a receiving signal of a kth user, calculating the signal-to-noise ratio of the kth user according to the obtained receiving signal, obtaining the realization rate of the kth user through a Shannon formula, summing to obtain a real reachable rate, and finally deducing a closed expression of the reachable rate of a downlink according to high-order statistics of a channel. The method specifically comprises the following steps:
as shown in fig. 1, it is a structure diagram of a Rician channel Massive MIMO relay system downlink model construction and performance analysis method based on low precision quantization. The system consists of a base station, a relay and K single-antenna users. Due to serious shadow and path LOSs, a direct link does not exist between the base station and the target user, a signal sent by the base station needs to pass through the relay to reach the target user, and LOS paths exist between the base station and the relay and the target user. The base station and the relay system are provided with a large number of antenna arrays, the number of the antennas is M respectively1And M2(assume M1≥M2≥K)。
Step 1: constructing a channel model: and modeling the channel coefficient from the base station to the relay and the channel from the relay to the target user into a Lass fading model.
The channel coefficients are written in the form of a matrix as follows:
Figure GDA0003406413690000061
Figure GDA0003406413690000062
wherein the content of the first and second substances,
Figure GDA0003406413690000063
and
Figure GDA0003406413690000064
fast fading matrix, M, for modeling base station to relay and relay to destination user1And M2Respectively representing the number of antennas of the base station and the relay, K being the number of users, and [ Hi]km＝hi,km,i＝1,2。D1And D2Represents a large scale fading diagonal matrix of K x K, and [ D1]kk＝αk,[D2]kk＝βk。
Fast fading channel matrix H1And H2Can be expressed as follows:
Figure GDA0003406413690000065
Figure GDA0003406413690000066
here, the
Figure GDA0003406413690000071
And
Figure GDA0003406413690000072
to representThe random component of the channel is the random component of the channel,
Figure GDA0003406413690000073
and
Figure GDA0003406413690000074
Figure GDA0003406413690000075
representing the deterministic component of the channel, omega1And Ω2The Rician-factor diagonal matrix of K multiplied by K can be expressed, and the Rician-factor of the K user can respectively express [ omega ]1]kk＝μkAnd [ omega ]2]kk＝εk。
Step 2: and processing the signal transmission process of the whole downlink: and the processing is sequentially carried out by dividing the time slot into two time slots, wherein the first time slot is a signal processing process from the base station to the relay, and the second time slot is a signal processing process from the relay to the target user.
The whole process is divided into two time slots.
In the first time slot, the base station transmits the source signal to the relay after performing Maximum Ratio Transmission (MRT) precoding processing. Assume a source signal of
Figure GDA0003406413690000076
And x satisfies the normalization E { x · x [ ] xH}＝IK，G1Is K M between base station and relay1The channel matrix comprises two parts of fast fading and large-scale fading. Signal to be transmitted y at base stationBSThat is, the source signal is simply processed through the MRT, i.e., the sum of x depends on
Figure GDA0003406413690000077
Of the receiving matrix
Figure GDA0003406413690000078
Multiplication:
Figure GDA0003406413690000079
p in the above formulauIs the transmit power of each user.
Therefore, the received signal at the relay end is:
Figure GDA00034064136900000710
wherein n isRSRepresents complex white Gaussian noise independently and equally distributed and
Figure GDA00034064136900000711
next, since the ADCs are configured at the relay end, the signal is quantized before further processing. In this model, we adopt a widely used Additive Quantization Noise Model (AQNM) to receive the signal yRSThe quantized signal obtained at the relay is:
Figure GDA00034064136900000712
where ξ ═ 1- ρ is the linear quantization gain, nqIs quantization noise, and yRSIs not relevant. ρ is the ratio of the quantizer error variance and the input variance, and since the channel input signal x is gaussian distributed, the received signal at the relay is also gaussian distributed. As shown in table 1 for b<5, the exact values of ρ are in table 1; for the case that b is more than or equal to 6, rho can be expressed by the formula
Figure GDA00034064136900000713
And (6) calculating. Further, n isqThe conditional covariance formula of (a) can be expressed as:
Figure GDA00034064136900000714
therefore, the temperature of the molten metal is controlled,
Figure GDA0003406413690000081
TABLE 1 quantization bit number b and quantization distortion factor
Figure GDA0003406413690000082
Subsequently, the signal y is receivedRS,qAnd performing power amplification at the relay, wherein the signals after power amplification are as follows:
yAF＝a·yRS,q
the signal y here being power amplifiedAFSatisfies E { yAF·yAF H}＝pRAnd a is an amplification factor that satisfies the total transmit power constraint at the relay. The amplification factor a that satisfies the total transmit power constraint at the relay, which can be obtained from the power constraint condition, is:
Figure GDA0003406413690000083
finally, mixing yAFProcessing the signals by MRT to obtain signals
Figure GDA0003406413690000084
Comprises the following steps:
Figure GDA0003406413690000085
in the second time slot, the relay will
Figure GDA0003406413690000086
Forwarded to the destination user, so the received signal to the destination user is:
Figure GDA0003406413690000087
where G is2Is that fast fading and large-scale fading are contained between the relay and the target user2The channel matrix of (a) is determined,nUis complex additive white gaussian noise at the destination user and
Figure GDA0003406413690000088
the user receiving signal based on the Rician channel Massive MIMO relay system can be obtained by expanding the above formula as follows:
Figure GDA0003406413690000089
and step 3: calculating the real achievable total rate of the model: and deducing the real total rate according to the received signal expression of the user and the Shannon formula.
Writing a received signal of a k-th destination user based on a user received signal of a Rician channel Massive MIMO relay system as follows:
Figure GDA00034064136900000810
suppose that user interference is gaussian distributed and xkRegardless, we can get the signal to interference plus noise ratio (SINR):
Figure GDA0003406413690000091
the achievable rate for the kth user can thus be found to be:
Rk＝1/2·E{log2(1+SINR)}
thus, the achievable rate for the kth user can be approximated as:
Rk≈1/2·log2(1+E{SINR})
the concrete expression is as follows:
Figure GDA0003406413690000092
and 4, step 4: calculating the theoretical total rate of the Rice fading model: a closed expression of the achievable total rate is derived using the high order statistics.
The achievable total rate of the Massive MIMO relay system under the Rician channel is as follows:
Figure GDA0003406413690000093
suppose that:
Figure GDA0003406413690000094
Figure GDA0003406413690000095
using delta1,k,Δ2,k,Φ1,ik,φ2,ik,γ1,ki,γ2,kiIs S in the above formulak,Ik,N1,k,N2,kCan be expressed as:
Figure GDA0003406413690000096
Figure GDA0003406413690000097
Figure GDA0003406413690000101
Figure GDA0003406413690000102
Figure GDA0003406413690000103
the following was demonstrated: the high order statistics are:
Figure GDA0003406413690000104
Figure GDA0003406413690000105
Figure GDA0003406413690000106
Figure GDA0003406413690000107
at RkIn the expression of
Figure GDA0003406413690000108
The following calculation can be made:
Figure GDA0003406413690000109
can pass through
Figure GDA00034064136900001010
The power of the desired signal is obtained as:
Figure GDA00034064136900001011
similarity can be calculated
Figure GDA00034064136900001012
Figure GDA00034064136900001013
Figure GDA0003406413690000111
Therefore, power I of inter-user interferencekCan be expressed in the following form:
Figure GDA0003406413690000112
the same principle is that:
Figure GDA0003406413690000113
the last term in the denominator is calculated as follows:
Figure GDA0003406413690000114
Figure GDA0003406413690000115
a using Delta1,k,Δ2,k,Φ1,ik,φ2,ik,γ1,ki,γ2,kiIt can be expressed as follows:
Figure GDA0003406413690000116
expression of true rate by a
Figure GDA0003406413690000117
The expectation of the ith element is:
Figure GDA0003406413690000121
thus obtaining the following components:
Figure GDA0003406413690000122
the third term in the denominator is:
Figure GDA0003406413690000123
in summary, in the downlink process, the model is considered as a leis fading channel model in the channels from the base station to the relay and from the relay to the user, and the leis fading channel model is more consistent with the actual communication environment compared with the traditional rayleigh channel model. And after the problem of higher hardware cost brought by multiple antennas is considered, low-precision quantized ADCs are configured in the relay so as to reduce cost and power consumption. The model also has the advantage that the channel of the entire model can be simplified according to the value of a particular Rician-factor, such as when Rician-factor is- ∞ dB (equivalent to Δ ∞ dB)1,k＝1、γ1,ki1) whose channel model changes from rice to rayleigh fading.
Fig. 2 is a simulation result of the total rate of the Rician channel Massive MIMO relay system based on low precision quantization according to the number of antennas in relay when the number of users K is 10 and Rician-factor is 10dB under perfect channel state information. Wherein the star points are the real rate obtained by taking 1000 Monte Carlo experiments, and the linear ones are the simulation results obtained by analysis. As can be seen from fig. 2, in this case, the curve obtained by the analysis almost coincides with the true curve of 1000 monte carlo simulations, which confirms the correctness of the analysis result.
Fig. 3 is a graph of the total rate as a function of Rician-factor for a number K of users of 10, a number of antennas at the relay of 200, and a transmission power of 10 dB. It can be seen from fig. 3 that the total achievable rate increases with increasing Rician-factor and the number of quantization bits. 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 30dB, the total rate no longer increases with increase of Rician-factor, thereby reaching a saturation state.
Fig. 4 is a graph showing the variation of the average rate of each user with the number of transmission bits for a relay antenna number of 200 and two Rician-factors of 10 dB. As can be seen from fig. 4, when the quantization bit number is less than 5, the average rate gradually increases with the increase of the quantization bit number, and when the quantization bit number is greater than 5, the average rate tends to be in a steady state and does not increase any more. Meanwhile, the performance degradation caused by the 1-bit quantization can be compensated by increasing the number of antennas.

Claims (4)

1. A Massive MIMO relay system downlink model construction method based on low-precision quantization is characterized by comprising the following steps:
(1) constructing a channel model: modeling a channel coefficient from a base station to a relay and a channel from the relay to a target user into a Leise fading model;
(2) processing the signal transmission process of the Rice fading model downlink: the method comprises the following steps that the two time slots are sequentially processed, wherein the first time slot is a signal processing process from a base station to a relay, and the second time slot is a signal processing process from the relay to a target user;
(3) calculating the true achievable total rate of the Rice fading model: deducing a real reachable total rate according to a received signal expression of a user and a Shannon formula;
(4) calculating the theoretical total rate of the Rice fading model: deducing a closed expression of the total rate by using the high-order statistic;
(5) obtaining system capacity by analyzing a closed expression of the achievable total rate;
the step (2) comprises the following steps:
(21) dividing the transmission signal of the whole downlink process into two time slots for processing;
(22) in the first time slot, the base station transmits the source signal to the relay after the maximum ratio transmission precoding processing, and the received signal of the relay end is as follows:
Figure FDA0003406413680000011
Figure FDA0003406413680000012
wherein the source signal is
Figure FDA0003406413680000013
And x satisfies the normalization E { x · x [ ] xH}＝IK，G1Is K M between base station and relay1The channel matrix comprises a fast fading part and a large-scale fading part; since MRT is used at the base station to process the signals, the precoding matrix is
Figure FDA0003406413680000014
Depend on
Figure FDA0003406413680000015
Figure FDA0003406413680000016
Is G1Conjugate transpose matrix of G1Is a base station to relay K x M1 channel matrix,
Figure FDA0003406413680000017
as a precoding matrix, yBSFor signals to be transmitted at the base station, puFor each user's transmit power, nRSRepresents complex white Gaussian noise independently and equally distributed and
Figure FDA0003406413680000018
(23) ADCs are configured at the relay terminal, and an additive quantization noise model is adopted to carry out on the received signal yRSAnd (3) quantification:
Figure FDA0003406413680000019
where ξ ═ 1- ρ is the linear quantization gain,nqis quantization noise, and yRSNot related; ρ is the ratio of the quantizer error variance and the input variance; receiving signal yRS，qAnd performing power amplification at the relay, wherein the signals after power amplification are as follows:
yAF＝a·yRS，q
wherein, yAFSatisfies E { yAF·yAF H}＝pRA is an amplification factor satisfying the total transmit power constraint at the relay end; the amplification factor a that satisfies the total transmit power constraint at the relay, which can be obtained from the power constraint condition, is:
Figure FDA0003406413680000021
will yAFProcessing the signals by MRT to obtain signals
Figure FDA0003406413680000022
Comprises the following steps:
Figure FDA0003406413680000023
(24) in the second time slot, the relay will
Figure FDA0003406413680000024
And forwarding to the destination user, wherein the received signals reaching the destination user are as follows:
Figure FDA0003406413680000025
wherein G is2Is that fast fading and large-scale fading are contained between the relay and the target user2Of the channel matrix nUIs complex additive white gaussian noise at the destination user and
Figure FDA0003406413680000026
based onThe user receiving signal of the Rician channel Massive MIMO relay system is as follows:
Figure FDA0003406413680000027
2. the method for constructing the Massive MIMO relay system downlink model based on the low-precision quantization according to claim 1, wherein the channel coefficients in the step (1) are written in a matrix form as follows:
Figure FDA0003406413680000028
Figure FDA0003406413680000029
wherein the content of the first and second substances,
Figure FDA00034064136800000210
and
Figure FDA00034064136800000211
fast fading matrix, M, for modeling base station to relay and relay to destination user1And M2Respectively representing the number of antennas of the base station and the relay, K being the number of users, and [ Hi]km＝hi，km，i＝1，2；D1And D2Represents a large scale fading diagonal matrix of K x K, and [ D1]kk＝αk，[D2]kk＝βk；
Fast fading channel matrix H1And H2Can be expressed as follows:
Figure FDA00034064136800000212
Figure FDA00034064136800000213
wherein the content of the first and second substances,
Figure FDA0003406413680000031
and
Figure FDA0003406413680000032
which represents the random component of the channel and,
Figure FDA0003406413680000033
and
Figure FDA0003406413680000034
representing the deterministic component of the channel, omega1And Ω2The Rician-factor diagonal matrix of K multiplied by K can be expressed, and the Rician-factor of the K user can respectively express [ omega ]1]kk＝μkAnd [ omega ]2]kk＝εk。
3. The method for constructing the downlink model of the Massive MIMO relay system based on the low precision quantization according to claim 1, wherein the step (3) is realized by the following steps:
the received signal of the kth destination user is as follows:
Figure FDA0003406413680000035
signal to interference plus noise ratio SINR:
Figure FDA0003406413680000036
the achievable rate for the kth user is:
Figure FDA0003406413680000037
wherein:
Figure FDA0003406413680000038
4. the method for constructing the downlink model of the Massive MIMO relay system based on the low precision quantization according to the claim 1, wherein the step (4) is realized by the following steps:
the achievable total rate of the Massive MIMO relay system under the Rician channel is as follows:
Figure FDA0003406413680000039
for ease of calculation, the following variables are defined:
Figure FDA00034064136800000310
Figure FDA00034064136800000311
using delta1，k，Δ2，k，Φ1，ik，φ2，ik，γ1，ki，γ2，kiIs S in the above formulak，Ik，N1，k，N2，kCan be expressed as:
Figure FDA0003406413680000041
Figure FDA0003406413680000042
Figure FDA0003406413680000043
Figure FDA0003406413680000044
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