CN108063634B - Optimal regular pre-coding method in low-precision quantitative large-scale MIMO - Google Patents

Optimal regular pre-coding method in low-precision quantitative large-scale MIMO Download PDF

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CN108063634B
CN108063634B CN201810103187.6A CN201810103187A CN108063634B CN 108063634 B CN108063634 B CN 108063634B CN 201810103187 A CN201810103187 A CN 201810103187A CN 108063634 B CN108063634 B CN 108063634B
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许威
徐锦丹
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Abstract

The invention discloses an optimal regular pre-coding method in low-precision quantization large-scale MIMO, wherein in a large-scale MIMO system, a base station needs to be configured with dozens or even hundreds of antennas. In order to reduce hardware cost and system power consumption, each antenna of the base station is configured with a DAC with low precision quantization, and the user side is generally configured with an ADC with limited precision quantization. In addition, because the number of antennas at the base station end is large and the volume of equipment is limited, the antenna array is densely arranged, the multi-antenna spatial channels are not independent, and correlation exists. The invention comprehensively considers the influence of low-precision quantization and channel correlation, and optimizes the regular precoding method of the base station end under the criterion of maximizing the received signal-to-interference-and-noise ratio of each user. Given the number of base station antennas, DAC quantization precision and signal-to-noise ratio, the invention can rapidly determine the optimal regular precoding calculation form. The method is simple in calculation and has positive significance for downlink transmission of a large-scale MIMO system.

Description

Optimal regular pre-coding method in low-precision quantitative large-scale MIMO
Technical Field
The invention relates to an optimal regular pre-coding method in a low-precision quantization large-scale multiple-input multiple-output (MIMO) system, and belongs to the technical field of wireless communication.
Background
The massive MIMO technology has the advantages of greatly increasing system capacity and improving frequency spectrum and power efficiency, and has been recognized as one of the key supporting technologies in future mobile communication systems. The original single-user MIMO technology can obtain multiple antenna diversity gains by deploying multiple transmit/receive antennas. However, in order to sufficiently multiplex spectrum and spatial resources, researchers have first proposed a multi-user MIMO transmission scheme. The transmission mode can lead a plurality of users to multiplex the same time-frequency resource for data transmission, and the data of different users are distinguished by precoding. Researchers such as Jindal, vishwatath, Goldsmith and the like give theoretical channel capacities of an uplink channel and a downlink channel of multi-user MIMO from the viewpoint of information theory at first, and give an optimal multi-user precoding design scheme, namely Dirty Paper Coding (DPC). The research results of the users firstly disclose the basic theory and the implementation method of the MIMO technology for the multi-user layer cooperative transmission. Although the optimal theory of multi-user cooperation is already well-defined, the nonlinear complex computation involved in the DPC-based multi-user precoding is not suitable for most of the current systems. In order to facilitate system implementation, researchers further propose a series of low-complexity linear precoding methods, which include maximum ratio combining, zero forcing, and regular precoding schemes. Maximum ratio combining precoding, while simple to implement, presents inter-user interference. Although zero-forcing precoding can eliminate inter-user interference, matrix inversion operation is required, and a power loss problem occurs when a channel matrix is ill-conditioned. The regularized precoding is introduced with regularized coefficients, so that the algorithm is stable and has good performance, and the regularized precoding is widely applied to a large-scale MIMO communication system. In the regular precoding scheme, the value of the regularization coefficient has a direct influence on the system performance. In the prior art, the regularization coefficients are typically set to the number of users/signal-to-noise ratio. The value of the coefficient needs to be further optimized if the characteristics of the actual system, such as the spatial correlation of the channel, the low-precision quantization of the signal, etc., are fully considered.
In a multi-user massive MIMO system, each rf link, i.e. each antenna, needs to be configured with a pair of analog-to-digital conversion unit (ADC) and digital-to-analog conversion unit (DAC) to quantize the real part and imaginary part of the complex signal, respectively, so the hardware and power consumption cost of the system increases greatly as the number of antennas increases. There are currently two solutions to this problem. One is to configure a low-precision ADC and DAC for the rf link. Since the power consumption of the ADC/DAC increases exponentially along with the increase of the quantization precision of the ADC/DAC, the low-precision ADC/DAC can be configured to effectively reduce the system power consumption. It has been shown that in some practical scenarios a 1-bit quantized ADC is sufficient to achieve near-optimal transmission rates. In addition, researchers have proposed a hybrid use of high and low precision ADC/DAC in an attempt to trade off system performance against power consumption cost. The second is to reduce the number of radio frequency links to reduce the number of ADC/DACs. The same radio frequency link serves a plurality of antennas, each antenna being provided with phase shifters to form a digital-analog hybrid transceiving structure. Clearly, both of the above approaches result in some loss of performance. The former brings quantization errors and the latter reduces antenna multiplexing gain.
Furthermore, the performance of massive MIMO systems is usually studied under independent channel assumptions. Many studies model the channel as a rayleigh fading model, with each element in the channel matrix obeying an independent iso-gaussian distribution. However, in an actual communication system, the number of antennas at the base station side is large, the size of the antenna array is very limited, and the interval between adjacent antenna units is usually very narrow, so that the channel vectors between different antennas and users do not satisfy independent distribution, and spatial correlation exists. Channel correlation can have a significant impact on the performance of a massive MIMO system. The smaller the antenna element spacing, the stronger the spatial correlation. It has been documented that a MIMO system with 4 wavelengths adjacent antenna spacing has twenty percent attenuation in channel capacity compared to a system without correlation. In the existing research, the commonly used channel correlation models include a Kronecker model, a unity-index-unity (uiu) model, and the like. For different forms of channel correlation matrix, the precoding scheme should be optimized correspondingly according to the correlation.
In large-scale MIMO downlink transmission, the invention comprehensively considers the spatial correlation of a channel and the low-precision quantization operation at the transmitting end and the receiving end, and adopts a Morse theory to analyze the quantization performance of a low-precision ADC/DAC, thereby optimizing the regularization coefficient in a regularized precoding scheme and improving the transmission rate of a system.
Disclosure of Invention
The invention provides an optimal regular precoding method in low-precision quantization large-scale MIMO aiming at the technical problems in the prior art, in a large-scale MIMO downlink with spatial correlation of a channel, a base station is configured with a low-precision DAC, a single-antenna user is configured with a limited-precision ADC, and a regular precoding coefficient in a regular precoding scheme directly influences the system performances such as user rate. The invention can rapidly determine the optimal regularization coefficient according to the signal-to-noise ratio of the system, the DAC quantization precision and the number of users, thereby obtaining the maximum single-user rate.
In order to achieve the above object, the technical solution of the present invention is as follows, an optimal regular precoding method in a low-precision quantized large-scale multiple-input multiple-output system (MIMO), comprising the following steps:
(1) in a large-scale MIMO system, a base station is configured with N transmitting antennas, wherein N is a positive real number, and each antenna is configured with a digital-to-analog conversion unit (DAC) with low precision quantization; the base station simultaneously serves M user terminals, wherein M is less than or equal to N, M is a positive real number, and each user terminal is provided with a single receiving antenna and an analog-to-digital conversion unit (ADC) with limited precision quantization; the downlink channel matrix H in the system can be represented as
Figure BDA0001566954030000021
Wherein
Figure BDA0001566954030000022
Representing an uncorrelated Rayleigh channel matrix with the dimension MxN, and R represents a correlation matrix of the base station side antenna array with the dimension NxN;
(2) the equivalent received signal-to-interference-and-noise ratio γ of each user in the downlink is calculated as follows:
Figure BDA0001566954030000031
wherein, γ0Representing the system signal-to-noise ratio; rhoADAnd ρDARespectively representing attenuation factors of the ADC and the DAC, and determining the value according to the quantization precision; the calculation formula for ζ, a and B is as follows:
Figure BDA0001566954030000032
Figure BDA0001566954030000033
Figure BDA0001566954030000034
wherein, λ represents the eigenvalue of the correlation matrix R, E {. can be used to solve the mathematical expectation for λ;
(3) in order to optimize the regular coefficient α in regular precoding to improve the system transmission rate, the following optimization problem is solved
maxαγ(6)
(4) Solving the equation aiming at the optimization problem in the step (3)
Figure BDA0001566954030000035
The calculation formula for obtaining the optimal value of the regularization coefficient alpha is as follows:
Figure BDA0001566954030000036
(5) during downlink transmission, regular precoding is adopted, and a precoding matrix calculation formula is as follows
P＝c(HHH+αI)-1HH(8)
The value of the regularization coefficient alpha is obtained by calculation according to a formula (7); c represents a power control parameter determined by
Figure BDA0001566954030000037
Wherein P represents transmission power, Tr {. cndot } represents the trace of the matrix, I represents the identity matrix, superscript ()HRepresents a conjugate transpose of the matrix;
(6) and (3) during downlink transmission, the base station multiplies the data vector to be transmitted by the precoding matrix P obtained in the step (5), and then transmits the data vector to obtain the optimal rate performance.
Compared with the prior art, the invention has the following beneficial effects: 1) according to the invention, the DAC with low precision and quantization is configured at the base station end, so that the hardware and power consumption cost of a large-scale MIMO system can be effectively reduced; 2) the invention considers the spatial correlation of the transmitting terminal antenna array in the MIMO downlink channel, and has guiding significance to the design of the actual communication system; 3) the invention adopts regular precoding, the performance is more stable compared with the traditional zero-forcing precoding scheme, and good system performance can be obtained even aiming at ill-conditioned channel matrixes; 4) the formula for calculating the optimal regularization coefficient is very simple, and the optimal regularization pre-coding method can be rapidly determined according to the DAC quantization precision, the number of users, the signal-to-noise ratio and the like.
Description of the drawings:
fig. 1 is a block diagram of a transmitting end and a receiving end of a downlink transmission link of a massive MIMO system according to the present invention.
Fig. 2 shows the equivalent received signal to interference plus noise ratio for each user.
Detailed Description
Example 1: an optimal canonical precoding method in a low-precision quantization large-scale multiple-input multiple-output (MIMO) system, the method comprising the steps of:
(1) in a large-scale MIMO system, a base station is configured with N transmitting antennas, and each antenna is configured with a digital-to-analog conversion unit (DAC) with low precision quantization; the base station serves M user terminals (M is less than or equal to N) at the same time, and each user terminal is provided with a single receiving antenna and an analog-to-digital conversion unit (ADC) with limited precision quantization; the downlink channel matrix H in the system can be represented as
Figure BDA0001566954030000041
Wherein
Figure BDA0001566954030000042
Representing an uncorrelated Rayleigh channel matrix with the dimension MxN, and R represents a correlation matrix of the base station side antenna array with the dimension NxN;
(2) the equivalent received signal-to-interference-and-noise ratio γ of each user in the downlink is calculated as follows:
Figure BDA0001566954030000043
wherein, γ0Representing the system signal-to-noise ratio; rhoADAnd ρDARespectively representing attenuation factors of the ADC and the DAC, and determining the value according to the quantization precision; ξ, A and B represent the influence parameters of the channel correlation on γ, which are calculated as follows:
Figure BDA0001566954030000044
Figure BDA0001566954030000045
Figure BDA0001566954030000046
wherein, λ represents the eigenvalue of the correlation matrix R, E {. can be used to solve the mathematical expectation for λ;
(3) in order to optimize the regular coefficient α in regular precoding to improve the system transmission rate, the following optimization problem is solved
maxαγ(6)
(4) Aiming at the optimization problem in the step (3), solving an equation
Figure BDA0001566954030000047
The calculation formula for obtaining the optimal value of the regularization coefficient alpha is as follows:
Figure BDA0001566954030000048
specifically, when γ is given0＝10dB，ρDA0.3633, and M16, calculated as α 11.65;
(5) during downlink transmission, regular precoding is adopted, and a precoding matrix calculation formula is as follows
P＝c(HHH+αI)-1HH(8)
Wherein according to step (4), α ═ 11.65; c represents a power control parameter determined by
Figure BDA0001566954030000049
Wherein P represents transmission power, Tr {. cndot } represents the trace of the matrix, I represents the identity matrix, superscript ()HRepresents a conjugate transpose of the matrix;
(6) during downlink transmission, the base station multiplies the data vector to be transmitted by the precoding matrix P obtained in the step (5), and then transmits the data vector to obtain the optimal rate performance;
referring to fig. 1, a base station serves as a transmitting endN antennas are configured, and each antenna is configured with a low-precision DAC; m users are used as receiving ends, each user is only provided with a single antenna, and each antenna is provided with a limited-precision ADC. At the transmitting end, M symbols s to be transmitted1,s2,…,sMFirstly, regular pre-coding is carried out to generate N digital signals { x }1,x2,…,xN}; then converted into an analog signal { x ] through a low-precision DACq1,xq2,…,xqN}; finally, the N antennas transmit the signals simultaneously; at the receiving end, all users receive the analog signal of y1,y2,…,yM}; generation of digital signal y by limited precision ADC quantizationq1,yq2,…,yqM}; finally, the original sending symbol is recovered through demodulation.
Fig. 2 shows the equivalent received signal to interference and noise ratio for each user, where γ varies with the regularization coefficient α. The abscissa is the normalized regularization coefficient α/N, where N-64 is the number of base station antennas. The number of users M is set to 16 in this example, and the signal-to-noise ratio γ is set0Setting 10dB, the DAC quantization precision is 1 bit, and the ADC quantization precision is 5, 4, 3 and 2 bits respectively. The channel correlation matrix R is a positive definite Toeplitz matrix, and the ith row and jth column elements of the matrix are v|i-j|Wherein ν is 0.5, the correlation coefficient is obtained. The five-pointed star in the graph represents the optimal regularization coefficient calculated according to the invention, and the maximum value of gamma at the point can be observed. The invention can effectively determine the optimal regular pre-coding method, so that the received signal-to-interference-and-noise ratio of each user is maximum. As can be seen from the figure, the optimal regularization coefficient is independent of the quantization precision of the ADC, which means that the base station can perform optimal regularized precoding without any information of the ADC at the user end.
It should be noted that the above-mentioned embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and all equivalent substitutions or substitutions made on the above-mentioned technical solutions belong to the scope of the present invention.

Claims (2)

1. An optimal canonical precoding method in a low-precision quantization large-scale multiple-input multiple-output (MIMO) system is characterized in that: the method comprises the following steps:
(1) in a large-scale MIMO system, a base station is configured with N transmitting antennas, wherein N is a positive real number, and each antenna is configured with a digital-to-analog conversion unit (DAC) with low precision quantization; the base station simultaneously serves M user terminals, wherein M is a positive real number, and each user terminal is provided with a single receiving antenna and an analog-to-digital conversion unit (ADC) with limited precision quantization; the downlink channel matrix H in the system can be represented as
Figure FDA0001566954020000011
Wherein
Figure FDA0001566954020000012
Representing an uncorrelated Rayleigh channel matrix with the dimension MxN, and R represents a correlation matrix of the base station side antenna array with the dimension NxN;
(2) the equivalent received signal-to-interference-and-noise ratio γ of each user in the downlink is calculated as follows:
Figure FDA0001566954020000013
wherein, γ0Representing the system signal-to-noise ratio; rhoADAnd ρDARespectively representing attenuation factors of the ADC and the DAC, and determining the value according to the quantization precision; ξ, A and B represent the influence parameters of the channel correlation on γ, which are calculated as follows:
Figure FDA0001566954020000014
Figure FDA0001566954020000015
Figure FDA0001566954020000018
wherein, λ represents the eigenvalue of the correlation matrix R, E {. can be used to solve the mathematical expectation for λ;
(3) in order to optimize the regular coefficient α in regular precoding to improve the system transmission rate, the following optimization problem is solved
maxαγ (6)
(4) Aiming at the optimization problem in the step (3), solving an equation
Figure FDA0001566954020000019
The calculation formula for obtaining the optimal value of the regularization coefficient alpha is as follows:
Figure FDA0001566954020000016
(5) during downlink transmission, regular precoding is adopted, and a precoding matrix calculation formula is as follows
P＝c(HHH+αI)-1HH (8)
The value of the regularization coefficient alpha is obtained by calculation according to a formula (7); c represents a power control parameter determined by
Figure FDA0001566954020000017
Wherein P represents transmission power, Tr {. cndot } represents the trace of the matrix, I represents the identity matrix, superscript ()HRepresents a conjugate transpose of the matrix;
(6) and (3) during downlink transmission, the base station multiplies the data vector to be transmitted by the precoding matrix P obtained in the step (5), and then transmits the data vector to obtain the optimal rate performance.
2. The optimal canonical precoding method in low-precision quantization large-scale multiple-input multiple-output (MIMO) system according to claim 1, wherein: m in the step (1) is less than or equal to N.
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