CN104617996A - Precoding design method of maximized minimum signal to noise ratio in large-scale MIMO (multiple input multiple output) system - Google Patents

Abstract

The invention relates to a precoding design method of a maximized minimum signal to noise ratio in a large-scale MIMO (multiple input multiple output) system. At first, according to an instant receiving signal to noise ratio of a sub-channel in every radio frequency port of a ZF (zero frequency) receiver used by a base station terminal in an uplink, a mean receiving signal to noise ratio is obtained by using a multivariate statistics method; the sub-channel is optimized on the basis of the maximized minimum mean receiving signal to noise ratio rule; according to the independence of distribution type MIMO ports, the optimization of the mean receiving signal to noise ratio is decomposed to be a precoding matrix design under the limit of independent power in ports and the total power restraint power distribution optimization design between ports; finally, the optimal precoding matrix is obtained. The precoding design method of the maximized minimum signal to noise ratio in the large-scale MIMO obtains the optimal porecoding matrix by bysing the statistical information of a channel only, and has low system feedback cost; meanwhile, in comparison to the traditional power distribution method, the method can obviously improve the mean symbol error rate performance of a system, and thereby promoting the feasibility of the method in actual application.

Description

The Precoding Design method of minimum signal to noise ratio is maximized in extensive mimo system

Technical field

The present invention relates to the Precoding Design method of communication technical field, specifically maximize the Precoding Design method of minimum signal to noise ratio in a kind of extensive MIMO (MassiveMultiple Input Multiple Output, Massive M-MIMO) system.

Background technology

Extensive MIMO technology is adopted as one of its core key technology by the 5th third-generation mobile communication, significantly can reduce power, elevator system performance and coverage, in large-scale distributed mimo system, because there is open structure and resource distribution feature more flexibly, so play important role in mobile communications.In recent years, communication system requirements message transmission rate at a high speed, makes to have carried out a lot of research work at this system regions.The feature of MIMO Signal with Distributed Transmit Antennas is the prevention at radio-frequency port of configuration many antennas, to be distributed in a community in each different region, each port experiences the impact of different path loss and large scale decline (such as shadow fading), and this brings certain difficulty to theoretical performance analysis and optimal design.

In conventional art, if each port can obtain the complete channel information of all of the port, associating precoding technique is used to increase substantially systematic function, but greatly can increase the overhead of feedback link, particularly when antenna number increases to extensive mimo system, white elephant can be brought to feedback link; The Space-Time Codes of any channel information and constant power distribution method is not utilized then to be difficult to effectively improve systematic function completely.Based on this, we propose a kind of Precoding Design method based on channel statistical information, with the obvious elevator system performance of lower overhead.

Summary of the invention

(1) problem that will solve

The technical problem to be solved in the present invention is to provide a kind of Precoding Design method maximizing minimum signal to noise ratio in extensive mimo system, distributed prevention at radio-frequency port different in the community cover same base station carries out power division between Precoding Design and port, to solve prior art Problems existing.

(2) technical scheme

For solving the problems of the technologies described above, the present invention by the following technical solutions:

Maximize the Precoding Design method of minimum signal to noise ratio in extensive mimo system, comprise the following steps:

S1: base station end obtains the compound channel information of all spaced antenna ports by channel estimating, comprises multipath fading H=ZR _t, launch correlation matrix R _t, large scale decline Ξ;

S2: each spaced antenna port obtains the channel statistical information of all of the port by base station feedback link, comprises multipath fading probability density distribution, correlation matrix, large scale fading probability density distribution and path loss coefficient;

S3: according to the instantaneous received signal to noise ratio of each port subchannel of base station end ZF receiver, Multivariable Statistical Methods is used to ask expectation to large scale decline, multipath fading respectively, obtain average received signal to noise ratio, based on the Optimality Criteria maximizing minimum average B configuration received signal to noise ratio, described average received signal to noise ratio is optimized;

The Optimal Decomposition of average received signal to noise ratio is pre-coding matrix design and total power constraint power division optimal design between the ports under independent power constraint in port by S4: according to the independence of port each in MIMO Signal with Distributed Transmit Antennas;

S5: under total power constraint, carry out optimizing between prevention at radio-frequency port, the power division optimization between port is carried out again according to the optimization solution of port inside, optimization solution between this port and the optimization solution in port are merged, finally obtains the optimum pre-coding matrix based on the Optimality Criteria maximizing minimum average B configuration received signal to noise ratio.

In S1, to a Ge Dan community MIMO Signal with Distributed Transmit Antennas, base station end antenna number is N, and in community, K port of different distance is equipped with M antenna, and K port sends data to base station simultaneously, and base station end adopts ZF receiver Received signal strength, and its expression formula is: wherein, y is the Received signal strength of base station end, and channel T is Composite Fading Channels, comprises multipath fading H, obeys plural rayleigh distributed i.i.dCN (0,1); Channels transmit correlation matrix is R _t=diag (R _t1, R _t2..., R _tK), large scale decline Ξ, obeys logarithm normal distribution: $\mathrm{\Ξ}=\mathrm{diag}({\mathrm{\Ξ}}_1/D_1^v{I}_M,{\mathrm{\Ξ}}_2/D_2^v{I}_M,...,{\mathrm{\Ξ}}_K/D_K^v{I}_M),$ Wherein, represent the path loss of a kth port, v is path loss coefficient, stochastic variable Ξ _kobeys logarithm normal distribution: ε _k> 0, wherein, μ _k, δ _kfor its average and variance, pre-coding matrix is F=diag (F ₁, F ₂..., F _k).

In S3, the instantaneous received signal to noise ratio of ZF receiver is wherein, N ₀for system noise; Multipath fading obey the distribution of card side: $\left(x_{\mathrm{km}}\right)=\frac{1}{\mathrm{\Γ}(N-\mathrm{KM}+1)}{x}_{\mathrm{km}}^{N-\mathrm{KM}}{e}^{-x_{\mathrm{km}}},$ X _km> 0, its expectation is

$E\left[\frac{1}{{\left[{\left(H^{H}H\right)}^{-1}\right]}_{\mathrm{km},\mathrm{km}}}\right]=N-\mathrm{KM}+1;$

The expectation of large scale decline item:

$E\left[{\mathrm{\Ξ}}_k\right]=\frac{e^{\frac{{\mathrm{\δ}}_k^2+2\mathrm{\η}{\mathrm{\μ}}_k}{2{\mathrm{\η}}^2}}}{D_k^v}=B_k;$

Therefore average received signal to noise ratio is:

$E\left[{\mathrm{\γ}}_{\mathrm{km}}\right]=\frac{C_k}{{\left[{\left(F^H{R}_{T}F\right)}^{-1}\right]}_{\mathrm{km},\mathrm{km}}},$

Wherein C _k=B _k(N-KM+1)/N ₀;

The Optimality Criteria of pre-coding matrix design is described maximization minimum average B configuration received signal to noise ratio criterion:

$\underset{F}{\max }\{\underset{1\≤k\≤K;1\≤m\≤M}{\min \left\{E\right[{\mathrm{\γ}}_{\mathrm{km}}\left]\right\}\left\}\right\}},$

Meet total transmit power constraint simultaneously:

tr(F ^HF)＝P _T。

In S4, in the independent power constraint situation of port, the power P of a kth emission port _kby temporarily given, make precoding F _kmeet and maximize minimum average B configuration received signal to noise ratio criterion:

$\underset{F_k}{\max }\underset{1\≤m\≤M}{\min }\left\{E\right[{\mathrm{\γ}}_{\mathrm{km}}\left]\right\},$

$\mathrm{tr}\left(F_k{F}_K^H\right)=P_k;$

Optimize under independent power constraint on average received signal to noise ratio basis, make total power configuration matrix P=diag (P ₁, P ₂..., P _k) meet maximization minimum average B configuration received signal to noise ratio criterion:

$\underset{P}{\max }\underset{1\≤k\≤K}{\min }\left\{{\stackrel{\‾}{\mathrm{\γ}}}_k\right\},$

$\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_k=P_T,$

Wherein for the average received signal to noise ratio after optimization in port.

In S5, power optimization coefficient between port $P_k=\frac{{\stackrel{\‾}{A}}_{\mathrm{kM}}^2{P}_T}{C_k{\stackrel{\‾}{W}}_{\mathrm{KM}}},{\stackrel{\‾}{W}}_{\mathrm{KM}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\stackrel{\‾}{A}}_{\mathrm{kM}}^2/C_k,{\stackrel{\‾}{A}}_{\mathrm{kM}}=\frac{1}{M}\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_{\mathrm{km}}^{-\frac{1}{2}};$ In port, pre-coding matrix form is wherein R _tk=V _kΛ _kv _k=V _kdiag (λ _k1, λ _k2..., λ _kM) V _k, P _k=diag (P _k1, P _k2..., P _kM), U is normalization discrete Fourier transform (DFT) matrix of M × M, power optimization coefficient power optimization coefficient final after amalgamation result is optimum pre-coding matrix is F=diag (F ₁, F ₂..., F _k).

(3) beneficial effect

For large-scale distributed mimo system, base station end uses ZF receiver, and Precoding Design method of the present invention uses the method such as multivariate statistics, convex optimization, obtains maximizing the optimum pre-coding matrix that minimum average B configuration received signal to noise ratio is criterion.The present invention does not need complete channel information making a start, only utilize the statistic channel information of channel to design the minimum average B configuration received signal to noise ratio that pre-coding matrix maximizes system, when sending gross power and being constant, significantly improve systematic function with lower system feedback expense, thus improve the method feasibility in actual applications.

Accompanying drawing explanation

Fig. 1 is workflow diagram of the present invention.

Fig. 2 is MIMO Signal with Distributed Transmit Antennas of the present invention transmission schematic diagram.

The average SER performance comparison figure of system of Precoding Design method of the present invention and conventional power distribution method when Fig. 3 is port transmitting coefficient correlation difference.

Fig. 4 be the total reception antenna number of system different with number of transmit antennas time Precoding Design method of the present invention and the average SER performance of system of conventional power distribution method to figure.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.

Under lower overhead prerequisite, effectively improve systematic function, and be conducive to applying in systems in practice, propose a kind of method for precoding based on channel statistical information.See Fig. 1 and Fig. 2, the invention provides a kind of Precoding Design method maximizing minimum signal to noise ratio in extensive mimo system, comprise the following steps:

S1: base station end obtains the compound channel information of all spaced antenna ports by channel estimating, comprises multipath fading H=ZR _t, launch correlation matrix R _t, large scale decline Ξ.

To a Ge Dan community MIMO Signal with Distributed Transmit Antennas, base station end antenna number is N, and in community, K port of different distance is equipped with M antenna, and K port sends data to base station simultaneously, and base station end uses ZF receiver Received signal strength, and its expression formula is: wherein, y is the Received signal strength of base station end, and channel T is Composite Fading Channels, comprises multipath fading H, obeys plural rayleigh distributed i.i.dCN (0,1); Channels transmit correlation matrix is R _t=diag (R _t1, R _t2..., R _tK), large scale decline Ξ, obeys logarithm normal distribution: $\mathrm{\Ξ}=\mathrm{diag}({\mathrm{\Ξ}}_1/D_1^v{I}_M,{\mathrm{\Ξ}}_2/D_2^v{I}_M,...,{\mathrm{\Ξ}}_K/D_K^v{I}_M),$ Wherein, represent the path loss of a kth port, v is path loss coefficient, stochastic variable Ξ _kobeys logarithm normal distribution: ε _k> 0, wherein, μ _k, δ _kfor its average and variance; Linear precoding matrix F=diag (the F designed ₁, F ₂..., F _k).

S2: each spaced antenna port obtains the channel statistical information of all of the port by base station feedback link, comprises multipath fading probability density distribution, correlation matrix, large scale fading probability density distribution and path loss coefficient.

S3: according to the instantaneous received signal to noise ratio of each port subchannel of base station end ZF receiver, use Multivariable Statistical Methods, expectation is asked to the multipath fading item in function expression and large scale decline item, obtain average received signal to noise ratio, based on the Optimality Criteria maximizing minimum average B configuration received signal to noise ratio, average received signal to noise ratio is optimized.

The instantaneous received signal to noise ratio of ZF receiver is wherein, N ₀for system noise, $X_{\mathrm{km}}=\frac{1}{{\left[{\left(H^{H}H\right)}^{-1}\right]}_{\mathrm{km},\mathrm{km}}},$ Obey the distribution of card side: $\left(x_{\mathrm{km}}\right)=\frac{1}{\mathrm{\Γ}(N-\mathrm{KM}+1)}{x}_{\mathrm{km}}^{N-\mathrm{KM}}{e}^{-x_{\mathrm{km}}},$ X _km> 0; The expectation of multipath fading is:

$E\left[\frac{1}{{\left[{\left(H^{H}H\right)}^{-1}\right]}_{\mathrm{km},\mathrm{km}}}\right]=N-\mathrm{KM}+1;$

The expectation of large scale decline item:

$E\left[{\mathrm{\Ξ}}_k\right]=\frac{e^{\frac{{\mathrm{\δ}}_k^2+2\mathrm{\η\μk}}{2{\mathrm{\η}}^2}}}{D_k^v}=B_k;$

Average received signal to noise ratio is:

$E\left[{\mathrm{\γ}}_{\mathrm{km}}\right]=\frac{C_k}{{\left[{\left(F^H{R}_{T}F\right)}^{-1}\right]}_{\mathrm{km},\mathrm{km}}},$

Wherein C _k=B _k(N-KM+1)/N ₀;

The Optimality Criteria of pre-coding matrix design is for maximizing minimum average B configuration received signal to noise ratio criterion:

$\underset{F}{\max }\{\underset{1\≤k\≤K;1\≤m\≤M}{\min \left\{E\right[{\mathrm{\γ}}_{\mathrm{km}}\left]\right\}\left\}\right\}},$

Meet total transmit power constraint simultaneously:

tr(F ^HF)＝P _T。

The Optimal Decomposition of average received signal to noise ratio is pre-coding matrix design and total power constraint power division optimal design between the ports under independent power constraint in port by S4: according to the independence of port each in MIMO Signal with Distributed Transmit Antennas.That is: maximization minimum average B configuration received signal to noise ratio criterion sub-channel is used to be optimized, under the constraint of port independent power, first diagonalization is decomposed to the channel correlation matrix use characteristic value of each port, then carry out power division optimization, finally use the gain between each sub-channels of DFT matrix equalization.

Under port independent power restraint condition, the power P of a kth emission port _kby temporarily given, make precoding F _kmeet and maximize minimum average B configuration received signal to noise ratio criterion:

$\underset{F_k}{\max }\underset{1\≤m\≤M}{\min }\left\{E\right[{\mathrm{\γ}}_{\mathrm{km}}\left]\right\},$

$\mathrm{tr}\left(F_k{F}_K^H\right)=P_k;$

Optimize under independent power constraint on average received signal to noise ratio basis, carry out power division optimization and make total power configuration matrix P=diag (P ₁, P ₂..., P _k) meet maximization minimum average B configuration received signal to noise ratio criterion:

$\underset{P}{\max }\underset{1\≤k\≤K}{\min }\left\{{\stackrel{\‾}{\mathrm{\γ}}}_k\right\},$

$\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_k=P_T,$

Wherein for the average received signal to noise ratio after optimization in port.

S5: under total power constraint, carry out optimizing between prevention at radio-frequency port, the power division optimization between port is carried out again according to the optimization solution of port inside, optimization solution between this port and the optimization solution in port are merged, finally obtain the optimum results in the optimum pre-coding matrix merging port based on the Optimality Criteria maximizing minimum average B configuration received signal to noise ratio and between port, obtain optimum pre-coding matrix.

Power optimization coefficient between port $P_k=\frac{{\stackrel{\‾}{A}}_{\mathrm{kM}}^2{P}_T}{C_k{\stackrel{\‾}{W}}_{\mathrm{KM}}},{\stackrel{\‾}{W}}_{\mathrm{KM}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\stackrel{\‾}{A}}_{\mathrm{kM}}^2/C_k,{\stackrel{\‾}{A}}_{\mathrm{kM}}=\frac{1}{M}\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_{\mathrm{km}}^{-\frac{1}{2}}.$ In port, pre-coding matrix form is wherein R _tk=V _kΛ _kv _k=V _kdiag (λ _k1, λ _k2..., λ _kM) V _k, P _k=diag (P _k1, P _k2..., P _kM), U is normalization discrete Fourier transform (DFT) matrix of M × M, power optimization coefficient power optimization coefficient final after amalgamation result is optimum pre-coding matrix is F=diag (F ₁, F ₂..., F _k).

The present invention proposes under each port in a kind of large-scale distributed mimo system experiences different small scales and large scale compound channel fading profiles, receiving terminal base station uses ZF (ZF) to receive the up-line system detected, to maximize minimum average B configuration received signal to noise ratio for Optimality Criteria, a kind of optimum method for precoding based on channel statistical information is proposed, when sending gross power and being constant, significantly improve systematic function with lower overhead.

The present invention does not need complete channel information making a start, only utilize the slow fading statistic channel information of channel to obtain optimum method for precoding and maximize minimum average B configuration received signal to noise ratio, the ensemble average error sign ratio of system or bit error rate performance are limited to the minimum subchannel performance of gain.When sending gross power and being constant, obviously can improve systematic function by lower overhead, thus improve the method feasibility in actual applications.This method considers the characteristic of channel of more realistic scene channel fading, the decline of each port experience compound channel, comprise multipath fading, launch correlation, large scale decline and path loss coefficient, receiving terminal uses zero-forcing detector (ZF), is Optimality Criteria to the maximum with system minimum average B configuration received signal to noise ratio, make a start and only need the statistical information of channel, reach the effect improving systematic function with lower expense.

Traditional antenna power distribution method is that every root antenna constant power of each port distributes, to the present invention is based on channel statistical information be each port design method for precoding, improves system error sign ratio performance to greatest extent.The precoding of a kth port is: r _tk=V _kΛ _kv _k=V _kdiag (λ _k1, λ _k2..., λ _kM) V _k, P _k=diag (P _k1, P _k2..., P _kM), wherein U is the normalization Discrete Fourier transform of M × M, and power optimization coefficient is wherein ${\stackrel{\‾}{A}}_{\mathrm{kM}}=\frac{1}{M}\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_{\mathrm{km}}^{-\frac{1}{2}},{\stackrel{\‾}{W}}_{\mathrm{KM}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\stackrel{\‾}{A}}_{\mathrm{kM}}^2/C_k,$

Wherein, N is base station receive antenna number, and K is port number, and M is port transmitting antenna number, D _kbe the distance of a kth port and base station, v is path loss coefficient.μ _k, δ _kthe expectation and variance for a kth emission port experience large scale decline logarithm normal distribution respectively.

SER average behavior comparison diagram shown in Figure 3, it is 10 that a kind of MIMO Signal with Distributed Transmit Antennas configuration is set to antenna for base station number, and have 4 spaced antenna ports being in different distance, distance is respectively: 0.5km, 1km, 1.5km, 2km, path loss coefficient is 4, in large scale decline shadow effect, the average of logarithm normal distribution and variance are respectively 4 and 2, each port arrangement 2 antennas, adopt QPSK modulation system, and receiving terminal adopts ZF to receive and detects; By employing the present invention carry power distribution method and traditional power distribution method performance contrasts, can as apparent from Fig. 3,0.1 is respectively at transmitting correlation coefficient ρ, 0., when 5 and 0.9, the average error sign ratio of system (SER) performance improves 3-5dB, and systematic function is significantly improved.

SER average behavior comparison diagram shown in Figure 4, it is 10 that a kind of large-scale distributed mimo system configuration is set to antenna for base station number, have 4 spaced antenna ports being in different distance, distance is respectively: 0.5km, 1km, 1.5km, 2km, path loss coefficient is 4, and in large scale decline shadow effect, the average of logarithm normal distribution and variance are respectively 4 and 2, each port arrangement 2 antennas, launch coefficient correlation and are respectively 0.9.Adopt 16QAM modulation system, receiving terminal adopts ZF to receive and detects; By employing the present invention carry power distribution method and traditional power distribution method performance contrasts, can as apparent from Fig. 4, base station receive antenna number and the total number of transmit antennas ratio beta of all of the port are 1.25, when 2 and 3, the average error sign ratio of system (SER) performance improves 4-5dB, and systematic function is significantly improved.

Claims (5)

1. maximize the Precoding Design method of minimum signal to noise ratio in extensive mimo system, it is characterized in that comprising the following steps:

S1: base station end obtains the compound channel information of all spaced antenna ports by channel estimating, comprises multipath fading H=ZR _t, launch correlation matrix R _t, large scale decline Ξ;

S2: each spaced antenna port obtains the channel statistical information of all of the port by base station feedback link, comprises multipath fading probability density distribution, correlation matrix, large scale fading probability density distribution and path loss coefficient;

S3: according to the instantaneous received signal to noise ratio of each port subchannel of base station end ZF receiver, Multivariable Statistical Methods is used to ask expectation to large scale decline, multipath fading respectively, obtain average received signal to noise ratio, based on the Optimality Criteria maximizing minimum average B configuration received signal to noise ratio, described average received signal to noise ratio is optimized;

The Optimal Decomposition of average received signal to noise ratio is pre-coding matrix design and total power constraint power division optimal design between the ports under independent power constraint in port by S4: according to the independence of port each in MIMO Signal with Distributed Transmit Antennas;

S5: under total power constraint, carry out optimizing between prevention at radio-frequency port, the power division optimization between port is carried out again according to the optimization solution of port inside, optimization solution between this port and the optimization solution in port are merged, finally obtains the optimum pre-coding matrix based on the Optimality Criteria maximizing minimum average B configuration received signal to noise ratio.

2. in extensive mimo system according to claim 1, maximize the Precoding Design method of minimum signal to noise ratio, it is characterized in that: in S1, to a Ge Dan community MIMO Signal with Distributed Transmit Antennas, base station end antenna number is N, in community, K port of different distance is equipped with M antenna, K port sends data to base station simultaneously, and base station end adopts ZF receiver Received signal strength, and its expression formula is: wherein, y is the Received signal strength of base station end, and channel T is Composite Fading Channels, comprises multipath fading H, obeys plural rayleigh distributed i.i.dCN (0,1); Channels transmit correlation matrix is R _t=diag (R _t1, R _t2..., R _tK), large scale decline Ξ, obeys logarithm normal distribution: $\mathrm{\Ξ}=\mathrm{diag}({\mathrm{\Ξ}}_1/D_1^v{I}_M,{\mathrm{\Ξ}}_2/D_2^v{I}_M,...,{\mathrm{\Ξ}}_K/D_K^v{I}_M),$ Wherein, represent the path loss of a kth port, v is path loss coefficient, stochastic variable Ξ _kobeys logarithm normal distribution: ε _k> 0, wherein, μ _k, δ _kfor its average and variance, pre-coding matrix is F=diag (F ₁, F ₂..., F _k).

3. maximize the Precoding Design method of minimum signal to noise ratio in extensive mimo system according to claim 2, it is characterized in that: in S3, the instantaneous received signal to noise ratio of ZF receiver is wherein, N ₀for system noise; Multipath fading obey the distribution of card side: $g\left(x_{\mathrm{km}}\right)=\frac{1}{\mathrm{\Γ}(N-\mathrm{KM}+1)}{x}_{\mathrm{km}}^{N-\mathrm{KM}}{e}^{-x_{\mathrm{km}}},$ X _km> 0, its expectation is

$E\left[\frac{1}{{\left[{\left(H^{H}H\right)}^{-1}\right]}_{\mathrm{km},\mathrm{km}}}\right]=N-\mathrm{KM}+1;$

The expectation of large scale decline item:

$E\left[{\mathrm{\Ξ}}_k\right]=\frac{e^{\frac{{\mathrm{\δ}}_k^2+2\mathrm{\η}{\mathrm{\μ}}_k}{2{\mathrm{\η}}^2}}}{D_k^v}=B_k;$

Therefore average received signal to noise ratio is:

$E\left[{\mathrm{\γ}}_{\mathrm{km}}\right]=\frac{C_k}{{\left[{\left(F^H{R}_{T}F\right)}^{-1}\right]}_{\mathrm{km},\mathrm{km}}},$

Wherein C _k=B _k(N-KM+1)/N ₀;

The Optimality Criteria of pre-coding matrix design is described maximization minimum average B configuration received signal to noise ratio criterion:

$\underset{F}{\max }\underset{1\≤k\≤K;1\≤m\≤M}{\left\{\min \right\{E\left[{\mathrm{\γ}}_{\mathrm{km}}\right]\left\}\right\}\}},$

Meet total transmit power constraint simultaneously:

tr(F ^HF)＝P _T。

4. maximize the Precoding Design method of minimum signal to noise ratio in extensive mimo system according to claim 3, it is characterized in that: in S4, in the independent power constraint situation of port, the power P of a kth emission port _kby temporarily given, make precoding F _kmeet and maximize minimum average B configuration received signal to noise ratio criterion:

$\underset{F_k}{\max }\underset{1\≤m\≤M}{\min }\left\{E\right[{\mathrm{\γ}}_{\mathrm{km}}\left]\right\},$

$\mathrm{tr}\left(F_k{F}_K^H\right)=P_k;$

Optimize under independent power constraint on average received signal to noise ratio basis, make total power configuration matrix P=diag (P ₁, P ₂..., P _k) meet maximization minimum average B configuration received signal to noise ratio criterion:

$\underset{P}{\max }\underset{1\≤k\≤K}{\min }\left\{{\stackrel{\‾}{\mathrm{\γ}}}_k\right\},$

$\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_k=P_T,$

Wherein for the average received signal to noise ratio after optimization in port.

5. maximize the Precoding Design method of minimum signal to noise ratio in extensive mimo system according to claim 4, it is characterized in that: in S5, power optimization coefficient between port $P_k=\frac{{\stackrel{\‾}{A}}_{\mathrm{kM}}^2{P}_T}{C_k{\stackrel{\‾}{W}}_{\mathrm{KM}}},{\stackrel{\‾}{W}}_{\mathrm{KM}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\stackrel{\‾}{A}}_{\mathrm{kM}}^2/C_k,{\stackrel{\‾}{A}}_{\mathrm{kM}}=\frac{1}{M}\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_{\mathrm{km}}^{-\frac{1}{2}};$ In port, pre-coding matrix form is wherein R _tk=V _kΛ _kv _k=V _kdiag (λ _k1, λ _k2..., λ _kM) V _k, P _k=diag (P _k1, P _k2..., P _kM), U is the normalization Discrete Fourier transform of M × M, power optimization coefficient power optimization coefficient final after amalgamation result is optimum pre-coding matrix is F=diag (F ₁, F ₂..., F _k).