CN104506256A - Performance evaluation method for MIMO (Multiple Input Multiple Output) multi-antenna system and multi-antenna system - Google Patents

Abstract

The invention discloses a performance evaluation method for an MIMO (Multiple Input Multiple Output) multi-antenna system and the multi-antenna system. The system assumes that a channel matrix complies with a zero-mean spatial white noise model at the transmitting end, and a group of linear arrays of which array elements are directional antennae are arranged at the receiving end of the system. According to the performance evaluation method for the MIMO multi-antenna system, the directional antenna array elements are introduced into linear antennae, so that a spatial statistics channel model is effectively expanded, the transmitting and receiving performances of an MIMO multi-antenna array are deepened, and the performances of a terminal antenna array and a wireless communication system are optimized; by introduction of spatial fading correlation coefficients and performance evaluation parameters such as MIMO multi-path channel capacity and error code rate, the advantages of a directional antenna array relative to an omnidirectional antenna array are analyzed, and the system performance of the directional antenna array is superior to that of the omnidirectional antenna array according to a relationship among the system performance, the distribution of arrival signals and the direction of a directional antenna beam.

Description

A kind of MIMO multiaerial system performance estimating method and multiaerial system

Technical field

The present invention relates to a kind of MIMO multiaerial system performance estimating method and multiaerial system, belong to terminal MIMO multiple element antennas directivity technical field.

Background technology

In recent years because mobile communication networking user increases sharply, make radio-frequency spectrum day by day crowded.Past we improve power system capacity to alleviate the jam situation in cellular system often through division cellular macro district or the method for Microcell, but it is high and need to reconfigure cellular system to divide cellular cell cost, and adaptivity antenna can effectively address this problem.Multiple-input and multiple-output (Multiple Input MultipleOutput, the MIMO) system be made up of adaptivity antenna can significantly improve message transmission rate by multipath signal is multiplexing, and can improve receptivity by diversity.Can increase exponentially MIMO multipath channel capacity in theory, and not need additionally to take system spectral resources, therefore MIMO multiple antennas transmit-receive technology has development prospect widely.Current MIMO technique has achieved in the application fixed and in mobile broadband wireless access, as Long Term Evolution (Long term evolution, LTE) system etc.

In adaptivity MIMO array antenna, the parameter of the classics such as array element directivity and efficiency has been not enough to for assessing the antenna array system performance of entirety.In the assessment to adaptive MIMO antenna system performance, not only multidiameter fading channel should be considered into, and must consider the directivity of each bay.Shafi etc. propose a kind of point-device two-way channel model for mimo system modeling and assessment, but because this model proposes based on system-level emulation, if only need to terminal (User Terminal, UT) aerial array compares the evaluation of level, and this model is just too complicated.Taga model is often used as the angular power spectrum model of terminal, aspect power spectrum (Azimuth PowerSpectrum is reached at Taga model medium wave, APS) be only equally distributed by hypothesis, but this being uniformly distributed is listed in the Random-Rotation on direction plane based on the MIMO multi-antenna array of terminal instead of because it is equally distributed that ripple reaches aspect power spectrum.A lot of research also thinks that ripple reaches aspect power spectrum APS and obeys to block Gaussian Profile.In fact usual to real mobile broadband wireless access networks network (Mobile Broadband WirelessAccess, MBWA) when system emulates, first must obtain the space channel statistical parameter of realistic channel circumstance, and then set up the correlated fading channels model of MIMO according to these parameters.Past is for carrying out the research of correlation fading channel when the convenient usual only consideration terminal MIMO multi-antenna array array element of research is omnidirectional antenna.But the directivity of mimo antenna array element can have an immense impact on to systematic function.

Summary of the invention

Technical problem to be solved by this invention is: provide a kind of MIMO multiaerial system performance estimating method and multiaerial system, introduce directional antenna array element in linear antenna, optimize the performance of terminal antenna array and system.

The present invention is for solving the problems of the technologies described above by the following technical solutions:

A kind of MIMO multiaerial system performance estimating method, described multiaerial system comprises transmitting terminal and receiving terminal, and transmitting end channel matrix H obeys zero-mean space White Noise Model, utilizes ergodic capacity C and error rate P _ethe performance of assessment MIMO multiaerial system, described receiving terminal is one group of array element is the linear array of directional antenna, and the spatial fading correlation matrix of this linear array is expressed as when system ripple reaches aspect power spectrum for being uniformly distributed, described spatial fading correlation matrix R _uTelement be $R_{\mathrm{mn}}=\frac{1}{3\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}\exp \left(\mathrm{jD}(m-n)\cos \mathrm{\ψ}\right)(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_m))(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_n))\mathrm{d\ψ},$ When to reach aspect power spectrum be cosine distribution to system ripple, spatial fading correlation matrix R _uTelement be $R_{\mathrm{mn}}=\frac{1}{3\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}\exp \left(\mathrm{jD}(m-n)\cos \mathrm{\ψ}\right)(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_m))(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_n))(1+\cos (\mathrm{\ψ}-{\mathrm{\ψ}}_0))\mathrm{d\ψ}$ , wherein, m=1,2 ... M _uT, n=1,2 ... M _uT, M _uTfor the array number of receiving terminal linear array, D=2 π d/ λ, d are the spacing between adjacent two array elements of receiving terminal, and λ is incoming signal wavelength, and j is imaginary unit, ψ ₀∈ [0,2 π) be the Bo Da signal center angle of arrival, ψ is azimuth parameter, α _m, α _nbe respectively the angle between receiving terminal m, n bay beam direction and receiving terminal linear array line.

A kind of MIMO multiaerial system, described multiaerial system comprises transmitting terminal and receiving terminal, transmitting end channel matrix H obeys zero-mean space White Noise Model, receiving terminal is one group of array element is the linear array of directional antenna, when system ripple reaches aspect power spectrum for being uniformly distributed, and the beam direction of each array element difference larger time, the best performance of described MIMO multiaerial system.

A kind of MIMO multiaerial system, described multiaerial system comprises transmitting terminal and receiving terminal, and transmitting end channel matrix H obeys zero-mean space White Noise Model, and receiving terminal is one group of array element is the linear array of directional antenna, be cosine distribution when system ripple reaches aspect power spectrum, and ψ ₀during=pi/2, there is maximum in the ergodic capacity of described MIMO multiaerial system.

A kind of MIMO multiaerial system, described multiaerial system comprises transmitting terminal and receiving terminal, transmitting end channel matrix H obeys zero-mean space White Noise Model, receiving terminal is one group of array element is the linear array of directional antenna, be cosine distribution when system ripple reaches aspect power spectrum, and during incoherent Binary Frequency Shift Keying modulation, system signal noise ratio is larger, and the average error rate of described MIMO multiaerial system is less.

A kind of MIMO multiaerial system, described multiaerial system comprises transmitting terminal and receiving terminal, transmitting end channel matrix H obeys zero-mean space White Noise Model, receiving terminal is one group of array element is the linear array of directional antenna, under incoherent Binary Frequency Shift Keying modulation case, when system ripple reaches aspect power spectrum for being uniformly distributed, multiaerial system average error rate is definite value; Be cosine distribution when system ripple reaches aspect power spectrum, and ripple reach signal angle consistent with bay beam direction time, multiaerial system average error rate is minimum.

The present invention adopts above technical scheme compared with prior art, has following technique effect:

1, MIMO multiaerial system performance estimating method of the present invention and multiaerial system, directional antenna array element is introduced in linear antenna, effective transmitting-receiving performance expanded spatial statistics channel model and goed deep into MIMO multi-antenna array, optimizes the performance of terminal antenna array and wireless communication system.

2, MIMO multiaerial system performance estimating method of the present invention and multiaerial system, by introducing spatial fading coefficient correlation, the performance evaluation parameter such as MIMO multipath channel capacity and the error rate, analyze the advantage of directional antenna array relative to omni-directional antenna arrays, the relation reached between signal distributions and directional antenna beams direction from systematic function and ripple finds, the systematic function of directional antenna array is better than the systematic function of omni-directional antenna arrays.

Accompanying drawing explanation

Fig. 1 is the structural representation of MIMO multiple antennas linear array of the present invention.

Fig. 2 is the directional diagram of directional antenna array element of the present invention.

Fig. 3 (a), (b) are that the present invention is uniformly distributed MIMO ULA spacing wave Fading correlation graph of a relation respectively, and wherein (a) is α ₁=α ₂, (b) is α ₂-α ₁=pi/2.

Fig. 4 (a)-(f) is cosine distribution MIMO ULA spacing wave Fading correlation graph of a relation of the present invention respectively, and wherein (a) is α ₁=α ₂, ψ ₀=0; B () is α ₁=α ₂, ψ ₀=π/4; C () is α ₁=α ₂, ψ ₀=pi/2; D () is α ₂-α ₁=pi/2, ψ ₀=0; E () is α ₂-α ₁=pi/2, ψ ₀=π/4; F () is α ₂-α ₁=pi/2, ψ ₀=pi/2.

Fig. 5 be under MRC diversity of the present invention cumulative distribution CDF with signal to noise ratio snr variation relation figure d/ λ=1/2, α=pi/2.

Fig. 6 be channel ergodic capacity of the present invention with signal to noise ratio snr variation relation figure α=pi/2, ψ ₀=pi/2, d/ λ=1/2.

Fig. 7 is that channel ergodic capacity of the present invention is with d/ λ variation relation figure ψ ₀=pi/2, ρ=20dB.

Fig. 8 be under cosine distribution of the present invention average error rate BER with signal to noise ratio snr variation relation figure a=1, α=pi/2, d/ λ=1/2.

Fig. 9 is that average error rate BER of the present invention reaches signal angle AOA variation relation figure a=1 with ripple, α=pi/2, d/ λ=1/2, ρ=20dB.

Embodiment

Be described below in detail embodiments of the present invention, the example of described execution mode is shown in the drawings, and wherein same or similar label represents same or similar element or has element that is identical or similar functions from start to finish.Being exemplary below by the execution mode be described with reference to the drawings, only for explaining the present invention, and can not limitation of the present invention being interpreted as.

The present invention introduces antenna element directivity while consideration spatial fading signal correlation, proposes a kind of terminal MIMO multiple antennas model of Corpus--based Method channel model and assesses its performance.Make to reach aspect power spectrum APS model at the ripple of terminal all can be applied in the mimo channel modeling of Kronecker.We find that the spatial fading relevant (SpatialFading Correlation, SFC) that ripple reaches between signal that signal arrives MIMO two array elements is the function reaching power spectrum signal, bay antenna pattern and antenna distance about ripple.Therefore this channel model is utilized, by analysis of simulation experiment, in terminal MIMO multiple antennas model, array element directivity affects systematic function, comprising the impact of spatial fading coefficient correlation to received signal, MIMO multipath channel capacity and the error rate (Bit Error Ratio, BER).The present invention is intended to the expansion past to the modeling of MIMO multi-antenna terminal, for the complicated mimo system of the mimo channel modeling analysis applying Kronecker and Simulated movable system are provided fundamental basis.

In order to achieve the above object, the present invention introduces directional antenna array element in wire antenna (Uniform Linear Array, ULA), supposes that two kinds of ripples reach aspect Power Spectrum Distribution simultaneously, is namely uniformly distributed and cosine distribution.By introducing spatial fading coefficient correlation, the performance evaluation parameter such as MIMO multipath channel capacity and the error rate, analyze the performance advantage of directional antenna array.

The present invention analyzes the performance advantage of directional antenna array based on three dimensions Correlation Theory, first provide three dimensions territory medium wave and reach the equation (1) and (2) that power spectrum signal, complex polarization direction meet in the distribution of azimuthal plane and elevation plane, provide the computational methods (3) of three dimensions territory Spatial Correlation simultaneously.The polarization considering to reach power spectrum signal to ripple in three dimensions territory in the vertical and horizontal direction component is defined as respectively with these two components must meet following equation:

${\∫}_0^{2\mathrm{\π}}{\∫}_0^{\mathrm{\π}}\{p_{{\mathrm{UT}}_{\mathrm{\θ}}}(\mathrm{\θ},\mathrm{\ψ})+p_{{\mathrm{UT}}_{\mathrm{\ψ}}}\left(\mathrm{\θ\ψ}\right)\}\sin \mathrm{\ψ\θ\ψ}=1---\left(1\right)$

The complex polarization direction defining m terminal MIMO multi-antenna array array element is with wherein represent vertical direction polarization, represent horizontal direction polarization, this can be used for the characterisitic parameter describing terminal MIMO multiple antennas, and they must meet:

$\frac{1}{4\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}{\∫}_0^{\mathrm{\π}}\{{\left|e_{{\mathrm{UT\θ}}_m}(\mathrm{\θ},\mathrm{\ψ})\right|}^2+{\left|e_{{\mathrm{UT\ψ}}_m}(\mathrm{\θ},\mathrm{\ψ})\right|}^2\}\sin \mathrm{\θd\θd\ψ}={\mathrm{\η}}_m---\left(2\right)$

η in formula (2) _mconsider path loss and the non-match condition efficiency in m interior terminal MIMO multi-antenna array array element.Signal fadeout correlation matrix R between terminal MIMO multiple element antennas _uTpower spectrum signal APS is reached and multi-antenna array array element complex polarization polarised direction calculates respectively by ripple, and terminal antenna efficiency eta _m≤ 1.

The mimo system fading signal correlation matrix R of terminal arrays _uTpower spectrum signal is reached and terminal antenna array each unit complex polarization polarised direction is calculated as respectively by ripple:

${\left[R_{\mathrm{UT}}\right]}_{\mathrm{mn}}={\∫}_0^{2\mathrm{\π}}{\∫}_0^{\mathrm{\π}}\{e_{{\mathrm{UT\θ}}_m}(\mathrm{\θ},\mathrm{\ψ})e_{{\mathrm{UT\θ}}_n}^{*}(\mathrm{\θ},\mathrm{\ψ})p_{\mathrm{UT\θ}(\mathrm{\θ},\mathrm{\ψ})}+e_{{\mathrm{UT\ψ}}_m}(\mathrm{\θ},\mathrm{\ψ})e_{{\mathrm{UT\ψ}}_n}^{*}(\mathrm{\θ},\mathrm{\ψ})p_{{\mathrm{UT}}_{\mathrm{\ψ}}(\mathrm{\θ},\mathrm{\ψ})}\}\sin \mathrm{\θd\θd\ψ}---\left(3\right)$

For simplifying computational complexity the present invention only on concentrating orientation ripple to reach aspect power spectrum APS in two dimensional surface and terminal multi-antenna array carries out research and analysis to the impact of mimo system performance.First the Distribution Statistics that two kinds of ripples reach signal APS is discussed, i.e. omnidirectional uniform power spectrum p _o(ψ) distribution and directed cosine power spectrum p _u(ψ, ψ ₀) distribution.Its statistical distribution functions may be defined as:

$p_o\left(\mathrm{\ψ}\right)=\frac{1}{2\mathrm{\π}}---\left(4\right)$

$p_U(\mathrm{\ψ},{\mathrm{\ψ}}_0)=\frac{1+\cos (\mathrm{\ψ}-{\mathrm{\ψ}}_0)}{2\mathrm{\π}}---\left(5\right)$

ψ in formula (5) ₀∈ [0,2 π), be defined as the Bo Da signal center angle of arrival (Angle of Arrival, AOA) because terminal produces in the rotation of aximuthpiston, the angle namely between signal incident direction as shown in Figure 1 and multi-antenna array coordinate system reference point.If only consider two-dimensional space territory, by bringing into simplified style (2):

$\frac{1}{4\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}{\∫}_0^{\mathrm{\π}}\{1+{\left|e_{{\mathrm{UT\ψ}}_m}(\frac{\mathrm{\π}}{2},\mathrm{\ψ})\right|}^2\}\mathrm{d\ψ}={\mathrm{\η}}_m---\left(6\right)$

If do not considering can obtain η under path loss and non-match condition _m=1.

Usually the MIMO multiple antennas receptivity in two kinds of situations is considered: one is when each array element of terminal multiple antennas is omnidirectional antenna in research in the past, due to space factor, to make same ripple reach signal different and produce phase of received signal difference in the time delay arriving different antenna element, and incoming signal steric direction vector when at this moment terminal multi-antenna array is classified as linear array ULA is:

$a{(\mathrm{\θ},\mathrm{\ψ})}_{\mathrm{ULA}}={[1,e^{\mathrm{jD}\cos \mathrm{\ψ}},\·\·\·,e^{\mathrm{iD}(M_{\mathrm{UT}}-1)\cos \mathrm{\ψ}}]}^T---\left(7\right)$

D=2 π d/ λ in formula (7), d is multiple element antennas spacing, and λ is incoming signal wavelength, M _uTreceiving terminal element number of array and [g] ^trepresenting matrix transposition; Another kind is when each array element of terminal multiple antennas is directional antenna, and the beam direction due to each bay is different also different to the ability to accept of same signal.If consider directional antenna array element, its pattern function can represent with such as formula (8) and (9) usually:

$e_{D2}\left(\mathrm{\ψ}\right)=\sqrt{\frac{2}{3}}(1-\cos \left(\mathrm{\ψ}\right))---\left(8\right)$

$e_{D2}\left(\mathrm{\ψ}\right)=\sqrt{\frac{2}{3}}(1+\cos \left(\mathrm{\ψ}\right))---\left(9\right)$

Suppose that terminal MIMO has M _uTindividual directional antenna array element, incoming signal steric direction vector when at this moment terminal multi-antenna array is classified as linear array ULA is:

$a{(\mathrm{\θ},\mathrm{\ψ})}_{\mathrm{ULA}}={[1\·\sqrt{\frac{2}{3}}(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_1)),e^{\mathrm{jD}\cos \mathrm{\ψ}}\·\sqrt{\frac{2}{3}}(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_2)),\·\·\·,e^{\mathrm{jD}(M_{\mathrm{UT}}-1)\cos \mathrm{\ψ}}\·\sqrt{\frac{2}{3}}(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_{M_{\mathrm{UT}}}))]}^T$

(10)

Element each in formula (10) is substituted into formula (6), and through deriving, easily checking incoming signal steric direction vector meets formula (6).Formula (10) and formula (4) or formula (5) are substituted into formula (3) respectively, and through deriving, the spatial fading coefficient correlation simplified when can try to achieve even APS and cosine APS respectively between multiple element antennas is:

${\left[R_{\mathrm{UT}}\right]}_{\mathrm{mn}}={\∫}_0^{2\mathrm{\π}}{e}_{{\mathrm{UT}}_{\mathrm{\ψm}}}\left(\mathrm{\ψ}\right)e_{{\mathrm{UT}}_{\mathrm{\ψn}}}^{*}{p}_{U{T}_{\mathrm{\ψ}}}\left(\mathrm{\ψ}\right)d\mathrm{\ψ}--\left(11\right)$

When power spectrum APS is for being uniformly distributed:

${\left[R\right]}_{\mathrm{mn}}=\frac{1}{3\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}\exp \left(\mathrm{jD}(m-n)\cos \mathrm{\ψ}\right)(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_m))(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_n))\mathrm{d\ψ}---\left(12\right)$

When power spectrum APS is cosine distribution:

${\left[R\right]}_{\mathrm{mn}}=\frac{1}{3\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}\exp \left(\mathrm{jD}(m-n)\cos \mathrm{\ψ}\right)(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_m))(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_n))(1+\cos (\mathrm{\ψ}-{\mathrm{\ψ}}_0))\mathrm{d\ψ}---\left(13\right)$

Wherein α _mor α _nit is the angle between tier beam direction and multi-antenna array coordinate system reference point.By formula (12) and (13) can computing terminal MIMO multi-antenna array fading signal correlation matrix be:

System Performance Analysis parameter: ergodic capacity and the error rate.Suppose that terminal antenna array has M _uTindividual array element, terminal MIMO multi-antenna array spatial fading correlation matrix is M _uT× M _uTsquare formation.In assessing radio channel capacity, usual MIMO multipath channel capacity can be used as a kind of mode weighed and comprise the channel quality of channel link end points.If in the known multipath channel information of receiving terminal, and during transmitting terminal the unknown, zero-mean space White Noise Model is obeyed in transmitting terminal hypothesis channel matrix H, maximize for making channel ergodic capacity, optimum strategy is assigned to by power averaging on each transmitting antenna unit, and can realize the maximized input covariance matrix of ergodic capacity is R _x=(ρ/M _bS) I _mBS, at this moment the ergodic capacity of channel can be:

$C=E_H\left[{\log }_2\det \right[I_{M_{\mathrm{UT}}}+\frac{\mathrm{\ρ}}{M_{\mathrm{BS}}}{\mathrm{HH}}^H\left]\right]---\left(15\right)$

M in formula (15) _uTterminal multi-antenna array array number, m _uTthe unit matrix of dimension, M _bSbase station (Base Station, BS) multi-antenna array array number, m _bSthe unit matrix of dimension, ρ sends Signal-to-Noise, and H is MIMO multipath channel matrix, H ^hthe conjugate transpose of channel matrix H, mathematic expectaion E _hthat mean analysis is carried out to the distribution of channel matrix H.For the mimo channel of space correlation, channel matrix H can utilize the spatial fading correlation matrix of receiving array and emission array and independent same distribution channel to be expressed as:

$H=R_{U/T}^{1/2}{H}_w{\left(R_{\mathrm{BS}}^{1/2}\right)}^T---\left(16\right)$

Wherein R _uTfor receiving terminal spatial fading correlation matrix, R _bSfor transmitting terminal spatial fading correlation matrix, subscript (.) ^tthe transposition of representing matrix, H _wit is multiple gaussian random matrix.

Even if under identical channel status, corresponding different mimo antenna array element, the spatial fading SFC that is correlated with also has very big-difference.Fading channel average error rate by average obtaining condition bit error probability on the probability-distribution function of signal to noise ratio γ:

$P_e={\∫}_0^{\∞}P\left(e\right|\mathrm{\γ})\·p\left(\mathrm{\γ}\right)\mathrm{d\γ}---\left(17\right)$

If at difference bi-phase shift keying (Differential Binary Phase Shift Keying, and incoherent Binary Frequency Shift Keying (Noncoherent Binary orthogonal frequency shift Keying DBPSK), NBFSK), in modulation, its condition error rate is:

P(e|γ)＝1/2exp(-αγ) (18)

α represents modulation constant in formula (18), corresponds to NBFSK when corresponding to DBPSK, α=1 during α=1/2.Then average error rate can be expressed as:

${\stackrel{\‾}{P}}_{\mathrm{eN}}=\frac{1}{2}{\∫}_0^{\∞}{e}^{-\mathrm{\α\γ}}p\left(\mathrm{\γ}\right)\mathrm{d\γ}=\frac{1}{2}{\mathrm{\Φ}}_{\mathrm{\γ}}\left(t\right){|}_{\mathrm{it}=-\mathrm{\α}}=\frac{1}{2}{|I_M+\frac{\mathrm{\α}\stackrel{\‾}{\mathrm{\γ}}}{m}{R}_{\mathrm{UT}}|}^{-m}---\left(19\right)$

In formula (19), M represents diversity order, I _mrepresent M rank unit matrix, m represents channel fading parameters and m>=1/2, m=1/2 and m=1 be corresponding monolateral Gaussian Profile and Rayleigh distribution respectively, and α is modulation constant, and γ is average signal-to-noise ratio, R _uTfor receiving terminal spatial fading correlation matrix, if therefore under given diversity order M, the error rate the polynomial form of coefficient correlation between bay can be reduced to.

As shown in Figure 1, the structural representation of MIMO multiple antennas linear array of the present invention, bay is wherein directional antenna array element, wherein, ψ ₀∈ [0,2 π) be the angle between signal incident direction and multi-antenna array coordinate system reference point, d is adjacent two multiple element antennas spacing.As shown in Figure 2, be the directional diagram of directional antenna array element.

As shown in Figure 3, reach power spectrum signal APS for being uniformly distributed at ripple, when terminal MIMO is linear array ULA, the spatial fading correlation of m=1, n=2 two between bay, wherein scheming (a) is tier parameter alpha ₁=α ₂, figure (b) is α ₁-α ₂=pi/2.Figure (a), figure (b) analyze again at α ₁=0, α ₁=π/4 and α ₁under=pi/2 three kinds of angles, two antenna elements receive the space correlation coefficient of fading signals, and spatial fading correlation when showing omnidirectional antenna array element array is under the same conditions to make comparisons.Analysis result shows that fading signal spatial coherence reduces along with the increase of antenna array elements spacing.

Consistent owing to setting two directional antenna beams directions in Fig. 3 (a), at α ₁when=0, Received signal strength spatial fading coefficient correlation is comparatively large, and at α ₁less during=pi/2.At α ₁=0 and α ₁during=π/4, between directional antenna array element, coefficient correlation is large compared with omnidirectional antenna, but at α ₁during=pi/2, between directional antenna array element, coefficient correlation is little compared with omnidirectional antenna.Fig. 3 (a) presentation space decline coefficient correlation curve has concussion and reduces phenomenon, and is zero in the integral multiple point place coefficient correlation of d=0.45 λ.Therefore, when directional antenna beams direction is consistent, adjustment bay beam direction and array manifold structure can reduce Received signal strength spatial fading correlation between array element, improve MIMO array multiple antennas performance of receiving system.Fig. 3 (b), due to two directional antenna beams direction difference pi/2s, makes α ₁=0, α ₂=pi/2 and α ₁=pi/2, α ₂=0 time space decline coefficient correlation curve co-insides.Because two directional antennas receive incoming wave signal from vertical direction instead of same direction, therefore nearly all coefficient correlation result is little compared with Fig. 3 (a).At α ₂-α ₁situation when coefficient correlation between directional antenna array element is less than omnidirectional antenna is there is, if d/ λ is from 0 to 0.25 during=pi/2.Therefore obtain at α ₁with α ₂when differing larger, Received signal strength spatial fading correlation is less, makes directional antenna MIMO array performance be better than omnidirectional antenna.

As shown in Figure 4, when to reach power spectrum signal APS be cosine distribution to ripple, the fading signal space correlation coefficient between terminal MIMO ULA array two unit.Figure (a), (b), (c) and figure (d), (e), (f) illustrate that again ripple reaches signal angle and is respectively ψ respectively ₀=0, ψ ₀=π/4 and ψ ₀=pi/2 three kinds of situations.Fig. 4 (a), (b), (c) are shown in ψ ₀=α ₁=α ₂time space decline coefficient correlation is minimum, and | ψ ₀-α | less, coefficient correlation is less.Because ripple reaches signal angle AOA and the more close then performance of tier beam direction is better.α can be found in Fig. 4 (d), (e), (f) ₂-α ₁during=pi/2, along with ψ ₀increasing makes whole MIMO multi-antenna terminal spatial fading coefficient correlation reduce, and makes the diversity performance of MIMO ULA multiple antennas receiving system better.

As shown in Figure 5, during the consistent and α=pi/2 of beam direction, when maximum-ratio combing (Maximal RatioCombining, MRC) receive diversity, cumulative distribution function CDF and signal to noise ratio snr relation.When power spectrum APS is for being uniformly distributed, the Cumulative Distribution Function CDF growth signal to noise ratio reached needed for 1 is about 10dB, at power spectrum APS for Cumulative Distribution Function during cosine distribution increases the signal to noise ratio Yin Boda signal angle AOA ψ reached needed for 1 ₀different and different.At ψ ₀be 12.5dB and ψ during=π/4 ₀=0 and ψ ₀consistent with result curve when being uniformly distributed during=pi/2.Can, when power spectrum APS is cosine distribution, suitable ripple be selected to reach signal angle ψ ₀, MIMO diversity system has better performance.

As shown in Figure 6, when MIMO multi-antenna-unit is directional antenna, ergodic capacity is with the change of signal to noise ratio snr.Along with signal to noise ratio increases, capacity almost linearly increases.The ergodic capacity that can draw when power spectrum APS is cosine distribution is greater than analysis result when being uniformly distributed.

As shown in Figure 7, channel ergodic capacity is with d/ λ result of variations.Increase to 1/2 at d/ λ by 0, capacity is that approximately linear increases; As d/ λ > 1/2, capability value tends towards stability maximum.When terminal MIMO multi-antenna array array element adopts directional antenna (α=pi/2), when ripple reaches signal angle ψ ₀increase to pi/2 from 0, channel capacity increases.At ψ ₀during=pi/2, ergodic capacity has maximum.Terminal MIMO can improve channel capacity about 10% in the method that directional antenna combines with phase difference.

As shown in Figure 8, when NBFSK (a=1) and cosine distribution average error rate BER with the performance change situation of signal to noise ratio snr.Increase BER with signal to noise ratio to reduce gradually; Along with diversity order M increases, mimo system can obtain better diversity gain; Large when the BER that m=0.5 is corresponding compares at m=1, reason is that m is less, and the more serious then corresponding BER of signal fadeout increases.Emulation experiment shows, when power spectrum APS is cosine distribution, systematic function is more excellent, directional antenna with the obvious advantage.

As shown in Figure 9, when NBFSK (a=1), average error rate BER reaches the situation of change of signal angle AOA with ripple.When power spectrum APS is for being uniformly distributed, BER and ripple reach signal angle AOA and have nothing to do for definite value.When power spectrum APS is cosine distribution, BER curve smoothing and present cosine distribution form.When getting α=pi/2, can find at ψ ₀during=pi/2, BER reaches minimum value, and reason is that ripple reaches signal angle AOA and beam array unit beam direction is consistent and causes optimum BER; When α=3 pi/2, the error rate reaches maximum, and reason is that ripple reaches the completely contrary Received signal strength poor effect that causes of signal angle AOA and beam array unit's beam direction and makes BER the poorest.

Above embodiment is only and technological thought of the present invention is described, can not limit protection scope of the present invention with this, and every technological thought proposed according to the present invention, any change that technical scheme basis is done, all falls within scope.

Claims (5)

1. a MIMO multiaerial system performance estimating method, described multiaerial system comprises transmitting terminal and receiving terminal, and transmitting end channel matrix H obeys zero-mean space White Noise Model, utilizes ergodic capacity C and error rate P _ethe performance of assessment MIMO multiaerial system, is characterized in that: described receiving terminal is one group of array element is the linear array of directional antenna, and the spatial fading correlation matrix of this linear array is expressed as

When system ripple reaches aspect power spectrum for being uniformly distributed, described spatial fading correlation matrix R _uTelement be $R_{\mathrm{mn}}=\frac{1}{3\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}\exp \left(\mathrm{jD}(m-n)\cos \mathrm{\ψ}\right)(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_m))(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_n))\mathrm{d\ψ},$

When to reach aspect power spectrum be cosine distribution to system ripple, spatial fading correlation matrix R _uTelement be

$R_{\mathrm{mn}}=\frac{1}{3\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}\exp \left(\mathrm{jD}(m-n)\cos \mathrm{\ψ}\right)(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_m))(1+\cos (\mathrm{\ψ}-{\mathrm{\α}}_n))(1+\cos (\mathrm{\ψ}-{\mathrm{\ψ}}_0))\mathrm{d\ψ}$ , wherein, m=1,2 ... M _uT, n=1,2 ... M _uT, M _uTfor the array number of receiving terminal linear array, D=2 π d/ λ, d are the spacing between adjacent two array elements of receiving terminal, and λ is incoming signal wavelength, and j is imaginary unit, ψ ₀∈ [0,2 π) be the Bo Da signal center angle of arrival, ψ is azimuth parameter, α _m, α _nbe respectively the angle between receiving terminal m, n bay beam direction and receiving terminal linear array line.

2. a MIMO multiaerial system, described multiaerial system comprises transmitting terminal and receiving terminal, transmitting end channel matrix H obeys zero-mean space White Noise Model, it is characterized in that: receiving terminal is one group of array element is the linear array of directional antenna, when system ripple reaches aspect power spectrum for being uniformly distributed, and the beam direction of each array element difference larger time, the best performance of described MIMO multiaerial system.

3. a MIMO multiaerial system, described multiaerial system comprises transmitting terminal and receiving terminal, transmitting end channel matrix H obeys zero-mean space White Noise Model, it is characterized in that: receiving terminal is one group of array element is the linear array of directional antenna, be cosine distribution when system ripple reaches aspect power spectrum, and ψ ₀during=pi/2, there is maximum in the ergodic capacity of described MIMO multiaerial system.

4. a MIMO multiaerial system, described multiaerial system comprises transmitting terminal and receiving terminal, transmitting end channel matrix H obeys zero-mean space White Noise Model, it is characterized in that: receiving terminal is one group of array element is the linear array of directional antenna, be cosine distribution when system ripple reaches aspect power spectrum, and during incoherent Binary Frequency Shift Keying modulation, system signal noise ratio is larger, and the average error rate of described MIMO multiaerial system is less.

5. a MIMO multiaerial system, described multiaerial system comprises transmitting terminal and receiving terminal, transmitting end channel matrix H obeys zero-mean space White Noise Model, it is characterized in that: receiving terminal is one group of array element is the linear array of directional antenna, under incoherent Binary Frequency Shift Keying modulation case, when system ripple reaches aspect power spectrum for being uniformly distributed, multiaerial system average error rate is definite value; Be cosine distribution when system ripple reaches aspect power spectrum, and ripple reach signal angle consistent with bay beam direction time, multiaerial system average error rate is minimum.