CN104506256B - Performance evaluation method for MIMO (Multiple Input Multiple Output) multi-antenna system and multi-antenna system - Google Patents
Performance evaluation method for MIMO (Multiple Input Multiple Output) multi-antenna system and multi-antenna system Download PDFInfo
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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
Technical field
The present invention relates to a kind of MIMO multiaerial systems performance estimating method and multiaerial system, belong to terminal MIMO many days
Linear array unit directionality technical field.
Background technology
In recent years as mobile communication networking user increases sharply so that radio-frequency spectrum is increasingly crowded.Past, we were normal
Power system capacity is improved usually through the method for division cellular macro area or Microcell to alleviate the jam situation in cellular system, but is divided
Split cellular cell high cost and needing and reconfigure cellular system, adaptivity antenna energy effectively solving this problem.By adaptive
Multiple-input and multiple-output (Multiple Input Multiple Output, the MIMO) system of answering property antenna composition can pass through many
Footpath signal multiplexing significantly improves message transmission rate, and can improve receptivity by diversity.In theory can be at double
MIMO multipath channel capacity is improved, and need not additionally take system spectral resources, therefore MIMO multiple antennas transmit-receive technologies are gathered around
There is extensive development prospect.MIMO technique has been realized in answering in fixation and mobile broadband wireless access at present
With such as Long Term Evolution (Long term evolution, LTE) system etc..
In adaptivity MIMO array antenna, the classical parameter such as array element directionality and efficiency has been not enough to for right
Overall antenna array system performance is estimated.The not only multipath fading in the assessment to adaptive MIMO antenna system performance
Channel should be considered into and it is necessary to consider the directionality of each bay.Shafi etc. is modeled and is commented for mimo system
Estimate and propose a kind of point-device two-way channel model, but be because that this model is proposed based on system-level emulation,
If the evaluation of level only need to be compared to terminal (User Terminal, UT) aerial array, this model is just excessively complicated.
Taga models are often used as the angular power spectrum model of terminal, reach aspect power spectrum (Azimuth in Taga models medium wave
Power Spectrum, APS) be only assumed be it is equally distributed, but this being uniformly distributed is many days of MIMO based on terminal
Random-Rotation of the linear array on direction plane rather than because ripple be equally distributed up to aspect power spectrum.It is many to study
It is to obey to block Gaussian Profile in grand area's honeycomb that ripple is also considered as up to aspect power spectrum APS.Actually generally to real
It is when mobile broadband wireless access networks network (Mobile Broadband Wireless Access, MBWA) system is emulated, first
First have to obtain the space channel statistical parameter for meeting actual channel environment, the phase of MIMO is then set up further according to these parameters
Close fading channel model.Past generally only considers to carry out when terminal MIMO multi-antenna array array element is omnidirectional antenna for research is convenient
The research of correlation fading channel.But the directionality of mimo antenna array element can have an immense impact on to systematic function.
The content of the invention
The technical problem to be solved is：A kind of MIMO multiaerial systems performance estimating method and multiple antennas are provided
System, introduces directional aerial array element in linear antenna, optimizes the performance of terminal antenna array and system.
The present invention is employed the following technical solutions to solve above-mentioned technical problem：
A kind of MIMO multiaerial systems performance estimating method, the multiaerial system include transmitting terminal and receiving terminal, transmitting terminal
Channel matrix H obeys zero-mean space White Noise Model, using ergodic capacity C and bit error rate PeThe property of assessment MIMO multiaerial systems
Can, the receiving terminal is the linear array that one group of array element is directional aerial, and the spatial fading correlation matrix table of the linear array
It is shown asWhen system ripple reaches aspect power spectrum to be uniformly distributed, the spatial fading
Correlation matrix RUTElement be
When it is cosine distribution that system ripple reaches aspect power spectrum, spatial fading correlation matrix RUTElement be, wherein, m
=1,2 ... MUT, n=1,2 ... MUT, MUTFor the array number of receiving terminal linear array, D=2 π d/ λ, d are receiving terminal adjacent two
Spacing between array element, λ are incoming signal wavelength, and j is imaginary unit, ψ0∈ [0,2 π) for Bo Da signal centers angle of arrival, ψ is
Orientation angular dimensions, αm、αnRespectively between m, n bay beam direction of receiving terminal and receiving terminal linear array line
Angle.
A kind of MIMO multiaerial systems, the multiaerial system include transmitting terminal and receiving terminal, transmitting end channel matrix H clothes
From zero-mean space White Noise Model, receiving terminal is the linear array that one group of array element is directional aerial, when system ripple reaches signal side
Position power spectrum to be uniformly distributed, and each array element beam direction difference it is bigger when, the best performance of the MIMO multiaerial systems.
A kind of MIMO multiaerial systems, the multiaerial system include transmitting terminal and receiving terminal, transmitting end channel matrix H clothes
From zero-mean space White Noise Model, receiving terminal is the linear array that one group of array element is directional aerial, when system ripple reaches signal side
Position power spectrum is cosine distribution, and ψ0During=pi/2, there is maximum in the ergodic capacity of the MIMO multiaerial systems.
A kind of MIMO multiaerial systems, the multiaerial system include transmitting terminal and receiving terminal, transmitting end channel matrix H clothes
From zero-mean space White Noise Model, receiving terminal is the linear array that one group of array element is directional aerial, when system ripple reaches signal side
Position power spectrum is cosine distribution, and during the modulation of incoherent Binary Frequency Shift Keying, system signal noise ratio is bigger, the MIMO multiple antennas
The average error rate of system is less.
A kind of MIMO multiaerial systems, the multiaerial system include transmitting terminal and receiving terminal, transmitting end channel matrix H clothes
From zero-mean space White Noise Model, receiving terminal be one group of array element be directional aerial linear array, incoherent binary frequency shift
In the case of keying modulation, when system ripple reaches aspect power spectrum to be uniformly distributed, multiaerial system average error rate is fixed
Value；When system ripple up to aspect power spectrum be cosine distribution, and ripple up to signal angle it is consistent with bay beam direction when, it is many
Antenna system average error rate is minimum.
The present invention adopts above technical scheme compared with prior art, with following technique effect：
1st, MIMO multiaerial systems performance estimating method of the present invention and multiaerial system, introduce orientation day in linear antenna
Linear array unit, has effectively expanded spatial statisticses channel model and its deep transmitting-receiving performance to MIMO multi-antenna arrays, has optimized end
The performance of end aerial array and wireless communication system.
2nd, MIMO multiaerial systems performance estimating method of the present invention and multiaerial system, by introducing spatial fading phase relation
Number, the performance evaluation parameter such as MIMO multipath channels capacity and the bit error rate, analysis directional antenna array is relative to omni-directional antenna arrays
Advantage, find from systematic function and ripple up to the relation between signal distributions and directional antenna beams direction, directional antenna array
Systematic function better than omni-directional antenna arrays systematic function.
Description of the drawings
Fig. 1 is the structural representation of MIMO multiple antennas linear array of the present invention.
Fig. 2 is the directional diagram of directional aerial array element of the present invention.
Fig. 3 (a), (b) they are that the present invention is uniformly distributed MIMO ULA spacing wave Fading correlation graphs of a relation respectively, wherein
A () is α1=α2, it is (b) α2-α1=pi/2.
Fig. 4 (a)-(f) is cosine distribution MIMO ULA spacing waves Fading correlation graph of a relation of the present invention respectively, wherein
A () is α1=α2, ψ0=0；B () is α1=α2, ψ0=π/4；C () is α1=α2, ψ0=pi/2；D () is α2-α1=pi/2, ψ0=0；
E () is α2-α1=pi/2, ψ0=π/4；F () is α2-α1=pi/2, ψ0=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 is channel ergodic capacity of the present invention with signal to noise ratio snr variation relation figure α=pi/2, ψ0=pi/2, d/ λ=1/2.
Fig. 7 is channel ergodic capacity of the present invention with d/ λ variation relation figures ψ0=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 figures a=1, α=pi/2, d/ λ=1/ with ripple
2, ρ=20dB.
Specific embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the drawings, wherein ad initio
Same or similar element or the element with same or like function are represented to same or similar label eventually.Below by ginseng
The embodiment for examining Description of Drawings is exemplary, is only used for explaining the present invention, and is not construed as limiting the claims.
The present invention introduces antenna element directivity while spatial fading signal correlation is considered, it is proposed that one kind is based on
The terminal MIMO multiple antennas model of statistical channel model is simultaneously assessed to its performance.So that the ripple in terminal reaches aspect
Power spectrum APS models are may apply in the mimo channel modeling of Kronecker.We have found that ripple reaches MIMO two up to signal
Spatial fading correlation (Spatial Fading Correlation, SFC) between the signal of individual array element is to reach signal with regard to ripple
The function of power spectrum, bay antenna pattern and antenna distance.Hence with this channel model, by emulation experiment point
In having analysed terminal MIMO multiple antennas model, array element directionality is affected on systematic function, including docking collection of letters spatial fading phase
The impact of relation number, MIMO multipath channels capacity and the bit error rate (Bit Error Ratio, BER).It is contemplated that propagating through
The modeling to MIMO multi-antenna terminals is gone, is mimo channel modeling analysis complexity mimo system and emulation using Kronecker
Mobile system is provided fundamental basis.
In order to achieve the above object, the present invention introduces orientation in wire antenna (Uniform Linear Array, ULA)
Bay, while assuming that two kinds of ripples reach aspect Power Spectrum Distribution, that is, is uniformly distributed and cosine distribution.By introducing space
Decline coefficient correlation, the performance evaluation parameter such as MIMO multipath channels capacity and the bit error rate, the performance for analyzing directional antenna array are excellent
Gesture.
The performance advantage of present invention analysis directional antenna array is based on three dimensions Correlation Theory, provides three-dimensional space first
Between domain medium wave up to power spectrum signal, complex polarization direction azimuthal plane and elevation plane the equation (1) that meets of distribution and
(2), while providing the computational methods (3) of three dimensions domain Spatial Correlation.Signal work(is reached to ripple in considering three dimensions domain
Component is respectively defined as in the vertical and horizontal direction for the polarization of rate spectrumWithThe two components are necessary
Meet below equation：
The complex polarization direction for defining m-th terminal MIMO multi-antenna array array element isWithIts
InVertical direction polarization is represented,Horizontal direction polarization is represented, it is many that this can be used for description terminal MIMO
The characterisitic parameter of antenna, and they must are fulfilled for：
η in formula (2)mIt is to consider path loss and mismatch case in m-th interior terminal MIMO multi-antenna array array
The efficiency of unit.Signal fadeout correlation matrix R between terminal MIMO multiple element antennasUTCan be by ripple up to power spectrum signal APS and many
Antenna array elements complex polarization polarised direction is calculating respectively, and terminal antenna efficiency etam≤1。
The mimo system fading signal correlation matrix R of terminal arraysUTPower spectrum signal and terminal antenna battle array can be reached by ripple
Row each unit complex polarization polarised direction is being calculated as respectively：
To simplify the computational complexity present invention only to concentrating orientation ripple to reach aspect power spectrum APS and end in two dimensional surface
End impact of the multi-antenna array to mimo system performance carries out research and analysis.Discuss two kinds of ripples up to the statistics of signal APS first
Distribution, i.e. omnidirectional's uniform power spectrum pO(ψ) it is distributed and orients cosine power spectrum pU(ψ,ψ0) distribution.Its statistical distribution functions can be determined
Justice is：
ψ in formula (5)0∈ [0,2 π), it is defined as the Bo Da signal centers that terminal is produced in the rotation of aximuthpiston
Angle of arrival (Angle of Arrival, AOA), i.e., signal incident direction as shown in Figure 1 are referred to multi-antenna array coordinate system
Angle between point.If only considering two-dimensional space domain, can be by bringing into Simplified style (2)：
If η can be obtained in the case where path loss and mismatch case is not consideredm=1.
MIMO multiple antennas receptivities in the case of generally considering two kinds in past research：One kind is when many days of terminal
The each array element of line is omnidirectional antenna, due to space factor so that same ripple reaches signal in the time delay difference of arrival different antenna element
Generation phase of received signal is poor, and incoming signal steric direction vector when at this moment terminal multi-antenna array is classified as linear array ULA is：
D=2 π d/ λ in formula (7), d are multiple element antennas spacing, and λ is incoming signal wavelength, MUTIt is receiving terminal element number of array
[g]TRepresenting matrix transposition；Another kind be when each array element of terminal multiple antennas be directional aerial, due to the wave beam of each bay
Direction is different also different to the ability to accept of same signal.If it is considered that directional aerial array element, generally its pattern function can use
Represent such as formula (8) and (9)：
Assume that terminal MIMO has MUTIndividual directional aerial array element, entering when at this moment terminal multi-antenna array is classified as linear array ULA
Penetrating signal space steering vector is：
(10)
Each element in formula (10) is substituted into into formula (6), Jing derives easily checking incoming signal steric direction vector meeting formula
(6).Formula (10) and formula (4) or formula (5) are substituted into into formula (3) respectively, Jing derives simplification and can try to achieve uniform APS and cosine APS respectively
When multiple element antennas between spatial fading coefficient correlation be：
When power spectrum APS is to be uniformly distributed：
When power spectrum APS is cosine distribution：
Wherein αmOr αnIt 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 matrixes be：
System Performance Analysis parameter：Ergodic capacity and the bit error rate.Assume that terminal antenna array has MUTIndividual array element, terminal MIMO
Multi-antenna array spatial fading correlation matrix is MUT×MUTSquare formation.In assessing to radio channel capacity, usual MIMO multipaths
Channel capacity can be used as a kind of mode for weighing the channel quality comprising channel link end points.If believed in multipath known to receiving terminal
Road information, and transmitting terminal it is unknown when, assume that channel matrix H obeys zero-mean space White Noise Model in transmitting terminal, to make channel
Ergodic capacity is maximized, and optimum strategy is that power averaging is assigned on each transmission antenna unit, you can realize that traversal is held
Maximized input covariance matrix is measured for Rx=(ρ/MBS)IMBS, at this moment the ergodic capacity of channel can be：
M in formula (15)UTIt is terminal multi-antenna array array number,It is MUTThe unit matrix of dimension, MBSIt is base station (Base
Station, BS) multi-antenna array array number,It is MBSThe unit matrix of dimension, ρ are sending signal signal to noise ratios, and H is MIMO many
Footpath channel matrix, HHIt is the conjugate transposition of channel matrix H, mathematic expectaion EHIt is that the distribution to channel matrix H carries out mean analysis.
For the mimo channel of space correlation, channel matrix H can utilize the spatial fading correlation matrix of receiving array and emission array with
And independent same distribution channel is expressed as：
Wherein RUTFor receiving terminal spatial fading correlation matrix, RBSFor transmitting terminal spatial fading correlation matrix, subscript (.)TTable
Show the transposition of matrix, HwIt is multiple Gauss random matrix.
Even if under identical channel status, the different mimo antenna array element of correspondence, spatial fading correlation SFC also have very
Big difference.Fading channel average error rate can be by averagely may be used to condition bit error probability on the probability-distribution function of signal to noise ratio γ
：
If in difference bi-phase shift keying (Differential Binary Phase Shift Keying, DBPSK) and
Incoherent Binary Frequency Shift Keying (Noncoherent Binary orthogonal frequency shift Keying,
NBFSK, in) modulating, its condition bit error rate is：
P (e | γ)=1/2exp (- α γ) (18)
In formula (18), α represents modulation constant, and DBPSK is corresponded to during α=1/2, and NBFSK is corresponded to during α=1.It is then average to miss
Code check is represented by：
In formula (19), M represents diversity order, IMM rank unit matrixs are represented, m represents channel fading parameters and m >=1/2, m=
1/2 and m=1 corresponds to monolateral Gaussian Profile and Rayleigh distributions respectively, and α is modulation constant, and γ is average signal-to-noise ratio, RUTTo connect
Receiving end spatial fading correlation matrix, if therefore under given diversity order M, the bit error ratePhase between bay can be reduced to
The polynomial form of relation number.
As shown in figure 1, the structural representation of MIMO multiple antennas linear array of the present invention, bay therein is orientation day
Linear array unit, wherein, ψ0∈ [0,2 π) for the angle between signal incident direction and multi-antenna array coordinate system reference point, d is phase
Adjacent two multiple element antennas spacing.As shown in Fig. 2 for the directional diagram of directional aerial array element.
As shown in figure 3, in ripple up to power spectrum signal APS to be uniformly distributed, when terminal MIMO is linear array ULA, m=1,
Spatial fading correlation between two bays of n=2, wherein figure (a) is tier parameter alpha1=α2, figure (b) is α1-
α2=pi/2.Scheme (a), figure (b) and analyze in α1=0, α1=π/4 and α1Under three kinds of angles of=pi/2, two antenna elements are received and are declined
The space correlation coefficient of falling signal, and spatial fading correlation when showing omnidirectional antenna array element array under the same conditions with
Make comparisons.Analysis result shows that fading signal spatial coherence reduces with the increase of antenna array elements spacing.
It is consistent due to setting two directional antenna beams directions in Fig. 3 (a), in α1Signal space decline is received when=0 related
Coefficient is larger, and in α1It is less during=pi/2.In α1=0 and α1During=π/4, between directional aerial array element, coefficient correlation is compared with omnidirectional antenna
Greatly, but in α1During=pi/2, between directional aerial array element, coefficient correlation is little compared with omnidirectional antenna.Fig. 3 (a) is presented spatial fading phase relation
There is number curve concussion to reduce phenomenon, and coefficient correlation is zero at the integral multiple point of d=0.45 λ.Therefore, directional antenna beams
When direction is consistent, adjustment bay beam direction and array manifold structure can reduce array element collection of letters spatial fading phase indirectly
Guan Xing, improves MIMO array multiple antennas performance of receiving system.Fig. 3 (b) differs pi/2 due to two directional antenna beams directions so that
α1=0, α2=pi/2 and α1=pi/2, α2=0 time space decline coefficient correlation curve co-insides.As two directional aerials are from Vertical Square
To rather than same direction receives incoming wave signal, therefore nearly all coefficient correlation result is less compared with Fig. 3 (a).In α2-α1
There is situation when coefficient correlation between directional aerial array element is less than omnidirectional antenna during=pi/2, such as d/ λ are from 0 to 0.25.Therefore obtain
In α1With α2When difference is bigger, signal space Fading correlation is received less so that directional aerial MIMO array performance is better than omnidirectional
Antenna.
As shown in figure 4, when it is cosine distribution that ripple reaches power spectrum signal APS, between terminal MIMO ULA arrays Unit two
Fading signal space correlation coefficient.Scheme (a), (b), (c) and figure (d), (e), (f) and ripple be shown respectively to be respectively ψ up to signal angle0
=0, ψ0=π/4 and ψ0Three kinds of situations of=pi/2.Fig. 4 (a), (b), (c) show in ψ0=α1=α2Time space decline coefficient correlation is most
It is little, and | ψ0- α | less, coefficient correlation is less.Because ripple is up to signal angle AOA with tier beam direction closer to then
Performance is better.Fig. 4 (d), (e), in (f) it can be found that α2-α1During=pi/2, with ψ0Increase causes whole MIMO multi-antenna terminal
Spatial fading coefficient correlation reduces, and makes the diversity performance of MIMO ULA multiple antennas reception systems preferable.
As shown in figure 5, beam direction is consistent and during α=pi/2, in maximum-ratio combing (Maximal Ratio
Combining, MRC) when receiving diversity, cumulative distribution function CDF and signal to noise ratio snr relation.It is to be uniformly distributed in power spectrum APS
When Cumulative Distribution Function CDF increase up to the about 10dB of the signal to noise ratio needed for 1, the cumulative distribution letter when power spectrum APS is cosine distribution
Number increases up to the signal to noise ratio Yin Boda signal angle AOA ψ needed for 10It is different and different.In ψ0It is 12.5dB and ψ during=π/40=
0 and ψ0It is consistent with result curve when being uniformly distributed during=pi/2.Can obtain when power spectrum APS is cosine distribution, select suitable ripple to reach
Signal angle ψ0, MIMO diversity systems have preferable performance.
As shown in fig. 6, when MIMO multi-antenna-units are directional aerial, change of the ergodic capacity with signal to noise ratio snr.With
Signal to noise ratio increases, and capacity almost linearly increases.The ergodic capacity when power spectrum APS is cosine distribution can be drawn more than uniform
Analysis result during distribution.
As shown in fig. 7, channel ergodic capacity is with d/ λ result of variations.1/2 is increased to by 0 in d/ λ, capacity increases in approximately linear
It is long；As d/ λ ＞ 1/2, capability value tends towards stability maximum.When terminal MIMO multi-antenna array array element adopts directional aerial (α=
Pi/2), when ripple reaches signal angle ψ0Pi/2, channel capacity increase are increased to from 0.In ψ0During=pi/2, ergodic capacity has maximum.Terminal
MIMO can improve channel capacity about 10% in the method that directional aerial is combined with phase difference.
As shown in figure 8, in NBFSK (a=1) and cosine distribution performance changes of the average error rate BER with signal to noise ratio snr
Situation.Increase BER with signal to noise ratio to be gradually reduced；As diversity order M increases, mimo system can obtain preferable diversity gain；In m
=0.5 corresponding BER ratios are big in m=1, and reason is that m is less, and the more serious BER that then corresponds to of signal fadeout increases.Emulation experiment table
It is bright, power spectrum APS be cosine distribution when systematic function it is more excellent, directional aerial it is with the obvious advantage.
As shown in figure 9, at NBFSK (a=1), average error rate BER reaches the situation of change of signal angle AOA with ripple.In work(
Rate spectrum APS is unrelated for definite value up to signal angle AOA with ripple for BER when being uniformly distributed.When power spectrum APS is cosine distribution, BER is bent
Line is smooth and cosine distribution form is presented.When α=pi/2 is taken, it can be found that in ψ0During=pi/2, BER reaches minimum of a value, and reason is ripple
Up to signal angle AOA and beam array unit, beam direction is consistent causes optimum BER；In α=3, during pi/2, the bit error rate reaches maximum, former
Because ripple up to signal angle AOA and beam array unit beam direction instead result in completely reception signal effect it is not good so that BER most
Difference.
Above example technological thought only to illustrate the invention, it is impossible to which protection scope of the present invention is limited with this, it is every
According to technological thought proposed by the present invention, any change done on the basis of technical scheme, the scope of the present invention is each fallen within
Within.
Claims (1)
1. a kind of MIMO multiaerial systems performance estimating method, the multiaerial system include transmitting terminal and receiving terminal, transmitting terminal
Channel matrix H obeys zero-mean space White Noise Model, using ergodic capacity C and bit error rate PeAssessment MIMO multiaerial systems
Performance, it is characterised in that：The receiving terminal is the linear array that one group of array element is directional aerial, and the space of the linear array declines
The correlation matrix that falls is expressed as
When system ripple reaches aspect power spectrum to be uniformly distributed, the spatial fading correlation matrix RUTElement be
When it is cosine distribution that system ripple reaches aspect power spectrum, spatial fading correlation matrix RUTElement be
Wherein, m=1,2 ... MUT, n=1,2 ... MUT, MUTFor the array number of receiving terminal linear array, D=2 π d/ λ, d are to connect
Spacing between adjacent two array element of receiving end, λ are incoming signal wavelength, and j is imaginary unit, ψ0∈ [0,2 π) for Bo Da signal centers
Angle of arrival, ψ be orientation angular dimensions, αm、αnRespectively m, n bay beam direction of receiving terminal and receiving terminal linear array
Angle between line.
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