CN101304275A - Wireless channel modeling and simulation method for mobile communication network - Google Patents

Abstract

The invention relates to a wireless channel modeling and simulation method for applying in the mobile communication network. The method is as follows: firstly, three basic conditions and the related characteristics which are used for satisfying the Gaussian stochastic sequence are introduced, wherein, the Gaussian stochastic sequence is used for producing the Raleigh fading waveforms that are accordant to small-sized wireless channel characteristics; an independent standard Gaussian stochastic sequence is produced by using the Monte Carlo method and is transferred to the Gaussian stochastic sequence that can satisfy the corresponding three basic conditions and the related characteristics through a linear transformation matrix; the module is taken out finally, thus obtaining the Raleigh fading waveform in the wireless channel; wherein, the linear transformation matrix is obtained through a way of recursion by column. The wireless channel modeling and simulation method of the invention is simple and practical, thus effectively producing the Raleigh fading waveforms that are accordant to small-sized wireless channel characteristics, satisfying the requirements of the related characteristics and stability; easily producing a plurality of mutually independent Raleigh fading waveforms; therefore, the invention provides conditions and possibilities for researching and analyzing the wireless communication system of various frequency diversities.

Description

Be applied to the wireless channel modeling and simulation method of mobile communications network

Technical field

The invention belongs to the cordless communication network technical field, particularly the wireless channel modeling and simulation method of mobile communications network.

Background technology

Influence owing to factors such as electromagnetic wave in the channel is reflected, diffraction, scattering, multipath transmisstions, the received signal of receiving terminal is that all directions arrive electromagnetic stack, make signal among a small circle, cause violent fluctuation, be referred to as multipath fading, also be called the small scale decline.The small scale decline has directly embodied the complexity and the randomness of wireless channel, is the basic problem of decision performance in wireless communication systems.Generally speaking, the envelope Rayleigh distributed of small scale fading channel response, and phase place is obeyed evenly distribution in (0,2 π).Therefore, the core of wireless channel modeling and key promptly are how to produce the Rayleigh fading envelope simply and effectively, and this also is the top priority of the various mobile communications networks of research and analysis.In recent years, the various models that are used for emulation small scale Rayleigh fading waveform continue to bring out.These models can roughly be divided into two classes: statistics class and definite class.

1. the statistics class model is based on the filtering shaping of the multiple Gaussian random process on time domain or the frequency domain being carried out power spectral density, this class model is suitable for generation to satisfy the Rayleigh fading waveform of various statistical properties, but the contrary discrete Fourier transform (DFT) (IDFT) that needs well-designed digital shaping filter and carry out big data quantity.This class methods implementation complexity height is unsuitable for the emulation of high-speed real-time.

2. determine that limited the cosine wave that class model is based on selecting meticulously on the time domain superposes.The most frequently used definite class model is Jakes model and modified model thereof, owing to its simplicity is used widely.But Jakes model and modified model thereof all are to be based upon on the hypothesis basis that reaches the quadrature component Gaussian distributed in the same way of generation.According to the requirement that is central-limit theorem, when N is tending towards infinite, reach the just genuine Gaussian distributed of quadrature component in the same way.Therefore, Jakes model and modified model thereof all are subjected to the restriction of central-limit theorem.

Summary of the invention

Technical problem: the wireless channel modeling and simulation method that the objective of the invention is to propose a kind of mobile communications network.This method is simple, practical, can produce the Rayleigh fading waveform that meets the small scale radio channel characteristic effectively, satisfy the requirement of autocorrelation performance and stationarity, and can easily produce a plurality of separate Rayleigh fading waveforms, thus for the various frequency diversity wireless communication systems of research and analysis provide condition with may.

Technical scheme: the wireless channel modeling and simulation method that is applied to mobile communications network of the present invention at first derives required satisfied three primary conditions of the gaussian random sequence that is used to produce the Rayleigh fading waveform that meets the small scale radio channel characteristic and autocorrelation performance, the separate standards gaussian random sequence that utilizes Monte Carlo method to produce, and be converted into the gaussian random sequence that satisfies corresponding three primary conditions and autocorrelation performance by a kind of matrix of a linear transformation, at last to its delivery, thereby draw Rayleigh fading waveform in the wireless channel; Wherein, the matrix of a linear transformation obtains by the mode by the row recursion.

Described three primary conditions are as follows:

1) real component is that in-phase component X (n) and imaginary part component are that all average is 0 to quadrature component Y (n), variance is σ ²Gaussian random process, wherein n represent discrete constantly;

2) in-phase component X (n) and quadrature component Y (n) add up independent at any time, i.e. their cross-correlation function E (X (n) * Y (n+m))=0, wherein E () expression peek term hopes, 0≤m≤N-1 be discrete time at interval;

3) in-phase component X (n), quadrature component Y (n) are generalized stationary random process, and its auto-correlation function equates and is R (m)=E (X (n) * X (n+m))=E (Y (n) * Y (n+M));

Autocorrelation performance is: in-phase component X (n) and quadrature component Y (n) auto-correlation coefficient satisfy $\mathrm{\ρ}\left(m\right)=\frac{R\left(m\right)}{{\mathrm{\σ}}^2}=J_0\left(2\mathrm{\π}{f}_{m}m{T}_s\right);$ Wherein, ρ (m) expression X (n) and Y (n) auto-correlation coefficient, J ₀() is first kind zeroth order Bei Saier function, f _mBe maximum doppler frequency, T _sBe sample time interval, σ ²Be variance.

The separate standards gaussian random sequence that utilizes Monte Carlo method to produce is one group of separate standard " be that average is 0, variance is 1 " Gaussian random variable sequence; Because the cumulative distribution function of Gaussian random variable can't provide with analytic expression, therefore utilize the rejection technique in the Monte Carlo method to produce the standard Gaussian random variable, its method is: make the probability density curve of standard Gaussian Profile, be positioned at area under the abscissa scope inner curve just corresponding to the probability of this scope; Have equally distributed two-dimensional random number under the standard Gaussian probability density curve in being selected at, then the standard Gaussian Profile is satisfied in the distribution corresponding to the point at abscissa place under the standard Gaussian probability density curve, and therefore this point promptly is the standard Gaussian random variable; Utilize said method to produce N random number and promptly get one group of separate standard Gaussian random variable, be designated as η=[η (n), 1≤n≤N]; η can obtain X promptly through linear transformation: X '=T η ', and here, transposition is got in [] ' expression, and T is the matrix of a linear transformation; Similarly, utilize Monte Carlo method to produce one group of separate standard Gaussian random variable κ=[κ (n), 1≤n≤N], can get Gaussian random process Y by formula Y '=T κ '; X (n) that said method produces and Y (n) satisfy three primary conditions and autocorrelation performance; Therefore, by $V\left(n\right)=\sqrt{X{\left(n\right)}^2+{Y\left(n\right)}^2,}$ Can satisfy the Rayleigh fading waveform V=[V (n) of small scale radio channel characteristic, 1≤n≤N].

The matrix of a linear transformation can obtain by the mode by the row recursion, and promptly available following recurrence formula obtains matrix of a linear transformation T:

T _i1＝σ ²ρ(i-1)，1≤i≤N a

$T_{\mathrm{ij}}=\frac{{\mathrm{\&sigma;}}^2\mathrm{\&rho;}(i-j)-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{T}_{\mathrm{ik}}{T}_{\mathrm{jk}}}{\sqrt{{\mathrm{\&sigma;}}^2-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{T}_{\mathrm{jk}}^2}},1<j\&le;i\&le;N---b$

Formula a is an initial value, and formula b is for pressing the row recurrence formula; At first obtain the matrix of a linear transformation T first row element T according to formula a ₁₁, obtain the matrix of a linear transformation T second row first column element T according to formula a then ₂₁And obtain the second row secondary series element T according to formula b ₂₂Thereby, obtain matrix of a linear transformation T second each column element [T of row ₂₁, T ₂₂], and the like, each row all at first utilizes formula a to obtain its first column element later on, utilizes formula b to obtain all the other each column elements then, thereby tries to achieve whole matrix of a linear transformation T.

Beneficial effect: innovative point of the present invention is as follows:

The present invention promptly is applied to the wireless channel modeling and simulation method of mobile communications network, its feature at first is to have derived required satisfied three primary conditions of the gaussian random sequence that is used to produce the Rayleigh fading waveform that meets the small scale radio channel characteristic and autocorrelation performance, the separate standards gaussian random sequence that utilizes Monte Carlo method to produce, and be converted into the gaussian random sequence that satisfies corresponding conditions and autocorrelation performance, thereby draw Rayleigh fading waveform in the wireless channel by a kind of matrix of a linear transformation.

According to the corresponding autocorrelation performance of gaussian random sequence, can obtain the matrix of a linear transformation by simple mode, and not need complicated matrixing or find the solution by the row recursion.

The present invention is simple, practical, can produce the Rayleigh fading waveform that meets the small scale radio channel characteristic effectively, satisfies the requirement of autocorrelation performance and stationarity.

The present invention can easily produce a plurality of separate Rayleigh fading waveforms, thereby be the various frequency diversity wireless communication systems of research and analysis (for example frequency hopping (FH) system, MC-CDMA (MC-CDMA) system, OFDM (OFDM) system) provide condition with may.

Description of drawings

Fig. 1 is a wireless channel modeling and simulation method flow diagram.

Embodiment

If Z (n)=X (n)+jY (n), n=1,2 ..., N is multiple Gaussian random process.Z (n) can be write as random vector form Z=[Z (1), Z (2) ..., Z (N)].Z (n) must satisfy following primary condition: 1) to be average be 0 to real component (being in-phase component) X (n) and imaginary part component (being quadrature component) Y (n), and variance is σ ²Gaussian random process.2) X (n) and Y (n) add up independent at any time, i.e. their cross-correlation function E (X (n) * Y (n+m))=0.3) X (n), Y (n) are generalized stationary random process, and its auto-correlation function equates and be R (m)=E (X (n) * X (n+m))=E (Y (n) * Y (n+m)) that 0≤m≤N-1 is the discrete time interval.

If the envelope of Z (n) $V\left(n\right)=\left|Z\left(n\right)\right|=\sqrt{X{\left(n\right)}^2+Y{\left(n\right)}^2}.$ Condition 1) with condition 2) unite and guaranteed that V (n) obeys average at any time and is

Variance is Rayleigh distributed, its probability density function is: $f_V\left(v\right)=\frac{v}{{\mathrm{\&sigma;}}^2}{e}^{{-v}^2/{2\mathrm{\&sigma;}}^2}(v\&GreaterEqual;0).$ Condition 3) further guaranteed the wide-sense stationarity of envelope V (n).

The implementation model of Rayleigh fading waveform is proposed based on the previous discussion, now.For obtaining to meet the Rayleigh fading waveform of small scale radio channel characteristic, the in-phase component X (n) of multiple Gaussian random process Z (n) and quadrature component Y (n) go up described three primary conditions of joint except that satisfying, and its power spectrum all should satisfy following formula:

$S\left(f\right)=\left\{\begin{array}{cc}\frac{{\mathrm{\&sigma;}}^2}{\mathrm{\&pi;}{f}_m\sqrt{1-{(f/f_m)}^2}}& \left|f\right|\&le;f_m\\ 0& \left|f\right|>f_m\end{array}\right.---\left(1\right)$

Wherein f is a frequency, f _mBe maximum doppler frequency.f _m=K/ λ=Kf ₀(K represents the translational speed of travelling carriage to/Ω, and λ represents carrier wavelength, f ₀Be carrier frequency, Ω is the light velocity 3 * 10 ⁸M/s).Formula (1) is exactly the U type power spectrum of Jakes, and the channel that satisfies this power spectrum is exactly usually said rayleigh fading channel.By getting X (n) and Y (n) auto-correlation function to formula S (f) inverse fourier transform and discretization (discrete sampling):

R(m)＝σ ²J ₀(2πf _mmT _s)(2)

T _sBe sample time interval, J ₀() is first kind zeroth order Bei Saier function.Therefore X (n) and Y (n) auto-correlation coefficient are:

$\mathrm{\&rho;}\left(m\right)=\frac{R\left(m\right)}{{\mathrm{\&sigma;}}^2}=J_0\left(2\mathrm{\&pi;}{f}_{m}m{T}_s\right)---\left(3\right)$

According to the theoretical foundation of front,, only need to produce Gaussian random process X (n) and the Y (n) that satisfies corresponding three primary conditions and autocorrelation performance (ρ (m)) coincidence formula (3) if will produce the Rayleigh fading waveform that satisfies the small scale radio channel characteristic.Because X (n) or Y (n) have similar character, be without loss of generality, be that example is introduced its production process with X (n) below.

At first, utilize Monte Carlo method to produce one group of separate standard (be that average is 0, variance is 1) Gaussian random variable, be designated as η (n), 1≤n≤N.Monte Carlo method is a kind of stochastic simulation or arbitrary sampling method.Rejection technique in the Monte Carlo method can produce effectively and satisfy independence required standard gaussian random sequence.Suppose the vector form η of η (n)=[η (1), η (2) ..., η (N)] and can obtain X=[X (1) through certain linear transformation, X (2) ..., X (N)] (vector form of X (n)) promptly:

X′＝Tη′(4)

Here, transposition is got in [] ' expression, and T is the matrix of a linear transformation.If it is all non-negative that T is lower triangular matrix and all elements,

Then:

Transition matrix T must satisfy following formula:

TT′＝E(X′X)(5)

Wherein E () expression is peeked respectively to each element in the matrix and is hoped in term.By preceding described, can get

According to formula (5), (6), we can find the solution transition matrix T with following recurrence formula:

T _i1＝σ ²ρ(i-1)，1≤i≤N (7-a)

$T_{\mathrm{ij}}=\frac{{\mathrm{\&sigma;}}^2\mathrm{\&rho;}(i-j)-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{T}_{\mathrm{ik}}{T}_{\mathrm{jk}}}{\sqrt{{\mathrm{\&sigma;}}^2-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{T}_{\mathrm{jk}}^2}},1<j\&le;i\&le;N---(7-b)$

Formula (7-a) is an initial value, and formula (7-b) is for pressing the row recurrence formula.According to these two formula, at first obtain transition matrix T first each column element T of row ₁₁, and then obtain transition matrix T second each column element [T of row ₂₁, T ₂₂], and the like, obtain capable each the column element [T of transition matrix T N at last _N1, T _N2..., T _NN], thereby try to achieve whole transition matrix T.

By formula (4) as can be seen, (1≤n≤N) linear combination by separate standard Gaussian random variable η (n) obtains X (n).Obviously, still Gaussian distributed and average are zero to the X of generation (n).Therefore and transition matrix T is obtained by top recurrence formula, has guaranteed that variance and the autocorrelation performance of the X (n) that produced by formula (4) satisfies formula (6).And then the X of generation (n) still has wide-sense stationarity.Similarly, utilize Monte Carlo method to produce one group of separate standard Gaussian random variable κ (n), 1≤n≤N (κ is its vector form) can get Gaussian random process Y (n) (Y is its vector form) by formula Y '=T κ '.Because κ (n) and η (n) separate at any time (being determined by Monte Carlo method), X of generation (n) and Y (n) add up independent at any time.Therefore the X (n) of said method generation satisfies three primary conditions and formula (6) regulation autocorrelation performance with Y (n).Therefore, by $V\left(n\right)=\left|Z\left(n\right)\right|=\sqrt{X{\left(n\right)}^2+{Y\left(n\right)}^2},$ Can satisfy the Rayleigh fading waveform V=[V (1) of small scale radio channel characteristic, V (2) ..., V (N)].

It is as follows that the present invention is applied to the wireless channel modeling and simulation method example of mobile communications network:

The first step: according to simulation requirements, Initial Channel Assignment parameter: variances sigma ², maximum doppler frequency f _m, the sample time interval T _s

Second step: the autocorrelation performance ρ (m) that calculates Gaussian random process X (n) and Y (n) by formula (3);

The 3rd step: reach (7-b) by pressing row recurrence formula (7-a), at first obtain transition matrix T first each column element T of row ₁₁, and then obtain transition matrix T second each column element [T of row ₂₁, T ₂₂], and the like, obtain capable each the column element [T of transition matrix T N at last _N1, T _N2..., T _NN], thereby try to achieve whole transition matrix T.

The 4th step: utilize the rejection technique in the Monte Carlo method to produce two groups of separate standard Gaussian random variable sequence η and κ.

The 5th step: according to formula (4), i.e. X '=T η ' and Y '=T κ '.Be met Gaussian random variable sequence X and the Y and the multiple Gaussian random variable sequence Z of the autocorrelation performance of three primary conditions and formula (3) regulation respectively.

The 6th step: by $V\left(n\right)=\left|Z\left(n\right)\right|=\sqrt{X{\left(n\right)}^2+Y{\left(n\right)}^2},$ Can satisfy the Rayleigh fading waveform V=[V (1) of small scale radio channel characteristic, V (2) ..., V (N)].

The present invention be mobile communications network wireless channel modeling and simulation method flow diagram as shown in Figure 1.

Following table has provided two separate Rayleigh fading waveform V that the present invention produces ₁(n) and V ₂The simulation value of probability density distribution (n), auto-correlation function and cross-correlation function thereof and the comparison measure of theoretical value (wherein auto-correlation function is meant the auto-correlation function of the corresponding gaussian random sequence of Rayleigh fading waveform).Emulation tool is VC++, and comparison measure is the ratio (relative error value) that the difference of simulation value and theoretical value accounts for theoretical value, and each comparison measure is the mean value of ten emulation.By this table as can be known, the present invention can produce a plurality of independently Rayleigh fading waveforms that satisfy radio channel characteristic preferably.

Claims (4)

1. wireless channel modeling and simulation method that is applied to mobile communications network, it is characterized in that, at first derive required satisfied three primary conditions of the gaussian random sequence be used to produce the Rayleigh fading waveform that meets the small scale radio channel characteristic and autocorrelation performance, utilize Monte Carlo method to produce the separate standards gaussian random sequence, and be converted into the gaussian random sequence that satisfies corresponding three primary conditions and autocorrelation performance by a kind of matrix of a linear transformation, at last to its delivery, thereby draw Rayleigh fading waveform in the wireless channel; Wherein, the matrix of a linear transformation obtains by the mode by the row recursion.

2. the wireless channel modeling and simulation method of mobile communications network according to claim 1 is characterized in that described three primary conditions are as follows:

1) real component is that in-phase component X (n) and imaginary part component are that all average is 0 to quadrature component Y (n), variance is σ ²Gaussian random process, wherein n represent discrete constantly;

2) in-phase component X (n) and quadrature component Y (n) add up independent at any time, i.e. their cross-correlation function E (X (n) * Y (n+m))=0, wherein E () expression peek term hopes, 0≤m≤N-1 be discrete time at interval;

3) in-phase component X (n), quadrature component Y (n) are generalized stationary random process, and its auto-correlation function equates and is R (m)=E (X (n) * X (n+m))=E (Y (n) * Y (n+m));

Autocorrelation performance is: in-phase component X (n) and quadrature component Y (n) auto-correlation coefficient satisfy $\mathrm{\&rho;}\left(m\right)=\frac{R\left(m\right)}{{\mathrm{\&sigma;}}^2}=J_0\left(2\mathrm{\&pi;}{f}_{m}m{T}_s\right);$ Wherein, ρ (m) expression X (n) and Y (n) auto-correlation coefficient, J ₀() is first kind zeroth order Bei Saier function, f _mBe maximum doppler frequency, T _sBe sample time interval, σ ²Be variance.

3. the wireless channel modeling and simulation method of mobile communications network according to claim 1, it is characterized in that utilizing Monte Carlo method to produce the separate standards gaussian random sequence, and be converted into the gaussian random sequence that satisfies corresponding three primary conditions and autocorrelation performance by a kind of matrix of a linear transformation, at last to its delivery, thereby draw Rayleigh fading waveform in the wireless channel; Utilize the method for the rejection technique generation standard Gaussian random variable in the Monte Carlo method to be: the probability density curve of making the standard Gaussian Profile; Be positioned at area under the abscissa scope inner curve just corresponding to the probability of this scope; Have equally distributed two-dimensional random number under the standard Gaussian probability density curve in being selected at, then the standard Gaussian Profile is satisfied in the distribution corresponding to the point at abscissa place under the standard Gaussian probability density curve, and therefore this point promptly is the standard Gaussian random variable; Utilize said method to produce N random number and promptly get one group of separate standard Gaussian random variable, be designated as η=[η (n), 1≤n≤N]; η can obtain X promptly through linear transformation: X '=T η ', and here, transposition is got in [] ' expression, and T is the matrix of a linear transformation; Similarly, utilize Monte Carlo method to produce one group of separate standard Gaussian random variable κ=[κ (n), 1≤n≤N], can get Gaussian random process Y by formula Y '=T κ '; X (n) that said method produces and Y (n) satisfy three primary conditions and autocorrelation performance; Therefore, by $V\left(n\right)=\sqrt{X{\left(n\right)}^2+Y{\left(n\right)}^2,}$ Can satisfy the Rayleigh fading waveform V=[V (n) of small scale radio channel characteristic, 1≤n≤N].

4. the wireless channel modeling and simulation method of mobile communications network according to claim 1 is characterized in that the matrix of a linear transformation can obtain by the mode by the row recursion, and promptly available following recurrence formula obtains matrix of a linear transformation T:

T _i1＝σ ²ρ(i-1)，1≤i≤N a

$T_{\mathrm{ij}}=\frac{{\mathrm{\&sigma;}}^2\mathrm{\&rho;}(i-j)-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{T}_{\mathrm{ik}}{T}_{\mathrm{jk}}}{\sqrt{{\mathrm{\&sigma;}}^2-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{T}_{\mathrm{jk}}^2}},1<j\&le;i\&le;N---b$

Formula a is an initial value, and formula b is for pressing the row recurrence formula; At first obtain the matrix of a linear transformation T first row element T according to formula a ₁₁, obtain the matrix of a linear transformation T second row first column element T according to formula a then ₂₁And obtain the second row secondary series element T according to formula b ₂₂Thereby, obtain matrix of a linear transformation T second each column element [T of row ₂₁, T ₂₂], and the like, each row all at first utilizes formula a to obtain its first column element later on, utilizes formula b to obtain all the other each column elements then, thereby tries to achieve whole matrix of a linear transformation T.

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