An average signal-to-noise ratio and bit error rate analysis method based on OCDM system

Abstract

The application discloses a kind of average signal-to-noise ratio and bit error rate analysis method based on OCDM system, comprising: step one, in multimedia wireless communication system, generate 4-QAM sending symbol, modulate on Chirp subcarrier to obtain sending signal;Step two, receive signal, obtain the statistical characteristics of multipath rayleigh channel, including the distribution and average power of path;Step three, according to physical channel information, construct channel circulation matrix, do eigenvalue decomposition to it, and use eigenvalue to express instantaneous signal-to-noise ratio;Step four, calculate the joint probability density function of eigenvalue, multiply with instantaneous signal-to-noise ratio and integrate to eigenvalue, obtain the general expression and specific expression of average SNR and BER of communication system under ZF equalization.The application solves the problem that it is difficult to directly and comprehensively evaluate the related performance of multimedia wireless communication system after passing through multipath rayleigh channel, and provides a reference for evaluating the transmission quality of picture, video and the like of communication system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of performance analysis of wireless communication systems, and particularly relates to an average signal-to-noise ratio and bit error rate analysis method based on an OCDM system. BACKGROUND

[0002] The sixth generation mobile communication (6G) technology is currently at the forefront of wireless communication research and development, and its goal is to achieve unprecedented data transmission speed, ultra-low latency and ultra-large-scale connection. In view of this goal, the academic and industrial circles have launched extensive research and exploration, especially in the field of coding and waveform modulation technology.

[0003] In the fifth generation mobile communication (5G) network, the orthogonal frequency division multiplexing (OFDM) technology is the most widely used air interface technology in today's wireless communication, which can realize high-speed wideband wireless access service. However, OFDM is susceptible to burst errors caused by channel zeros or interference, which seriously affects its average error performance. This may not guarantee that it meets the reliability constraints of ultra-reliable low-latency communication. In addition, since the massive machine type communication network operates on unlicensed frequency bands, the operation of the OFDM system will inevitably be limited by interference, and there will also be a significant out-of-band leakage problem using OFDM modulation. For the above reasons, the industry and academia have vigorously promoted the exploration of the transition variant of OFDM modulation to cope with the increasing traffic and lower tolerance to interference that future generations of wireless networks will encounter. And the spread spectrum scheme, such as the orthogonal chirp division multiplexing (OCDM) technology, shows considerable application prospect in solving these problems.

[0004] Chirp signal, also known as chirp signal, is widely used in radar or communication field due to its wideband spectrum and good autocorrelation characteristics. Meanwhile, Chirp multicarrier can realize superimposed transmission of multicarrier by using its orthogonality in time domain or frequency domain, thereby maximizing its spectral efficiency, i.e. OCDM system. At present, OCDM system has been proved to exhibit better performance than OFDM in multipath channel, thereby providing more accurate data transmission performance. OCDM system has been concerned by academia in many aspects, such as attenuation spectrum leakage, channel estimation, channel equalization, and also includes the expectation and variance of effective signal to noise ratio (ESNR), signal to noise ratio (SNR) and bit error rate (BER) at the receiving end of OCDM system.

[0005] However, the current research does not consider the expression of average SNR and BER of OCDM system through multipath Rayleigh channel after time domain zero-forcing (ZF) equalization, especially the case of L-path arbitrary distribution. b / N0, wherein E b is the transmit power per bit, and N0 is the average noise power at the receiving end. Due to the complexity of calculation, most researches consider the approximate Q function to obtain the approximate expression of BER, or obtain the upper bound of BER, without giving the accurate general expression or the calculation expression under special channel environment. SUMMARY

[0006] The present application provides an average signal to noise ratio and bit error rate analysis method based on OCDM system, which solves the problem that the prior art does not analyze the average SNR and BER performance of OCDM system after ZF equalization in multipath Rayleigh channel, especially without considering the L-path arbitrary distribution.

[0007] Technical scheme: In order to achieve the purpose of the present application, the technical scheme adopted by the present application is as follows: an average signal to noise ratio and bit error rate analysis method based on OCDM system, comprising the following steps:

[0008] Step one, in a multimedia wireless communication system, the transmitting end generates 4-QAM sending symbols, and modulates on Chirp subcarriers to obtain OCDM sending signals;

[0009] Step two, the receiving end processes the received signals by ZF equalization to obtain the statistical characteristics of multipath Rayleigh channel, wherein the statistical characteristics include the distribution and average power of path;

[0010] Step three, according to the physical channel information, construct the channel circulation matrix, do eigenvalue decomposition, and use the eigenvalue to express the instantaneous SNR;

[0011] Step four, calculate the joint probability density function of the eigenvalue, multiply it with the instantaneous SNR, and integrate the eigenvalue to get the expression of the average SNR and BER of the communication system under the ZF equalization;

[0012] Step five, according to the expression obtained in step four, get the relationship between the system parameters and the average SNR and BER, and evaluate the signal transmission quality of the current multimedia wireless communication system.

[0013] Further, the step three process is as follows:

[0014] 4-QAM sending symbol s = [s0, s1, …, s N-1 ], where N is the number of OCDM subcarriers, s i is the i-th sending symbol of s, i = 0, 1, …, N-1;

[0015] Multiply s by the inverse discrete Fresnel transform matrix Φ H on the left to get N-point sending signal x = [x0, x1, …, x N-1 ], where x i is the i-th point sending signal of x, i = 0, 1, …, N-1, (·) H represents Hermitian transpose;

[0016] At the receiving end, the received signal is processed by ZF equalization, and the channel impulse response CIR is h L = [h0, h1, …, h L-1 , 0, …, 0], where L is the maximum delay spread, h l is the l-th element of h L , l = 0, 1, …, L-1, and h L corresponds to the channel circulation matrix H;

[0017] After diagonalizing the matrix H by the fast Fourier transform matrix F, the vector λ = [λ0, λ1, …, λ N-1 ] composed of N eigenvalues of the matrix H and the per-bit SNR γ are used to express the instantaneous SNR ρ λ at the receiving end, where λ i is the i-th eigenvalue in λ, i = 0, 1, …, N-1;

[0018] The instantaneous SNR ρ λ at the receiving end is expressed by using the eigenvalue and the per-bit SNR, and the method is as follows:

[0019] The continuous waveform expression of the OCDM subcarrier in the time domain is: where t is time variable, k is subcarrier index value, ranging from 0 to (N-1), T is a whole OCDM symbol duration;

[0020] At a single sampling rate, one OCDM symbol is sampled at N points, and the sampling time point is n = 0, 1, …, N-1, the element of the nth row and the kth column of the discrete Fresnel transform matrix Φ is expressed as:

[0021]

[0022] where n = 0, 1, …, N-1, k = 0, 1, …, N-1; assuming that the constellation modulation mode is power normalized 4-QAM, that is, the energy E of each bit of s b = 1 / 2, the generated OCDM symbol x is calculated by the following formula:

[0023] x = Φ H s (2)

[0024] After the transmission signal passes through a multipath Rayleigh channel, the channel impulse response CIR is: Σ h is the covariance matrix of h L ; the noise signal at the receiving end is n = [n(0), n(1), …, n(N-1)], where n(i) is the ith noise component of n, i = 0, 1, …, N-1, then the signal at the receiving end is

[0025] y = HΦ H s + n (3)

[0026] After ZF equalization, the estimated constellation point is expressed as

[0027]

[0028] Then the instantaneous signal-to-noise ratio ρ is expressed as

[0029]

[0030] where represents the expectation operation, x k is the kth point of the transmission signal of x, k = 0, 1, …, N-1; assuming that F is an N×N discrete Fourier transform matrix, then H and H -1 in formula (5) are expressed as

[0031] H = F H DF,H -1 = F H DF (6)

[0032] where D is an N×N diagonal matrix, and the elements of D are calculated as​L The N-point Fourier transform of

[0033]

[0034] where h k It is h L The kth channel coefficient, k=0,1,…,L-1,λ i is the eigenvalue of H, i = 0, 1, ..., N-1;

[0035] Define the signal-to-noise ratio per bit Among them E b is the energy per bit of the 4-QAM transmitted symbol s, is the average power of the multipath Rayleigh channel; using λ i After ZF equalization, the instantaneous signal-to-noise ratio ρ is given by λ The general expression for :

[0036]

[0037] Furthermore, step 4 calculates the joint probability density function f of λ λ , and the instantaneous signal-to-noise ratio ρ λ By multiplying and integrating with respect to λ, we can obtain the expected general expression of the signal-to-noise ratio at the receiving end under any L-bar diameter. The process is as follows:

[0038] Let h L The power of each path is equal, and the real and imaginary parts of each path obey independent and identically distributed Gaussian distributions with mean 0 and variance σ 2 ;

[0039] The process of formula (7) is to linearly combine the channel coefficients of L stripes into N eigenvalues. The linear mapping matrix is ​​the first L columns of F, denoted as F L ,have

[0040] λ=F L h L (9)

[0041] F L It obeys the multivariate Gaussian distribution with a mean of 0 and a covariance matrix of ∑ λ The rank is L, that is, among the N eigenvalues, the first L eigenvalues ​​λ L As the base eigenvalue, it is used to linearly represent the remaining NL eigenvalues;

[0042] Let g ij Represented by λ i Represents λ j The coefficient of time, then the instantaneous SNR is expressed as

[0043]

[0044] The process of solving the joint probability density function f of N eigenvalues is transformed into solving the joint PDF of L eigenvalues, where the mapping matrix is F λ L The first L rows of F LL ;

[0045] The real and imaginary parts of F LL ,λ L ,h L are denoted as And the vector composed of the real and imaginary parts of CIR is denoted as The vector composed of the real and imaginary parts of eigenvalues is denoted as The mapping relationship from CIR to eigenvalues is denoted as

[0046]

[0047] The elements of h RI are independent and identically distributed, and the covariance matrix of h RI is denoted as

[0048]

[0049] Where I 2L is a 2L×2L identity matrix, σ 2 is the average power of the elements of h RI , and the joint PDF of λ RI is denoted as

[0050]

[0051] Equation (14) is the general expression of the joint PDF of the eigenvalues of the channel matrix of L paths of Rayleigh channel; combined with equation (10) and equation (14), the general expression of the expectation of the SNR at the receiving end is

[0052]

[0053] Further, combined with the expression of the bit error rate (BER) of M-QAM in a white noise channel, the integral of λ is obtained, which is the general expression of the BER under any L paths; the process is as follows:

[0054] The expression of the BER of M-QAM in a white noise channel is

[0055]

[0056] Where P b is the bit error rate, is the Gaussian Q function, M is the modulation order, k and i are both index variables, k = 1, …, u1, i = 0, 1, …, u2, and

[0057]

[0058] The conditional bit error rate of the 4-QAM modulation mode under the current channel is expressed as Substitute formula (10) and formula (14) into formula (16), and integrate with respect to RI to obtain the general expression of BER under ZF equalization

[0059]

[0060] Advantages: Compared with the prior art, the technical scheme of the present application has the following advantages:

[0061] The present application provides a comprehensive and in-depth analysis of the average SNR and BER performance of the OCDM system after ZF equalization in the multipath Rayleigh channel, especially considering the case of L paths arbitrarily distributed, that is, mapping the L independent and identically distributed (Independent and Identically Distributed, i.i.d.) channel coefficients of CIR into N eigenvalues of channel matrix H, by discussing the joint PDF of the N eigenvalues, the calculation method of the above performance under 4-QAM modulation mode is given. In particular, the general expression of the average SNR and BER under arbitrary L paths is given, and based on this, two special cases are given: single-path Rayleigh channel and two-path Rayleigh channel, wherein the average SNR calculation method when the two paths are arbitrarily distributed is also discussed, and the above performance accurate calculation formula when n = N / 2; finally, in the subsequent simulation, combined with the general expression, the average SNR numerical integration result when the path distribution is in the first L = 1, 2 position of CIR is given. All the above derivation and numerical integration results verify the accuracy and effectiveness of the performance analysis method. In the actual multimedia wireless communication scene, the above analysis and evaluation of the transmission performance of the communication device in different data transmission environments can provide an important reference for optimizing data transmission, thereby improving the stability of data transmission. The present application takes the actual single-transmitting single-receiving OCDM communication system as an example, and gives the analysis method and general expression of the average SNR and BER at the receiving end under ZF equalization, which can be used to directly evaluate the quality of the signal in the current multimedia wireless communication scene, and solves the problem that the existing technology cannot comprehensively analyze the performance of the OCDM system according to the statistical characteristics of the channel in the multipath Rayleigh channel, thereby optimizing the transmission quality. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 is the general flowchart of the method of the present application.

[0063] Figure 2 is the theoretical value of average SNR about γ compared with simulation value.

[0064] Figure 3 is the theoretical value of average SNR about γ compared with simulation value of single path, two path Rayleigh channel.

[0065] Figure 4 is the theoretical value of BER about γ compared with simulation value of single path, two path Rayleigh channel. DETAILED DESCRIPTION

[0066] The technical solutions of the present application are further described below in combination with the drawings and examples.

[0067] The average signal-to-noise ratio and bit error rate analysis method based on the OCDM system provided by the present application is based on the actual multimedia wireless communication scene, and studies the performance analysis method of the single-transmitting and single-receiving OCDM system under the ZF equalization, thereby providing an important reference for optimizing data transmission and solving the problem that it is difficult to directly and comprehensively evaluate the transmission quality according to the statistical characteristics of the multipath Rayleigh channel. Assuming that N is the number of subcarriers of the OCDM system, H is diagonalized through the Fourier transform matrix, the instantaneous signal-to-noise ratio at the receiving end can be expressed by the N eigenvalues of H, and the general expressions of the average SNR and BER under the multipath Rayleigh fading channel can be derived by performing multidimensional variable integration on the eigenvalues. The accurate expressions of the above performances under the single-path Rayleigh channel and the two-path Rayleigh channel are derived. In addition, the average SNR at the receiving end when L=1, 2 is verified by numerical integration, and the reliability of the analysis method is proved. The flow is shown in Figure 1 and the specific implementation steps are as follows:

[0068] Step one, obtain 4-QAM sending symbols s=[s0, s1, …, s N-1 ], wherein N is the number of OCM subcarriers, s i is the i-th sending symbol of s, i=0, 1, …, N-1, and left multiply the inverse discrete Fresnel transform (Inverse Discrete Fresnel Transform, iDFnT) matrix Φ H , to obtain N-point sending signal x=[x0, x1, …, x N-1 ], wherein x i is the i-th point sending signal of x, i=0, 1, …, N-1, and (·) H represents Hermite transpose.

[0069] Step two, process the received signal at the receiving end by ZF equalization, and assume that the channel impulse response (Channel Impulse Response, CIR) is h L =[h0, h1, …, h L-1,0,…,0], where L is the maximum delay spread, h l is the lth element of h L , l = 0, 1,…, L-1, h L The corresponding channel circulant matrix is H.

[0070] Step three, after diagonalizing H by fast Fourier transform matrix F, the general expression of the received instantaneous signal-to-noise ratio p N-1 can be expressed by the vector λ = [λ0, λ1,…, λ λ N-1] composed of N eigenvalues of H and the per-bit signal-to-noise ratio γ, where λ i is the ith eigenvalue of λ, i = 0, 1,…, N-1; the specific process is as follows:

[0071] The continuous waveform expression of the OCDM subcarrier in the time domain is: where t is the time variable, k is the subcarrier index value, ranging from 0 to (N-1), and N is assumed to be even here; T is the duration of an entire OCDM symbol. At a single sampling rate, an OCDM symbol is sampled at N points, and the sampling time points are n = 0, 1,…, N-1, then the element in the nth row and the kth column of the Discrete Fresnel Transform (DFnT) matrix Φ can be expressed as:

[0072]

[0073] where n, k = 0, 1,…, N-1. Assuming that the constellation point modulation mode is power-normalized 4-QAM, i.e., the energy E b of each bit of s is 1 / 2, the generated OCDM symbol x can be calculated by:

[0074] x = Φ H s (2)

[0075] After the transmitted signal passes through the multipath Rayleigh channel, assuming that the CIR is: Σ h h L h H is the covariance matrix of h , assuming that the received noise signal is n = [n(0), n(1),…, n(N-1)], where n(i) is the ith noise component of n, i = 0, 1,…, N-1, and the average power is

[0076] The received signal is

[0077] After ZF equalization, the estimated constellation point is expressed as

[0078]

[0079] Then the instantaneous signal-to-noise ratio ρ can be expressed as

[0080]

[0081] in represents the expectation operation, x k is the signal sent at the kth point of x, k=0,1,…,N-1. Let F be the N×N Discrete Fourier Transform (DFT) matrix, then H and H in formula (5) are -1 It can be expressed as

[0082] H=F H DF,H -1 =F H DF (6)

[0083] Where D is an N×N diagonal matrix, and the elements of D are calculated as h L The N-point Fourier transform of

[0084]

[0085] where h k It is h L The kth channel coefficient, k=0,1,…,L-1,λ i It is also the N eigenvalues ​​of H, i = 0, 1, ..., N-1. Define the signal-to-noise ratio per bit You can use λ i and γ give the general expression of the instantaneous signal-to-noise ratio λ after ZF equalization

[0086]

[0087] Step 4: Calculate the joint probability density function (PDF) f of λ λ , and the instantaneous signal-to-noise ratio ρ λ By multiplying and integrating with respect to λ, we can obtain the expected universal expression for the receiver signal-to-noise ratio under any L-path. Combining the expression for the bit error rate (BER) of M-QAM in an additive Gaussian white noise (AWGN) channel and integrating with respect to λ, we can obtain the universal expression for the BER under any L-path. The specific process is as follows:

[0088] Let h L Each path has equal power, and the real and imaginary parts of each path obey independent and identically distributed Gaussian distributions with mean 0 and variance σ2 The process of equation (7) is essentially to linearly combine the channel coefficients of L paths into N eigenvalues, and the linear mapping matrix is the first L columns of F, denoted as F L , and

[0089] λ = F L h L (9)

[0090] Since h L obeys a multi-dimensional Gaussian distribution, its linear combination F L also obeys a multi-dimensional Gaussian distribution, and its mean is 0 and its covariance matrix is ∑ λ The rank of F l is L, which means that among the N eigenvalues, the first L eigenvalues λ ij can be used as the base eigenvalues to linearly represent the remaining N-L eigenvalues. Let g i represent the coefficients when λ j is expressed in terms of λ λ , then the instantaneous SNR can be expressed as

[0091]

[0092] Therefore, the process of solving the joint probability density function (PDF) f L of the N eigenvalues is converted into solving the joint PDF of the L eigenvalues, and the mapping matrix at this time is the first L rows of F LL , denoted as F LL . Since the integral of the L eigenvalues should be converted into the integral of the real part and the imaginary part respectively, the solution of the general expression is a 2L-dimensional multi-variable integral process. Let the real part and the imaginary part of F L , λ L , h be denoted as and the vector composed of the real part and the imaginary part of the CIR be denoted as , and the vector composed of the real part and the imaginary part of the eigenvalue be denoted as

[0093]

[0094] Since the elements of F are independent and identically distributed (i.i.d.), the covariance matrix of h RI is

[0095]

[0096] where I2L is a 2Lx2L identity matrix, and 2 is h RI the average power of each element, and RI The joint PDF of

[0097]

[0098] Further, it can be expressed as

[0099]

[0100] The above formula is the general expression of the joint PDF of the eigenvalues of the channel matrix of the L-path Rayleigh channel, which contains 2L i.i.d. variables. In particular, when L=N, which means that the N real parts and N imaginary parts corresponding to the N eigenvalues after mapping are also independent of each other. In combination with formula (10) and formula (14), the general expression of the expectation of the SNR at the receiving end is

[0101]

[0102] Next, the general expression of the BER at the receiving end is determined. The BER expression of M-QAM under white noise channel is

[0103]

[0104] wherein is the Gaussian Q function, M is the modulation order, k and i are both index variables, k=1,…,u1, i=0,1,…,u2, and

[0105]

[0106] Therefore, if the instantaneous signal-to-noise ratio at the receiving end is p, the conditional bit error rate P b of 4-QAM modulation under the current channel can be expressed as Similarly, substituting formula (10) and formula (14) into formula (16), and integrating RI , the general expression of the BER under ZF equalization can be obtained

[0107]

[0108] Step five, by calculating the closed-form expressions under single-path and two-path Rayleigh channels, as well as the numerical integration results, and comparing them with the simulation values, the correctness of the analysis method can be verified. The specific process is as follows:

[0109] 5.1 In combination with the general expression, the accurate expressions of the average SNR and BER at the receiving end after ZF equalization under the single-path Rayleigh channel are derived. At this time, the CIR is represented as

[0110] h L = [h0, 0,..., 0] (19)

[0111] Mapping matrix F LL = 1, all eigenvalues can be expressed as: λ i = h0, i = 0, 1,..., N-1. At this time, formula (10) and formula (14) can be expressed as

[0112]

[0113] Substituting formula (20) into formula (15), the average SNR at this time can be obtained as

[0114]

[0115] Substituting formula (20) into formula (18), combined with the Gaussian Q function transformation equation: φ is an arbitrary variable, and M. K. Simon et al. proposed the identity

[0116]

[0117] The closed expression of BER under the single-path Rayleigh channel can be derived as

[0118]

[0119] 5.2 The average SNR and BER after the ZF equalization of the receiving end under the two-path Rayleigh channel are derived. First, consider the general expression of CIR

[0120]

[0121] The mapping matrix at this time is a 2x2 submatrix of F, denoted as:

[0122]

[0123] Where F(i,j) is the element of the i-th row and j-th column of F. Similarly, λ0, λ1 are the base eigenvalues, and λ m can be expressed as

[0124]

[0125] Substituting formula (10) can obtain the current And F RI can be expressed as

[0126]

[0127] Substituting formula (14) can obtain the current with The average SNR of the two-path Rayleigh channel can be obtained by multiplying and integrating the above equation. Based on this, consider the special case of n = N / 2. In this case

[0128]

[0129] can be expressed as

[0130]

[0131] And can be expressed as

[0132]

[0133] Substitute and into equation (15), and after some mathematical operations, the average SNR in this case is

[0134]

[0135] Substitute and into equation (18), and the BER expression is

[0136]

[0137] Rewrite the variables into polar coordinate representation, where x, y, θ0, θ1 are intermediate integral variables, and x, y ∈ (0, ∞), θ0, θ1 ∈ (-π, π), and combine equation (22), the above equation can be simplified to

[0138]

[0139] where b = 2γσ 2 sin 2 ψ, ψ is an arbitrary variable. Thus, the BER expression of the OCDM system after the two-path Rayleigh channel and ZF equalization is derived.

[0140] As shown in Figure 2 , L = 1, σ 2 = 4, L = 2, σ 2 = 2, and L = 3, σ 2When =1, the average SNR of the receiving end after ZF equalization is compared with the theoretical value and the measured value about γ. It can be seen from the figure that the theoretical value and the measured value can be closely fitted whether it is single path, two paths or three paths. In addition, the γ of each curve covers a range of 16dB, proving that the SNR analysis method can be established whether the SNR per bit is high or low;

[0141] As shown in Figure 3 , the average SNR of the receiving end after ZF equalization is compared with the theoretical value and the measured value about γ under single path and two path Rayleigh channels. Wherein, σ 2 ∈{1 / 2,1}, the two path Rayleigh channel corresponds to the case of n=N / 2 in formula (24). It can be seen from the figure that the theoretical value can be closely fitted with the measured value whether it is single path or two path Rayleigh channel. In addition, the average SNR increases with the increase of γ, and the γ of each curve covers a range of 16dB, which also proves that the SNR analysis method can be established whether the SNR per bit is high or low;

[0142] As shown in Figure 4 , the BER of the receiving end after ZF equalization is compared with the theoretical value and the measured value about γ under single path and two path Rayleigh channels. Wherein, σ 2 ∈{1 / 2,1}, the two path Rayleigh channel still corresponds to the case of n=N / 2 in formula (24). It can be seen from the figure that the BER decreases with the increase of γ, and the γ of each curve covers a range of 16dB, verifying that the BER analysis method can be established whether the SNR per bit is high or low.

Claims

1. A method for analyzing average signal-to-noise ratio and bit error rate based on OCDM system, characterized in that, The steps are as follows: Step one, in a multimedia wireless communication system, a transmitting end generates 4-QAM sending symbols, and modulates on Chirp subcarriers to obtain an OCDM sending signal; Step two, a receiving end processes a receiving signal by using a ZF equalization, and acquires statistical characteristics of a multipath Rayleigh channel, the statistical characteristics including a distribution and average power of a path; Step three, according to physical channel information, a channel circulation matrix is constructed, eigenvalue decomposition is performed on the channel circulation matrix, and an instantaneous signal-to-noise ratio is represented by using eigenvalues; Step four, a joint probability density function of the eigenvalues is calculated, the instantaneous signal-to-noise ratio is multiplied by the joint probability density function, and integration is performed on the eigenvalues to obtain an expression of an average SNR and BER of the communication system under the ZF equalization; Step five, according to the expression obtained in step four, a relationship between system parameters and the average SNR and BER is acquired, and signal transmission quality of the current multimedia wireless communication system is evaluated.

2. The average signal-to-noise ratio and bit error rate analysis method based on the OCDM system according to claim 1, characterized in that: The step three process is as follows: 4-QAM transmit symbol s = [s0, s1,..., s N-1 N-1], where N is the number of OCDM subcarriers, s i is the i-th transmit symbol of s, i = 0, 1,..., N-1; Multiply s by the inverse discrete Fresnel transformation matrix Φ H , we get the N-point sending signal x=[x0,x1,...,x N-1 ], where x i Send a signal for the i-th point of x, i = 0, 1, ..., N-1, (·) H represents the Hermitian transpose; The received signal is processed by ZF equalization at the receiving end, and the channel impulse response CIR is h L =[h0, h1,..., h L-1 L-1, 0,..., 0], where L is the maximum delay spread, h l is the lth element of h L , l = 0, 1,..., L-1, and h L The corresponding channel circulation matrix is H; After the matrix H is diagonalized by the fast Fourier transform matrix F, a vector λ = [λ0, λ1,..., λN-1] composed of N eigenvalues of the matrix H and a signal-to-noise ratio γ per bit are used to express the instantaneous signal-to-noise ratio ρ of the receiving end N-1 ] and a signal-to-noise ratio γ per bit λ where λ i is the i-th eigenvalue in λ, i = 0, 1,..., N-1; The received instantaneous signal-to-noise ratio ρ is expressed by the eigenvalue and the signal-to-noise ratio per bit λ The method is as follows: The continuous wave expression of OCDM sub-carrier in time domain is: Wherein, t is time variable, k is sub-carrier index value, the range is 0~(N-1), and T is a whole OCDM symbol duration. At the single sampling rate, one OCDM symbol is sampled at N points, and the sampling time points are The element of the nth row and the kth column of the discrete Fresnel transform matrix Φ is represented as: where n=0, 1,..., N-1, k=0, 1,..., N-1; assuming the constellation modulation is power normalized 4-QAM, i.e. the energy of each bit of s E b = 1 / 2, the generated OCDM symbol x is calculated by the following formula: x = Φ H s(2) After the transmitted signal passes through a multipath Rayleigh channel, the channel impulse response CIR: ∑ h is the covariance matrix of h L ; the received noise signal is n = [n(0), n(1),..., n(N-1)], where n(i) is the ith noise component of n, i = 0, 1,..., N-1, and the received signal is y = HΦ H s + n (3) After ZF equalization, the constellation points are estimated are represented as The instantaneous signal-to-noise ratio ρ is represented as wherein represents a desired operation, x k is the kth point transmitted signal of x, k = 0, 1,..., N - 1; let F be an N x N discrete Fourier transform matrix, then H and H -1 is expressed as H = F HDF,H-1 = F H DF (6) where D is an N x N diagonal matrix, the elements of D are computed as h L N-point Fourier transform of x, i.e., where h k is the kth channel coefficient of h L , k = 0, 1,..., L - 1, λ i is an eigenvalue of H, i = 0, 1,..., N - 1; Definition of energy per bit where E b is the energy per bit for a 4-QAM transmitted symbol s, is the average power of the multipath Rayleigh channel; and λ i and γ give the general expression of the instantaneous signal-to-noise ratio ρ λ after ZF equalization.

3. The OCDM system based average SNR and BER analysis method of claim 2, wherein, Step four: Compute the joint probability density function f of λ λ , and the instantaneous signal-to-noise ratio ρ λ , and integrate over λ, to obtain the general expression for the expected signal-to-noise ratio at the receiver for any L bins; the procedure is as follows: Let h L be the complex Gaussian random variable with equal power for each ray, and the real and imaginary parts of each ray obey independent Gaussian distribution with mean 0 and variance σ 2 ; The process of equation (7) is to linearly combine L paths of channel coefficients into N eigenvalues, and the linear mapping matrix is the first L columns of F, denoted as F L , there are λ = F LhL (9) F L Subject to the multivariate Gaussian distribution, and the mean is 0, the covariance matrix is ∑ λ The rank of L, that is, among the N eigenvalues, the first L eigenvalues λ L As the base eigenvalue, the remaining N-L eigenvalues are linearly represented; Let g ij representing λ i representing λ j the coefficients at time t, then the instantaneous SNR is represented as Solve the joint probability density function f of N eigenvalues λ The process is transformed into solving the joint PDF of L eigenvalues. The mapping matrix at this time is F L The first L rows of LL ; Recall that LL , the real and imaginary parts of L , and L and let the vector consisting of the real and imaginary parts of CIR be The vector consisting of the real and imaginary parts of the eigenvalue is The mapping of CIR to eigenvalue at this time is represented as​ are independently and identically distributed, h RI the covariance matrix of where I 2L is the 2L x 2L identity matrix, σ 2 is h RI the average power of each element, λ RI The joint PDF of the elements is given by The formula (14) is a general expression of the joint PDF of the eigenvalues of the channel matrix of the L-path Rayleigh channel; in combination with the formula (10) and the formula (14), a general expression of an expectation of the SNR of the receiving end is 4. The OCDM system based average SNR and BER analysis method of claim 3, wherein, In combination with a bit error rate BER expression of M-QAM under a white noise channel, integration is performed on λ to obtain a general expression of the BER under any L-path; the process is as follows: The BER expression of M-QAM under the white noise channel is where P b is the bit error rate, is the Gaussian Q-function, M is the modulation order, k and i are both index variables, k = 1,..., u1, i = 0, 1,..., u2, and The conditional bit error rate of 4-QAM modulation under the current channel is expressed as Substitute formula (10) and formula (14) into formula (16), and integrate with respect to λ RI to obtain the general expression of BER under ZF equalization

Images