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

Abstract

The invention discloses an average signal-to-noise ratio and bit error rate analysis method based on an OCDM system, and the method comprises the steps: 1, generating a 4-QAM transmission symbol in a multimedia wireless communication system, and modulating the 4-QAM transmission symbol on a Chirp subcarrier to obtain a transmission signal; step 2, receiving a signal, and obtaining statistical characteristics of a multipath Rayleigh channel, including path distribution and average power; step 3, constructing a channel cyclic matrix according to physical channel information, performing eigenvalue decomposition on the channel cyclic matrix, and representing an instantaneous signal-to-noise ratio by eigenvalues; and step 4, calculating a joint probability density function of the characteristic value, multiplying the joint probability density function by the instantaneous signal-to-noise ratio, and integrating the characteristic value to obtain a general expression and a specific expression of the average SNR and BER of the communication system under ZF equalization. The problem that the related performance of the multimedia wireless communication system passing through the multipath Rayleigh channel is difficult to directly and comprehensively assess is solved, and reference is provided for the communication system to assess the transmission quality of pictures, videos and the like.

Description

Technical Field

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

[0002] The Sixth Generation Mobile Communication (6G) technology is currently at the forefront of wireless communication research and development, with the goal of achieving unprecedented data transmission speeds, ultra-low latency, and ultra-large-scale connections. To achieve this goal, academia and industry have conducted extensive research and exploration, especially in the field of coding and waveform modulation technology.

[0003] In the fifth generation mobile communication (5G) network, Orthogonal Frequency Division Multiplexing (OFDM) is the most widely used air interface technology in wireless communication today, enabling high-speed broadband wireless access services. However, OFDM is susceptible to burst errors caused by channel zeros or interference, which seriously affects its average bit error performance. This may not guarantee that it meets the reliability constraints of ultra-reliable low-latency communication. In addition, since massive machine-type communication networks operate on unlicensed frequency bands, the operation of OFDM systems will inevitably be limited by interference, and the use of OFDM modulation will also have significant out-of-band leakage problems. For the above reasons, industry and academia have vigorously promoted the exploration of transitional variants of OFDM modulation to cope with the increasing traffic and lower tolerance to interference that will be encountered in future generations of wireless networks. Spread spectrum schemes, such as Orthogonal Chirp Division Multiplexing (OCDM) technology, have shown considerable application prospects in solving these problems.

[0004] Chirp signal, also known as chirp signal, is widely used in radar or communication fields because of its wideband spectrum and good autocorrelation characteristics. At the same time, Chirp multi-carrier can use its orthogonality in the time domain or frequency domain to realize the superposition transmission of multiple carriers, thereby maximizing its spectrum efficiency, that is, OCDM system. At present, OCDM system has been proven to be able to show better performance than OFDM under multipath channels, thereby providing more accurate data transmission performance; many research aspects of OCDM system have also been concerned by the academic community, such as attenuation spectrum leakage, channel estimation, channel equalization, and also include the effective signal to noise ratio (ESNR), signal to noise ratio (SNR) expectation and variance, bit error rate (BER) and other aspects of OCDM system at the receiving end.

[0005] However, the current research does not consider the average SNR and BER of the OCDM system after zero-forcing (ZF) equalization in the time domain through the multipath Rayleigh channel. b / N0 expression, especially without considering the case of arbitrary distribution of L bar diameter, where E b is the power per bit at the transmitter, and N0 is the average noise power at the receiver. Due to computational complexity, most studies consider approximate Q functions to obtain approximate expressions for BER, or obtain upper bounds for BER, but do not provide precise general expressions or computational expressions under special channel environments. Summary of the invention

[0006] Purpose of the invention: The present invention proposes an average signal-to-noise ratio and bit error rate analysis method based on an OCDM system, which solves the problem that the prior art does not analyze the average SNR and BER performance of the OCDM system after ZF equalization in a multipath Rayleigh channel, and especially does not consider the arbitrary distribution of L-bar diameters.

[0007] Technical solution: To achieve the purpose of the present invention, the technical solution adopted by the present invention is: a method for analyzing the average signal-to-noise ratio and bit error rate based on an OCDM system, comprising the following steps:

[0008] Step 1: In a multimedia wireless communication system, a transmitter generates a 4-QAM transmission symbol and modulates it on a Chirp subcarrier to obtain an OCDM transmission signal;

[0009] Step 2: Process the received signal with ZF equalization at the receiving end to obtain the statistical characteristics of the multipath Rayleigh channel, wherein the statistical characteristics include the distribution and average power of the paths;

[0010] Step 3: construct a channel circulant matrix based on the physical channel information, perform eigenvalue decomposition on it, and use the eigenvalue to represent the instantaneous signal-to-noise ratio;

[0011] Step 4: Calculate the joint probability density function of the eigenvalues, multiply it by the instantaneous signal-to-noise ratio and integrate the eigenvalues ​​to obtain the expressions of the average SNR and BER of the communication system under ZF equalization;

[0012] Step 5: According to the expression obtained in step 4, the relationship between the system parameters and the average SNR and BER is obtained to evaluate the signal transmission quality of the current multimedia wireless communication system.

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

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

[0015] 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 to the i-th point of x, i = 0, 1, ..., N-1, (·) H represents the Hermitian transpose;

[0016] At the receiving end, the ZF equalizer is used to process the received signal, 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 Yes L The lth element of L The corresponding channel circulant matrix is ​​H;

[0017] After the matrix H is diagonalized by the fast Fourier transform matrix F, the vector λ=[λ0,λ1,…,λ N-1 ] and the signal-to-noise ratio per bit γ represent the instantaneous signal-to-noise ratio ρ at the receiving end λ , where λ i is the i-th eigenvalue in λ, i = 0, 1, …, N-1;

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

[0019] The continuous waveform expression of 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 T is the duration of a whole OCDM symbol;

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

[0021]

[0022] Where n = 0, 1, ..., N-1, k = 0, 1, ..., N-1; Assume that the constellation point modulation mode is 4-QAM after power normalization, that is, the energy per bit of s is E b =1 / 2, the generated OCDM symbol x is calculated by the following formula:

[0023] x=Φ H s (2)

[0024] After the transmitted signal passes through the multipath Rayleigh channel, the channel impulse response CIR is: Σ h h L The covariance matrix of the receiving end noise signal is n = [n(0), n(1), ..., n(N-1)], where n(i) is the i-th noise component of n, i = 0, 1, ..., N-1, then the receiving end signal is

[0025] y=HΦ H s+n (3)

[0026] After ZF equalization, the constellation points are estimated Expressed as

[0027]

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

[0029]

[0030] 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 matrix, then H and H in formula (5) -1 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 hL The N-point Fourier transform of

[0033]

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

[0035] Defining the signal-to-noise ratio per bit Where 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 of is:

[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 λ, we can get the expected general expression of the signal-to-noise ratio at the receiving end under any L bar diameters; the process is as follows:

[0038] Assume 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 a mean of 0 and a variance of 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 by F L ,have

[0040] λ=F L h L (9)

[0041] F L It obeys multivariate Gaussian distribution with mean 0 and covariance matrix is ∑ 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] Assume g ij Represented by λ i Represents λ j The coefficient at time , then the instantaneous SNR is expressed as

[0043]

[0044] Solve for the joint probability density function f of N eigenvalues λ The process is transformed into solving the joint PDF of L eigenvalues. At this time, the mapping matrix is ​​F L The first L rows of LL ;

[0045] Remember F LL ,λ L ,h L The real and imaginary parts are And the vector composed of the real and imaginary parts of CIR is The vector consisting of the real and imaginary parts of the eigenvalue is Then the mapping relationship from CIR to eigenvalue is expressed as

[0046]

[0047] Each element of h is independent and identically distributed. RI The covariance matrix of

[0048]

[0049] Among them, I 2L is the 2L×2L unit matrix, σ 2 Yes RI The average power of each element, λ RI The joint PDF of

[0050]

[0051] Formula (14) is the general expression of the joint PDF of the channel matrix eigenvalues ​​of the L-path Rayleigh channel; Combining formula (10) and formula (14), the general expression of the expected SNR at the receiving end is

[0052]

[0053] Furthermore, combined with the bit error rate BER expression of M-QAM in a white noise channel, the BER general expression under any L-bar diameter is obtained by integrating λ; the process is as follows:

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

[0055]

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

[0057]

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

[0059]

[0060] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0061] The present invention provides a comprehensive and in-depth analysis of the average SNR and BER performance of the OCDM system after ZF equalization in a multipath Rayleigh channel, especially considering the case of arbitrary distribution of L paths, that is, mapping the L independent and identically distributed (iid) channel coefficients of the CIR to the N eigenvalues ​​of the channel matrix H. By discussing the joint PDF of these N eigenvalues, a calculation method for the above performance under the 4-QAM modulation mode is given. In particular, a general expression of the average SNR and BER under arbitrary L paths is given, and based on this, two special cases are given: a single-path Rayleigh channel and a two-path Rayleigh channel, in which the latter also discusses the average SNR calculation method when the two paths are arbitrarily distributed, and the precise calculation formula for the above performance when n=N / 2; finally, in subsequent simulations, combined with the general expression, the numerical integration results of the average SNR when the paths are distributed at L=1,2 positions before the CIR are given. All the above derivations and numerical integration results verify the accuracy and effectiveness of this performance analysis method. In actual multimedia wireless communication scenarios, the above analysis and evaluation of the transmission performance of communication equipment in different data transmission environments can provide an important reference for optimizing data transmission, thereby improving the stability of data transmission. This method takes the actual single-transmit single-receive 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 scenario, solving the problem that it is difficult for existing technologies to comprehensively analyze the performance of the OCDM system based on the statistical characteristics of the channel under multipath Rayleigh channels, thereby optimizing the transmission quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is the overall flow chart of the method of the present invention.

[0063] Figure 2 It is a comparison chart of the theoretical value and simulation value of the average SNR with respect to γ ​​for L=1,2,3.

[0064] Figure 3 This is a comparison chart of the theoretical and simulated values ​​of the average SNR with respect to γ ​​for single-path and two-path Rayleigh channels.

[0065] Figure 4 This is a comparison chart of the theoretical and simulated values ​​of BER with respect to γ ​​for single-path and two-path Rayleigh channels. DETAILED DESCRIPTION

[0066] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0067] The present invention describes an average signal-to-noise ratio and bit error rate analysis method based on an OCDM system. It studies the performance analysis method of a single-transmit single-receive OCDM system under ZF equalization based on actual multimedia wireless communication scenarios, provides an important reference for optimizing data transmission, and solves the problem of difficulty in directly and comprehensively evaluating transmission quality based on the statistical characteristics of multipath Rayleigh channels. Let N be the number of subcarriers in the OCDM system, and diagonalize H through the Fourier transform matrix. The instantaneous signal-to-noise ratio at the receiving end can be represented by the N eigenvalues ​​of H. By integrating the eigenvalues ​​in multiple dimensions, the general expressions of the average SNR and BER under multipath Rayleigh fading channels can be derived; the precise expressions of the above performance under single-path Rayleigh channels and two-path Rayleigh channels are derived; in addition, numerical integration verifies the average SNR of the receiving end when L=1,2, proving the reliability of the analysis method. The process is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0068] Step 1: Get 4-QAM transmission symbol s = [s0, s1, ..., s N-1 ], where N is the number of OCDM subcarriers, s i is the i-th transmitted symbol of s, i=0,1,…,N-1, and multiplied on the left by the inverse discrete Fresnel transform (iDFnT) matrix Φ H , we get the N-point sending signal x=[x0,x1,…,x N-1 ], where x i Send a signal to the i-th point of x, i = 0, 1, ..., N-1, (·) H represents the Hermitian transpose.

[0069] Step 2: Use ZF equalization to process the received signal at the receiving end, assuming that the channel impulse response (CIR) is h L =[h0,h1,…,h L-1,0,…,0], where L is the maximum delay spread, h l Yes L The lth element of L The corresponding channel circulant matrix is ​​H.

[0070] Step 3: After H is diagonalized by the fast Fourier transform matrix F, the vector λ = [λ0,λ1,…,λ N-1 ] and the signal-to-noise ratio per bit γ represent the instantaneous signal-to-noise ratio ρ at the receiving end λ The general expression of i is the i-th eigenvalue of λ, i=0,1,…,N-1; the specific process is as follows:

[0071] The continuous waveform expression of 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), where N is an even number; T is the duration of an entire OCDM symbol. Under single sampling rate, an OCDM symbol is sampled at N points, and the sampling time point is n=0,1,…,N-1, then the elements of the nth row and kth column of the Discrete Fresnel Transform (DFnT) matrix Φ can be expressed as:

[0072]

[0073] Where n, k = 0, 1, ..., N-1. Assume that the constellation point modulation mode is 4-QAM after power normalization, that is, the energy per bit of s is E b =1 / 2, the generated OCDM symbol x can be calculated by the following formula:

[0074] x=Φ H s (2)

[0075] After the transmitted signal passes through the multipath Rayleigh channel, let CIR be: Σ h h L The covariance matrix of the receiver is: Assume that the noise signal at the receiving end is n = [n(0), n(1), ..., n(N-1)], where n(i) is the i-th noise component of n, i = 0, 1, ..., N-1, and the average power is The receiving end signal is

[0076] y=HΦ H s+n (3)

[0077] After ZF equalization, the constellation points are estimated 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 Yes L The k-th 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 λ, we can get the expected general expression of the signal-to-noise ratio at the receiving end under any L-path. Combined with the bit error rate (BER) expression of M-QAM in white noise channel (Additive Gaussian White Noise, AWGN), we can integrate λ to get the general expression of BER under any L-path. The specific process is as follows:

[0088] Assume h L All paths have 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 formula (7) is essentially to linearly combine the channel coefficients of L stripes into N eigenvalues, and the linear mapping matrix is ​​the first L columns of F, denoted by F L ,have

[0089] λ=F L h L (9)

[0090] Because h L Obeys multivariate Gaussian distribution, and its linear combination F L It also obeys a multivariate Gaussian distribution with a mean of 0 and a covariance matrix of ∑ λ The rank is L, which means that among the N eigenvalues, the first L eigenvalues ​​λ l As the base eigenvalue, de-linearize the remaining NL eigenvalues. Let g ij Represented by λ i To express λ j The instantaneous SNR can be expressed as

[0091]

[0092] Therefore, solve the joint probability density function (PDF) f of the N eigenvalues λ The process is transformed into solving the joint PDF of L eigenvalues. At this time, the mapping matrix is ​​F L The first L rows of LL Since the integration of L eigenvalues ​​should be transformed into the integration of their real and imaginary parts, respectively, solving the general expression is a 2L-dimensional multivariable integration process. LL ,λ L ,h L The real and imaginary parts are And the vector composed of the real and imaginary parts of CIR is The vector consisting of the real and imaginary parts of the eigenvalue is Then the mapping relationship from CIR to eigenvalue can be expressed as

[0093]

[0094] because The elements of h are independent and identically distributed (iid), so h RI The covariance matrix of

[0095]

[0096] Among them, I2L is the 2L×2L unit matrix, σ 2 Yes RI The average power of each element, and λ RI The joint PDF of can be expressed as

[0097]

[0098] Further, it can be expressed as

[0099]

[0100] The above formula is the general expression of the joint PDF of the channel matrix eigenvalues ​​of the L-path Rayleigh channel, which contains 2L iid variables. In particular, when L = N, That is, the N real parts and N imaginary parts corresponding to the N eigenvalues ​​after mapping are also unrelated. Combining formula (10) and formula (14), the general expression of the expected SNR at the receiving end is as follows:

[0101]

[0102] Next, we determine the general expression for the BER at the receiving end. The BER expression for M-QAM in a white noise channel is:

[0103]

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

[0105]

[0106] Therefore, if the instantaneous signal-to-noise ratio at the receiving end is ρ, the conditional bit error rate P of the 4-QAM modulation method under the current channel is b It can be expressed as Similarly, substitute formula (10) and formula (14) into formula (16), and RI By integrating, we can get the general expression of BER under ZF equilibrium.

[0107]

[0108] Step 5: 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 Combined with the general expression, the precise expression of average SNR and BER after ZF equalization at the receiving end in a single-path Rayleigh channel is derived. At this time, CIR is expressed as

[0110] h L =[h0,0,…,0] (19)

[0111] Mapping Matrix F LL =1, all eigenvalues ​​can be expressed as: 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), we can get the average SNR at this time:

[0114]

[0115] Substitute formula (20) into formula (18) and combine it with the Gaussian Q function transformation equation: φ is an arbitrary variable, and the identity proposed by MkSimon et al.

[0116]

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

[0118]

[0119] 5.2 The average SNR and BER after ZF equalization at the receiver in a two-path Rayleigh channel are derived. First, consider the general expression of CIR:

[0120]

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

[0122]

[0123] where F(i,j) is the element in the i-th row and j-th column of F. Similarly, taking λ0 and λ1 as the basis eigenvalues, then λ m It can be expressed as

[0124]

[0125] Substituting into formula (10) we can get the current And F RI It can be expressed as

[0126]

[0127] Substituting into formula (14) we can get the current and By multiplying and integrating, we can get the general expression of the average SNR in a two-path Rayleigh channel. Based on this, consider the special case of n = N / 2.

[0128]

[0129] It can be expressed as

[0130]

[0131] and It can be expressed as

[0132]

[0133] Will and Substituting into formula (15) and performing some mathematical operations, we can obtain the average SNR in this case as

[0134]

[0135] Will and Substituting into formula (18), we can get the BER expression as follows:

[0136]

[0137] Rewrite the variables in polar coordinates. Where x, y, θ0, θ1 are intermediate integral variables, and x, y∈(0,∞), θ0, θ1∈(-π,π), and combined with formula (22), the above formula can be simplified to

[0138]

[0139] Where b = 2γσ 2 sin 2 ψ, ψ are arbitrary variables. From this, the BER expression of the OCDM system after passing through the two-path Rayleigh channel and ZF equalization is derived.

[0140] like Figure 2 As shown, it describes L = 1, σ 2 =4, L = 2, σ 2 =2 and L = 3,σ 2= 1, after ZF equalization, the theoretical value and measured value of the average SNR of the receiving end are compared with each other. As can be seen from the figure, whether it is single-path, two-path or three-path, the theoretical value and the measured value are closely matched; in addition, the γ of each curve covers a range of 16dB, proving that the SNR analysis method is valid regardless of whether the signal-to-noise ratio per bit of the transmitter is high or low;

[0141] like Figure 3 As shown in the figure, the theoretical and measured values ​​of the average SNR of the receiver after ZF equalization are compared with respect to γ ​​in single-path and two-path Rayleigh channels. 2 ∈{1 / 2,1}, the two-path Rayleigh channel is the case where n=N / 2 in formula (24). It can be seen from the figure that, regardless of single-path or two-path Rayleigh channels, the theoretical values ​​are also closely aligned with the measured values. In addition, the average SNR increases with the increase of γ, and the γ of each curve covers a range of 16 dB, which also proves that the SNR analysis method is valid in the case of high or low signal-to-noise ratio per bit.

[0142] like Figure 4 As shown in the figure, the comparison between the theoretical value and the measured value of BER about γ after ZF equalization in single-path and two-path Rayleigh channels is described. 2 ∈{1 / 2,1}, the two-path Rayleigh channel still corresponds to the case where n=N / 2 in formula (24). As can be seen from the figure, the BER decreases with the increase of γ, and the γ of each curve covers a range of 16dB, which verifies that the BER analysis method is valid when the signal-to-noise ratio per bit is high or low.

Claims

1. A method for analyzing average signal-to-noise ratio and bit error rate based on an OCDM system, characterized in that: Here are the steps: Step 1: In a multimedia wireless communication system, a transmitter generates a 4-QAM transmission symbol and modulates it on a Chirp subcarrier to obtain an OCDM transmission signal; Step 2: Process the received signal with ZF equalization at the receiving end to obtain the statistical characteristics of the multipath Rayleigh channel, wherein the statistical characteristics include the distribution and average power of the paths; Step 3: construct a channel circulant matrix based on the physical channel information, perform eigenvalue decomposition on it, and use the eigenvalue to represent the instantaneous signal-to-noise ratio; Step 4: Calculate the joint probability density function of the eigenvalues, multiply it by the instantaneous signal-to-noise ratio and integrate the eigenvalues ​​to obtain the expressions of the average SNR and BER of the communication system under ZF equalization; Step 5: According to the expression obtained in step 4, the relationship between the system parameters and the average SNR and BER is obtained to evaluate the signal transmission quality of the current multimedia wireless communication system.

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 process of step three is as follows: 4-QAM transmission symbol s = [s0, s1, ..., s N-1 ], where N is the number of OCDM subcarriers, s i is the i-th transmitted symbol of s, i = 0, 1, ..., N-1; Multiply s by the inverse discrete Fresnel transformation matrix Φ H , we get the N-point transmission signal x=[x0, x1,..., x N-1 ], where x i Send a signal to the i-th point of x, i = 0, 1, ..., N-1, (·) H represents the Hermitian transpose; At the receiving end, the ZF equalizer is used to process the received signal, 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 Yes L The lth element of L The corresponding channel circulant matrix is ​​H; After the matrix H is diagonalized by the fast Fourier transform matrix F, the vector λ=[λ0,λ1,...,λ N-1 ] and the signal-to-noise ratio per bit γ represent the instantaneous signal-to-noise ratio ρ at the receiving end λ , where λ i is the i-th eigenvalue in λ, i = 0, 1, ..., N-1; The instantaneous signal-to-noise ratio ρ at the receiving end is expressed using the eigenvalue and the signal-to-noise ratio per bit λ , the method is as follows: The continuous waveform expression of 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 T is the duration of a whole OCDM symbol; At a single sampling rate, an OCDM symbol is sampled at N points, and the sampling time point is Then the elements of the nth row and kth column of the discrete Fresnel transformation matrix Φ are expressed as: Where n = 0, 1, ..., N-1, k = 0, 1, ..., N-1; Assume that the constellation point modulation mode is 4-QAM after power normalization, that is, the energy per bit of s is 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 the multipath Rayleigh channel, the channel impulse response CIR is: ∑ h h L The covariance matrix of 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 receiving end signal is y=HΦ H s+n (3) After ZF equalization, the constellation points are estimated Expressed as Then the instantaneous signal-to-noise ratio ρ is expressed as 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 matrix, then H and H in formula (5) -1 Expressed as H=F H DF,H -1 =F H DF (6) Where D is an N×N diagonal matrix, and the elements of D are calculated as h L The N-point Fourier transform of where h k Yes L The k-th channel coefficient, k = 0, 1, ..., L-1, λ i is the eigenvalue of H, i = 0, 1, ..., N-1; Define the signal-to-noise ratio per bit Where 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 of is:

3. The average signal-to-noise ratio and bit error rate analysis method based on the OCDM system according to claim 2 is characterized in that: Step 4 Calculate the joint probability density function f of λ λ , and the instantaneous signal-to-noise ratio ρ λ By multiplying and integrating λ, we can get the expected general expression of the signal-to-noise ratio at the receiving end under any L bar diameters; the process is as follows: Assume 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 a mean of 0 and a variance of σ 2 ; 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 by F L ,have λ=F L h L (9) F L It obeys multivariate Gaussian distribution with mean 0 and covariance matrix is ∑ 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; Assume g ij Represented by λ i Represents λ j The coefficient at time , then the instantaneous SNR is expressed as Solve for the joint probability density function f of N eigenvalues λ The process is transformed into solving the joint PDF of L eigenvalues. At this time, the mapping matrix is ​​F L The first L rows of LL ; Remember F LL ,λ L ,h L The real and imaginary parts are And the vector composed of the real and imaginary parts of CIR is The vector consisting of the real and imaginary parts of the eigenvalue is Then the mapping relationship from CIR to eigenvalue is expressed as Each element of h is independent and identically distributed. RI The covariance matrix of Among them, I 2L is the 2L×2L unit matrix, σ 2 Yes RI The average power of each element, λ RI The joint PDF of Formula (14) is the general expression of the joint PDF of the channel matrix eigenvalues ​​of the L-path Rayleigh channel; Combining formula (10) and formula (14), the general expression of the expected SNR at the receiving end is 4. The average signal-to-noise ratio and bit error rate analysis method based on the OCDM system according to claim 3 is characterized in that: Combined with the bit error rate BER expression of M-QAM in a white noise channel, integrating λ, we can get the general expression of BER under any L stripe lengths; the process is as follows: The BER expression of M-QAM in white noise channel is: Among them, P b is the bit error rate, is the Gaussian Q function, M is the modulation order, k and i are index variables, k=1,...,u1, i=0,1,...,u2, The conditional bit error rate of 4-QAM modulation in the current channel is expressed as Substitute formula (10) and formula (14) into formula (16), and RI Integrate and obtain the general expression of BER under ZF equilibrium

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