阅读说明：本技术 双Gamma湍流信道下FTN传输系统平均信道容量的计算方法 (Method for calculating average channel capacity of FTN transmission system under double-Gamma turbulent channel ) 是由 曹明华 武鑫 王惠琴 孙剑锋 吕佳芸 王博 李亚婷 于 2019-07-15 设计创作，主要内容包括：双Gamma湍流信道下FTN传输系统平均信道容量的计算方法,目的是将FTN技术引入Gamma-Gamma湍流信道中,使符号速率大于Nyquist速率有效提高系统平均容量,改善大气传输系统的性能。FTN信号的形成是将输入的比特信息a<Sub>n</Sub>进行QPSK映射后经过FTN成形滤波器生成FTN信号。系统信道容量的计算是利用接收信号传输模型计算得出信道容量,然后对其周期归一化后得到FTN系统平均容量。在此基础上,根据QPSK调制特性推导出QPSK调制格式下Gamma-Gamma湍流信道下超奈奎斯特光传输系统的平均容量的表达式。该超奈奎斯特光传输系统的构建有效的提高了系统频谱效率。(A method for calculating the average channel capacity of an FTN transmission system under a double-Gamma turbulent channel aims to introduce an FTN technology into a Gamma-Gamma turbulent channel, so that the symbol rate is greater than the Nyquist rate, the average channel capacity of the system is effectively improved, and the performance of an atmospheric transmission system is improved. The FTN signal is formed by inputting bit information a n And after QPSK mapping, generating an FTN signal through an FTN shaping filter. The calculation of the system channel capacity is to calculate the channel capacity by utilizing a received signal transmission model, and then to normalize the period of the channel capacity to obtain the average capacity of the FTN system. On the basis, an expression of the average capacity of the super-Nyquist optical transmission system under a Gamma-Gamma turbulent channel under a QPSK modulation format is deduced according to QPSK modulation characteristics. The construction of the super-Nyquist optical transmission system effectively improves the spectral efficiency of the system.)

1. Method for calculating average channel capacity of FTN transmission system under double-Gamma turbulent channelthe method is characterized in that the average capacity C of the super-Nyquist system is calculated after the channel capacity C is used for periodic normalization_FTNFurther calculating to obtain the average capacity C under the QPSK modulation format_FTN-QPSKAnd finally, obtaining the average capacity of the super-Nyquist transmission system under the Gamma-Gamma turbulent flow channel according to the Gamma-Gamma turbulent flow distribution model.

2. The method for calculating the average channel capacity of the FTN transmission system under the double-Gamma turbulent channel according to claim 1, is characterized by comprising the following specific steps:

Step 1: at the transmitting end, the binary information sequence a_nFirstly, mapping the signals into complex signals respectively, and generating FTN signals x (t) after the signals pass through an FTN shaping filter;

wherein, a_nis a complex symbol, E_SIs the sign pulse energy, g (t) is the signal pulse shape, andk is 0, ± 1, ± 2, ·, τ (0 < τ < 1) is an acceleration factor;

Two paths of FTN signals are respectively modulated onto laser through an IQ modulator to form polarization signals, and then the polarization signals are transmitted through an optical antenna; when signals are transmitted in the atmosphere, the signals are influenced by atmosphere turbulence, the light intensity fading follows Gamma-Gamma distribution, and the probability density function of the signals is f (h);

Step 2: the laser signal reaches a receiving end after atmospheric transmission, after coherent receiver and sampling, the pulse shaping filter is used for generating an FTN signal with tau T as a period, and then intersymbol interference caused by FTN is compensated through a digital signal processing technology; the received signal can then be expressed as:

Wherein, y_kFor the signal sampled by the matched filter at the receiving end, g_n-kFor the introduced intersymbol interference impulse response, z_kIs zero mean additive white Gaussian noise with variance of sigma²＝N₀2; i is the corresponding light intensity when the transmission signal is 1, h is the fading coefficient of the light intensity of the signal light, eta is the photoelectric conversion coefficient, P_tIs the average emitted optical power, P_LIs the local oscillator optical power;

And step 3: according to a transmission model of the FTN system, firstly, calculating a channel capacity C of the system under a Gaussian channel; calculating the average capacity C of the FTN system after the obtained C period is normalized_FTNThe average capacity C of the FTN-QPSK system is deduced according to the channel capacity characteristics of QPSK modulation_FTN-QPSKFinally, the average capacity C of the FTN communication system under the Gamma-Gamma turbulent flow channel is obtained by utilizing the Meijer G function property_FTN-GGNamely:

Technical Field

The invention relates to a method for calculating the average capacity of an FTN transmission system under a Gamma-Gamma turbulent flow channel, belonging to the technical field of wireless optical communication.

Background

In recent years, Free Space Optical communication (FSO) has become a significant research hotspot due to advantages such as large communication capacity, high transmission rate, and good security. With the development of 5G and 6G and the increasing technical demands of information networks for high capacity and high spectral efficiency, more technologies need to be developed to improve the transmission performance of wireless optical communication. Researchers have made a lot of research on this problem, such as using wavelength division multiplexing, high modulation formats, and the like. However, as the modulation order increases, the sensitivity of the system decreases. The fast peak Nyquist (FTN) technique is a non-orthogonal transmission technique, and its high spectral efficiency makes it one of the important techniques for high-speed communication links. The FTN technology is applied to the FSO communication system to improve the spectrum efficiency of the system, and is an effective solution.

although FSO has many advantages, when a laser signal is transmitted in an atmospheric channel, the signal is easily affected by atmospheric turbulence, which may cause phenomena such as spot drift, light intensity fluctuation (flicker), etc. of a transmitted light beam, and scattering and refraction caused by aerosol in the atmosphere may also cause delay and pulse broadening of the signal, further causing problems such as increase of bit error rate and reduction of channel capacity of a wireless optical communication system, thereby affecting the application of FTN technology in a free space optical communication system. Therefore, it is necessary to study the influence of the atmospheric turbulence intensity, the receiver aperture diameter and the transmission distance of the FTN after the signal waveform is transmitted through the atmospheric channel after the FTN artificially introduces the inter-symbol interference on the average bit error rate and the average capacity performance of the system.

Disclosure of Invention

The invention aims to introduce the FTN technology into a Gamma-Gamma turbulent flow channel, so that the symbol rate is greater than the Nyquist rate, the average capacity of the system is effectively improved, and the performance of an atmospheric transmission system is improved.

the invention discloses a method for calculating average channel capacity of an FTN transmission system under a double-Gamma turbulent channel, which is characterized in that the average capacity C of a super-Nyquist system is calculated after periodic normalization is carried out by utilizing the channel capacity C_FTNFurther calculating to obtain the average capacity C under the QPSK modulation format_FTN-QPSKand finally, obtaining the average capacity of the super-Nyquist transmission system under a Gamma-Gamma turbulent flow channel according to a Gamma-Gamma turbulent flow distribution model.

the invention has the advantages that: by utilizing the non-orthogonal characteristic of the FTN technology, the limitation of the Nyquist criterion is broken through, and the spectral efficiency of the Gamma-Gamma communication system is effectively improved. The average capacity of the FTN system is calculated by utilizing the channel capacity of the system, so that the average capacity of the FTN communication system under a Gamma-Gamma turbulent flow channel can be deduced, the influence of parameters such as turbulent flow intensity, transmission distance, receiver aperture diameter, average signal-to-noise ratio and the like on the system performance is further effectively analyzed, and a certain reference value is provided for the design of a wireless optical communication system in actual engineering.

Drawings

FIG. 1 is a block diagram of an FSO communication system based on FTN-QPSK signals, FIG. 2 is a flow chart of the method of the present invention, FIG. 3 is the BER of the system under different transmission distances L, FIG. 4 is the BER and C when γ is 10dB_FTNIn relation to the transmission distance, FIG. 5 shows BER and C when γ is 15dB_FTNIn relation to the transmission distance, FIG. 6 shows BER and C when γ is 20dB_FTNthe relation to the transmission distance.

Detailed Description

The invention discloses a method for calculating average channel capacity of an FTN transmission system under a double-Gamma turbulent channel, which is characterized in that the average capacity C of a super-Nyquist system is calculated after periodic normalization is carried out by utilizing the channel capacity C_FTNFurther calculating to obtain the average capacity C under the QPSK modulation format_FTN-QPSKAnd finally, obtaining the average capacity of the super-Nyquist transmission system under a Gamma-Gamma turbulent flow channel according to a Gamma-Gamma turbulent flow distribution model.

in the invention, the average capacity C of the FTN system is calculated after the channel capacity C is used for periodic normalization_FTNFurther calculating to obtain the average capacity C under the QPSK modulation format_FTN-QPSKFinally, obtaining the average capacity of the super-Nyquist transmission system under a Gamma-Gamma turbulent flow channel according to a Gamma-Gamma turbulent flow distribution model; the method comprises the following specific steps:

Step 1: at the transmitting end, the binary information sequence a_nFirstly, the signals are respectively mapped into complex signals, and the complex signals are processed by an FTN shaping filter to generate FTN signals x (t), namely:

wherein, a_nis a complex symbol, E_SIs the sign pulse energy, g (t) is the signal pulse shape, andk is 0, ± 1, ± 2, ·, τ (0 < τ < 1) is an acceleration factor.

The two FTN signals are modulated to laser through an IQ modulator to form polarization signals, and then the polarization signals are transmitted through an optical antenna. When signals are transmitted in the atmosphere, the signals are influenced by atmosphere turbulence, the light intensity fading follows Gamma-Gamma distribution, and the probability density function of the signal is f (h).

Step 2: the laser signal reaches a receiving end after atmospheric transmission, after coherent receiver and sampling, the pulse shaping filter is used for generating FTN signal with period of tau T, and then the digital signal processing technology is used for compensating the intersymbol interference caused by FTN. The received signal can then be expressed as:

Wherein, y_kFor the signal sampled by the matched filter at the receiving end, g_n-kFor the introduced intersymbol interference impulse response, z_kis zero mean additive white Gaussian noise with variance of sigma²＝N₀/2. I is the corresponding light intensity when the transmission signal is 1, h is the fading coefficient of the signal light intensity, eta is the photoelectric conversion coefficient, P_tIs the average emitted optical power，P_LIs the local oscillator optical power.

and step 3: according to a transmission model of the FTN system, firstly, calculating the channel capacity C of the system under a Gaussian channel; calculating the average capacity C of the FTN system after normalizing the obtained C period_FTNThe average capacity C of the FTN-QPSK system is deduced according to the channel capacity characteristics of QPSK modulation_FTN-QPSKfinally, the average capacity C of the FTN communication system under the Gamma-Gamma turbulent flow channel is obtained by utilizing the Meijer G function property_FTN-GGNamely:

The invention provides a method for calculating the average capacity of an FTN transmission system under a Gamma-Gamma turbulent flow channel. The method utilizes the channel capacity of the FTN system and the channel capacity characteristic of the QPSK modulation format to calculate the average capacity of the FTN-QPSK system, and the introduction of the FTN technology greatly improves the spectrum efficiency of the atmospheric turbulence system. The present invention will be described in detail below with reference to specific embodiments thereof.

The invention is achieved by the following technical measures:

1. The basic assumption is that:

the present invention assumes an average emitted optical power P_tlocal oscillator optical power P_LOthe channel is a flat slow fading channel. Assuming that the background light has been filtered out by the filter, only polarization noise is considered. This assumption is typical of such systems and is not a particular requirement of the present invention.

2. the method comprises the following specific implementation steps:

Step 1: at the transmitting end, the binary sequence a_nand forming an FTN complex signal through QPSK mapping and an FTN shaping filter. Setting symbol period as tau (tau is more than 0 and less than 1) as acceleration factor), and X, Y two branches are not orthogonal any more, and FTN complex signal is expressed as:

wherein, a_nIs a complex symbol, E_SIs a symbolsignal pulse energy, g (t) is signal pulse waveform, andk ═ 0, ± 1, ± 2, ·. Fourier transforming G (t) into G (f), normalized power signal power spectrum density | G (f) & ltY & gt²And folding spectrum | G_fo(f)|²The relationship of (c) can be expressed as:

Laser signals are subject to atmospheric turbulence when transmitted in an atmospheric channel. Let y (t) be hs (t) + z (t) as the optical antenna reception signal. Where z (t) represents a noise signal. h is the light intensity fading coefficient caused by the atmospheric turbulence, and the probability density function obeys the distribution as follows:

Wherein, K_v(. cndot.) is a V-order second-class modified Bessel function, Gamma (. cndot.) is a Gamma function, and alpha and beta are respectively a large-scale scattering coefficient and a small-scale scattering coefficient. α, β can be expressed as:

In the formula, the Rytov variance Is the structural constant of the refractive index of the atmosphere;d isThe diameter of the aperture of the receiver, lambda is the wavelength, and L is the transmission distance of the laser beam.

Step 2: the laser signal reaches a receiving end after atmospheric transmission, and after coherent receiver and sampling, the pulse shaping filter is used for generating an FTN signal with tau T as a period, and then intersymbol interference caused by FTN is compensated through a digital signal processing technology. The received signal can then be expressed as:

Wherein, y_kFor the signal sampled by the matched filter at the receiving end, g_n-kFor the introduced intersymbol interference impulse response, z_kis zero mean additive white Gaussian noise with variance of sigma²＝N₀/2. I is the corresponding light intensity when the transmission signal is 1, h is the fading coefficient of the light intensity of the signal light, eta is the photoelectric conversion coefficient, P_tIs the average emitted optical power, P_Lis the local oscillator optical power.

And step 3: FTN system capacity C, which can be derived from the FTN transmission model of equation (6), is represented as:

Wherein, y^NTo receive a sequence, a^Nfor transmit sequences and for Gaussian distributions, I (y)^N；a^N) Is y^NAnd a^NAmount of mutual information between, N being the length of the sequence, P_a(a) For transmitting a sequence a^NThe probability of (c), sup is the upper bound of the distribution,G (λ) is the power spectral density of the intersymbol interference, expressed as:

The capacity of the FTN system can be obtained after C period normalization:

The average capacity of the FTN system can be obtained by substituting equations (7) and (8) into equation (9), that is:

C_FTNThe achievable transmission rate of a transmission system incorporating FTN technology is provided, with this concept, for a particular order-M modulation format, the achievable rate of an FTN-QPSK system employing QPSK modulation is given according to equation (10):

Wherein γ is 2 η²I²P_LP_t/N₀Is the signal to noise ratio.

Then the reaction is carried out by the formula (3), the formula (11),And the operation property of the Meijer G function can obtain the average capacity of the FTN-QPSK transmission system under the Gamma-Gamma channel:

In order to further illustrate the influence of parameters such as turbulence intensity, transmission distance, receiver aperture diameter, average signal-to-noise ratio and the like on the system bit error rate and average capacity, the method is subjected to simulation verification by adopting a Monte Carlo (Monte Carlo) method. The simulation conditions are as follows, (1) the transmitted signal is modulated by QPSK; (2) average emitted light power P_t1, photoelectric conversion efficiency η 0.5, wavelength λ 1550nm, transmission rate 22G baud, acceleration factor τ 0.75, pulse energy E_s2, local oscillator optical power P_LO1 is ═ 1; (3) turbulence intensity:Take values of 5 × 10 respectively^-14m^-2/3， 1.13×10^-13m^-2/3And 5X 10^-13m^-2/3。

Fig. 3 is a graph of the variation of the bit error rate with the OSNR under three conditions of turbulent intensity when L is 1500m,2000m and 2500 m. It can be seen that the transmission distance has less effect on BER as the turbulence intensity increases. When L is 1500m,2000m, under the condition of weak turbulencethe average bit error rate performance of the method is respectively superior to that under the condition of medium turbulence1.1dB and 1.2 dB.

FIG. 4 shows the aperture diameter (D0.2 m,0.1m, 0.05m) and transmission distance L versus BER and C under different turbulence intensity conditions at γ of 10dB_FTNThe influence of (c). As can be seen from fig. 4, the aperture diameter has less effect on BER and average capacity performance at lower average osnr. It can be seen from fig. 4.(a) that when γ is 10dB, the system BER performance is poor even atWhen D is 0.2m, system BER>3.8×10^-3Normal transmission of data cannot be satisfied. Meanwhile, as can be seen from fig. 4 (b), the average capacity is less affected by the transmission distance; when D is 0.1m,0.2m, inUnder the condition, when the transmission distance reaches a certain value, the average capacity is not reduced by the increase of the transmission distance. When D is 0.05m,when the transmission distance is increased from 800m to 3500m, the average capacity is reduced by 0.61 bit/s/Hz; and when the transmission distance is 3500m, the system can transmit 1.21 bit/s/Hz.

in order to make the data normally transmittable, the average signal-to-noise ratio can be increased appropriately. Fig. 5 and 6 show the effect of aperture diameter (D0.2 m,0.1m, 0.05m) and transmission distance on BER and average capacity under conditions of 15dB for γ and 20dB for γ and different turbulence intensities, respectively. From fig. 5, (a), it can be seen that when γ is 15dB, there is a certain improvement in system BER performance compared to fig. 4, (a). In thatwhen D is 0.2m, BER<3.8×10^-3Then, the maximum transmission distance can reach 2400 m; however, when transmitting longer distances (2600m), the BER>3.8×10^-3. Therefore, it is necessary to further improve the average signal-to-noise ratio and improve the system error performance. In fig. 6, (a) γ is 20dB, and D is 0.2m,Under the condition, when 3600m is transmitted, the average BER of the system<3.8×10^-3. Meanwhile, as can be seen from fig. 5 (b), as the average signal-to-noise ratio increases, the average capacity also increases significantly. When D is 0.05m and L is 1500m, the process is carried outUnder the condition, the average capacity is 2.45bit/s/Hz, and the average capacity is improved by about 0.5bit/s/Hz compared with gamma which is 10 dB. Higher average capacity performance can be obtained when γ is 20dB in fig. 6 (b); under three different turbulence intensity conditions with three aperture diameters (D ═ 0.05m,0.1m,0.2m), the average capacity of the FTN transmission system can exceed 2.07bit/s/Hz when the transmission distance is increased from 800m to 3500 m.

From the above description of the embodiments, it is clear for a person skilled in the art that the present invention can be implemented in software or by hardware. Based on the above understanding, the contribution of the technical solution of the present invention to the prior art can be realized by software or hardware to execute the method of the embodiment of the present invention.