CN114204990B - Adaptive MIMO-FSO multi-mode transmission method based on channel capacity - Google Patents
Adaptive MIMO-FSO multi-mode transmission method based on channel capacity Download PDFInfo
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- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
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- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
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Abstract
The invention discloses a self-adaptive MIMO-FSO multi-mode transmission method based on channel capacity, which comprises the steps of establishing an FSO composite atmospheric channel model; establishing a baseband signal model of the self-adaptive MIMO-FSO system; calculating the average channel capacity function formula when the system is respectively under the space multiplexing, diversity and mixed mode; obtaining average channel capacity data of three modes under different scenes; establishing a receiving end signal-to-noise ratio threshold lookup table for mode switching based on data; calculating the instantaneous signal-to-noise ratio of a receiving end under the conditions of different atmospheric turbulence intensities, comparing the signal-to-noise ratio with the available signal-to-noise ratio threshold value in the lookup table, and selecting the applicable optimal transmission mode; the receiving end transmits the selected mode to the self-adaptive control module of the transmitting end through the feedback link, and the self-adaptive control module is switched continuously among different modes. The invention can improve the system throughput to the maximum extent and ensure the reliability of the system in the whole range of the signal-to-noise ratio.
Description
Technical Field
The invention belongs to the technical field of wireless optical communication (FSO), and particularly relates to a self-adaptive MIMO-FSO multi-mode transmission method based on channel capacity.
Background
Wireless laser communication, also known as free space optical communication (FSO), provides a point-to-point wireless connection by using infrared laser transmitters. Compared with wireless communication, the wireless communication system has the advantages of large bandwidth, small size, good confidentiality, convenience and flexibility in construction and the like. However, with the rapid development of services such as big data, cloud computing, internet of things and the like, the existing communication network also faces many challenges such as channel blockage, insufficient transmission capacity and the like. Seamless connectivity of wireless laser communication and future communication networks has become a necessary trend.
Laser signals are affected by various factors in the complex atmospheric environment as they propagate through the atmospheric channel. In the optical communication process, due to the fluctuation of temperature and pressure in the atmosphere, the refractive index changes, and finally, the rapid fluctuation (called flicker) of the transmission signal, namely, the atmosphere turbulence, is caused. Thermal expansion, dynamic wind loading, weak earthquakes, etc. all cause building sway, which results in the vibration of the transmitter's beam, causing alignment errors between the transmitter and receiver, known as pointing errors. In addition, the light beam propagating in free space is also absorbed, scattered, or moved by the atmosphere, which makes the optical signal worse, i.e., the atmospheric path loss. These factors can cause the FSO link quality to change over time, which severely affects the reliability and throughput of the communication.
In recent years, the air channel influence and suppression technology has been the hot spot of FSO communication research. The self-adaptive transmission technology provides a feasible solution for inhibiting the influence of atmospheric turbulence on laser signal transmission and improving the communication performance of the system under various channel conditions. In a MIMO link, different spatial transmission strategies may provide different degrees of multiplexing and diversity performance, which makes the design of link adaptive transmission strategies more challenging. Meanwhile, a new adaptive dimension is introduced in a complex atmospheric channel, so that switching between different spatial modes to obtain a high data rate also becomes a key technical problem. MIMO modes are roughly divided into three categories: spatial multiplexing, spatial diversity, and hybrid modes. In spatial multiplexing mode, the system transmits independent parallel data streams through multiple transmit apertures to increase the data rate. In spatial diversity mode, the system transmits the same data stream through multiple transmit apertures to extract the diversity gain. In the hybrid mode, a trade-off is made between diversity and multiplexing gain to ensure that the link is balanced between reliability and data rate.
Disclosure of Invention
The invention aims to provide a channel capacity-based adaptive MIMO-FSO multi-mode transmission method, which solves the problem that a free space optical communication system is low in communication reliability and throughput in a composite atmospheric channel.
The technical scheme adopted by the invention is as follows: the adaptive MIMO-FSO multi-mode transmission method based on the channel capacity comprises the following steps:
step 1, establishing an FSO (free space optical) composite atmospheric channel model, and giving an irradiance probability density function of the composite channel model by considering the combined influence of atmospheric turbulence, pointing error and path loss;
and 7, continuously working in a feedback mode to ensure that the system performs continuous self-adaptive mode switching.
The present invention is also characterized in that,
the step 1 specifically comprises the following steps: the light intensity fluctuation is described by a Malaga atmospheric turbulence probability density function, and the adjusting parameters are respectively used for simulating a Gamma-Gamma distribution channel sigma I 2 =0.5, lognormal distribution channel σ I 2 =0.2 and K distribution channel σ I 2 The probability density function of the fluctuation of the light intensity of the Malaga atmospheric turbulence is specifically as follows:
in the formulae (1) to (3), α is a positive parameter; beta is the number of the natural fading parameters; k n (.) is a second class modified Bessel function of order n; line-of-sight transmitted independent scattered component
Has an average power of
The average power of the total scattered portion is
Rho is the scattering power coupled to the line-of-sight part, and is greater than or equal to 0 and less than or equal to 1; Ω' is the coherent average power; gamma (·) is a Gamma function;
irradiance h taking into account pointing error p Is expressed as:
in formula (4), g = w zeq /(2σ s ) Is the equivalent beam radius w at the receiver zeq Quasi deviation sigma from jitter s The ratio of (A) to (B); a. The 0 ＝[erf(v)] 2 Where erf (·) is an error function,
a is the radius of the circular detection aperture, w z Is the beam waist radius;
path loss h l Is expressed as:
h l ＝exp(-σL) (5)
in the formula (5), σ is an attenuation coefficient, and L is a path length;
and (3) giving an irradiance probability density function of the composite channel model by considering the joint influence of atmospheric turbulence, pointing error and path loss:
the number of the sending end and the receiving end of the self-adaptive MIMO-FSO system in the step 2 is respectively M and N, and M independent data signals are generated to be x under the spatial multiplexing A ＝(x 1 ,x 2 ,...,x M ) T (ii) a In diversity mode, M identical data signals are generated as x B ＝(x 1 ,x 1 ,...,x 1 ) T (ii) a In a hybrid mode, t parallel data signals are transmitted over M transmission apertures, M and N are multiples of t, and t repetition codes are transmitted over M/t different sets of sequences, the transmission signal being x C ＝(x 1 ,x 2 ,...,x t ) T Wherein x is i Representing a repeating signal stream at M/t.
The baseband signal model of the adaptive MIMO-FSO system established in the step 2 is as follows:
in the formula (8), P T Is the total optical emission power, η is the electro-optic conversion constant; w is within the range of R N Represents additive white Gaussian noise, and w i ～N(0,N 0 /2),i＝1,2,...,N，N 0 Representing a bilateral power spectral density; h e R M×N Representing the fading channel matrix, whose element h ij (i =1, 2.. N, j =1, 2.. M) represents a channel gain between the jth transmit aperture and the ith receive aperture.
The specific steps of step 3 are:
step 3.1, in the space multiplexing, different antennas send different information; the maximum degree of freedom is min (M, N) = M, and the channel matrix is simplified to a diagonal form:
H＝diag{h 1 ,h 2 ,...,h M } (11)
substituting the expression (11) into the instantaneous channel capacity expression to obtain the instantaneous channel capacity in the spatial multiplexing mode as follows:
substituting the expressions (12) and (6) into the expression of the average channel capacity to obtain the function formula of the average channel capacity of the system in the spatial multiplexing mode, wherein the function formula is as follows:
from the MeijerG function properties, equation (13) translates to:
step 3.2, in the diversity mode, different antennas send the same information; in this mode, equation (8) in step 2 is written as:
the channel matrix H is written in the following format:
substituting equation (16) into the instantaneous channel capacity expression yields the instantaneous channel capacity in diversity mode as:
substituting the expressions (17) and (6) into the average channel capacity expression, the average channel capacity function expression of the score set mode is:
by the nature of the MeijerG function, equation (18) is written again:
step 3.3, combining diversity and spatial multiplexing in a mixed mode, and constructing t parallel streams through M transmitting holes; the repetition codes are transmitted over M/t different apertures; the ith received signal at the ith stream is:
in the formula (20), h ij l Is the channel coefficient from the jth transmitting hole to the ith receiving hole in the ith stream, and the channel matrix H is:
substituting equation (21) into the instantaneous channel capacity expression, the instantaneous channel capacity of the mixed mode is:
substituting the expressions (22) and (6) into the average channel capacity expression to obtain the average channel capacity function expression of the mixed mode as follows:
by nature of the MeijerG function, equation (23) is expressed as:
the invention has the beneficial effects that: the adaptive MIMO-FSO multi-mode transmission method based on the channel capacity, provided by the invention, supports three modes of MIMO space diversity, multiplexing and mixing, provides the average channel capacity of the three modes at different receiving and transmitting end numbers, different turbulence intensities and different weather conditions, establishes a receiving end signal-to-noise ratio threshold lookup table for carrying out mode switching, and determines a switching threshold. The method of the invention can adaptively configure the appropriate MIMO technology, improve the system throughput to the maximum extent and ensure the reliability of the system in the whole signal-to-noise ratio range.
Drawings
Fig. 1 (a) is a graph of the average channel capacity of a 4 × 4MIMO system with K distributed channels in an embodiment of the present invention;
fig. 1 (b) is a graph of the average channel capacity of a 6 × 6MIMO system with K distributed channels in an embodiment of the present invention;
FIG. 2 (a) is a diagram of w of K distribution channels in an embodiment of the present invention z /a＝10,σ s A 4 × 4MIMO system average channel capacity curve of/a = 1.5;
FIG. 2 (b) is a diagram of w of K distribution channels in an embodiment of the present invention z /a＝5,σ s A 4 × 4MIMO system average channel capacity curve of/a = 2;
FIG. 3 (a) is a graph of the average channel capacity of a 4 × 4MIMO system with Gamma-Gamma distribution channels according to an embodiment of the present invention;
fig. 3 (b) is a graph of the average channel capacity of a 4 × 4MIMO system of Lognormal distribution channels in the embodiment of the present invention;
FIG. 4 (a) is a graph of the average channel capacity of a 4 × 4MIMO system with Gamma-Gamma distribution channels in haze days according to an embodiment of the present invention;
FIG. 4 (b) is a graph of the average channel capacity in foggy days for a 4 × 4MIMO system with Gamma-Gamma distribution channels in an embodiment of the present invention;
fig. 5 is a block diagram of an adaptive MIMO-FSO communication system in an embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a self-adaptive MIMO-FSO multi-mode transmission method based on channel capacity, which is implemented according to the following steps:
a complete adaptive MIMO-FSO system comprises: the system comprises a transmitting end, a receiving end, an adaptive control module and a feedback link unit. The transmitting end sends information through M antennas, and the receiving end receives information through N antennas. The self-adaptive control module is positioned at the transmitting end, and the feedback links are arranged at the transmitting end and the receiving end. In operation, in the case of different levels of atmospheric turbulence, the receiving end first calculates the instantaneous signal-to-noise ratio (SNR), which is a function of fading. The signal-to-noise ratio is compared to a signal-to-noise ratio threshold available in a look-up table (LUT) and the best transmission mode (i.e., one of spatial multiplexing, diversity, hybrid modes) is selected accordingly. The selected mode is then communicated to the transmitting end via a feedback link and adaptively switched between different MIMO modes. The main method steps of the adaptive modulation strategy are as follows:
step 1, establishing an FSO composite atmospheric channel model. The light intensity fluctuation is described by a Malaga atmospheric turbulence probability density function, and the adjusting parameters can be respectively used for simulating a Gamma-Gamma distribution channel (sigma) I 2 = 0.5), lognormal distribution channel (σ) I 2 = 0.2) and K distribution channel (σ) I 2 = 2). The probability density function of the light intensity fluctuation of the Malaga atmospheric turbulence is specifically as follows:
wherein α is a positive parameter; beta represents the number of natural fading parameters; k n () is a second class modified Bessel function of order n; line-of-sight transmitted independent scattered component
Has an average power of
The average power of the total scattered part is
Rho is the scattering power coupled to the line-of-sight part, and is greater than or equal to 0 and less than or equal to 1; Ω' is the coherent average power; Γ () is a Gamma function.
Irradiance h taking into account pointing error p Is expressed as:
wherein g = w zeq /(2σ s ) Is the equivalent beam radius w at the receiver zeq Quasi deviation sigma from jitter s In-line with the above and (4) the ratio. A. The 0 ＝[erf(v)] 2 Where erf (·) is an error function,
a is the radius of the circular detection aperture, w z Is the beam waist radius.
Path loss h l Is expressed as:
h l ＝exp(-σL) (5)
where σ is the attenuation coefficient and L is the path length.
Considering the joint influence of various factors such as atmospheric turbulence, pointing error and path loss, and giving an irradiance probability density function of the composite channel model:
and 2, establishing a baseband signal model of the self-adaptive MIMO-FSO system. The number of the transmitting end and the receiving end of the self-adaptive MIMO-FSO system is M and N respectively. Under spatial multiplexing, M independent data signals are generated as x A ＝(x 1 ,x 2 ,...,x M ) T . In diversity mode, M identical data signals are generated as x B ＝(x 1 ,x 1 ,...,x 1 ) T . In a hybrid mode, t parallel data signals are transmitted over M transmission apertures, M and N are multiples of t, and t repetition codes are transmitted over M/t different sets of sequences, the transmission signal being x C ＝(x 1 ,x 2 ,...,x t ) T Wherein x is i Representing a repetitive signal flow at M/t. The baseband signal model is:
wherein, P T Is the total optical emission power, and η is the electro-optic conversion constant. w is formed by R N Represents additive white Gaussian noise, and w i ～N(0,N 0 /2),i＝1,2,...,N，N 0 Representing the bilateral power spectral density. H e R M×N Representing a fading channel matrix, whose element h ij (i =1, 2.. N, j =1, 2.. M) represents a channel gain between the jth transmit aperture and the ith receive aperture.
And 3, deriving average channel capacity function formulas when the system is respectively under spatial multiplexing, diversity and mixed mode according to the formula (9). In equation (9), t =1 and t = M correspond to the average channel capacities of the diversity mode and the spatial multiplexing mode, respectively; when t belongs to the divisor set of M and t ≠ 1, t ≠ M, equation (10) is an expression of instantaneous channel capacity, corresponding to the average channel capacity of the mixed mode (see steps 3.1-3.3 for specific derivation).
The method comprises the following specific steps:
and 3.1, in the spatial multiplexing, different antennas send different information. The maximum degree of freedom is min (M, N) = M, and the channel matrix is simplified to a diagonal form:
H＝diag{h 1 ,h 2 ,...,h M } (11)
the instantaneous channel capacity in the spatial multiplexing mode obtained by substituting equation (11) for equation (10) is:
when equation (12) and equation (6) are substituted for equation (9), the average channel capacity function of the system in the multiplexing mode is given by:
by the MeijerG function property, equation (13) can be converted to:
step 3.2, in the diversity mode, different antennas send the same information. In this mode, equation (8) in step 2 can be written as:
the channel matrix H may be written in the following format:
the instantaneous channel capacity in the diversity mode obtained by substituting equation (16) for equation (10) is:
substituting equations (17) and (6) for equation (9), the average channel capacity function of the score set mode is:
by the nature of the MeijerG function, equation (18) is written again:
and 3.3, combining diversity and spatial multiplexing by using a mixed mode, and constructing t parallel streams through M transmitting holes. The repetition codes are transmitted over M/t different apertures. The ith received signal at the ith stream is:
wherein h is ij l Is the channel coefficient from the jth transmitting hole to the ith receiving hole in the ith stream, and the channel matrix H is:
when equation (21) is substituted into equation (10), the instantaneous channel capacity of the hybrid mode is:
substituting the formula (22) and the formula (6) into the formula (9) to obtain a mixed-mode average channel capacity function formula as follows:
by nature of the MeijerG function, equation (23) can be expressed as:
and 4, obtaining average channel capacity data of three modes under different receiving and transmitting terminal antenna numbers, different Malaga turbulence distribution channels and different weather conditions (clear days, fog days and haze days), and establishing a receiving terminal signal-to-noise ratio threshold value lookup table for mode switching according to the average channel capacity data.
And step 5, under the condition of different atmospheric turbulence intensities, the receiving end calculates the instantaneous signal-to-noise ratio which is a fading function. The snr is compared to the snr thresholds available in the look-up table and the best transmission mode for the snr is selected.
And 6, the receiving end transmits the selected mode to the self-adaptive control module of the transmitting end through the feedback link, and switching is carried out among different modes.
And 7, continuously working in a feedback mode to enable the system to continuously switch the self-adaptive mode.
Fig. 1 (a) and (b) show the average channel capacities of three modes of the 4 × 4MIMO system and the 6 × 6MIMO system under the K distribution, respectively. The LUT is constructed to specify the signal-to-noise ratio region that should be used for each transmission mode (see table 1). FIG. 1 shows that in 4 × 4MIMO system, the average SNR γ is received 0 <24dB, the diversity mode has significant advantages, which can provide the best under poor channel conditionsHigh data rates. When the SNR is between 24-33 dB, a hybrid mode is used to ensure that the link is balanced between reliability and data rate. When the SNR is greater than 33dB, the multiplexing mode is selected to ensure the highest data rate. In a 6 × 6MIMO system, diversity mode should be activated for SNR values less than 22.4dB. And a hybrid mode with t =2 or t =3 may be used with SNR ranging from 22.4 to 36.7dB. For SNR values greater than 36.7dB, the multiplexing mode may be selected.
TABLE 1 adaptive SNR threshold lookup table for different apertures under K distribution
Table 1 can see that the performance of 4 × 4 and 6 × 6MIMO systems is similar, but the mixed mode of the 6 × 6MIMO system provides two areas to provide more flexibility (see t =2 and t =3 in fig. 1 (b)). When gamma is 0 The multiplexing mode for the 40db,6 x 6MIMO link can achieve a data rate of 7.5bit/s, while this value for the 4 x 4MIMO link is equal to 6bit/s. It is clear that the data rate of a 6 x 6MIMO link is higher than in the 4 x 4MIMO case. In addition, the operating mode division of the SNR region is also different, and it can be seen that γ is the diversity mode of the 4 × 4MIMO link 0 <24dB, but for the diversity mode of the 6 x 6MIMO link, the signal-to-noise ratio γ 0 <22.4dB. Indicating that the greater the number of transmit and receive apertures, the smaller the signal-to-noise ratio required to employ diversity mode.
FIGS. 2 (a), (b) show different standard deviations σ of jitter s And different beam waist radii w z Average channel capacity of the 4 × 4MIMO system. In conjunction with fig. 1 (a), a LUT can be built as shown in table 2. From the numerical results in combination with the graph, when w z A is 5, σ s As aa increases from 1.5 to 2, the minimum signal-to-noise ratio required for the system to operate in each mode becomes large. When sigma is s A is 1.5,w z As aa increases from 5 to 10, the signal-to-noise threshold for each mode of the system also increases and increases by a much greater degree than in the previous case. For example, only change σ s At/a, the signal-to-noise threshold in diversity mode increases from 24dB to 25.5dB,however, only change w z The signal-to-noise threshold at/a increases from 24dB to 34.2dB. With a s And w z The increase of the number of the effective light beams received by the receiving end becomes less, and the communication quality becomes poor.
TABLE 2 different w under K distribution z And σ s 4 x 4MIMO system self-adaptive transmission signal-to-noise ratio threshold lookup table
FIGS. 3 (a) and (b) are Gamma-Gamma (σ), respectively I 2 = 0.5) distribution and Lognormal (σ) I 2 = 0.2) average channel capacity of three modes of a 4 × 4MIMO system under distribution. As can be seen from FIG. 3 (a), in a medium turbulent environment, when gamma is present 0 <6.4dB, the average channel capacity of the diversity mode has a weak advantage. When gamma is equal to 0 >6.4dB, the average channel capacity for the reuse mode is clearly much higher than for the diversity and hybrid modes as the signal-to-noise ratio increases. As can be seen in fig. 3 (b), in the environment of weak turbulence, the average channel capacity of the multiplexing mode is always at the highest position, and the rising speed is fast. However, the capacity of the diversity mode is much lower than the other two and changes slowly. An LUT (see table 3) for three distributions of Malaga atmospheric turbulence was constructed in conjunction with fig. 1 (a).
Table 3 adaptive transmission snr threshold lookup table for 4 × 4MIMO system under three turbulence distributions of Malaga channel
From Table 3, it can be seen that the flicker index σ is dependent on the intensity I 2 The environment of the channel is increasingly poor. In this case, the advantage of the diversity mode in a poor channel environment is more obvious. Thus, when in the K profile, the LUT switches among three modes to achieve high data rates. While with decreasing turbulence intensity, in the Lognormal distribution, the system only selects the multiplexing mode that is already sufficient to ensure the highest data rate.
Fig. 4 (a) and (b) show the average channel capacity of a 4 × 4MIMO system under Gamma-Gamma distribution in haze and fog days. In conjunction with fig. 3 (a), LUTs for different weather were constructed (see table 4). In conjunction with graph analysis, the system only works in hybrid or reuse mode during Clear weather. However, when the weather conditions become Haze and Fog, the channel environment becomes worse and worse, the operation mode of the system is switched from diversity to mixing and multiplexing as the signal-to-noise ratio increases, and the multiplexing mode has a very high average channel capacity. Also, in diversity mode of Haze, γ 0 <3.2dB, while for the diversity mode of Fog this increases to γ 0 <34dB. I.e., at Fog, the time the system is in diversity mode becomes significantly longer, which also fully accounts for the reliability of diversity mode in poor channel environments and the high data rate of multiplexing mode in better communication environments.
Fig. 5 is a block diagram of an adaptive MIMO-FSO communication system. The transmitting end sends information through M antennas, and the receiving end receives information through N antennas. The self-adaptive control module is positioned at the transmitting end, and the feedback links are arranged at the transmitting end and the receiving end. In operation, in the case of different levels of atmospheric turbulence, the receiving end first calculates the instantaneous signal-to-noise ratio (SNR), which is a function of fading. The signal-to-noise ratio is compared to the signal-to-noise ratio threshold available in a look-up table (LUT) and the best transmission mode (i.e., one of spatial multiplexing, diversity, hybrid mode) is selected accordingly. The selected mode is then communicated to the transmitting end via a feedback link and adaptively switched between different MIMO modes
Table 4 table look-up table for adaptive snr threshold of 4 × 4MIMO system under Gamma-Gamma distribution in three weather
Claims (1)
1. The adaptive MIMO-FSO multi-mode transmission method based on the channel capacity is characterized by comprising the following steps of:
step 1, establishing an FSO (free space optical) composite atmospheric channel model, and giving an irradiance probability density function of the composite channel model by considering the combined influence of atmospheric turbulence, pointing error and path loss;
step 2, establishing a baseband signal model of the self-adaptive MIMO-FSO system;
step 3, solving average channel capacity function formulas of the system respectively under spatial multiplexing, diversity and mixed modes based on the instantaneous channel capacity expression, the average channel capacity expression, the irradiance probability density function obtained in the step 1 and the baseband signal model obtained in the step 2;
step 4, when the number of antennas at different transceiving ends, different Malaga turbulence distribution channels and different weather conditions exist, obtaining average channel capacity data of the system respectively under spatial multiplexing, diversity and mixed modes based on the average channel capacity function formula obtained in the step 3, and establishing a receiving end signal-to-noise ratio threshold lookup table for mode switching according to the average channel capacity data; selecting a mode with large average channel capacity as a current working mode all the time within the range of the signal-to-noise ratio of a receiving end;
step 5, under the condition of different atmospheric turbulence intensities, the receiving end calculates the instantaneous signal-to-noise ratio, compares the signal-to-noise ratio with the available signal-to-noise ratio threshold value in the lookup table, and selects the applicable optimal transmission mode;
step 6, the receiving end transmits the selected mode to a self-adaptive control module of the transmitting end through a feedback link, and switching is carried out among different modes;
step 7, the feedback mode continuously works to enable the system to continuously switch the self-adaptive mode;
the step 1 specifically comprises: the fluctuation of light intensity is described by a Malaga atmospheric turbulence probability density function, and the adjusting parameters are respectively used for simulating a Gamma-Gamma distribution channel sigma I 2 =0.5, lognormal distribution channel σ I 2 =0.2 and K distribution channel σ I 2 The probability density function of the fluctuation of the light intensity of the Malaga atmospheric turbulence is specifically as follows:
in the formulae (1) to (3), α is a positive parameter; beta represents the number of natural fading parameters; k n () is a second class modified Bessel function of order n; line-of-sight transmitted independent scattered components
Has an average power of
The average power of the total scattered portion is
Is coupled to the LOS component; rho is the scattering power coupled to the line-of-sight part, and is greater than or equal to 0 and less than or equal to 1; Ω' is the coherent average power; gamma (·) is a Gamma function;
irradiance h taking into account pointing error p Is expressed as:
in formula (4), g = w zeq /(2σ s ) Is the equivalent beam radius w at the receiver zeq Quasi deviation sigma from jitter s A ratio of; a. The 0 ＝[erf(v)] 2 Where erf (·) is an error function,
a is the radius of the circular detection aperture, w z Is the beam waist radius;
path loss h l Is expressed as:
h l ＝exp(-σL) (5)
in the formula (5), σ is an attenuation coefficient, and L is a path length;
and (3) giving an irradiance probability density function of the composite channel model by considering the joint influence of atmospheric turbulence, pointing error and path loss:
in the formula (6), the reaction mixture is,
is the MeijerG function;
the number of the sending end and the receiving end of the self-adaptive MIMO-FSO system in the step 2 is M and N respectively, and M independent data signals are generated to be x under the spatial multiplexing A ＝(x 1 ,x 2 ,...,x M ) T (ii) a In diversity mode, M identical data signals are generated as x B ＝(x 1 ,x 1 ,...,x 1 ) T (ii) a In a hybrid mode, t parallel data signals are transmitted over M transmission apertures, M and N are multiples of t, and t repetition codes are transmitted over M/t different sets of sequences, the transmission signal being x C ＝(x 1 ,x 2 ,...,x t ) T Wherein x is i Representing a repetitive signal flow at M/t;
the baseband signal model of the adaptive MIMO-FSO system established in the step 2 is as follows:
in the formula (8), P T Is the total optical emission power, η is the electro-optic conversion constant; w is formed by R N Represents additive white Gaussian noise, and w i ～N(0,N 0 /2),i＝1,2,...,N，N 0 Representing a bilateral power spectral density; h e R M×N Representing the fading channel matrix, whose element h ij (i =1, 2.. N, j =1, 2.... M) represents a channel gain between the jth transmit aperture and the ith receive aperture;
said step 3, according to equation (9), deriving the average channel capacity function formula when the system is under the spatial multiplexing, diversity, mixed mode, respectively, in equation (9), t =1 and t = M correspond to the average channel capacity of the diversity mode and the spatial multiplexing mode, respectively; when t belongs to the divisor set of M and t ≠ 1, t ≠ M, corresponding to the average channel capacity of the mixed mode, equation (10) is the instantaneous channel capacity expression:
the method comprises the following specific steps:
step 3.1, in the space multiplexing, different antennas send different information; the maximum degree of freedom is min (M, N) = M, and the channel matrix is simplified to a diagonal form:
H＝diag{h 1 ,h 2 ,...,h M } (11)
substituting the expression (11) into the expression of the instantaneous channel capacity obtains the instantaneous channel capacity in the spatial multiplexing mode as follows:
in formula (12), γ 0 Is the average signal-to-noise ratio;
substituting the expressions (12) and (6) into the expression of the average channel capacity to obtain the function formula of the average channel capacity of the system in the spatial multiplexing mode, wherein the function formula is as follows:
in the formula (13), h l Is the path loss; from the MeijerG function properties, equation (13) translates to:
in the formula (14), the compound represented by the formula (I),
is the MeijerG function;
step 3.2, in the diversity mode, different antennas send the same information; in this mode, equation (8) in step 2 is written as:
the channel matrix H is written in the following format:
substituting equation (16) into the instantaneous channel capacity expression yields the instantaneous channel capacity in the diversity mode as:
substituting the expressions (17) and (6) into the average channel capacity expression, the average channel capacity function expression of the score set mode is:
by the nature of the MeijerG function, equation (18) is written again:
step 3.3, combining diversity and spatial multiplexing in a mixed mode, and constructing t parallel streams through M transmitting holes; the repetition codes are transmitted over M/t different apertures; the ith received signal at the ith stream is:
in the formula (20), h ij l Is the channel coefficient from the jth transmitting hole to the ith receiving hole in the ith stream, and the channel matrix H is:
substituting equation (21) into the instantaneous channel capacity expression, the instantaneous channel capacity of the mixed mode is:
substituting the expressions (22) and (6) into the average channel capacity expression to obtain the average channel capacity function expression of the mixed mode as follows:
by nature of the MeijerG function, equation (23) is expressed as:
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