Method for evaluating channel capacity of MISO-UWOC system with timing jitter error and ocean turbulence effect

Abstract

The invention discloses a channel capacity evaluation method for an MISO-UWOC system with a timing jitter error and an ocean turbulence effect, and belongs to the technical field of underwater wireless optical communication. The method comprises the following steps: firstly, modeling a channel model of composite fading factors such as GGD ocean turbulence, FFIR implicit path loss and multipath effect, and obtaining a PDF mathematical expression fh (h) of a merged equivalent fading channel coefficient h at a target node according to an equal gain merging technology (EGC); secondly, depicting deterministic jitter by using a double Dirac function, describing random jitter by using a Gaussian distribution function, and convolving the deterministic jitter and the random jitter to obtain a PDF expression f xi (xi) of a total timing jitter error xi; and finally, deducing the channel capacity expression of the MISO-UWOC system after the EGC combination is adopted by the MISO-UWOC system by using the Shannon classical channel capacity theorem. According to the method, the defect that timing jitter is ignored in traditional underwater wireless optical communication is overcome, and the actual high-speed communication requirement is better met.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless optical communications and relates to an underwater wireless optical communication (UWOC) system using a multiple-input single-output (MISO) diversity transmission system, and a channel capacity evaluation method when the system has timing jitter errors and ocean turbulence effects. Background Art

[0002] When the laser beam in a MISO-UWOC system using a diversity transmission scheme is transmitted in an ocean environment, it is affected by complex channel fading caused by ocean turbulence and device timing jitter. Experimental test data show that among the existing probability density function (PDF) models used to describe the statistical characteristics of ocean turbulence fading, the generalized gamma distribution (GGD) can achieve an excellent fit between the measured data and the theoretical curve of the turbulent channel. Therefore, this model is often used to describe the ocean turbulence effects caused by changes in temperature and salinity gradients.

[0003] Timing jitter refers to the deviation between the actual received signal and its ideal position, and is commonly seen in high-speed communication systems. Specifically, when a system transmits high-speed data, timing errors in the system clock or oscillator waveform can limit the maximum rate of a digital I / O interface, leading to inter-symbol interference (ISI) and an increase in the bit error rate (BER). Timing jitter can be categorized as deterministic jitter and random jitter. Deterministic jitter is described using a dual-Dirac function, while random jitter can be modeled as a Gaussian process. The combined effect of these two factors constitutes total timing jitter. Timing jitter is the additional loss introduced by hardware clock errors when designing for high-speed transmission applications. Researching this issue has important engineering applications and practical value.

[0004] According to research, to date, UWOC systems generally consider the impact of fading caused by ocean turbulence on system performance, but no analysis has been conducted on the adverse effects of the objective "timing jitter" factor on system performance during actual high-speed transmission. Given the extremely high carrier frequency and high-speed transmission characteristics of UWOC (usually ≥1Gbps), it is necessary to propose a MISO-UWOC system channel capacity evaluation method that comprehensively considers timing jitter error and ocean turbulence fading, thereby providing rapid calculation support for the performance evaluation and optimization design of the UWOC system channel capacity at the theoretical level. Summary of the Invention

[0005] Purpose of the invention: In order to make up for the deficiency of the current UWOC system in the lack of consideration of the timing jitter fading factor in channel modeling, the present invention proposes a MISO-UWOC system channel capacity evaluation method that integrates timing jitter error and ocean turbulence effect. According to the derived closed-form expression of system capacity, the influence of the actual fading factor of the ocean high-speed transmission environment on the system communication rate can be measured more comprehensively and quickly from a theoretical level, thereby improving the theoretical basis for the channel capacity analysis of the UWOC system.

[0006] Technical solution: A method for evaluating the channel capacity of a MISO-UWOC system that comprehensively considers timing jitter error and ocean turbulence effects includes the following steps:

[0007] Considering the channel environment with composite fading factors such as timing jitter error, GGD ocean turbulence, and fading-free channel impulse response (FFIR) implicit path loss and multipath effects, a MISO-UWOC system with equal gain combining (EGC) technology at the receiver is considered. First, the PDF expression of the composite fading channel h after equal gain combining and the PDF expression of the timing jitter error ξ are calculated; secondly, based on the matched filter output of the received signal, the signal-to-interference-and-noise ratio of the equivalent received signal after EGC combining, which takes into account the timing jitter error and ocean turbulence effects, is calculated. Finally, the classic Shannon channel capacity theorem is used to obtain the average channel capacity of the MISO-UWOC system taking into account the above-mentioned composite fading factors after statistical averaging.

[0008] As a preferred solution, the average channel capacity of the composite fading MISO-UWOC system considering timing jitter error, GGD ocean turbulence, FFIR hidden path loss and multipath effect is The expression is as follows:

[0009]

[0010] In the above formula, the integrated current noise variance is Here T b is the symbol width of On-off Keying (OOK), Among them, K, T, B, R L They represent the Boltzmann constant, Kelvin temperature, filter bandwidth, and system load resistance respectively; ξ represents the jitter error per unit time; h is the equivalent attenuation after EGC merging; f h (h) and f ξ (ξ) are the statistical expressions of the PDFs of random variables h and ξ respectively; symbol Eξ,h [·] represents the operation of finding the mathematical expectation of random variables ξ and h.

[0011] As a preferred solution, the PDF of the equivalent channel fading h after EGC merging, which takes into account GGD ocean turbulence, FFIR implicit path loss and multipath effects, is approximately expressed as follows:

[0012]

[0013] In the above formula, Where μ1 and μ2 are the first-order and second-order origin moments of h, respectively, and Variables in the formula Here a i ,c i and b i They represent the shape parameter and scale parameter of the GGD fading distribution from the source node to the target node of the i-th branch of the MISO system. Without loss of generality, they are independent of i. N is the number of source nodes. Function d k (x,y)=Γ(x+k / y) / Γ(x), k=1,2; Γ(·) represents the gamma function; the equivalent fading coefficient h satisfies in represents the GGD turbulence attenuation coefficient experienced by the i-th branch, GG(·) represents Obey parameter a i ,b i ,c i The GGD distribution of is the matched filter output of the desired current waveform signal on the i-th branch, R is the responsivity of the photodetector, represents the received signal waveform after the pulse shaping function P(t) passes through the corresponding link FFIR, where That is, FFIR from the i-th source node to the target node, and the symbol * is the convolution operation; To satisfy the higher transcendental FoxH function with parameters m,n,p,q.

[0014] As a preferred solution, the PDF expression of the timing jitter error ξ can be expressed as follows:

[0015]

[0016] In the above formula, ξ=Δ / T b represents the jitter error per unit time, Δ represents the offset from the ideal clock during the measurement time, σ represents the random jitter deviation, and A is the jitter amplitude of the deterministic jitter error.

[0017] As a preferred solution, the signal to interference noise ratio The expression is as follows:

[0018]

[0019] As a preferred solution, the GGD ocean turbulence decay The FoxH function description of the PDF is as follows:

[0020]

[0021] In the above formula, b i is the scale parameter, a i and c i is the shape parameter, represents a random variable that follows a GGD distribution.

[0022] As a preferred solution, the non-fading channel impulse response FFIR data can be obtained by simulating photon motion using a computer Monte Carlo method under given system transceiver parameters, such as ocean water quality, transmission distance, receiver aperture, and emission light source wavelength.

[0023] Beneficial effects:

[0024] Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects: a method for evaluating the average channel capacity of a MISO-UWOC system provided by the present invention can quickly calculate the theoretical system channel capacity of the proposed MISO-UWOC system when adopting EGC merging in a complex marine communication environment that takes into account comprehensive factors such as delay jitter error, GGD ocean turbulence fading, and FFIR implicit path loss and multipath effect, thereby providing theoretical guidance for the upper-layer network planning research of the diversity transmission UWOC system. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a block diagram of the principle implementation of a MISO-UWOC system channel capacity assessment method that comprehensively considers timing jitter error and ocean turbulence effects, as proposed in the present invention;

[0026] Figure 2 This is a schematic diagram of the implementation structure of the MISO-UWOC system with timing jitter error and ocean turbulence effect. i represents the source node, DN represents the target node, From the source node SN i FFIR to the target node, d i is the length of the corresponding path (assuming they are all equal, denoted as d).

[0027] Figure 3The theoretical value of the average channel capacity of the MISO-UWOC system changes with the transmit power when the value of σ, i.e., random jitter deviation, is changed, taking into account the timing jitter error and ocean turbulence effect (the simulation parameters are uniformly set as: number of source nodes N = 4, deterministic jitter amplitude A = 0.5, transmission distance d = 13m, GGD turbulence shape parameter c = 3);

[0028] Figure 4 It is the variation of the theoretical value of the average channel capacity of the MISO-UWOC system with the transmission power when the A value, i.e. the deterministic jitter amplitude, is changed, considering the timing jitter error and ocean turbulence effect (the simulation parameters are uniformly set to: number of source nodes N = 4, random jitter deviation σ = 0.2, transmission distance d = 13m, GGD turbulence shape parameter c = 3). DETAILED DESCRIPTION

[0029] The present invention will be further described below with reference to specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0030] This invention is a method for rapidly evaluating the average channel capacity performance of a diversity transmission MISO-UWOC system in a marine communication environment that comprehensively considers complex fading factors such as high-speed transmission timing jitter errors, GGD ocean turbulence, FFIR implicit path loss, and multipath effects. Its specific implementation method and application examples are described below:

[0031] Step 1: Model the mathematical model of the received current signal that has experienced complex fading factors such as GGD ocean turbulence, FFIR hidden path loss and multipath effect. The PDF expression of the GGD random variable is converted into a higher-level transcendental FoxH function form. Based on the fact that the sum of N independent and not necessarily identically distributed GGD random variables still obeys the GGD distribution, the PDF mathematical expression f of the combined equivalent fading channel coefficient h at the target node is obtained according to the EGC merging technology. h (h);

[0032] Step 2: Use the dual Dirac function to characterize deterministic jitter and the Gaussian distribution function to describe random jitter. Convolve the two to obtain the PDF expression of the total timing jitter error ξ: ξ (ξ);

[0033] Step 3: Based on the current receiving signal model obtained in step 1, the instantaneous signal-to-interference-and-noise ratio expression is obtained under the condition that the influence of timing jitter error on signal power is considered. Shannon’s classical channel capacity theorem is then used to derive the instantaneous channel capacity of the MISO-UWOC system after EGC merging. Finally, the PDF of the equivalent fading channel coefficient h and the timing jitter error ξ obtained in steps one and two are combined to obtain the final system average channel capacity.

[0034] First, the GGD model is used to describe the ocean turbulence effect caused by the temperature and salinity gradient changes on the i-th path. Its PDF can be expressed as:

[0035]

[0036] Where b i is the scale parameter, a i and c i is the shape parameter, Γ(·) represents the gamma function. For the convenience of subsequent calculations, the above formula is rewritten as the equivalent form of the FoxH function:

[0037]

[0038] In the above formula, To satisfy the higher transcendental FoxH function with parameters m, n, p, q

[0039] According to the basic principle of matched filtering, the integrated current of the OOK signal received by the i-th branch, taking into account the inter-symbol interference caused by FFIR, at the 0th time slot interval can be expressed as

[0040]

[0041] Where b0 is the OOK symbol sent in time slot 0; is the matched filter output of the required current waveform signal on the i-th branch, T b is the OOK symbol width; is the inter-symbol interference (ISI) caused by channel time dispersion on branch i; L i is the channel memory length of the corresponding branch i, which is related to ISI; n i is the integrated current noise, with a mean of 0 and a variance of When the ocean water quality is non-turbid or the light source beam divergence angle is relatively small, the inter-symbol interference (ISI) term is relatively weak and is closely related to the useful signal term. In contrast, the interference The received signal expression at this time can be further expressed as:

[0042]

[0043] make because and is a constant, then That is h i Still obeys the generalized Gamma distribution. Therefore, h i The probability density function of is:

[0044]

[0045] According to the gain combining principle such as EGC, the mixed fading h on i branches can be i Merger, that is Therefore, the useful signal weighted term obtained by EGC merging is used The PDF of the equivalent fading coefficient h in can be approximated as

[0046]

[0047] In the above formula, μ1 and μ2 are the first and second order origin moments of h respectively. Define the function in

[0048] Next, consider the impact of receiver timing jitter error on system performance. According to the definition, timing jitter can be divided into two categories: deterministic jitter and random jitter. Deterministic jitter can be characterized by a dual Dirac function, while random jitter follows a Gaussian distribution. Specifically, the PDF of deterministic jitter can be expressed as Where δ(ξ) is the Dirac function and A is the deterministic jitter amplitude. The PDF expression of random jitter is: Where σ represents the deviation of random jitter. The total timing jitter is the convolution of deterministic jitter and random jitter. The PDF expression of the total timing jitter is:

[0049]

[0050] Because the above formula satisfies symmetry, when ξ>0, it can be written as:

[0051]

[0052] According to the received signal expression (4), the signal-to-noise ratio of the combined signal can be expressed as: In the presence of additional timing jitter error, the signal power is only (1-ξ)h 2 Part is the effective part, and the rest ξh 2 Part of it will become the interference signal on the next bit (considered as additional noise). The signal-to-interference-noise ratio at this time can be expressed as:

[0053]

[0054] According to the classic point-to-point Shannon channel capacity formula, the average channel capacity of the MISO-UWOC system after EGC merging is

[0055]

[0056] An example of a simulation application of the MISO-UWOC system channel capacity assessment method considering timing jitter error and ocean turbulence effects:

[0057] Next, we comprehensively consider the presence of timing jitter error, GGD ocean turbulence, FFIR implicit path loss and multipath effect in a composite fading channel, and use the average channel capacity calculation formula of the MISO-UWOC system derived in the previous article to quantitatively measure the degree to which the system is affected by turbulence effects and timing jitter error. This further illustrates the effectiveness of the above-mentioned proposed and derived method for evaluating the average channel capacity of the MISO-UWOC system in the presence of timing jitter error and ocean turbulence effect when facing the requirements of underwater high-speed communication transmission.

[0058] The core simulation parameters are set as follows: the coastal water quality is selected, and its absorption and scattering coefficients are (0.179, 0.219) m -1 ; Transmission distance d = 13m; Transceiver location is deep sea; Turbulence scintillation index The wavelength of the light source at the transmitting end is 532nm, and the beam waist radius is W r =3mm blue-green laser; receiver half divergence angle θ div =40°, system load resistance R L =100Ω, transmission rate R b =1Gbps; To simplify the analysis of the problem, it is assumed that the scale parameter b of the GGD ocean turbulence i , and shape parameter a i and c i It is not affected by the selection of transmission branch i, that is, its subscript i can be ignored.

[0059] Figure 3 and Figure 4 The influence of timing jitter error on the average channel capacity of the system is demonstrated when the number of source nodes N=4 and the GGD turbulence intensity is fixed. Figure 3 The variation of the system average channel capacity with transmit power for different values ​​of random jitter deviation σ is shown. As the value of σ increases, the random jitter component of the timing jitter increases, and the average channel capacity decreases accordingly. This shows that it is very necessary to consider random timing jitter errors in high-speed communication systems. Figure 4The variation of the system average channel capacity with the transmission power under different deterministic jitter amplitude A values ​​is given, and a similar conclusion can be drawn that the system average capacity decreases with the increase of jitter amplitude. All of this shows that timing jitter, including random jitter and deterministic jitter, does have the potential to greatly deteriorate the effective transmission rate of the system during the high-speed communication process of the UWOC system. In addition, compared Figure 3 and Figure 4 It can also be concluded that as the random jitter deviation σ increases, the system average channel capacity deteriorates by approximately 21.4%, while as the deterministic jitter amplitude A increases, the system average channel capacity decreases by approximately 35.6%. This shows that deterministic jitter in timing jitter has a greater impact on system performance than random jitter.

[0060] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for evaluating the channel capacity of a MISO-UWOC system in the presence of timing jitter errors and ocean turbulence effects, characterized by: The steps include: Considering a channel environment with composite fading factors such as timing jitter error, GGD ocean turbulence, implicit path loss from the fading-free impulse response (FFIR), and multipath effects, a MISO-UWOC system using equal gain combining (EGC) technology at the receiver is considered. First, the PDF expression of the composite fading channel h after equal gain combining and the PDF expression of the timing jitter error ξ are calculated. Secondly, based on the matched filter output of the received signal, the signal-to-interference-noise ratio of the equivalent received signal after EGC merging is calculated, taking into account the timing jitter error and ocean turbulence effect. Finally, the classic Shannon channel capacity theorem is used to obtain the average channel capacity of the MISO-UWOC system taking into account the above-mentioned composite fading factors after statistical averaging.

2. The MISO-UWOC system channel capacity considering timing jitter error and ocean turbulence effects according to claim 1 is characterized by: Average channel capacity of composite fading MISO-UWOC system considering timing jitter error, GGD ocean turbulence, FFIR implicit path loss and multipath effect The expression is as follows: In the above formula, the thermal noise variance is T b is the On-off Keying (OOK) symbol width, Among them, K, T, B, R L They represent the Boltzmann constant, Kelvin temperature, filter bandwidth, and system load resistance respectively; ξ represents the jitter error per unit time; h is the equivalent attenuation after EGC merging; f h (h) and f ξ (ξ) are the statistical expressions of the PDFs of random variables h and ξ respectively; symbol E ξ,h [·] represents the operation of finding the mathematical expectation of random variables ξ and h.

3. The method for evaluating the channel capacity of a MISO-UWOC system in the presence of timing jitter errors and ocean turbulence effects according to claim 1, characterized in that: The PDF of the equivalent channel fading h after EGC merging, which takes into account GGD ocean turbulence, FFIR implicit path loss, and multipath effects, is approximately expressed as follows: In the above formula, Where μ1 and μ2 are the first-order and second-order origin moments of h, respectively, and Variables in the formula Here a i ,c i and b i They represent the shape parameter and scale parameter of the GGD fading distribution from the source node to the target node of the i-th branch of the MISO system. Without loss of generality, they are independent of i. N is the number of source nodes. Function d k (x,y)=Γ(x+k / y) / Γ(x), k=1,2; Γ(·) represents the gamma function; the equivalent fading coefficient h satisfies in represents the GGD turbulence attenuation coefficient experienced by the i-th branch, GG(·) represents Obey parameter a i ,b i ,c i The GGD distribution of is the matched filter output of the desired current waveform signal on the i-th branch, R is the responsivity of the photodetector, represents the received signal waveform after the pulse shaping function P(t) passes through the corresponding link FFIR, where That is, FFIR from the i-th source node to the target node, and the symbol * is the convolution operation; To satisfy the higher transcendental FoxH function with parameters m,n,p,q.

4. The method for evaluating the channel capacity of a MISO-UWOC system in the presence of timing jitter errors and ocean turbulence effects according to claim 1, wherein: The PDF expression of the timing jitter error ξ can be expressed as follows: In the above formula, ξ=Δ / T b represents the jitter error per unit time, Δ represents the offset from the ideal clock during the measurement time, σ represents the random jitter deviation, and A is the jitter amplitude of the deterministic jitter error.

5. The method for evaluating the channel capacity of a MISO-UWOC system in the presence of timing jitter errors and ocean turbulence effects according to claim 1, characterized in that: The signal-to-interference-and-noise ratio The expression is as follows:

6. The method for evaluating the channel capacity of a MISO-UWOC system in the presence of timing jitter errors and ocean turbulence effects according to claim 3, characterized in that: The GGD ocean turbulence decay The FoxH function description of the PDF is as follows: In the above formula, b i is the scale parameter, a i and c i is the shape parameter, represents a random variable that follows a GGD distribution.

7. The method for evaluating the channel capacity of a MISO-UWOC system in the presence of timing jitter errors and ocean turbulence effects according to claim 3, characterized in that: The non-fading channel impulse response FFIR data can be obtained by simulating photon motion using a computer Monte Carlo method under given system transceiver parameters, such as ocean water quality, transmission distance, receiver aperture, and emission light source wavelength.

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