CN103177181B - For estimating the method for electromagnetic wave normalization attenuation by fog - Google Patents

Abstract

When the wavelength of the electromagnetic wave is much larger than the droplet size, the Rayleigh absorption approximation model can be used to calculate the attenuation of the fog on the electromagnetic wave. Although the calculation result is accurate, the calculation is too complicated. The present invention proposes an experience for estimating the normalized fog attenuation of the electromagnetic wave Formula: <maths num="0001"> </maths> The applicable temperature range of this formula is -8~20°C, and the frequency range is 30~100GHz. Compared with the existing empirical formula, the empirical formula has better calculation accuracy and higher correlation coefficient. The calculation results show that The maximum value of the absolute value of the relative error between the empirical formula proposed by the invention and the Rayleigh absorption approximation model is not more than 4.48%.

Description

For estimating the method for electromagnetic wave normalization attenuation by fog

(1) technical field

The present invention relates to the method for a kind of estimation 30 ~ 100GHz electromagnetic wave normalization attenuation by fog, belong to wave transmissions field, troposphere.

(2) background technology

Millimeter wave and microwave system almost have same long history, but due to the cause that millimetre wavelength is shorter, make its loss in atmospheric propagation process comparatively large, and the Primary Components such as power source slower development always before this, it is extensive that the application that result in millimeter-wave technology can not show a candle to microwave technology.In recent years, the development of the technology such as millimeter wave solid state source, novel high-power millimeter wave electrovacuum source and breakthrough, make millimeter-wave systems again receive the concern of numerous scholar.

At present, millimeter wave frequency band temporarily without definite definition, generally by 30 ~ 300GHz(correspondence, 1 ~ 10mm wavelength) frequency domain become millimeter wave.

Can be subject to serious decay when millimeter wave transmits in an atmosphere, mist is exactly one of them important influence factor.Present stage, calculate electromagnetic wave normalization attenuation by fog K _l(unit dB/km/g/m ³) method mainly contain two kinds: Mie scattering theory and Rayleigh and absorb approximate model.

Mie scattering theory hypothesis suspended particle is approximately spheroid, can be used for the electromagnetic wave attenuation value that calculating rain, mist, sand and dust etc. cause, result of calculation is accurate, but computation complexity is very high, calculating process relates to the complicated function such as Bessel's function, Hunk function, and result of calculation is easily dispersed.

Compared to Mie scattering theory, it is simple that Rayleigh absorbs approximate model computation process, and specific formula for calculation is as follows:

K _l＝(0.819f)/[ε _i(1+η ²)](1)

η＝(2+ε _r)/ε _i(2)

ε _r＝(ε ₀-ε ₁)/[1+(f/f _p) ²]+(ε ₁-ε ₂)/[1+(f/f _s) ²]+ε ₂(3)

ε _i＝[f*(ε ₀-ε ₁)]/{f _p*[1+(f/f _p) ²]}+[f*(ε ₁-ε ₂)]/{f _s*[1+(f/f _s) ²]}(4)

f _p＝20.09-142.4(θ-1)+294(θ-1) ²(5)

ε ₀＝77.66+103.3(θ-1)(6)

ε ₁＝5.48(7)

θ＝300/T(8)

Wherein, the unit of absolute temperature T is Kelvin.

If electromagnetic wavelength is much larger than droplet sizes, Rayleigh can be used to absorb the very high Mie scattering theory of approximate model replacement complexity for calculating normalization attenuation by fog.From formula (1) ~ (8): although relative to Mie scattering theory, it is comparatively simple that Rayleigh absorbs approximate model, and computation process is still aobvious complicated.Apply for simplifying computation process further and facilitating in engineering, several scholar's suggestion can under the prerequisite of loss part precision, and the approximate expression (experimental formula) using the less Rayleigh of complexity to absorb approximate model estimates normalization attenuation by fog.At present, existing experimental formula comprises: Staellin experimental formula (1966), Benoit experimental formula (nineteen sixty-eight), Altshuler experimental formula (1984), Liebe experimental formula (1989) and Zhao Zhen tie up experimental formula (2000).The concrete form of each formula is as follows:

Staellin： $K_{l\_\mathrm{Staellin}}=4.34\&times;\frac{{10}^{0.0122(291-T)-1}}{{{\mathrm{\&lambda;}}_0}^2}---\left(9\right)$

Benoit：K _{l_Benoit}＝f ^1.95e ^{-6.866(1+0.0045t)}(10)

Altshuler：K _{l_Altshuler}＝-1.347+11.152/f+0.06f-0.022t(11)

Liebe： $K_{l\_\mathrm{Liebe}}=(2.18\&times;{10}^{-3}f+3.9\&times;{10}^{-4}{f}^2){\mathrm{\&theta;}}^{9.73-0.0892f+1.73\&times;{10}^{-4}{f}^2}---\left(12\right)$

Zhao Zhenwei: $K_{l\_\mathrm{zhao}}=(6.0826\&times;{10}^{-4}{f}^{1.8963}){\mathrm{\&theta;}}^{7.8087-0.01565f-3.073\&times;{10}^{-4}{f}^2}---\left(13\right)$

In formula (9) ~ (13), T is absolute temperature, unit Kelvin (K); T is Celsius temperature, degrees Celsius (° C); λ ₀for wavelength, unit centimetre (cm).

Although existing 5 experimental formulas at present, above-mentioned experimental formula has best frequency range, the temperature range be suitable for separately, and result of calculation shows that above-mentioned experimental formula is larger at the maximal value ABS of the absolute relative error of millimeter wave frequency band.The people such as Liebe are learnt by calculating: the upper limiting frequency that droplet radius difference can cause Rayleigh model to be suitable for changes, but concerning the millimeter wave frequency band of 30 ~ 100GHz, Rayleigh model can be used in most cases to obtain accurate normalization attenuation by fog value.The present invention passes through the new electromagnetic wave normalization attenuation by fog experimental formula of proposition one, can be used for simplifying the calculating that Rayleigh absorbs approximate model, and compared to existing 5 experimental formulas, experimental formula calculated results proposed by the invention and the ABS of actual value less, related coefficient is higher.The temperature range that this experimental formula is suitable for is-8 ~ 20 ° of C, frequency range is 30 ~ 100GHz.

(3) summary of the invention

The object of the invention is to the electromagnetic wave attenuation by fog experimental formula that proposition ABS is less, related coefficient is higher, this formula is convenient to engineer applied, and applicable temperature range is-8 ~ 20 ° of C, frequency range is 30 ~ 100GHz.

Below detailed technology scheme of the present invention is described.

The present invention proposes one for estimating the experimental formula of electromagnetic wave normalization attenuation by fog, when temperature range is-8 ~ 20 ° of C, can be used for estimating that the frequency range caused by mist is the electromagnetic pad value of 30 ~ 100GHz; It is characterized in that the formula model chosen is

K _{l_new}＝A(f)θ ^B(f)(14)

Wherein, K _{l_new}represent the normalized value of electromagnetic wave attenuation by fog, unit (dB/km)/(g/m ³); θ=300/T, absolute temperature T unit is Kelvin; A (f) and B (f) form are

A(f)＝para1+para2*f ^para3(15)

B(f)＝para4+para5*f+para6*f ²(16)

In formula, para1 ~ para6 is 6 undetermined parameters.

Determine that the concrete grammar of parameter p ara1 ~ para6 is as follows:

A) θ=1 is made, now K _{l_new}=A (f), in 0 ~ 1000GHz, choose arbitrarily the frequency range (such as 25 ~ 305GHz) comprising 30 ~ 100GHz, utilize Rayleigh to absorb the normalization attenuation by fog data K of this frequency range when approximate model (ideal model) calculates θ=1 _{l_R}, utilize A (f) to above-mentioned K _{l_R}data carry out matching, the K of gained matching formula under calculating 30 ~ 100GHz frequency range _{l_new}(one-dimension array) and Rayleigh absorb the K of approximate model _{l_R}the ABS of (one-dimension array), the ABS of the matching formula in comparative analysis 0 ~ 1000GHz corresponding to all frequency ranges comprising 30 ~ 100GHz, choose the minimum matching formula of wherein ABS as best A (f), utilize said method can proper frequency range when getting 23 ~ 100GHz ABS be 1.37%, now gained matching formula is best, and para1=-0.10606, para2=0.0016174, para3=1.69238;

B) on a) basis, also need to determine para4 ~ para6, this seasonal temperature t (unit ° C) equals-8 ,-719,20 respectively, obtaining 29 by formula (1), temperature independent (now temperature is constant, t is respectively-8 ,-719,20) model, all frequency ranges comprising 30 ~ 100GHz are chosen with a) method is similar, corresponding each frequency range, due to the difference that temperature is chosen, 29 matching formulas can be obtained, calculate the K in 30 ~ 100GHz frequency range ,-8 ~ 20 ° of C temperature ranges _{l_new}(two-dimensional array) and K _{l_R}(two-dimensional array), calculates the ABS of 29 matching formulas respectively, and chooses the minimum matching formula of corresponding A BS as alternative matching formula; The ABS of the alternative matching formula in comparative analysis 0 ~ 1000GHz corresponding to all frequency ranges comprising 30 ~ 100GHz, choose the minimum alternative matching formula of wherein ABS as best-fit formula, result of calculation shows, when temperature chooses 21 ~ 154GHz for-4 ° of C, frequency ranges, ABS is 4.4709%, and now matching formula is best, and para4=9.2419, para5=-0.068303, para6=3.5235 × 10 ^-5;

To sum up, final experimental formula is $K_{l\_\mathrm{new}}=(-0.10606+0.0016174f^{1.69238})*{\mathrm{\&theta;}}^{9.2419-0.068303f+3.5236\&times;{10}^{-5}{f}^2}.$

(4) accompanying drawing explanation

Fig. 1 is for determining the process flow diagram of parameter p ara1 ~ para3 in formula (15).

Fig. 2 is for determining the process flow diagram of parameter p ara4 ~ para6 in formula (16).

Fig. 3 is when temperature is-8 ° of C, the relative error curve map of four kinds of experimental formulas.

Fig. 4 is when temperature is 0 ° of C, the relative error curve map of four kinds of experimental formulas.

Fig. 5 is when temperature is 10 ° of C, the relative error curve map of four kinds of experimental formulas.

Fig. 6 is when temperature is 20 ° of C, the relative error curve map of four kinds of experimental formulas.

(5) embodiment

Determine formula (15) and the parameter in formula (16) respectively according to process flow diagram shown in Fig. 1 and Fig. 2, the experimental formula that final known the present invention proposes is $K_{l\_\mathrm{new}}=(-0.10606+0.0016174f^{1.69238})*{\mathrm{\&theta;}}^{9.2419-0.068303f+3.5236\&times;{10}^{-5}{f}^2}.$

For the experimental formula that inspection the present invention proposes, choose following 3 indexs and contrast new experimental formula and existing 5 experimental formulas before this.Explanation and the result of these 3 indexs are as follows:

A) make Celsius temperature t equal-8 respectively ,-7.519.5,20, in 30 ~ 100GHz frequency range, determine the ABS of each experimental formula and theoretical value (being calculated by Rayleigh model) according to 6 kinds of experimental formula calculated results.The computing formula of ABS is as follows:

$\mathrm{ABS}=\max |\frac{K_l-K_R}{K_R}\&times;100\%|---\left(17\right)$

In formula, K _lfor utilizing certain experimental formula calculated normalization attenuation by fog value (array), K _rfor the theoretical value (array) utilizing Rayleigh model to obtain, || represent and take absolute value, max represents the maximal value asked in array.

This index reflect each experimental formula at the corresponding temperature with the maximum deviation of theoretical value, table 1 provides concrete data.By under same temperature in table 1, the minimum value runic of the ABS that 6 kinds of experimental formulas are corresponding is indicated, as seen in-8 ~ 20 ° of C, compared to all the other 5 kinds of experimental formulas, the ABS of new experimental formula is minimum.

Table 1 at each temperature, the ABS that 6 kinds of experimental formulas are corresponding

Temperature (° C)	New formula (%)	Zhao Zhenwei (%)	Liebe(%)	Altshuler(%)	Staelin(%)	Benoit(%)
							-8	4.45	8.59	9.64	9.89	93.94	106.31
-7.5	3.77	7.79	8.96	9.72	90.96	102.86
							-7	3.11	7.03	8.32	9.56	88.09	99.53
-6.5	2.49	6.3	7.71	9.39	85.31	96.3
							-6	1.9	6.15	7.14	9.21	82.62	93.18
-5.5	1.93	6.02	6.6	9.03	80.02	90.17
							-5	1.99	5.89	6.09	8.85	77.5	87.25
-4.5	2.05	5.78	5.62	8.67	75.07	84.42
							-4	2.13	5.67	5.17	8.49	72.72	81.69
-3.5	2.22	5.58	4.76	8.31	70.44	79.04
							-3	2.32	5.49	4.37	8.13	68.23	76.48
-2.5	2.42	5.41	4.34	7.94	66.1	73.99

-2	2.53	5.33	4.48	7.76	64.03	71.58
							-1.5	2.64	5.27	4.62	7.58	62.03	69.25
-1	2.75	5.21	4.76	7.4	60.08	66.99
							-0.5	2.86	5.16	4.9	7.22	58.2	64.79
0	2.96	5.12	5.04	7.04	56.37	62.66
							0.5	3.12	5.09	5.17	6.86	54.6	60.59
1	3.33	5.06	5.29	6.69	52.88	58.58
							1.5	3.52	5.04	5.41	6.52	51.2	56.62
2	3.69	5.02	5.53	6.35	49.58	54.72
							2.5	3.84	5.01	5.64	6.18	48	52.87
3	3.97	5.01	5.75	6.04	46.46	51.07
							3.5	4.09	5.01	5.84	6.07	44.96	49.32
4	4.19	5.01	5.93	6.16	43.5	47.61
							4.5	4.28	5.02	6.02	6.29	42.08	45.94
5	4.35	5.03	6.1	6.45	40.7	44.31
							5.5	4.4	5.04	6.17	6.64	39.34	42.73
6	4.44	5.06	6.23	6.85	38.02	41.18
							6.6	4.47	5.08	6.29	7.08	36.74	39.66
7	4.48	5.1	6.33	7.33	35.48	38.18
							7.5	4.48	5.12	6.37	7.59	34.24	36.73
8	4.47	5.14	6.41	7.86	33.04	35.32
							8.8	4.45	5.17	6.43	8.14	31.86	33.93
9	4.42	5.19	6.45	8.43	30.7	32.57
							9.5	4.38	5.22	6.45	8.73	29.57	31.24
10	4.38	5.24	6.45	9.02	28.46	29.93
							10.5	4.4	5.27	6.44	9.34	27.37	28.64
11	4.4	5.3	6.43	9.64	26.3	27.38
							11.5	4.4	5.33	6.4	9.96	25.25	26.15
12	4.38	5.36	6.36	10.28	24.21	24.93
							12.5	4.37	5.39	6.32	10.6	23.2	23.74
13	4.34	5.42	6.27	10.92	22.2	22.56
							13.5	4.31	5.45	6.21	11.24	21.21	21.4
14	4.27	5.49	6.14	11.57	20.24	20.26
							14.5	4.23	5.52	6.07	11.9	19.29	19.14
15	4.18	5.56	5.98	12.23	18.35	18.03
							15.5	4.12	5.6	5.89	12.56	17.42	16.94
16	4.06	5.64	5.79	12.88	16.5	15.86
							16.5	3.99	5.69	5.68	13.21	15.59	14.8
17	3.91	5.74	5.56	13.54	14.7	13.75
							17.5	3.83	5.79	5.44	13.87	13.82	12.72
18	3.74	5.85	5.3	14.19	12.94	11.7
							18.5	3.65	5.91	5.16	14.52	12.19	10.69
19	3.55	5.97	5.02	15.27	12.47	9.69
							19.5	3.45	6.04	5.15	16.66	12.75	8.74
20	3.33	6.11	5.37	18.11	13.03	9.17

B) at each temperature, each experimental formula and Rayleigh absorb the related coefficient of approximate model, and concrete data are in table 2.By under same temperature in table 2, the maximal value runic of the related coefficient that 6 kinds of experimental formulas are corresponding is indicated, as seen in-8 ~ 20 ° of C, compared to all the other 5 kinds of experimental formulas, the related coefficient of new experimental formula is maximum, illustrates that the fitting effect of new experimental formula and theoretical model is better.

Table 2 at each temperature, the related coefficient of 6 kinds of experimental formulas and Rayleigh model

Temperature (° C)	New formula	Zhao Zhenwei	Liebe	Altshuler	Staelin	Benoit
							-8	0.999914	0.999387	0.997469	0.998326	0.983786	0.984948

-7.5	0.999926	0.99943	0.997577	0.99851	0.984379	0.985519
							-7	0.999937	0.999471	0.997683	0.998683	0.984959	0.986078
-6.5	0.999946	0.99951	0.997785	0.998843	0.985524	0.986622
							-6	0.999954	0.999546	0.997884	0.998991	0.986075	0.987151
-5.5	0.999961	0.999581	0.99798	0.999127	0.98661	0.987665
							-5	0.999966	0.999613	0.998072	0.999251	0.98713	0.988164
-4.5	0.99997	0.999643	0.99816	0.999363	0.987634	0.988647
							-4	0.999973	0.999671	0.998245	0.999464	0.988122	0.989115
-3.5	0.999975	0.999696	0.998326	0.999554	0.988595	0.989567
							-3	0.999976	0.99972	0.998403	0.999633	0.989051	0.990004
-2.5	0.999976	0.999742	0.998476	0.999702	0.989492	0.990425
							-2	0.999975	0.999762	0.998546	0.99976	0.989917	0.99083
-1.5	0.999973	0.99978	0.998612	0.99981	0.990327	0.991221
							-1	0.999971	0.999797	0.998674	0.99985	0.990722	0.991597
-0.5	0.999968	0.999812	0.998733	0.999881	0.991101	0.991958
							0	0.999965	0.999826	0.998788	0.999904	0.991466	0.992305
0.5	0.999962	0.999839	0.998841	0.999919	0.991817	0.992638
							1	0.999958	0.99985	0.99889	0.999927	0.992154	0.992957
1.5	0.999954	0.99986	0.998936	0.999927	0.992478	0.993263
							2	0.99995	0.999869	0.998979	0.999922	0.992788	0.993557
2.5	0.999946	0.999876	0.99902	0.99991	0.993086	0.993838
							3	0.999942	0.999883	0.999058	0.999892	0.993371	0.994107
3.5	0.999938	0.999889	0.999093	0.999869	0.993644	0.994364
							4	0.999935	0.999894	0.999126	0.999841	0.993906	0.994611
4.5	0.999931	0.999899	0.999156	0.999808	0.994157	0.994846
							5	0.999928	0.999903	0.999184	0.999771	0.994397	0.995072
5.5	0.999925	0.999906	0.99921	0.99973	0.994627	0.995287
							6	0.999922	0.999908	0.999235	0.999685	0.994847	0.995493
6.6	0.99992	0.99991	0.999257	0.999637	0.995057	0.995689
							7	0.999918	0.999911	0.999277	0.999586	0.995259	0.995877
7.5	0.999917	0.999912	0.999296	0.999532	0.995451	0.996056
							8	0.999916	0.999912	0.999313	0.999476	0.995635	0.996228
8.8	0.999915	0.999911	0.999328	0.999417	0.995811	0.996391
							9	0.999914	0.99991	0.999342	0.999357	0.99598	0.996547
9.5	0.999914	0.999909	0.999355	0.999295	0.996141	0.996696
							10	0.999915	0.999907	0.999366	0.999231	0.996294	0.996838
10.5	0.999915	0.999905	0.999376	0.999165	0.996442	0.996974
							11	0.999916	0.999902	0.999385	0.999099	0.996582	0.997104
11.5	0.999917	0.999898	0.999392	0.999031	0.996717	0.997227
							12	0.999919	0.999895	0.999398	0.998963	0.996845	0.997345
12.5	0.999921	0.99989	0.999403	0.998894	0.996968	0.997458
							13	0.999923	0.999885	0.999407	0.998824	0.997086	0.997565
13.5	0.999925	0.99988	0.99941	0.998754	0.997198	0.997668
							14	0.999928	0.999874	0.999412	0.998684	0.997306	0.997766
14.5	0.999931	0.999867	0.999413	0.998613	0.997409	0.997859
							15	0.999934	0.99986	0.999413	0.998542	0.997507	0.997949
15.5	0.999937	0.999852	0.999412	0.998472	0.997601	0.998034
							16	0.99994	0.999843	0.999411	0.998401	0.997691	0.998115
16.5	0.999943	0.999834	0.999408	0.99833	0.997777	0.998193
							17	0.999946	0.999824	0.999405	0.99826	0.99786	0.998267
17.5	0.999949	0.999814	0.9994	0.99819	0.997938	0.998338
							18	0.999952	0.999803	0.999395	0.99812	0.998014	0.998405
18.5	0.999955	0.999791	0.999389	0.998051	0.998086	0.99847
							19	0.999958	0.999778	0.999382	0.997982	0.998155	0.998532
19.5	0.99996	0.999765	0.999374	0.997914	0.998222	0.998591
							20	0.999963	0.999751	0.999366	0.997846	0.998285	0.998647

C) when temperature is-8 ° of C, 0 ° of C, 10 ° C and 20 ° C (the normalization attenuation by fog of these four kinds of temperature computation is that document widely uses), provide 4 kinds of experimental formulas (Staellin experimental formula and Benoit experimental formula error larger, this time be not used further to compare) relative error curve map, result is as shown in Fig. 3 ~ Fig. 6.

Comprehensive These parameters, the experimental formula that known the present invention proposes has better superior function when the electromagnetic wave normalization attenuation by fog of estimation 30 ~ 100GHz frequency range.

Claims (1)

1. the present invention proposes a kind of method for estimating electromagnetic wave normalization attenuation by fog, when temperature range is-8 ~ 20 DEG C, can be used for estimating that the frequency range caused by mist is the electromagnetic pad value of 30 ~ 100GHz; It is characterized in that the formula model chosen is

K _{l_new}＝A(f)θ ^B(f)(1)

Wherein, K _{l_new}represent the normalized value of electromagnetic wave attenuation by fog, unit (dB/km)/(g/m ³); θ=300/T, absolute temperature T unit is Kelvin; A (f) and B (f) form are

A(f)＝para1+para2*f ^para3(2)

B(f)＝para4+para5*f+para6*f ²(3)

In formula, para1 ~ para6 is 6 undetermined parameters;

Wherein, determine that the concrete grammar of parameter p ara1 ~ para6 is as follows:

A) θ=1 is made, now K _{l_new}=A (f), chooses arbitrarily the frequency range comprising 30 ~ 100GHz in 0 ~ 1000GHz, utilizes the normalization attenuation by fog data K of this frequency range during Rayleigh absorption approximate model calculating θ=1 _{l_R}, utilize A (f) to above-mentioned K _{l_R}data carry out matching, the one-dimension array K of gained matching formula under calculating 30 ~ 100GHz frequency range _{l_new}the one-dimension array K of approximate model is absorbed with Rayleigh _{l_R}the maximal value ABS of absolute relative error, the ABS of the matching formula in comparative analysis 0 ~ 1000GHz corresponding to all frequency ranges comprising 30 ~ 100GHz, choose the minimum matching formula of wherein ABS as best A (f), utilize said method can proper frequency range when getting 23 ~ 100GHz ABS be 1.37%, now gained matching formula is best, and para1=-0.10606, para2=0.0016174, para3=1.69238;

B) on a) basis, also need to determine para4 ~ para6, this seasonal temperature t equals-8 ,-719,20 respectively, 29 temperature independent models are obtained by formula (1), now temperature is constant, t is respectively-8 ,-719,20, wherein t unit is DEG C, all frequency ranges comprising 30 ~ 100GHz are chosen with a) method is similar, corresponding each frequency range, due to the difference that temperature is chosen, 29 matching formulas can be obtained, calculate the two-dimensional array K in 30 ~ 100GHz frequency range ,-8 ~ 20 DEG C of temperature ranges _{l_new}with two-dimensional array K _{l_R}, calculate the ABS of 29 matching formulas respectively, and choose the minimum matching formula of corresponding A BS as alternative matching formula; The ABS of the alternative matching formula in comparative analysis 0 ~ 1000GHz corresponding to all frequency ranges comprising 30 ~ 100GHz, choose the minimum alternative matching formula of wherein ABS as best-fit formula, result of calculation shows, when temperature for-4 DEG C, frequency range choose 21 ~ 154GHz time, ABS is 4.4709%, and now matching formula is best, and para4=9.2419, para5=-0.068303, para6=3.5235 × 10 ^-5;

To sum up, final experimental formula is $K_{l\_new}=(-0.10606+0.0016174f^{1.69238})*{\mathrm{\&theta;}}^{9.2419-0.068303f+3.5236\&times;{10}^{-5}{f}^2}.$