1、 Rec. ITU-R SM.1134-1 1 RECOMMENDATION ITU-R SM.1134-1*Intermodulation interference calculations in the land-mobile service (Question ITU-R 44/1) (1995-2007) Scope This Recommendation serves as a basis for the calculation of a maximum of three intermodulation interference that are created at the out
2、put of a receiver under influence of intensive unwanted signals at the receiver input due to non-linearity of an amplitude response of the receiver. The ITU Radiocommunication Assembly, considering a) that, in the most typical cases, the major factors which determine interference in the land-mobile
3、service include: in-band intermodulation products which are generated by two (or more) high-level interfering signals; unwanted emission that can occur in a transmitter when any other signal from another transmitter is also presented at the input of RF stages of the influenced transmitter; the wante
4、d and interfering signal levels are random variables; b) that two (or more) unwanted signals must have specific frequencies so that the intermodulation products fall into the frequency band of a receiver; c) that the probability of occurrence of intermodulation interference due to more than two high
5、-level unwanted signals is very small; d) that the intermodulation interference calculation procedure will offer a useful means of promoting efficient spectrum utilization by the land-mobile service, recommends 1 that the receiver intermodulation model presented in Annex 1 should be used for intermo
6、dulation interference calculations in the land-mobile service; 2 that intermodulation interference calculations should follow the following procedure, details of which are presented in Annex 1; 2.1 to determine mean value and dispersion of a random wanted signal power at the receiver input; 2.2 to d
7、etermine mean value and dispersion of a random intermodulation interference signal power at the receiver input; 2.3 to determine the probability that the intermodulation products generated both in the receiver itself and as a result of the intermodulation in the transmitter will occur during the rec
8、eption; *This Recommendation should be brought to the attention of Radiocommunication Study Group 8. 2 Rec. ITU-R SM.1134-1 3 that the zones affected by intermodulation interference and relevant necessary geographical separation of interfering transmitters and receivers should be determined on the b
9、asis of a given value of the interference probability, as it is described in Annex 1. Annex 1 Intermodulation models This Annex describes two intermodulation models; the receiver intermodulation (RXIM) model and the transmitter intermodulation (TXIM) model. It is divided into five sections. Section
10、1 outlines the general formula for calculating receiver intermodulation interference. Section 2 describes the RXIM measurement procedure. Section 3 outlines a procedure for evaluating receiving intermodulation interference using the general formula. Section 4 outlines the formula for transmitter int
11、ermodulation interference. Section 5 describes how the probabilities of RXIM and TXIM interference are calculated. 1 Receiver intermodulation analysis model The two-signal, third-order intermodulation interference power is given by the following formula (ex-CCIR Report 522-2, Dsseldorf, 1990): ()( )
12、1,222112 KPPPino+= (1) where: P1and P2: powers of the interfering signals at frequencies f1and f2, respectively Pino: power of the third-order intermodulation product at frequency f0(f0= 2f1 f2) K2,1: third-order intermodulation coefficient, may be computed from third-order intermodulation measureme
13、nts or obtained from equipment specifications 1and 2: RF frequency selectivity parameters at frequency deviations f1and f2from the operating frequency f0, respectively. The values of 1and 2for example can be obtained from the equation to calculate the attenuation of a signal at an off-tune frequency
14、. +=221 log 60)(RFBff (2) where BRFis the RF bandwidth of the receiver. It is worth noting that for a particular set of third-order intermodulation measurements for land mobile analogue radio receivers operating in the VHF and lower UHF bands, equation (1) may be manipulated to derive the following
15、formula McMahon, 1974: ()fPPPino+= log6010221(3) Rec. ITU-R SM.1134-1 3 where f is the mean frequency deviation (MHz) and is equal to: 221ff +2 Receiver intermodulation interference characteristics In Fig. 1, Gsis the signal generator of the wanted signal (WS). GI1and GI2are the signal generators of
16、 the interfering signals (IS) which constitute the RXIM product. These signals are applied to the input of the receiver (RX). When measuring the RX intermodulation characteristic, there are two IS with equal levels from the generators GI1and GI2and the WS with level Psr, from the generator Gsthat ar
17、e carried to the RX input. The frequency detuning of the first IS is chosen equal f0, as for the second IS it is approximately equal 2f0. The level of both IS at the RX input is increased until PI(IM) is reached when the reception quality of the WS should not reduce below a specified value. The rece
18、ption quality is definitely connected with protection ratio A. Note that: Psr: sensitivity of radio receiver (dBW) PI(IM): the sensitivity to intermodulation, that was measured for the receiver (dBW). Therefore, according to equation (1): () ()( )1,200223 KffIMPPIino= (4) This level is related to Ps
19、ras follows: inosrPAP = (5) K2,1is therefore: () ()( ) APffIMPKsrI+=001,2223 (6) 4 Rec. ITU-R SM.1134-1 3 Procedure for receiver intermodulation analysis 3.1 General model Interferences caused by intermodulation products (IMP) in the receiver occur when the following two conditions are fulfilled: IF
20、RIMPIFRBFfBF + 5.05.0 (7) and APPinos+ (9) where: 1,22102 KAR += (10) 3.2 IMP calculation method based on intercept points 3.2.1 In cases of absence of an opportunity of measurement of the receiver 2,1 factor, for determination of IMP interference it is expedient to take advantage of such parameters
21、 as IPi intercept points of i-th order, where i = 2, 3 and 5, and Iifactors of the same orders for microcircuits which are used in input stages (preselectors and mixers) of modern receivers. Parameters IPiand Iiare available from corresponding specifications. The most widespread is parameter IP3(ITU
22、 Handbook on Spectrum Monitoring, 2002, 6.5) “the third-order intercept point“ a theoretical level, at which the level of 3rd order IMP is equal to individual levels of incoming signals (two equal signals generating IMP such as 2f1 f2and 2f2 f1) recalculated to the output of a non-linear element (se
23、e Fig.2). Parameters IPicharacterize degree of linearity of input stages of the receiver in the sense of their ability to generate IMP of corresponding orders. The higher IPilevels, the better linearity of the receiver and wider its dynamic range and, therefore, the greater levels of incoming signal
24、s at which IMP are produced and better protection of the receiver against IMP interferences. Iifactors characterize a susceptibility of the receiver to IMP of corresponding orders. They represent relation of IMP level at the receiver output to a level of incoming signals at its input (two equal sign
25、als generating IMP at the output). Rec. ITU-R SM.1134-1 5 FIGURE 2 Third-order intercept point IP3 Average values and variation limits of parameters of microcircuits used as input stages of receivers (preselectors and mixers), provided by the most known manufacturers, are presented in Table 1. Indiv
26、idual values of these parameters can be obtained from the engineering specifications on relevant equipment. Parameter G in Table 1 represents amplification factor of the preselector, and dBc designates decibels relative to the unmodulated carrier power of the emission. TABLE 1 Parameters of microcir
27、cuits of input stages of receivers G (dB) IP3(dBm) IM2(dBc) IM3(dBc) IM5(dBc) 12 5 28 5 24 5 30 5 35 5 Calculating formulas for IMP components that can fall into IF passband of the receiver are given in Table 2 which presents: fIMP: IMP frequencies of 2nd, 3rd and 5th orders generated by two or thre
28、e incoming signals Pe-in: the power of the equivalent incoming signal at the input of the receiver two or three incoming signals at the input of the receiver with equal levels Pe-inare generating the same IMP as incoming signals with different levels P1, P2, P3PIMP: IMP levels of 2nd, 3rd and 5th or
29、ders resulted by two or three incoming signals at the input, where P1, P2, P3 powers of incoming signals at frequencies f1, f2, f3correspondingly. Values of PIMP are expressed in terms of IPiand IMi. 6 Rec. ITU-R SM.1134-1 TABLE 2 IMP interferences of 2nd, 3rd and 5th orders under 2 or 3 unwanted in
30、coming signals Frequency, fIMPfg fh(fg fh) 2fg fhfk+ fl fm3fg 2fh2fk 2fl+ fmThe order and type of products 2 (1; 1) 3 (2; 1) 3 (1; 1; 1) 5 (3; 2) 5 (2; 2; 1) Pe-in(dBm) (Pg+ Ph)/2 (2Pg+ Ph)/3 (Pk + Pl + Pm)/3 (3Pg+ 2Ph)/5 (2Pk + 2Pl + Pm)/5 2 (Pe-in+ Gi IP23 (Pe-in+ G) 2.IP33 (Pe-in + G) 2.IP3+ 6 5
31、(Pe-in+ G) 4.IP55 (Pe-in+ G) 4.IP5+ 9.5 PIMP (dBm) IM2+ Pe-inIM3+ Pe-inIM3+ Pe-in+ 6 IM5+ Pe-inIM5+ Pe-in+ 9.5 In Table 2 for frequencies of IMP fIMPand for IMP levels Pe-inof various subscript indexes are determined as follows. For two incoming signals: each index g and h accepts one of two values
32、1 or 2 under the condition: g + h = 3 For three incoming signals: each index k, l and m accepts one of three values 1, 2 or 3 under the condition: k+ l + m = 6 Calculations of IMP levels Pe-infor various IMP components should be made for the same distributions of indexes as for calculation of freque
33、ncies fIMPof these components. Table 2 also shows the number of components fIMPand possible number of different IMP levels Pe-inof various orders under different levels of incoming signals. From formulas for Pe-init can be concluded that at different levels of incoming signals different IMP componen
34、t at the output for the same order also have various levels which lend themselves to calculation by this method. Relationships between IPiand Iilevels can be found by equating PIMPvalues in Table 2: IP2= Pe-in+ 2G IM2IP3= Pe-in+ 0.5 (3G IM3) IP5= Pe-in+ 0.25 (5G IM5) The equivalent IMP level recalcu
35、lated to the input of the receiver Pinois equal: Pino= PIMP G To attenuate unwanted incoming interfering signals, diplexing or passband filters are usually installed at receiver inputs before preselectors. Parameters of filters (under trapezoidal shapes of their characteristics) are: the passband BR
36、F1, the border of the attenuation band BRF2and attenuation of incoming signals (f) outside the passband (at f 0.5BRF2 the attenuation is considered as to be constant and equal LFdB). Rec. ITU-R SM.1134-1 7 In that case insertion losses of the filter (dB) are: ()+=fBLBfBcfaBffRFFRFRFRF22115.0at5.05.0
37、at5.0at0where: |f | frequency offset of the incoming signal at the receiver input a = LF/0.5 (BRF2 BRF1) c = 0.5 . a .BRF1The power of the signal at the input of the preselector Pjat frequency fj(j = 1; 2; 3) equals: Pj= Pj-in (f) where Pj-in: the power of the incoming signal at the input of the rec
38、eiver. 3.2.2 Procedure of IMP interference calculation contains the following steps Step 1: Determination of attenuation of incoming signals acting at the input of the receiver by input filters (fj), j = 1; 2; 3. Step 2: Calculation of levels of the incoming signals acing at the input of the presele
39、ctor Pj. Step 3: Determination of IMP levels at the output of the mixer PIMP. Step 4: Estimation of the equivalent IMP level recalculated to the input of the receiver Pino. Step 5: Calculation of the signal interference ratio at the input of the receiver R. Step 6: Comparison of the signal interfere
40、nce ratio R with the protection ratio A for determination of compatibility conditions of the receiver with other radio-electronic systems in the particular electromagnetic environment. 3.2.3 Example of calculations Let us suppose that it is required to calculate IMP interference of a kind f1+ f2 f3i
41、n the receiver and to estimate its harmful effect. Entries: IP3= 24 dBm; G = 15 dB; P1-in= 50 dBm; P2-in= 10 dBm; P3-in= 15 dBm; Ps= 114 dBm;A = 9 dB; LF= 30 dB. Let frequency offsets of the incoming signals at the input of the receiver |fj| = |FR fj | are: |f1| 0.5BRF1; |f2| 0.5BRF2and |f3| 0.5BRF2
42、, i.e. one incoming signal lies in the passband of the input filter of the receiver and other two incoming signals outside of the passband. In this case: (f1) = 0; (f2) = (f3) = 30 dB Pj= Pj-in (fj); P1= 50 dBm; P2= 40 dBm; P3= 45 dBm Lets calculate Pe-inand PIMPwith the help of equations of Table 2
43、: Pe-in= (50 40 45)/3 = 45 dBm PIMP= 3 (45 + 15) 2.24 + 6 = 132 dBm Pino= PIMP G = 132 15 = 147 dBm R = Ps Pino= 114 (147) = 33 dBm 8 Rec. ITU-R SM.1134-1 R A and, therefore, in accordance with equation (8) compatibility is provided. 4 Power of transmitter intermodulation products The power Piof the
44、 intermodulation product occurring in the transmitter and subsequently reaching the receiver input may be written as: 101),2(10122LKPPi= (11) where: 2P: interfering transmitter power (with frequency f2) at the output terminals of the affected transmitter (with frequency f1), in which the intermodula
45、tion products occur (dBW) 12, 10: attenuation due to the output and antenna circuits of the affected transmitter at frequency f1to interfering transmitter at frequency f2, and to intermodulation product at frequency f0, respectively (dB) K(2),1: intermodulation conversion losses in the transmitter (
46、dB) which is different from K2,1in equation (1) L10: attenuation of intermodulation product on the path between the transmitter with frequency f1and the receiver (dB). Interference caused by TXIM occurs when: APPis (13) Rec. ITU-R SM.1134-1 9 where: AKT +=1),2(10120The mean value T and dispersion 2T
47、 of the random quantity: 102LPPTs= are equal respectively to: 212222102+=sTmsmmLPPTwhere: mP2 , Psm, L10m: mean values 21222, s: dispersions of the random quantities102, LPPs . 5.3 Probability of intermodulation products The probability that intermodulation products, generated both in the receiver i
48、tself and as a result of intermodulation in the transmitter (conditions (9) and (13), respectively), will occur during reception is equal to: =xtt2de /2-2(14)()RRRx = /0: on determination of the probability of intermodulation products occurring in receivers (condition (9); ()TTTx = /0: on determinat
49、ion of the probability of interference due to intermodulation products occurring in transmitters (condition (13). In determining the zones affected by intermodulation interference on the basis of a given value of probability of interference , the value of x is first determined from equation (14). Then for a known value of Psm
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