A5.3 INTERMODULATION REJECTION CALCULATION

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Last updated: Jan 10, 2018
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ETSI defines the intermodulation response rejection as a measure of the capability of the receiver to receive a wanted modulated signal, without exceeding a given degradation due to the presence of two or more unwanted signals with a specific frequency relationship to the wanted signal frequency ‎[18].

In SEAMCAT, it is called the intermodulation rejection, and in the presence of more than one interfering system applying its own frequency distribution, a theoretically unlimited number of intermodulation products exist, caused by the non-linearity of the VLR.  In practice, just the products close to the frequency of the VLR are of importance, of which the products of the so called 3rd order[1] are the most dominant and therefore considered by SEAMCAT. The frequency conditions for the intermodulation products of the 3rd order are

               (Eq. 98)

with

                                      f_VLR-b/2≤f_0≤f_VLR+b/2              (Eq. 99)

where

  • b           : is the bandwidth of the VLR;
  • f_0        : the trialed frequency of the victim system;
  • f_1, f_2   : the trialed frequencies of pairs of interfering systems in case more than two systems are to be taken into account.


As an example consider a victim system with a desired signal at frequency f0, a channel separation Df and interfering signals Ei1 and Ei2  at frequencies f0+n∆f and f0+2n∆f, respectively. The receiver non-linearity produces an intermodulation product Eif of third order at the frequency f0 as shown below in Figure 372.

    (Eq. 100)




Figure 372: Illustration of intermodulation product Eif of third order at the frequency f0


The signal strength Eif of the intermodulation product is given by

                                         (Eq. 101)


with some constant k to be determined. For signal levels (measured in dB), Eif becomes  and the equation above reads


 (Eq. 102)


From the measurement procedure which is described e.g. in the ETSI standard ETSI 300-113, clause 8.8, we can derive the calculation algorithm. The method is similar to the contribution for blocking interference. ETSI 300-113 defines via the intermodulation response Limr the interfering signal levels iRSSi1 = iRSSi2 at which bit errors due to intermodulation just start to be recorded.

Figure 373: Illustration of intermodulation product from ETSI 300-113


This means, for iRSSi1 and iRSSi2, we have an intermodulation product  relative to the noise floor (0 dB), due to the noise augmentation (N+I)/N of 3 dB corresponds to an I/N of 0 dB. Transferring Figure 371 into a formula gives the relation

                                              (Eq. 103)

from which we can derive the calculation algorithm for this example

                           (Eq. 104)


where for interferer i-th, at frequency x:

  (Eq. 105)

where

  • P^output_ILT: power supplied to the ILT antenna (before power control);
  • g^PC_ILT: power control gain for the ILT with the power control function, see ‎ANNEX 14;
  • PL_ILT->VLR: path loss between the interfering link transmitter i and the victim link receiver;
  • G_ILT->VLR: ILT antenna gain in the direction of the VLR;
  • G_VLR->ILT: VLR antenna gain in the direction of the ILT;
  • MCL : Minimum coupling loss given by the system parameter definition.


For any other consistent combination of (N+I)/N and I/N this becomes

 (Eq. 106)


For the computation of the intermodulation products in the victim link receiver two different interfering systems (i-th and j-th) are required and the total intermodulation product is


   (Eq. 107)

where:

  • iRSS^(i,j)_intermod: intermodulation product at the frequency f0;
  • L_inter: the attenuation given by the input parameter 'Intermodulation rejection'. This attenuation applies inside the bandwidth of the VLR. It is therefore advisable to set a constant value as intermodulation rejection;
  • L_sens: the sensitivity of the VLR given by the system parameter definition;
  • (N+I)/N: Noise augmentation given by the system parameter definition;
  • I/N: interference to noise ratio given by the system parameter definition.


In case the intermodulation product does not fit the frequency condition  , a value of -1000 dBm is returned in SEAMCAT.

The EPP Demo9 (Figure 374) allows you to see the behaviour of this equation.

 

Figure 374: EPP Demo 9 – intermodulation internals




[1] the order is given by the sum of the absolute values of the coefficients, here 2 + |1| = 3