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 3^rd order[1] are the most dominant and therefore considered by SEAMCAT. The frequency conditions for the intermodulation products of the 3^rd 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 E_i1 and E_i2 at frequencies f₀+n∆f and f₀₊2n∆f, respectively. The receiver non-linearity produces an intermodulation product E_if of third order at the frequency f₀ as shown below in Figure 372.

(Eq. 100)

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

The signal strength E_if of the intermodulation product is given by

(Eq. 101)

with some constant k to be determined. For signal levels (measured in dB), E_if 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 L_imr the interfering signal levels iRSS_i1 = iRSS_i2 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 iRSS_i1 and iRSS_i2, 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

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