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	A5.3
	A5.3

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 ‎[1618].

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

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body	${{f}_{0}}=2\times {{f}_{1}}\pm {{f}_{2}}$

(Eq. 98)

with

f_VLR-b/2≤f_0≤f_VLR+b/2 (Eq. 99)

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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.

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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 thirdorder at the frequency f₀ as shown below in Figure 370.

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372.

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body	{{f}_{0}}=2({{f}_{0}}+n\Delta f)-({{f}_{0}}+2n\Delta f)

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body n=\pm 1,\pm 2,...
(Eq. 100)

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Figure 370372: 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
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body ${{E}_{if}}=kE_{i1}^{2}{{E}_{i2}}$
    (Eq. 101)

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

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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.
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Figure 371373: 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

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body $0=2({{L}_{imr1}}+3dB+{{L}_{sens}})+({{L}_{imr2}}+3dB+{{L}_{sens}})+20\log k$
(Eq. 103)
from which we can derive the calculation algorithm for this example
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(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

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where:
iRSS^(i,j)_intermod: intermodulation product at the frequency f0;
LL_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;
II/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 372374) allows you to see the behaviour of this equation.
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Figure 372374: 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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