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 [16].
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 370.
(Eq. 100)
Figure 370: 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 371: 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 372) allows you to see the behaviour of this equation.
Figure 372: EPP Demo 9 – intermodulation internals
[1] the order is given by the sum of the absolute values of the coefficients, here 2 + |1| = 3