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A7.3 A7.3

Figure 377 375 shows the principle of the determination of the interfering power. If  f_ILT =f_ VLR then the interfering frequencies fall exactly in the receiving band of the victim link receiver (co-channel interference).

For simplification within the algorithms the mask function p_m_ILT is normaliSed normalized to 1 Hz reference bandwidth:

 

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body ${{p}_{n\_ILT}}={{p}_{m\_ILT}}(\Delta f)-10{{\log }_{10}}\left( \frac{b}{1Hz} \right)$

   (                        Image Added              (Eq. 110)

The bandwidth b is the bandwidth used for the emission mask. The total received interfering power emission_ILT can easily be calculated by integration over the receiver bandwidth from  to

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body $powe{{r}_{ILT}}=10{{\log }_{10}}\left\{ \int\limits_{a}^{b}{{{10}^{\left( {{p}_{n\_ILT}}(\Delta f)/10 \right)}}}d\Delta f \right\}$

              Image Added                     (Eq. 111)

with p_n_ILT denoting the normalized mask in dBm/Hz. Using 1 Hz reference bandwidth the integral can be replaced by a summation

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body $powe{{r}_{ILT}}=10{{\log }_{10}}\left\{ \sum\limits_{i=a}^{b}{{{10}^{\left( {{p}_{n\_ILT}}(\Delta {{f}_{i}})/10 \right)}}} \right\}$

                        Image Added               (Eq. 112)

where power_ILT is given in dBm.

Note:  The interfering power of a radio system having a different bandwidth can be estimated by the aforementioned algorithms. This calculation is only required for the interference due to unwanted emissions but not for blocking and intermodulation.

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F377F375F377 F375

Figure 377375: Integration of the unwanted emissions in the victim link receiver band

The total interfering power relative to carrier  Image Removedcan be calculated by integration over the receiver bandwidth from Image Removed to Image Removed

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body

...

\

...

mathit{emission\_rel_{ILT}}

 can be calculated by integration over the receiver bandwidth from Image Added to Image Added

    Image Added                    (Eq. 113)

with  denoting the normaliSed normalized user-defined mask in dBc/Hz.

This mask is expressed as an array of N+1 points  and assumed linear between these points.

                             

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body $P_{rel}^{dBc}\left( \Delta f \right)={{P}_{i}}+\frac{\Delta {{f}_{{}}}-\Delta {{f}_{i}}}{\Delta {{f}_{i+1}}-\Delta {{f}_{i}}}\left( {{P}_{i+1}}-{{P}_{i}} \right)$

    (                Image Added        (Eq. 114)

This leads to:

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body $emission\_re{{l}_{it}}=10\log \left\{ \sum\limits_{i=0}^{N-1}{\int_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}{{{10}^{\frac{P_{rel}^{dBc}\left( \Delta f \right)}{10}}}d\Delta f}} \right\}$

     (              Image Added                   (Eq. 115)

where:

                                                   

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body $\Delta {{f}_{0}}=a={{f}_{VLR}}-{{f}_{ILT}}-{{B}_{VLR}}/2$

                                     Image Added                  (Eq. 116)

                                                  

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body $\Delta {{f}_{N}}=b={{f}_{VLR}}-{{f}_{ILT}}+{{B}_{VLR}}/2$

                                Image Added                      (Eq. 117)

Intermediate calculation

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body $\begin{align} & emission\_rel_{i}^{dBc}=\int_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}{{{10}^{\frac{P_{rel}^{dBc}\left( \Delta f \right)}{10}}}d\Delta f} \\ & emission\_rel_{i}^{dBc}={{10}^{\frac{{{P}_{i}}}{10}}}\int_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}{{{\left[ {{10}^{\frac{{{P}_{i+1}}-{{P}_{i}}}{10\left( \Delta {{f}_{i+1}}-\Delta {{f}_{i}} \right)}}} \right]}^{\left( \Delta {{f}_{{}}}-\Delta {{f}_{i}} \right)}}d\Delta f} \\ & emission\_rel_{i}^{dBc}=\frac{{{10}^{\frac{{{P}_{i}}}{10}}}}{{{K}^{\Delta {{f}_{i}}}}}\int_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}{{{K}^{\left( \Delta {{f}_{{}}}-\Delta {{f}_{i}} \right)}}d\Delta f},\quad K={{10}^{\frac{{{P}_{i+1}}-{{P}_{i}}}{10\left( \Delta {{f}_{i+1}}-\Delta {{f}_{i}} \right)}}} \\ & emission\_rel_{i}^{dBc}=\frac{{{10}^{\frac{{{P}_{i}}}{10}}}}{{{K}^{\Delta {{f}_{i}}}}}\left[ {{e}^{\ln K}} \right]_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}=\frac{{{10}^{\frac{{{P}_{i}}}{10}}}}{\ln K}\left[ {{K}^{\Delta {{f}_{i+1}}-\Delta {{f}_{i}}}}-1 \right],\quad \ln K=\frac{\ln 10}{10}.\frac{{{P}_{i+1}}-{{P}_{i}}}{\Delta {{f}_{i+1}}-\Delta {{f}_{i}}} \\ & \\ \end{align}$

    (Eq. 118)

      

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body $emission\_rel_{i}^{dBc}=\frac{10}{\ln 10}\frac{{{10}^{{{P}_{i+1}}}}-{{10}^{{{P}_{i}}}}}{{{P}_{i+1}}-{{P}_{i}}}\left( \Delta {{f}_{i+1}}-\Delta {{f}_{i}} \right)$

    (Eq. 119)

Eventually:

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body $emission\_re{{l}_{ILT}}=10\log \left\{ \frac{10}{\ln 10}\sum\limits_{i=0}^{N-1}{\frac{\left( P_{i+1}^{linear}-P_{i}^{linear} \right)\left( \Delta {{f}_{i+1}}-\Delta {{f}_{i}} \right)}{\left( P_{i+1}^{dBc}-P_{i}^{dBc} \right)}} \right\}$

    Image Added    (Eq. 118)

                      Image Added         (Eq. 119)

Eventually:

  Image Added                  (Eq. 120)