Power Spectral Densities of Noise Sources in ETSI Model

 In this section, expressions will be obtained for the power spectral density of the noise produced by the two branches of the ETSI noise model at points just before the summation block.

 

Figure 5.1:   Power Spectral Densities in Noise Model implemented on SPW

Consider first the top branch of the noise model as shown in figure 5.1 with a white Gaussian noise source of power spectral density

$$S_{WGN}(f)=\frac{1}{2}\eta$$ (34)

The power spectral density of the noise once it has passed through filters A and B can be found.

 

Figure 5.2:   Power Spectral Density Relationship

By considering figure 5.1 and using the relation

 

S_out(f)=|H(f)|² S_in(f)

as shown in figure 5.2 it is evident that

S_out<<1134>>f(f)=S_WGN(f) |K_f H_A(f) H_B(f)|²

Substituting the transfer functions for filters A and B (2.2), (2.3) one obtains

$$S_{out_{f}}(f)\approx \frac{1}{2}\eta \vert K_F\vert^2 \left... ...}{s}}\right\vert^2 \left\vert\frac{\beta}{s+\beta}\right\vert^2$$

which may be simplified to  

$$S_{out_{f}}(f)=\frac{1}{2}\eta \cdot K_f^2 \frac{f_0}{f}\frac{B^2}{f^2 + B^2}$$ (37)

A similar analysis for the lower branch yields the expression  

$$S_{out_{w}}(f)=\frac{1}{2}\eta K_w^2\frac{f^2}{f^2 + B^2}$$ (38)

Finally, $\eta$ can be related to parameters in the ETSI noise model. The noise sources referred to in section 2.4 have a noise bandwidth B_n=5Hz and standard deviation $\sigma=1ns$. It can be shown [17] that  

$$\eta=\frac{\sigma^2}{B_n}$$ (39)

Thus equations (5.4) and (5.5) become