10 Estimation of the overall compression rate

The overall compression rate (efficiency) is the average of $C_{{\rm r}}$ ( $\eta_{{\rm c}}$) over the full set of detectors. Appendix A illustrates the mathematical aspects of such average. From Eq. (A4):

$$% \overline{\mbox{$C_{{\rm r}}$ }}(\mbox{$N_{{\rm c}}$ }) = ... ...ox{$C_{{\rm r}}$ }_{,\nu}(\mbox{$N_{{\rm c}}$ })}\right]^{-1}.$$ (15)

We will limit ourselves to the most probable case $\mbox{$N_{{\rm c}}$ } = 1$ and to the most effective compressor arith-n1. The compression parameters $C_{{\rm r},1}$ and ${\mathcal{S}}_{1}$ at 30 GHz and 100 GHz are derived from our simulations, while $C_{{\rm r},1}$ and ${\mathcal{S}}_{1}$ at 44 GHz and 70 GHz are obtained by linear interpolation of the simulated values as a function of $\ln \sigma_\nu$. After that we obtain:

$$% \overline{\mbox{$C_{{\rm r}}$ }} \approx \frac{2.66}{1+0.271 \times \ln \mbox{${{\rm VOT}}$ }}\cdot$$ (16)

As expected the overall compression rate is dominated by the 100 GHz channel. Taking in account the conservative ${{\rm VOT}}$ distribution considered in Eq. (A8) the overall compression rate becomes: $\overline{\mbox{$C_{{\rm r}}$ }} \approx 2.63$ which represents a $\approx 2 \%$ correction only. It is likely that this correction will be even smaller, since the amplifiers gain will be adjusted in order to cover a smaller ${{\rm VOT}}$ interval. So this $2\%$ correction represents our greatest uncertainty in our estimation of the expected compression rate in the present conditions, and we may conservatively conclude that:

$$% \overline{\mbox{$C_{{\rm r}}$ }}_{,{\rm arith-n1}} \approx 2.65 \pm 0.02\cdot$$ (17)

Recently a new evaluation of the expected instrumental sensitivity leads to some change in the expected white noise rms. These changes affect in particular the 30 GHz channel, but does not change significantly the 100 GHz channel so that the overall compression rate will be practically unaffected.