# Channel Impulse Response is zero mean Gaussian random variable?

In the Paper "Key Generation From Wireless Channels" the channel estimation is given as: $$\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||S_B||^2}$$, $$\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||S_A||^2}$$

So the different $$\tilde{h}_{1,x}$$ are zero mean Gaussian random variables with some variance.

At the end, they calculate the secret key rate by

$$R_s = \frac{1}{T} I \left( \tilde{h}_{1,A}, \tilde{h}_{1,B} \right) = \frac{1}{2T} \log\left( {1+\frac{\sigma_1^4 P^2 T^2}{4(\sigma^4+\sigma^2+\sigma_1^2PT)}} \right)$$, there P is power and T is the coherence time.

I would like to calculate that for WiFi at 2.4 GHz. I'm searching for a typical value for the variances $$\sigma$$ and $$\sigma_1$$. In addition, a value for 60 GHz would be also awesome.

• Those variances can go from 0 (for a static environment) to very large... they depend on the properties of the specific channel you're measuring on. – MBaz Jan 30 '20 at 22:14
• @MBaz, thanks for your response. But I'm searching for a typical value for 2.4 GHz and 60 Ghz. I don't core how precise that is. :) – user674907 Jan 31 '20 at 11:02