NextGen relies on Global Positioning System $($GPS$)$ satellite signals to determine each aircraft's precise position in the sky$.$ Aircraft then use Automatic Dependent Surveillancebroadcast $($ADS$-$B$)$ technology to periodically broadcast their location information to other aircraft and air traffic control towers in the vicinity.

Suppose that an ADS$-$B transmitter broadcasts a binary signal $\backslash ($ x $\backslash$in$\backslash \{-1,1\backslash \}\backslash )$ and that an ADS$-$B receiver receives the signal as

$\backslash [$

Y$=$a x$+$N

$\backslash ]$

where $\backslash ($ a$>0\backslash )$ represents the strength of the received signal after propagating through space and $\backslash ($ N $\backslash )$ is additive noise, which is normally distributed with mean $0$ and variance $\backslash (\backslash$sigma$^\{2\}\backslash ).$ For example, if the transmitter broadcasts the signal $\backslash ($ x$=1\backslash )$ and $\backslash ($ a$=0\mathrm{.}1\backslash ),$ then $\backslash ($ Y$=$a x$+$N$=0\mathrm{.}1+$N $\backslash ).$ Notice that the signal attenuation becomes larger as $\backslash ($ a $\backslash )$ decreases. At large attenuations $($small values of $\backslash ($ a $\backslash )),$ the received signal eventually gets lost in the noise $($i$.$e$.,$ the received signal will eventually become smaller than the noise $\backslash ($ N $\backslash ),$ which will make it harder for the receiver to correctly interpret it$).$

The ADS$-$B receiver uses a likelihood ratio test to decode the received message based on the following binary hypothesis testing problem:

$-\backslash ($ H$\_\{0\}$: Y$=$a$+$N $\backslash )$

$-\backslash ($ H$\_\{1\}$: Y$=-$a$+$N $\backslash )$