The relation of sub-carrier and FDMA

Question

In Mengyu Liu, Yuan Liu, "Charge-then-Forward: Wireless Powered Communication for Multiuser Relay Networks", it is said that

while information signals are conveyed by using FDMA over $N$ sub-carriers (SCs) in the next phase of WIT(wireless information transmission). For information transmission, we define a binary SC allocation variable $x_{k,n}$ with $x_{k,n} = 1 $ representing that SC $n$ is allocated to pair $k$ for WIT and $x_{k,n} = 0 $ otherwise. Each SC is allocated to at most one pair at slot 1 for WIT to avoid interference

Does it mean that if the source transmits information to relay, it needs a carrier to help it send the message, so if I have $K$ source, then I have $K$ subcarrier?

If so, why does it still need two different variables? And I can't understand that if my thinking is right, why does it still have two situations, $x_{k,n}=0$ and $x_{k,n}=1$, for that?

Answer 1

Does it mean that if the source transmits information to relay, it needs a carrier to help it send the message, so if I have K source, then I have K subcarrier?

There's $K$ pairs of nodes, if you read the text closely. That means you can have, for example, one source with four information sinks, or four sources and three sinks, or…

Answer 2

A pair $k$ is the link $S_k\rightarrow R \rightarrow D_k$. Since you have $K$ pairs, you need to use orthogonal channels to avoid interference between the difference pairs. In FDMA this is done by assigning different subcarrier to each pair that is orthogonal to other subcarriers. Since you have $K$ pairs and $N$ subcarriers, you need to specify which subcarrier is assigned to which pair. If subcarrier $n$ is assigned to pair $k$, then $x_{k,n}=1$, otherwise it's zero. You need $K$ subcarriers for the transmission, but $N\geq K$, where other subcarriers maybe used for other things, like control channels, or guard intervals between the subcarriers ... etc.