Wireless devices usually have several types of constraints. A commonly studied constraint is that the powers (or energies) of the inputs satisfy (see (2.4))
A more severe type of constraint is
where the per-symbol energy is constrained.
A second constraint is similar to the wireline port constraint (3.1). Note that the model defined by (3.3a) and (3.3b) implicitly lets node 2 transmit and receive at the same time in the same frequency band. However, this is often not possible due to the large differences in transmit and receive energies at the antenna of node 2. Most practical wireless devices operate under a half-duplex constraint that we can model as
Note the similarity between (3.1) and (3.7).
A third constraint is that, because the channel changes over time, a device usually does not know the internode distances duv or channel gains huv ahead of time. A simple approach is to assume that each node knows the gain huv between itself and the nodes with which it cooperates. However, the validity of this assumption depends strongly on the speed of channel variations. Learning the channel and network parameters is usually a challenging task even for nodes near each other. In general, different models must be considered for different scenarios. For example, there might be two tiers of nodes: one tier with high capacity to neighboring nodes and therefore sufficient channel and network knowledge, and a second tier that lacks such knowledge. The communications theory for the latter case is fascinating in its own right, and we refer to [115, 117, 135, 184] for further information.
