## Sum-rate maximization for two-way active channels.

##### Abstract

In this thesis, the term passive channel refers to the conventional parallel wireless
channel model, where there is no control over the gain of each individual subchannel.
We de ne an active channel as a parallel channel where by injecting power into
the subchannels, somewhere between a transmitter and a receiver, the gain of the
subchannels are adjusted. We herein study the problem of joint power allocation
and channel design over a reciprocal two-way active channel. Assuming the channel
is reciprocal, we consider the sum-rate maximization problem under the assumption
that the powers of transceivers as well as the channel power are limited. The goal is to
jointly optimize the power of each subchannel as well as the allocated power by each
transceiver to each subchannel. We use the KKT conditions to nd the necessary
conditions for the optimality. Then we devise a semi-closed-form solution for the
problem by searching over the set of the solutions provided by the KKT conditions.
We show that for a two-way active channel, the sum-rate maximization problem has a
unique global solution. We prove that at the optimum the power should be allocated
uniformly only to a subset of parallel subchannels.
Next we consider the sum-rate maximization problem for a reciprocal two-way active
channel, when the total power of the network is limited. In our system model, the
total power of the network is de ned as the summation of the total power of each
transceiver and the power of the active channel. We show that at the optimum, half
of the total power of the network should be allocated to the active channel, while the
remaining half should be distributed equally between the two transceivers.
Furthermore, we analyze the non-reciprocal two-way active channels. We consider
the sum-rate maximization problem over a non-reciprocal two-way active channel. To
solve this problem, without loss of optimality, we break the maximization problem into
two sub-problems. Then using the solution to the sum-rate maximization problem
for the one-way reciprocal active channels, we nd the optimal power distribution.
Finally, in the simulation result section, we analyze several passive channels as well
as several active channels. As shown in our numerical results two-way active channels
outperform the passive channels in terms of sum-rate under the same total network
power.