Resource Allocation in OFDM Based Wireless Relay Networks ...

2.4 Generalization to Multiple Relay Scenario
Here, U, B and C denote the sets of users, sub-carriers on MU-to-RS link, and
sub-carriers on RS-to-BS link, respectively, and χ(t) represents the t-th element
of the set χ. In the first step, both MUs and RS equally distribute the available
power to K sub-carriers, such that p m,k = P m
K
, ∀m and q j = Q . In the second step,
K
sub-carrier allocation among different users is found by selecting K best sub-carriers
among all MK sub-carriers, such that each sub-carrier is allocated to a unique
user that has the best channel gain for this particular sub-carrier. This requires
a complexity of O(MK).
sub-carrier pairing is done in step 3, where the best
sub-carrier on MU-to-RS link is paired with the best sub-carrier on RS-to-BS link,
with total complexity of O(2K). For τ and π found from step 2 and step 3, we can
derive the power allocation in step 4. The dual variables are found from sub-gradient
method.
If the solution converges after I ′ sub-gradient updates, the total complexity of
suboptimal scheme becomes O(K(I ′ + M + 2)). Considering I ′ close to I, because
both are iterations for gradient type search, we can see that the complexity of
suboptimal approach is much less than that of joint resource allocation scheme,
where later in the simulations it can be observed that the suboptimal algorithm
yields closed performance to the joint resource allocation scheme.
2.4 Generalization to Multiple Relay Scenario
In the previous section, we developed the resource allocation algorithm for multi-user
single RS scenario. In this section, we extend our previous results to the uplink
scenario with N RSs. The multi-relay uplink system model is shown in Fig. 2.2.
The protocol is described as follows: MUs transmit the signals based on
OFDMA over different sub-carriers to more than one RS, whereas a particular RS
can serve more than one MUs. To avoid interference, an OFDMA transmission is
adopted on the second hop such that different relays will only forward the received
signals over different sub-carriers.
Let h m,n,k , p m,n,k , and σm,n,k 2 denote the channel coefficient, power allocation
31