Resource Allocation in OFDM Based Wireless Relay Networks ...

2.4 Generalization to Multiple Relay Scenario
Figure 2.2: Multi-user multi-relay uplink system model.
and the variance of the additive noise over the k-th sub-carrier between the m-th
MU and the n-th RS. Moreover denote g n,j as the channel coefficient of sub-carrier
j between the n-th RS and BS. Based on the proposed protocol, one sub-carrier
pair (k, j) can only be assigned to one MU-RS pair (m, n). The corresponding data
throughput is given by
r (m,n),(k,j) = 1 2 log 2
(
)
p m,n,k a m,n,k q n,j b n,j
1 +
, (2.39)
1 + p m,n,k a m,n,k + q n,j b n,j
where a m,n,k h m,n,k
, b
σm,n,k
2 n,j g n,j
, and q
σn,j
2 n,j , σn,j 2 are the power allocation and the
variance of the additive noise over the j-th sub-carrier during the second hop,
respectively. Let τ (m,n),(k,j) be a binary variable indicating the sub-carrier pair
allocation, i.e., τ (m,n),(k,j) = 1 if sub-carrier pair (k, j) is allocated to MU-RS pair
(m, n) and it must satisfy
N∑
n=1 m=1
M∑
τ (m,n),(k,j) = 1, ∀(k, j). (2.40)
Meanwhile, each node has limited transmission power, i.e.,
N∑
n=1 k=1
K∑
p m,n,k ≤ P m , ∀ m,
K∑
q n,j ≤ Q n , ∀n, (2.41)
j=1
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