Resource Allocation in OFDM Based Wireless Relay Networks ...

3.3 Problem Formulation
signals received at the m-th user pair can be written as
ym,j A =
√p R˜h √
√
j m,j ρ j p A m,k h m,kx A m,k + p R j ρ j˜h m,j wk RS +
√p R˜h √
j m,j ρ j p B m,k g m,kx B m,k
+ wm,j, A (3.2)
√
√
√
ym,j B =
√p R j ρ j˜g m,j p B m,k g m,kx B m,k + p R j ρ j˜g m,j wk RS +
√p R j ˜g m,jρ j p A m,k h m,kx A m,k
+ w B m,j, (3.3)
where ρ j √ 1
p A m,k |h m,k| 2 +p B m,k |g m,k| 2 +σ 2
is the scaling factor to keep the power
constraint, while w A m,j and w B m,j are the received additive white Gaussian noises
(AWGN) at A m and B m , respectively, both with variance σ 2 . Assuming a perfect
self-interference cancellation, the corresponding SNRs can be written as
SNR A m,j = pR j |˜h m,j | 2 ρ 2 jp B m,k |g m,k| 2
(
) , (3.4)
p R j ρ2 j |˜h m,j | 2 + 1 σ 2
SNR B m,j = pR j |˜g m,j | 2 ρ 2 jp A m,k |h m,k| 2
(
p
R
j ρ 2 j |˜g m,j| 2 + 1 ) σ 2 . (3.5)
3.3 Problem Formulation
Due to the exclusive tone matching constraint, each sub-carrier in MAP can only
be paired with one sub-carrier in BCP. We then define π (k,j) ∈ {0, 1} as the binary
variable for the sub-carrier pairing such that π (k,j) = 1 if the k-th sub-carrier is
paired with the j-th sub-carrier, while π (k,j) = 0 otherwise. Further, we define
binary variables τ m,(k,j) ∈ {0, 1}, such that τ m,(k,j) = 1 if sub-carrier pair (k, j) is
allocated to the m-th MU pair while τ m,(k,j) = 0 otherwise.
We seek to jointly optimize the sub-carrier allocation, sub-carrier pairing, and
the power allocation such that the overall system throughput is maximized under
individual power constraints at MUs and RS. Let P Am , P R , and P Bm denote the
total available powers at A m , RS, and B m , respectively. The optimization can be
49