  In OFDM relay networks with IQ imbalances and full-duplex relay station (RS),
how to optimize pilot pattern and power allocation using the criterion of
minimizing the sum of mean square errors (Sum-MSE) for the frequency-domain
least-squares channel estimator has a heavy impact on self-interference
cancellation. Firstly, the design problem of pilot pattern is casted as a
convex optimization. From the KKT conditions, the optimal analytical expression
is derived given the fixed source power and RS power. Subsequently, an optimal
power allocation (OPA) strategy is proposed and presented to further alleviate
the effect of Sum-MSE under the total transmit power sum constraint of source
node and RS. Simulation results show that the proposed OPA performs better than
equal power allocation (EPA) in terms of Sum-MSE, and the Sum-MSE performance
gain grows with deviating $\rho$ from the value of $\rho^o$ minimizing the
Sum-MSE, where $\rho$ is defined as the average ratio of the residual SI
channel at RS to the intended channel from source to RS. For example, the OPA
achieves about 5dB SNR gain over EPA by shrinking or stretching $\rho$ with a
factor $4$. More importantly, as $\rho$ decreases or increases more, the
performance gain becomes more significant.
