Channel Estimation for Self-Interference Cancellation in Full-Duplex Wireless Systems

Abstract

In this paper, analog cancellation with a self-interference channel estimation scheme is proposed for full-duplex wireless systems. The aim of the proposed scheme is to cancel the self-interference signal at a full-duplex node for orthogonal frequency division multiplexing systems in a multipath self-interference channel with small delay spread. In the proposed scheme, the analog self-interference signal is emulated on the basis of baseband channel estimation. Assuming that a multipath self-interference channel has small delay spread, the proposed channel estimator provides effective channel gain and effective delay estimates of the self-interference channel on the basis of the maximum-likelihood criterion. Numerical results indicate that the self-interference suppression performance of the proposed analog cancellation scheme is better than the performance of the conventional schemes in a small delay spread multipath environment.

Appendix

Because the phase rotation [6] and JGD schemes focus on baseband channel estimation for the strongest path in the self-interference channel, $\bar{H}[k]$ in (7) can be approximated as

$$\bar{H}[k]=\varGamma e^{-j 2 \pi f_k \tau _1}+\frac{1}{P} \sum _{i=2}^{N_P} G_i e^{-j 2 \pi f_k \tau _i} \approx \varGamma e^{-j 2 \pi f_k \tau _1}, $$

(23)

where $\varGamma =\frac{G_1}{P}$. For baseband channel estimation in (23), the phase rotation scheme in [6] uses estimates of $\varGamma$ and $\theta _k=2 \pi f_k \tau _1$. For the JGD scheme, the log-likelihood function for the parameters $(\varGamma , \tau _1)$ is obtained by

$$\varLambda (\bar{R}[k]; \tilde{\varGamma }, \tilde{\tau _1})=N \ln (\pi \sigma _W^2) - \frac{1}{\sigma _W^2} \sum _{k=-N/2}^{N/2-1} \left| \bar{R}[k] - \tilde{\varGamma } e^{-j 2 \pi (f_c+k\varDelta f)\tilde{\tau }_1} X^P[k] \right| ^2, $$

(24)

where $\tilde{\varGamma }$ and $\tilde{\tau }_1$ are the trial values of $\varGamma$ and $\tau _1$, respectively. Then, the joint ML estimates of $\tau _1$ and $\varGamma$ can be obtained by

$$ \hat{\tau }_1=\arg \max _{\tilde{\tau }_1} \left( {\mathfrak{R}}\left\{ e^{j 2 \pi f_c \tilde{\tau }_1} \varPsi (\tilde{\tau }_1) \right\} \right) ^2, $$

(25)

and

$$ \hat{\varGamma }=\frac{1}{\varUpsilon } {\mathfrak{R}}\left\{ e^{j 2 \pi f_c \hat{\tau }_1} \varPsi (\hat{\tau }_1) \right\} , $$

(26)

respectively. Note that $\left( {\mathfrak{R}}\left\{ e^{j 2 \pi f_c \tilde{\tau }_1} \varPsi (\tilde{\tau }_1) \right\} \right) ^2$ in (25) is maximized for $\tilde{\tau }_1$ that satisfies ${\mathfrak{R}}\left\{ e^{j 2 \pi f_c \tilde{\tau }_1} \varPsi (\tilde{\tau }_1) \right\} >0$ because $\hat{\varGamma }=\frac{1}{\varUpsilon } {\mathfrak{R}}\left\{ e^{j 2 \pi f_c \hat{\tau }_1} \varPsi (\hat{\tau }_1) \right\} >0$. Here, the JGD scheme provides the ML estimates of the gain and delay when the only strongest path exists in a self-interference channel.