# A Full-Duplex 60 GHz Transceiver with Digital Self-Interference Cancellation
## 3 Design and Implementation
### Digital SI Cancellation Scheme  
The SI power should be less than \(-\)67.6 dBm to ensure the FD operation has benefits compared to the HD operation for a 3 m communication distance. This is challenging to achieve using only the RF isolation approach. This section focuses on a digital SI cancellation scheme to relax the RF-related leakage optimization requirement. To simplify the digital SI cancellation (DSIC) scheme, only a linear transformation is adopted in this work, and the dominant SI leakage source considered is from the PA's output to the LNA's input. So, the transmitter signal \(\mathrm{S_{tx}}\) can be expressed as in (1), where I and Q are the baseband signals, \(\omega_{0}\) is the LO carrier frequency, and \(\varphi_{\mathrm{tx}}\) and \(\theta_{\mathrm{tx}}\) are the phase noise and the initial phase of the transmitter LO, respectively. \[S_{tx}=I\cdot\cos((\omega_{0}+\varphi_{tx})t+\theta_{tx})+Q\cdot\sin((\omega_{ 0}+\varphi_{tx})t+\theta_{tx}) \tag{1}\]  
The transmitted RF signal \(\mathrm{S_{tx}}\) loops back to the LNA's input through an undesired SI leakage path and will be down-converted through the receiver chain by using the same LO \(\omega_{0}\) but with the phase noise \(\varphi_{\mathrm{rx}}\) and an initial phase \(\theta_{\mathrm{rx}}\). The received I/Q baseband signal is captured by an analog-to-digital converter (ADC) in the baseband processor. The captured baseband signal before the ADC can be expressed as follows:  
\[I_{rx}=1/2[(I\times\cos((\varphi_{tx})t-\theta_{tx})\cdot Q\times\sin((\varphi_ {tx})t-\theta_{tx} \tag{2}\]  
\[Q_{rx}=1/2[(Q\times\cos((\varphi_{tx})t-\theta_{tx})\cdot I\times\sin((\varphi_ {tx})t-\theta_{tx})] \tag{3}\]  
where \(\varphi_{\mathrm{tx}}=\varphi_{\mathrm{tx}}-\varphi_{\mathrm{rx}}\) and \(\theta_{\mathrm{tx}}=\theta_{\mathrm{tx}}-\theta_{\mathrm{rx}}\). It is clearly seen that the SI signal is related to the LO phase noise, and it is rotated depending on the initial phase \(\theta_{\mathrm{tx}}\). Equations (2) and (3) shows that the phase noise is effectively doubled as \(\varphi_{\mathrm{tx}}\) and \(\varphi_{\mathrm{rx}}\) are not related to each other, and there is a constant phase rotation in the received I/Q signal. At the same time, the propagation delay of the signal causes an offset between the sampling time of the receiver's ADC and the ideal sampling time. The time-domain equalization filter is used after the phase rotation and symbol synchronization to minimize the error  
Figure 4: The fabricated PCB with two antennas. between the received leakage signal and the estimated value. Here, the propagation delay and channel effect of the SI leakage channel are assumed to be fixed across the time and input signals. Figure 5 shows the block diagram of the proposed DSIC scheme. The design is implemented in MATLAB with four times the oversampling data captured by an oscilloscope. \(\mathrm{I_{rx}}\) and \(\mathrm{Q_{rx}}\) are received as baseband signals, and \(\mathrm{I_{rx}}\) and \(\mathrm{Q_{rx}}\) are the original signals from the transmitter. The data sequence is separated into a training period and an SI cancellation period as shown in Figure 5. During the training period, only the SI leakage signal is available in the receiver chains. The IEEE 802.11 ad-based frame packages are used as training sequences. Firstly, the I/Q data-related correlation is calculated in the phase rotation module to detect the package and estimate the initial phase simultaneously. Then, the Gardner filter is used for symbol synchronization after the phase rotation. It helps to correct the sampling time offset. Finally, a symmetrical filter with 21 multipliers is implemented as a 41-tapped finite impulse response (FIR) filter to do time-domain equalization among 10 symbols. The FIR-based recursive least squares (RLS) algorithm is used as an adaptive filter to optimize the equalization filter. The FIR filter coefficients are calculated during the training period and maintained for the SI cancellation period.