## 2 System Overview  
In this study, we implement a basic IBFD system prototype that consists of several constitute parts including an antenna unit, two AC boards, two software defined radio (SDR) devices, and a digital processing unit. The block diagram of the proposed IBFD system implementation is shown in Figure 2. In the following paragraphs, the functionalities of the constitute blocks of the proposed system implementation are introduced with more details. \begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Description** \\ \hline \(a\) & Scalar variable \\ \(A\) & Scalar constant \\ \(f(x)\) & Function of \(x\) \\ \(a^{*}\) & Complex conjugate of \(a\) \\ \(\mathbf{a}\) & Vector \\ \(\mathbf{A}\) & Matrix \\ \(\mathbf{A}^{\mathrm{T}}\) & Transpose of \(\mathbf{A}\) \\ \(\mathrm{A}^{\mathrm{H}}\) & Hermitian of \(\mathbf{A}\) \\ \(||\mathbf{a}||\) & Norm of \(\mathbf{a}\) \\ \(\mathbb{E}\{a\}\) & Expectation function of random variable \(a\) \\ \(\mathbf{\
abla_{\mathbf{a}}}\) & Derivation with respect to \(\mathbf{a}\) \\ \(\mathrm{tr}\{\mathbf{A}\}\) & Trace of \(\mathbf{A}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mathematical notation list. Firstly, the digital processing unit is implemented by a high-performance computer with high computational capability. The programming of the digital processing is realized by the MATLAB program platform, which can be connected to the following USRP stage via high-speed ethernet connections. The digital processing unit is responsible for the transmitter (TX) process, receiver (RX) process, SI cancellation with adaptive filter in digital domain, and calculating two performance metrics including error vector magnitude (EVM) and BER of RX signal. The TX process is operating random bit generation, QPSK modulation, and OFDM modulation, while the RX process is processing QPSK and OFDM demodulation. The detailed illustration of the digital SI cancellation using an adaptive filter is provided in Section 3. The next stage connected to the digital processing unit consists two software-defined radio (SDR) devices responsible for converting digital signals into radio signals. The SDR devices can be customized by users, which makes the evaluations of complicated wireless systems like IBFD easy. Besides for validation of system practicality, the system development can be more effective by using SDR devices. The SDR devices adopted in the proposed system implementation are universal software radio peripheral (USRP) devices. There are two USRP devices included in our implemented system prototype. One serves as a transmitter acting as the desired signal and SI sources. Another one serves as the UL receiver, which receives and processes the combined signal of desired UL signal and SI. The USRP devices adopted in the implemented system prototype are NI USRP 2954R devices, which transmit and receive radio signals at the intermediate frequency (IF) 2.15 GHz. The functional blocks connected to the USRP devices are AC boards, which are responsible for up-converting and down-converting of the operating frequency, Additionally, there is an analog-domain SI cancellation functionality implemented in the AC boards. The up-converting of the operating frequency is shifting the USRP output IF signal with 2.15 GHz to radio frequency (RF) 4.7 GHz for the antennas, while the down-converting of the operating frequency is shifting the 4.7 GHz RF signal from antennas to IF 2.15 GHz for USRP. In addition to the up-converting and down-converting functionalities, the AC boards are implemented with analog SI cancellation functionality proving about maximum 30 dB analog SI cancellation performance.