# An Ultra-Wideband Microwave Photonic Channelized Receiver with Zero-IF Architecture
## 2 Principle
The polarization multiplexed signal output from the DP-QPSK modulator is sent to the OBPF, and the optical frequency comb and the positive second-order optical sideband are filtered out and can be expressed as:  
\[E_{OBPF}(t)=\left| \begin{array}{c}\frac{E_{in}(t)}{2}\left[\begin{array}{c} \cos AJ_{0}(B)+\cos(\frac{\pi V_{1B}}{2V_{n}})e^{\frac{\pi V_{1E}}{V_{n}}}\\ +\sin AJ_{1}(B)e^{i(\omega_{LO1}t+\frac{\pi}{2})}+\sin AJ_{1}(B)e^{i(\omega_{LO1 }t-\frac{\pi}{2})}\\ +\cos AJ_{2}(B)e^{j2\omega_{LO1}t}+\cos AJ_{2}(B)e^{-j2\omega_{LO1}t}\\ \frac{\pi V_{E_{in}}(t)}{2}J_{2}(\mathfrak{m}_{LO2})[\exp(j2\omega_{LO2}t)] \end{array}\right|\\ \end{array} \right. \tag{19}\]  
The output port of the OBPF is connected to the single polarization MZM. The wideband RF signal sent to the single polarization MZM consists of five vector signals with a symbol rate of 500 MSym/s and a modulation format of hexadecimal quadrature amplitude modulation (16 QAM) and center frequencies of 18.8 GHz, 19.4 GHz, 20 GHz, 20.6 GHz, and 21.2 GHz, respectively. The RF signal can be expressed as \(V_{RF}(t)\sin[\omega_{RF}t+\varphi(t)]\). The wideband RF signal is only modulated by the _TM_ mode (positive second-order optical sideband) and is not modulated by the _TE_ mode (optical frequency comb). The DC bias of the single-polarized MZM is set to be operated at the MITP to realize the double-side band modulation with carrier suppression. The signal output from the single polarization MZM modulation can be expressed as:  
\[E_{out} =\frac{E_{DPMZM2}(t)}{2}\left\{ \begin{array}{c}\exp[jm_{RF}\sin( \omega_{RF}t+\varphi(t))]\\ -\exp[-jm_{RF}\sin(\omega_{RF}t+\varphi(t))]\end{array} \right\} \tag{20}\] \[=\frac{E_{DPMZM2}(t)}{2}\left\{ \begin{array}{c}\cos\begin{array} []{c}J_{n}(m_{RF})\exp[jn(\omega_{RF}t+\varphi(t))]\\ \mathfrak{n}=-\infty\end{array}J_{n}(m_{RF})\exp[-jn(\omega_{RF}t+\varphi(t))] \end{array} \right\}\]  
Since the center frequency of the broadband RF signal is equal to twice the frequency of the \(LO_{2}\), the center frequency of the lower sideband of the modulated broadband RF signal is equal to the center frequency of the optical frequency comb. The output of the single polarization MZM is divided into five channels by the optical splitter. Each channel passes through the narrowband OBPF with different center frequencies. The center frequencies of the five channels are 193.0988 THz, 193.0994 THz, 193.1 THz, 193.1006 THz, and 193.1012 THz, respectively, and the bandwidth is 600 MHz, which realizes simultaneous segmentation of wideband signals and optical frequency combs. The following is an example of down-conversion for a sub-channel with the center frequency of 21.2 GHz. The OBPF1 filters out the negative second-order band of the RF signal on the first-line of the optical comb. The sub-RF signal can be expressed as \(V_{RF1}(t)\sin[\omega_{RF1}t+\varphi_{1}(t)]\), and the optical signal output from OBPF1 is expressed as  
\[E_{OBPF1}(t) =\left| \begin{array}{c}E_{-2}(t)\\ E_{\omega_{RF1}}(t)\end{array} \right| \tag{21}\] \[=\frac{E_{in}(t)}{2}\left| \begin{array}{c}\cos AJ_{2}(B)\exp(-j 2\omega_{LO1}t)\\ \sqrt{2}J_{2}(\mathfrak{m}_{LO2})\exp(j2\omega_{LO2}t)\cdot J_{1}(m_{RF1}) \exp[-j(\omega_{RF1}t+\varphi_{1}(t))]\end{array} \right|\]An optical splitter can be used to split the optical signal into two channels. Each channel has a PC and a PBS which can generate the following two different optical signals:  
\[E_{1}(t)=\frac{E_{in}(t)}{2}\left\{ \begin{array}{l}\cos AJ_{2}(B)\exp(-j2\omega_{ LO1}t)\cos\alpha\\ +\sqrt{2}J_{2}(\text{m}_{LO2})\exp(j2\omega_{LO2}t)\\ \cdot J_{1}(m_{RF1})\exp[-j(\omega_{RF1}t+\varphi_{1}(t))]\sin\alpha\exp(j\phi) \end{array} \right\} \tag{22}\]  
\[E_{2}(t)=\frac{E_{in}(t)}{2}\left\{ \begin{array}{l}\cos AJ_{2}(B)\exp(-j2 \omega_{LO1}t)\sin\alpha\\ -\sqrt{2}J_{2}(\text{m}_{LO2})\exp(j2\omega_{LO2}t)\\ \cdot J_{1}(m_{RF1})\exp[-j(\omega_{RF1}t+\varphi_{1}(t))]\cos\alpha\exp(j\phi )\end{array}