# An Ultra-Wideband Microwave Photonic Channelized Receiver with Zero-IF Architecture
## 2 Principle  
Figure 1 shows the schematic diagram of the proposed microwave photonic channelized receiver with zero-IF architecture. It mainly consists of a laser diode (LD), a DP-QPSK modulator, two LO signals (LO\({}_{1}\) and LO\({}_{2}\)), a set of optical bandpass filters (OBPFs), a single polarization MZM, several polarization controllers (PCs), several polarization beam splitters (PBSs), and several pairs of balanced photodiodes (BPDs). In the proposed system, the DP-QPSK modulator is integrated by two parallel DPMZMs (DPMZM1 and DPMZM2) and a polarization beam combiner (PBC). Each DPMZM is composed of two parallel sub-MZMs (MZMa and MZMb) and a main modulator (MZMc). The LD generates a continuous light wave with a frequency of 193.1 THz and a power of 20 dBm, and the continuous light wave is launched into the DP-QPSK modulator as a carrier. Supposing the light wave generated from the LD is expressed as \(E_{\rm in}(t)=E_{0}\exp(j\omega_{\rm c}t)\) where \(E_{0}\) and \(\omega_{\rm c}\) are the amplitude and angular frequency, respectively. After equal power splitting, two light waves are modulated by the \(LO_{1}\) and \(LO_{2}\) signals, respectively. In DPMZM1, only \(LO_{1}\) signal with a frequency of 0.6 GHz is applied to drive MZMa and a push-pull configuration of the sub-MZMs is assumed. The \(LO_{1}\) signal can be expressed as \(V_{LO1}=V_{0}\sin(\omega_{LO1}t)\). \(V_{1a}\), \(V_{1b}\), and \(V_{1c}\) represent the three DC bias voltages respectively. The output field of the DPMZM1 can be expressed as [18]:  
\[E_{\rm DPMZM1}=\frac{E_{in}(t)}{2}\Big{\{}\cos\!\Big{[}\frac{\pi V_{0}}{2V_{ \pi}}\sin(\omega_{LO1}t)+\frac{\pi V_{1a}}{2V_{\pi}}\Big{]}+\cos\!\Big{(}\frac {\pi V_{1b}}{2V_{\pi}}\Big{)}e^{i\frac{\pi V_{1c}}{V_{\pi}}}\Big{\}} \tag{1}\]  
where \(V_{\pi}\) is the half-wave voltage of the modulators. Based on Jacobi-Anger expansion to the output field, the optical carrier, first-order and second-order sidebands can be expressed as follows. \[E_{0}=\frac{E_{in}(t)}{2}\Big{[}\cos AJ_{0}(B)+\cos\!\Big{(}\frac{\pi V_{1b}}{2 V_{\pi}}\Big{)}e^{i\frac{\pi V_{1c}}{V_{\pi}}}\Big{]} \tag{2}\]  
\[E_{+1}=\frac{E_{in}(t)}{2}\sin AJ_{1}(B)e^{i(\omega_{LO1}t+\frac{\pi}{2})} \tag{3}\]  
\[E_{-1}=\frac{E_{in}(t)}{2}\sin AJ_{1}(B)e^{i(\omega_{LO1}t-\frac{\pi}{2})} \tag{4}\]  
\[E_{+2}=\frac{E_{in}(t)}{2}\cos AJ_{2}(B)e^{i2\omega_{LO1}t} \tag{5}\]  
\[E_{-2}=\frac{E_{in}(t)}{2}\cos AJ_{2}(B)e^{-j2\omega_{LO1}t} \tag{6}\]  
where \(A=\pi V_{1a}/2V_{\pi}\), \(B=\pi V_{0}/2V_{\pi}\), \(\omega_{LO1}=2\pi f\), and \(J_{n}(x)\) represent the \(n\)th-order Bessel function. The optical carrier, first-order and second-order sidebands together can form five comb lines. The amplitude of each comb directly affects the flatness of the five comb lines. Therefore, Equations (2)-(6)  
Figure 1: Schematic diagram of proposed microwave photonic channelization receiver with zero-intermediate frequency (IF) architecture, which mainly consists of polarization multiplexed signals generation, photonic microwave in-phase/quadrature (I/Q) mixing, and balanced detection. LD: laser diode; DPMZM: dual parallel Mach–Zehnder modulator; LO: local oscillator; PBC: polarization beam combiner; OBPF: optical bandpass filter; RF: radio frequency; PC: polarization controller; PBS: polarization beam splitter; BPD: balanced photodiode. can also be regarded as the expression of the five combs.