## 3 Proposed MDM-MIMO-IIR Photonic Radar Modeling  
The proposed photonic radar system's schematic diagram, which is intended for multiple target detection, is presented in Figure 1. The modeling of the proposed MDM-MIMO-IIR system was conducted utilizing OptiSystem(tm) (V 18) and MATLAB(tm) (R 2022) software. These tools are instrumental in simulating and analyzing the performance of the system, providing a comprehensive understanding of its capabilities and efficiency. As shown in Figure 1, the proposed 2 \(\times\) 2 MIMO-IIR-based photonic radar is configured in homodyne formation. Homodyne radar has several advantages over heterodyne radar in terms of simplicity, performance, and cost-effectiveness, namely, better signal-to-noise ratio (SNR), simpler design, improved range resolution, and faster data processing. The transmitter has three sections--a linear frequency modulator (LFM) section, an optical source, and a modulator section. The LFM section produces a saw-tooth waveform, which undergoes frequency modulation via an LFM modulator. This modulator operates at a frequency of 77 GHz and has a bandwidth capacity of 4 GHz. The output signal is divided into two parts, with one part going towards the optical modulator and the other acting as a reference signal for the receiver. The continuous wave (CW) laser signal is fed into the mode generator component where transverse modes are encoded onto the signal. In this setup, two distinct transmitters are used, each of which transmits on a specific Laguerre-Gaussian (LG) transverse mode. Transmitter 1 operates on the LG 20 mode, while Transmitter 2 operates on the LG 30 mode. These modes refer to different spatial light patterns characterized by their specific angular momentum and radial node properties, which are key in applications like mode division multiplexing. Figure 2 presents the intensity distribution for the LG 20 and LG 30 optical modes. The LG 20 mode image displays a central bright spot surrounded by two concentric rings of light, which corresponds to its mode structure with two radial nodes. The LG 30 mode shows a similar central peak but with three surrounding concentric rings, denoting its three radial nodes. LG 20 and LG 30 modes are specific types of Laguerre-Gaussian (LG) modes, which are a family of laser beam modes characterized by their azimuthal and radial properties. In other words, they have 20 and 30 nodes in the radial and azimuthal directions, respectively. The LFM signal is modulated by the dual-port Mach-Zehnder modulator (DMZM), using the transverse optical signal as the carrier signal. The mathematical representation of the DMZM output is denoted as \(E(t)\) in Equation (1) [21; 22]:  
\[E(t)=\frac{E_{in}(t)}{10^{\frac{17}{20}}}\times\left(\gamma\times e^{(\frac{i \pi\pi_{2}(t)}{\
abla_{nRF}}+\frac{i\pi_{2n_{2}}(t)}{\
abla_{nDC}})}+(1- \gamma)\times e^{(\frac{i\pi\pi_{1}(t)}{\
abla_{nRF}}+\frac{i\pi_{2n_{2}}(t)} {\
abla_{nDC}})}\right) \tag{1}\]  
The term \"\(L\)\" denotes the insertion loss, whereas \(V_{nRF}\) and \(V_{nDC}\) refer to the switching modulation voltage and switching bias voltage, respectively. For signal transmission towards the target in open space, the output from each transmitter is merged through a power combiner. Following this combination, the signals are intensified using an optical amplifier, which boasts a gain of 20 dB and a noise figure of 4 dB, before being projected through a lens. It is important to note that the Gamma-Gamma fading channel was considered for this work and is expressed mathematically as Equation (2) [22; 23]:  
\[P_{Received}=P_{Transmitted}\times\frac{d_{R}^{2}}{\left(d_{T}+\theta_{R} \right)^{2}}10^{-\alpha^{\frac{B}{10}}} \tag{2}\]Figure 1: Schematic diagram of proposed MDM-based MIMO photonic radar. (**a**) Photonic radar transmitter and receiver. (**b**) Concept of MDM in MIMO photonic radar for multiple target detection. MZM: Mach–Zehnder modulator; EA: electronic amplifier; LFM: low-frequency modulator; Tx: transmitter; and Rx: receiver.