## 3 Experimental Setup and Dataset  
In this work, the jammer effect on two laser mode families is investigated in direct detection FSO system. Figure 2b shows the demonstrated experimental setup used in this investigation. The information carrier link is built using a Teraxion continuous wave (CW) laser source operating at 1550 nm (LD1). The laser output power is boosted up to \(\sim\)20 dBm using an Erbium doped fiber amplifier (EDFA) before collimated in free space using Thorlabs F230 FC-1550. A free space set of a half wave plate (HWP) and a polarizer (P) is used to maximize the intensity and align the polarization of the collimated light, respectively. An Hamamatsu (X13138-08) programmed liquid crystal on silicon-spatial light modulator (LCOS-SLM) is utilized to modulate the phase of the horizontally polarized incident Gaussian beam. According to the \(M\)-ary order, a computer (PC1) is used to program the LCOS-SLM with different hologram sets to convert the incident Gaussian mode into LG, Mux-LG, and/or HG modes. On the other side, the jamming link is a standard Gaussian beam generated using another CW laser source (LD2) working in C-band with an output power varying from 8 to 15 dBm to change the signal-to-jamming ratios (SJRs). A 15x Thorlabs GBE-15C beam magnifier (BM) is used to adjust the beam diameter of the jamming signal. Both mode pattern and jamming signals are transmitted over a free space link of 1-meter inside the lab. The free space direct detection receiver is constructed using a Thorlabs LB1471-C convex lens of 50 mm focal length and a charge-coupled device (CCD) detector (Ophir-Spiricon LBP2-IR2) that captures and stores the intensity profiles of the different jammed modes in PC2. Moreover, a beam splitter is used initially to measure the the power of the received pattern and jamming signals and to adjust the SJR values. Figure 3 compares the received beam width diameters statistically measured by D4\(\sigma\) method (i.e., four times beam profile standard deviation in \(x\) or \(y\) directions) [21], for left-hand jammer, LG, Mux-LG, and HG mode profiles. The measured beam diameter of the jamming signal is 3 mm, see Figure 3a, whereas the measured beam widths of the LG/Mux-LG modes varying from \(\sim\)2.3 mm (LG\({}_{01/0\pm 1}\)) to 4.2 mm (LG\({}_{08/0\pm 8}\)), as shown in Figure 3b,c. For HG modes, the beam diameters change from \(\sim\)1 mm (HG\({}_{00}\)) to 4.5 mm (HG\({}_{33}\)) in \(x\) and \(y\) directions. Figure 2: **(a)** Laboratory-generated transverse intensity profiles of LG, superposition-LG and HG modes, **(b)** Experimental setup of M-ary structure pattern transmission with Gaussian jammer. LD: Laser diode; Coll. : Collimator; HWP: Half-wave plate; M: Mirror; SLM: Spatial light modulator; BM: Beam magnifier; PC: Computer; BS: Beam splitter; PD: Photodiode; CCD: Charge-coupled device. Inset is a photograph of the laboratory setup. In order to mimic the random wandering-around of a jammer, a 3-axis translation stage is used to randomly change the incident position of the jammer. Besides, in this investigation, both the left- and right-hand jammer direction-of-arrivals (DoAs) are considered. A dataset of the jammed patterns was created by recording the received intensity profiles using the CCD detector. The CCD recorded the received profiles with a frame rate of 1 frame/sec (which is sufficient to capture the slow jammer wandering), for a duration of 200 s (\(\sim\)3.3 min). In addition, the profiles was recorded at different SJRs varying from \(-5\) to 3 dB with a step size of 1 dB. It is worth noting that the choice of the lower (\(-5\) dB) and upper (3 dB) SJR values is owing to the devices power limitations and the performance consistency, respectively. This creates a data set of 14,400, 28,800, and 57,600 frames for 8-ary LG/Mux-LG, 16-ary HG/LG+Mux-LG, and 32-ary LG+Mux-LG+HG modes, respectively. Figure 4 shows examples of the various intensity profiles of the randomly jammed mode pattern at SJRs of \(-5\), 0, and 3 dB, of a left-hand DoA jammer.