This paper introduces the first mathematical investigation on utilizing a single inline optical amplifier in the 2-D time-spreading wavelength-hopping (TW) code division multiple access (OCDMA) system. The study adopts a non-ideal erbium-doped fiber amplifier (EDFA), where the optical gain depends on the input power of the amplifier. Three en/decoders representing different loss levels are examined. In addition, the paper highlights the significance of the power budget in the amplified TW systems to ensure the accomplishment of two concurrent conditions. First, the total input power from all users to the inline amplifier should fall within the amplifier input power range to gain sufficient amplification. Hence, the transmitted chip power from users is the key contributor. The second condition is the ordinary case where the desired received power should meet the required bit error rate (BER). The number of central splitter/combiner ports (Nsys) is an additional important system parameter, representing the upper bound of the available number of simultaneous users (K). The analysis supported by the Optisystem simulation results shows that the best location for the inline amplifier is close to the central system's combiner. The results also reveal that, for low-user system capacities, employing a single inline optical amplifier in the 2-D TW OCDMA system is effective for the low-loss TW en/decoders but with increased code weights (w). For an 8-user system (i.e., Nsys = 8), transmitted chip power of 15 dBm, and EDFA amplification gain of 28 dB, the system can support the full-user capacity (at a BER <= 10-9) when w = 29. On the contrary, the performance of the higher system capacities sustains only a particular number of simultaneous users, accommodating up to 60 % of the full-user capacity when Nsys = 16.
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