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Two optimisation models established for a wireless optical communication system based on the four-level pulse amplitude modulation scheme were recently reported. Both models were expressed in terms of multiple improper integrals. To improve the computational efficiency, the closed-form in terms of the incomplete gamma function is derived that is supported by most mathematical software packages, including MATLAB. The previously reported optimisation models are solved with the new method. The solutions are presented.Introduction: In a recent paper [1], a wireless optical communication (WOC) system based on the multi-level pulse amplitude modulation scheme was investigated and two optimisation models were developed. One of the primary metrics in these models is the average bit error probability (BEP) [1]:

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