We address the problem of detection in a multiple-beam orbital angular momentum (OAM)-based free-space optical communication link. Based on experimental channel observations, we extract a statistical model for the coaxial multimode OAM channel affected by atmospheric turbulence. We employ solutions to least square problems to compensate for the interference among optical modes. A solution based on Fincke-Pohst Enumeration Algorithm for least square problems is presented. In addition, Moore-Penrose based analytical solutions are considered (e.g. Zero Forcing). Finally, we provide bit error rate analysis for the channel under investigation.