This paper studies the characteristics of the singular modes of a scalar wave system, in which two arrays communicate with each other in the presence of multi-object scattering. The channel matrix between the arrays is determined by rigorously solving Helmholtz equations subject to boundary conditions using the integral equation method. The singular value decomposition of the channel matrix results in the system's source and field modes, each of which has a unique array factor associated. The results reveal how various system modes target the scattering objects with their radiation beams, suggesting a potential application of using these singular modes to localize objects.