An amplify-and-forward (AF) relay network has been studied extensively, but a closed form of an optimal AF relaying matrix is not available yet for the distributed AF relay network with the destination power constraint (DPC) and the following adverse environments: (a) partial-band noise jamming (PBNJ), (b) node geometry (NG), and (c) channel uncertainty (CU). Hence, this paper presents a closed form of an optimum AF relaying matrix consisting of a one-source-one-destination pair and N relay nodes under such adverse PBNJ, NG, CU, and DPC environments, based on the minimum mean square error (MMSE). By adopting the optimal relay amplifying matrix, the MMSE cost function behaviors are analytically and numerically studied.