A noncooperative amplify-and-forward (AF) wireless relay network consisting of a one-source-one-destination pair and N relays is investigated. The objective of this paper is to analytically derive the explicit optimal noncooperative relay amplifying matrices (or vector) under both jamming and no-jamming environments, with the relay power constraint based on the minimum mean square error (MMSE) criterion. The MMSE cost function behaviors will be analytically and numerically investigated using the relay amplifying vectors derived. Finally, the relay selection scheme for the noncooperative AF wireless relay network is presented using the maximum signal-to-noise ratio (SNR) criterion under both jamming and no-jamming environments.