This paper proposes amplify-and-forward (AF) relay strategies for two-way wireless distributed relay networks consisting of two sources with a single antenna per source and multiple N relays with a single antenna per relay. The objective of this paper is to determine optimal relay amplifying matrices (or vectors) under global and local power constraints at the relays based on the minimum mean square error (MMSE) criterion with/without the perfect cancelation of self-interference. With the derived optimal relay amplifying vectors, performances of the
proposed two-way AF distributed relay system are investigated by presenting average bit error rate (BER), average MMSE behavior, and the sum of the achievable rate.