MMSE-based Distributed Beamforming in AF Relay System under Network Power Constraint

An amplify-and-forward (AF) wireless relay strategy consisting of a source with multiple IT antennas, distributed N relays with only a single antenna, and a destination with multiple L antennas is investigated in this paper. This paper presents an optimal relay amplifying matrix at the relays, transmit beam forming vector at the source, and receive beamtbrming vector at the destination under the network power constraint of the source and relays using the minimum mean square error (MMSE) criterion. Then, this paper proves that, for the considered amplify-and-forward (AF) wireless relaying system, minimizing the mean square error (MSE) is equivalent to maximizing the signal-to-noise ratio (SNR). Additionally, this paper presents the relationship between the achievable rate and the MMSE. This paper also investigates the relay amplifying matrix, SNR, and MMSE cost function (CF) behaviors numerically and analytically. Finally, this paper numerically and analytically shows that the MMSE CF values are less than 1 at all times, regardless of N.