Most of the existing distributed beamforming algorithms for relay networks require global channel state information (CSI) at relay nodes and the overall computational complexity is high. In this paper, a new class of adaptive algorithms is proposed which can achieve a globally optimum solution by employing only local CSI. A reference signal based (RSB) scheme is first derived, followed by a constant modulus (CM) based scheme when the reference signal is not available. Considering individual power transmission constraint at each relay node, the corresponding constrained adaptive algorithms are also derived as an extension. An analysis of the overhead and stepsize range for the derived algorithms are then provided and the excess mean square error (EMSE) for the RSB case is studied based on the energy reservation method. As demonstrated by our simulation results, a better performance has been achieved by our proposed algorithms and they have a very low computational complexity and can be implemented on low cost and low processing power devices.
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