Bounds and algorithms for multiple frequency offset estimation in cooperative networks

Abstract—The distributed nature of cooperative networks may result in multiple carrier frequency offsets (CFOs), which make the channels time varying and overshadow the diversity gains promised by collaborative communications. This paper seeks to address multiple CFO estimation using training sequences in space-division multiple access (SDMA) cooperative networks. The system model and CFO estimation problem for cases of both decode-and-forward (DF) and amplify-and-forward (AF) relaying are formulated and new closed-form expressions for the Cramer-Rao lower bound (CRLB) for both protocols are derived. The CRLBs are then applied in a novel way to formulate training sequence design guidelines and determine the effect of network protocol and topology on CFO estimation. Next, two computationally efficient iterative estimators are proposed that determine the CFOs from multiple simultaneously relaying nodes. The proposed algorithms reduce multiple CFO estimation complexity without sacrificing bandwidth and training performance. Unlike existing multiple CFO estimators, the proposed estimators are also accurate for both large and small CFO values. Numerical results show that the new methods outperform existing algorithms and reach or approach the CRLB at mid-to-high signal-to-noise ratio (SNR). When applied to system compensation, simulation results show that the proposed estimators significantly reduce average-bit-error-rate (ABER). Index Terms—Cooperative communications, synchronization, car-rier frequency offset estimation, Cramer-Rao Lower Bound (CRLB)