ML-estimator and CRLB on carrier-frequency offset in TDM receivers for direction finding

Recently switched antenna array, sometimes also called Time Division Multiplexing (TDM), receivers have found their way in systems suitable for, e.g. indoor positioning. Such systems use low-power and low-cost transmitters and receivers, having significant differences in their local reference clocks. Consequently, the received signal in the base-band carries a carrier-frequency offset (CFO). This CFO has to be estimated from the observed signal and compensated for. In this paper Cramér-Rao lower bounds on the CFO for two data models of switched antenna array receivers signals are derived. Furthermore a closed form Maximum Likelihood Estimator (MLE) for the CFO and the antenna data is proposed. The derived CRLBs are used to study the statistical performance of the maximum likelihood estimator.