A ML-BASED ESTIMATION OF CFO IN NON-CIRCULAR COMPLEX-VALUED AR (1) MULTIPLICATIVE NOISE

This paper addresses the carrier-frequency offset (CFO) estimation in non-circular complex-valued colored multiplicative noise channels. The non-circular multiplicative noise is modeled as a non-circular complex-valued first-order autoregressive (NCAR(1)) model. The primary aim is to characterize the significant gains in terms of CFO estimation that can be provided by exploiting the non-circularity property of the channel model. A high signal-to-noise-ratio (SNR) approximation time domain scheme for joint CFO and fast-fading NC-AR(1) channel parameters estimation is proposed based on the maximum likelihood (ML) principle. Using this approach, the CFO estimate is first obtained by solving a one-dimensional optimization problem. We also derive an approximate high-SNR ML CFO estimation approach under a quasi-static non-circular channel model. To evaluate the performance of these approaches, we derive closedform expressions of the exact Cramér-Rao lower bound (CRLB) of the CFO estimate for both slow-fading and fast-fading channel models. Analytical sensitivity analysis is performed for NC-AR(1) parameters by deriving high-SNR approximate expressions of the CRLBs. Finally, theoretical analysis and simulation results show that the proposed estimators provide significant performance as compared to the conventional circular CFO estimation schemes and the existing squaring loop algorithm.