We address the problem of nondata aided frequency offset estimation for noncircular transmissions over frequency-selective channels in a linear precoder-based communications context. Linear precoding is representative of a downlink direct-sequence code division multiple access (DS-CDMA) system or of an orthogonal frequency division multiplexing (OFDM) system. We observe that twice the frequency offset is a cyclic frequency of the received signal. We thus introduce an estimator relying on the maximization of the empirical cyclocorrelations. We analyze its asymptotic behavior and obtain a closed-form expression for the asymptotic covariance. This enables us to design relevant system parameters. Numerical illustrations are provided and confirm our theoretical assertions. Comparisons with existing methods are also, reported.
Ciblat, P., & Vandendorpe, L. (2003). Blind, carrier, frequency offset estimation for noncircular constellation-based transmissions. IEEE Transactions on Signal Processing, 51(5), 1378-1389. https://doi.org/10.1109/TSP.2003.810287 (Original work published 2003)