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On the Achievable Rates of OFDM With Common Phase Error Compensation in Phase Noise Channels

This paper considers the problem of analytically assessing the maximum achievable rates (capacity) of orthogonal frequency division multiplexing (OFDM) transmissions when the receiver, for complexity reasons, only accounts for the common phase error (CPE) effect due to phase noise impairments with inter-carrier interference (ICI) treated as noise. By recognizing that the functional form of the CPE with respect to the phase noise realization is actually a free design parameter, determination of the capacity is posed as a functional optimization problem with respect to the, so-called, CPE function. A simple lower bound of the capacity is obtained, revealing the performance degradation due to the unknown CPE at the receiver, as well as the suboptimal performance achieved in severe phase noise conditions by the conventional CPE function that is routinely employed in previous works. The existence of an optimal number of subcarriers that balances the effects of the (unknown) CPE and ICI is highlighted and critical system design/operation issues, such as selection of the CPE function and effect of unknown channel on the achievable rate, are discussed. The analysis in this paper can be employed for determining the suitability of OFDM in phase noise channels and provides a tractable utility function for resource allocation purposes.