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

Abstract

This paper considers the problem of analytically assessing the maximum achievable rates (capacity) of 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.

Existing System

Compensation Algorithm.

Proposed System

This paper addresses the problem of analytical determination of the maximum achievable rate (capacity) of OFDM transmissions in frequency selective channels with PN, which serves as an upper bound for the performance of any estimation/compensation/decoding scheme employed in practice. The receiver is assumed to account only for the CPE effect, ignoring the explicit dependence of the ICI on data. No a-priori knowledge of the CPE is assumed, which, as expected, translates to a reduction of achievable rates, an effect that is not captured by the analysis of previous works assuming ideal CPE knowledge. In addition, in contrast to previous works, no a-priori assumption on the form of the CPE is considered. In particular, even though all previous works routinely consider a specific form of the CPE as function of the phase noise (PN) realization, it is noted that this function (what is referred in this paper as CPE function) is actually a free design parameter. Therefore, the CPE function is treated in this work as an optimization variable with respect to (w.r.t.) capacity maximization. As an exact determination of the system capacity in closed form is difficult, if not impossible, analysis considers bounding expressions for the capacity under various simplifying assumptions. In particular, a lower capacity bound is derived in a simple closed form expression that holds for asymptotically small PN levels and/or operational signal-to-noise-ratio (SNR). Its value represents a rate that can be achieved by OFDM using certain design choices w.r.t. CPE function and signal distribution and clearly demonstrates the loss of performance due to unknown CPE as well as the significance of optimally selecting the number of OFDM subcarriers towards balancing the conflicting requirements of rate loss due to the unknown CPE and rate loss due to ICI. The latter observation has system design implications for operational conditions requiring a small cyclic prefix length allowing for the potential use of a small number of subcarriers, which is preferable in the sense of reducing ICI power. However, system performance does not monotonically increase with decreasing number of subcarriers as the effect of unknown CPE becomes dominant when this number becomes too small, resulting in performance degradation. Numerical results confirm the validity of the bound for all operational regimes, rendering it a reasonable metric over which OFDM performance under PN is evaluated. The analysis is complemented by a discussion on properties of well-selected CPE functions and performance under unknown channel, which provide guidelines for system design under operational conditions affected by PN.

Architecture