Abstract-We study joint estimation of the channel impulse response (CIR) and of the carrier frequency offset (CFO) for linear channels in which both the CIR and the noise statistics vary periodically in time. This model corresponds to interferencelimited communications as well as to power line communication and doubly selective channels. We first consider the joint maximum likelihood estimator (JMLE) for the CIR and the CFO and show it has a high computational complexity and relatively low spectral efficiency. This motivates the derivation of two estimation schemes with higher spectral efficiency and lower computational complexity compared to the JMLE, obtained by exploiting both the periodicity of the channel and the fact that, typically, the delay-Doppler spreading function of the CIR is approximately sparse, without requiring a-priori knowledge of the sparsity pattern. The proposed estimation schemes are numerically tested and the results demonstrate that substantial benefits can be obtained by properly accounting for the approximate sparsity and periodicity in the design of the estimation scheme.

Communications over power lines in the frequency range above 2 MHz, commonly referred to as broadband (BB) power line communications (PLC), has been the focus of increasing research attention and standardization efforts in recent years. BB-PLC channels are characterized by a dominant colored non-Gaussian additive noise, as well as by periodic variations of the channel impulse response and the noise statistics. In this work we study the fundamental rate limits for BB-PLC channels by bounding their capacity while accounting for the unique properties of these channels. We obtain explicit expressions for the derived bounds for several BB-PLC noise models, and illustrate the resulting fundamental limits in a numerical analysis.Index terms-Power line communications, MIMO systems, channel capacity. noise. We emphasize that all the works mentioned above, i.e., [7], [10], [26], derived expressions assuming Gaussian noise, while major works have concluded that the noise is non-Gaussian, see, e.g., [4], [8], [9]. We also note the work [28], which derived an approximate expression for the achievable rates when using Gaussian inputs and when using inputs with discrete amplitudes, for memoryless channels with additive GM noise, which were used for modelling communications in the presence of co-channel interference. Finally, we note that the capacity of PLC channels in the narrowband frequency range (0−500 kHz), modeled as additive noise channels in which the CIR is modeled as an LPTV filter and the noise is a cyclostationary Gaussian process, was derived in [29]. To the best of our knowledge, the fundamental limits for BB-PLC channels, accounting for their unique characteristics, including the non-Gaussianity and the temporal correlation of the noise, as well as the periodic variations of the CIR and of the noise statistics, have not been characterized to date. In this work we aim to address this gap. Main Contributions:In this work we study the fundamental rate limits of discrete-time (DT) BB-PLC channels. We consider a general channel model accounting for a wide range of the characteristics of BB-PLC channels, in which the CIR is modeled as an LPTV filter, and the additive noise is modeled as a temporally correlated non-Gaussian cyclostationary process 1 . Accordingly, we characterize an upper bound and two lower bounds on the capacity of these channels. We note that when the noise is not a Gaussian process, obtaining a closed-form expression for the capacity is generally a very difficult task, even for stationary and memoryless channels, and the common approach is to characterize upper and lower bounds on the capacity, see, e.g., [30, Ch. 7.4]. To facilitate the derivation, we first derive bounds on the capacity of a general LTI MIMO channel with additive non-Gaussian stationary noise. Then, we prove that the capacity of BB-PLC channels can be obtained from the capacity of non-Gaussian LTI MIMO channels by properly setting the parameters of the model, and finally we apply the bounds on the capacity of the latter model to ob...

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