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Orthogonal frequency-division multiplexing (OFDM) is widely used in modern communication systems thanks to the ease of its implementation as well as to a simple design of channel estimation methods. Pilot-based schemes are commonly employed to recover channel information and implement efficient channel equalisation. From the symbols transmitted over the pilot carriers, the channel coefficients for a whole OFDM are estimated. In this paper, we propose a method to compute in a closed form the mean square estimation error of different linear approximation and interpolation algorithms in the time-frequency domain. Specifically, by exploiting the linear relationship between the estimated channel coefficients for the whole frame and those relative to the pilots, the proposed approach permits to obtain the mean square error relative to all OFDM symbols in a frame. The method can be used for any linear frequency/time interpolation/approximation method and for any choice of pilot positions and channel statistics. Thanks to our derivations, several pilot-aided channel estimation and interpolation algorithms can be compared without resorting to burdensome computer simulations. In order to demonstrate the effectiveness of the method, the downlink of the long term evolution system is taken as a case study: some popular channel estimators have been selected and the best strategy in a realistic wireless scenario is investigated. The performance of the method is also verified by computing, by means of simulations, bit error rate (BER) curves for the long term evolution (LTE) multiple input multiple output (MIMO) downlink, using 2 2 and 4 4 Alamouti space-frequency coding configurations, in both uncoded and coded communications. Copyright

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Abstract-Orthogonal Frequency Division Multiplexing (OFDM) transmission technique has been considered for the 4G LTE-Advanced system because of its high performance and low complexity. In the new 5G scenario this type of modulation is not properly suited because of the additional requirements for very high spectral efficiency, low latency and low out-of-band (OOB) emissions. Thus, new waveforms have been chosen to replace it and effectively deal with these problems. Particularly, recently proposed multicarrier techniques as the Generalized Frequency Division Multiplexing (GFDM) and the Filter Bank Multicarrier (FBMC) modulations are two of the main candidates techniques for the new 5G standard. As for classical OFDM technique, the channel estimation is a crucial functionality for the all multicarrier approaches. In this paper we generalize a recently proposed method for the computation of the MSE on the time-frequency domain for pilot based channel estimation techniques in multicarrier system. This method permits to determine the most suitable channel estimation algorithm for a given wireless channel as well as to define the suitable pilot density in order to afford a target MSE value for a given SNR level. Hence, in this paper a general design tool for multicarrier systems is proposed.