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Orthogonal Frequency-Division Multiplexing (OFDM) has been employed in several current and future 4-th Generation (4G) wireless standards. Frequency offsets in OFDM introduce Inter-Carrier Interference (ICI). Channel estimations are also required. This paper focuses on the channel and frequency offset estimation for OFDM-based systems. For cooperative-relay OFDM with frequency offsets, where Inter-Relay Interference (IRI) exists, channel estimation is developed. Optimal pilot designs are proposed by minimizing the IRI in the Mean Square Error (MSE) of the Least Square (LS) channel estimation. The impact of frequency offset on the channel estimation accuracy is derived. The Pairwise Error Probability (PEP) with both the frequency offset and channel estimation errors is evaluated.
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