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This paper provides an extension of RS-OFDM for transmission over Rayleigh fading channels with additive white Gaussian noise (AWGN). RS-OFDM is a combination of Reed-Solomon (RS) codes and orthogonal frequency division multiplexing (OFDM), in which part of the RS code operates as an OFDM front-end. Apart from other advantages such as low peak to average power ratio (PAPR), this scheme benefits mainly from the fact that the overall code is an RS code, leading to optimal performance. This result was obtained previously under the constraint of impulse noise and a fixed integer valued channel. This paper shows that these constraints can be removed by splitting the equalization in two stages: the first stage encompasses a partial equalization in the complex field, which avoids noise amplification. This complex field equalizer also ensures that the residual channel response has integer coefficients. It is calculated using a minimum mean square error (MMSE) criterion. The residual ISI is removed by a Galois field equalizer in the second stage, posterior to the RS decoding removing the noise. Finally, the performance of the RS-OFDM system is further evaluated by simulations showing the performance gain of the RS-OFDM system compared to a traditional coded OFDM or single carrier with cyclic prefix (SC-CP) scheme.