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One of the most serious problems in relay systems is power constraint. Due to this limitation, complex algorithms are replaced by cost efficient techniques. In conventional orthogonal frequency division multiplexing (OFDM) systems at the relays, signal processing techniques, such as equalization is performed considering signalling in the frequency domain. Employing such techniques, the received OFDM time signals in the first hop have to be converted into frequency domain at the relays, equalized and converted back to time domain again via the next hop for retransmission. In this paper, by employing the Toeplitz matrix structure that converts frequency selective channels into an equivalent channel matrix, the convolution of input signal and the channel is transferred into multiplication of input signal with the equivalent channel matrix causing the removal of the OFDM procedure at the relay. Since the span of the channel is calculated by a channel matrix, the signal length is not increased causing the transmission rate to be increased without the loss of full system BER. [ABSTRACT FROM PUBLISHER]