A Pre-Equalized Transmission Based on Basefield Hartley Transform over Multi-Path Fading Channels

This paper proposes a pre-equalized transmission scheme based on a finite field transform. Unlike orthogonal frequency division multiplexing (OFDM) which transmits signals on orthogonal sub- carriers at the transmitter and explores post-equalization to migrate the effect of multi-path fading at the receiver, in the proposed scheme, signals are processed with the finite field transform called basefield Hartley transform (BHT) before transmission. Since BHT has similar convolution property as discrete Fourier transform (DFT), the inter-symbol interference (ISI) can be mitigated by applying a finite field pre-equalizer and quantization pre-equalizer at the transmitter. By allowing the padded redundancy to take values in finite field, the proposed scheme has the inherent error correction capability with various coding rate. Since the received signals are equivalent to certain block error correction codes, only a decoding scheme is required to recover the source data without any DFT operations that are used in conventional OFDM receiver, which leads to a simple receiving structure with low process complexity. Our simulation results show that the proposed scheme reduces the peak-to-average power ratio (PAPR) and provides better bit error rate (BER) performance at the high signal-to-noise ratio (SNR) in comparison with the coded OFDM system.