An iterative FFT approach to Tomlinson-Harashima precoding

An FFT block-based implementation of Tomlinson-Harashima precoding (THP) is presented. We propose that the modulo operation in THP is computed iteratively by identifying clipped samples and removing them by addition of correction factors known as the precoding sequence. It is shown that the proposed FFT implementation is more efficient than traditional THP for minimum-phase coefficients at the precoder. On average, the number of operations is reduced from O(L²) to O(κL · log(L)) where κ is number of iterations required to remove all clips and is dependent on the impulse response of the channel and L + 1 is the number of coefficients in the channel impulse response. Simulations show that κ is approximately 6.2 iterations for a copper wireline model channel with 33 taps (L = 32). We also analyse the complementary cumulative distribution function (CCDF) and average power of the precoded sequence as clips are successively removed. CCDF and average power results show that the number of clip-removal iterations can be reduced - and hence computational speed-up achieved - at the cost of slight increase in transmit power.