Low-Complexity Chromatic Dispersion Compensation Using High-Radix Fermat Number Transform

The emergence of advanced technologies has spurred the development of high-capacity, long-distance, and high-speed coherent optical communication systems. However, Chromatic Dispersion (CD) is the major challenge of coherent optical communication leading to high power consumption at the receiver which impedes the adoption of the technology. The existing systems adopt a high-complexity FFT-based CD equalization consuming around 20% power in the receiver. In this paper, we propose DFNT-TrDE, an efficient Transform Domain Equalization (TrDE) method that reduces the computational complexity of the CD compensation by leveraging the Fermat Number Transform (FNT, where Fermat number
$F_{n} = 2^{b}+1=2^{2^{n}}+1$
) with diminished-1 representation. We adopt various techniques in the system design. Specifically, we propose High-Radix (HR) FNT to further reduce the complexity for large transform lengths. Moreover, we compare the complexity of 1D circular convolution between 1D-R2, 1D-HR, 2D-R2 and 2D-HR FNT at the granularity of adder level. We furthermore provide recommendations for radix and dimension settings tailored to different transform lengths. The results of our implementation show that the DFNT-TrDE (with
$b=8$
) achieves 62% complexity savings compared to 12-bit split-radix FFT-FDE at a similar Bit Error Rate (BER). The DFNT-TrDE (with
$b=16$
) also achieves 51% complexity savings compared to 16-bit split-radix FFT-FDE at a better BER.