Fixed-point FPGA Implementation of the FFT Accumulation Method for Real-time Cyclostationary Analysis

The spectral correlation density (SCD) is an important tool in cyclostationary signal detection and classification. Even using efficient techniques based on the fast Fourier transform (FFT), real-time implementations are challenging because of the high computational complexity. A key dimension for computational optimization lies in minimizing the wordlength employed. In this article, we analyze the relationship between wordlength and signal-to-quantization noise in fixed-point implementations of the SCD function. A canonical SCD estimation algorithm, the FFT accumulation method (FAM) using fixed-point arithmetic, is studied. We derive closed-form expressions for SQNR and compare them at wordlengths ranging from 14 to 26 bits. The differences between the calculated SQNR and bit-exact simulations are less than 1 dB. Furthermore, an HLS-based FPGA design is implemented on a Xilinx Zynq UltraScale+ XCZU28DR-2FFVG1517E RFSoC. Using less than 25% of the logic fabric on the device, it consumes 7.7 W total on-chip power and has a power efficiency of 12.4 GOPS/W, which is an order of magnitude improvement over an Nvidia Tesla K40 graphics processing unit (GPU) implementation. In terms of throughput, it achieves 50 MS/sec, which is a speedup of 1.6 over a recent optimized FPGA implementation.