Low-Computation-Cycle, Power-Efficient, and Reconfigurable Design of Recursive DFT for Portable Digital Radio Mondiale Receiver

Low-cost, fast-computational, power-efficient, and reconfigurable design for recursive discrete Fourier transform (RDFT) is proposed in this brief. The proposed method is the first integration that collated both the prime factor algorithm (PFA) and the Chinese reminder theorem (CRT) into a recursive algorithm. Hence, a multicycle RDFT algorithm (PFA + CRT + RDFT) and its hardware implementation are produced and presented here in great detail. Compared with some well-known recursive algorithms, the significant improvements for the proposed algorithm can be summarized as follows: 1) The number of computational cycles of the proposed algorithm can be saved by up to 88.5%; 2) The number of multiplications and additions for the proposed algorithm is dramatically reduced by up to 85.2% and 85.2%, respectively; 3) The amount of coefficient read-only memory for storing the twiddle factors totally takes 694 words fewer than those of other existing RDFT algorithms; 4) The hardware cost of the proposed algorithm only takes four real multipliers and eight real adders. This design is more suitable for digital radio mondiale (DRM) systems, such as coded orthogonal frequency-division-multiplexing modulation. The proposed RDFT algorithm was designed and fabricated using a 0.18-μm 1P6M CMOS process. The core area is 521 × 508 μm², and this hardware accelerator only consumes 8.44 mW at 25 MHz. Furthermore, the performance index of power for this design is three times discrete Fourier transform (DFT) per energy of previous work. Additionally, it can calculate the 288/256/176/112-point DFTs for a portable DRM receiver.