Multidimensional DFT IP generators for FPGA platforms

Multidimensional (MD) discrete Fourier transform (DFT) is a key kernel algorithm in many signal processing applications, such as radar imaging and medical imaging. Traditionally, a two-dimensional (2-D) DFT is computed using Row-Column (RC) decomposition, where one-dimensional (1-D) DFTs are computed along the rows followed by 1-D DFTs along the columns. However, architectures based on RC decomposition are not efficient for large input size data which have to be stored in external memories based Synchronous Dynamic RAM (SDRAM). In this dissertation, first an efficient architecture to implement 2-D DFT for large-sized input data is proposed. This architecture achieves very high throughput by exploiting the inherent parallelism due to a novel 2-D decomposition and by utilizing the row-wise burst access pattern of the SDRAM external memory. In addition, an automatic IP generator is provided for mapping this architecture onto a reconfigurable platform of Xilinx Virtex-5 devices. For a 2048x2048 input size, the proposed architecture is 1.96 times faster than RC decomposition based implementation under the same memory constraints, and also outperforms other existing implementations. While the proposed 2-D DFT IP can achieve high performance, its output is bit-reversed. For systems where the output is required to be in natural order, use of this DFT IP would result in timing overhead. To solve this problem, a new bandwidth-efficient MD DFT IP that is transpose-free and produces outputs in natural order is proposed. It is based on a novel decomposition algorithm that takes into account the output order, FPGA resources, and the characteristics of off-chip memory access. An IP generator is designed and integrated into an in-house FPGA development platform, AlgoFLEX, for easy verification and fast integration. The corresponding 2-D and 3-D DFT architectures are ported onto the BEE3 board and their performance measured and analyzed. The results shows that the architecture can maintain the maximum memory bandwidth throughout the whole procedure while avoiding matrix transpose operations used in most other MD DFT implementations. The proposed architecture has also been ported onto the Xilinx ML605 board. When clocked at 100 MHz, 2048x2048 images with complex single-precision can be processed in less than 27 ms. Finally, transpose-free imaging flows for range-Doppler algorithm (RDA) and chirp-scaling algorithm (CSA) in SAR imaging are proposed. The corresponding implementations take advantage of the memory access patterns designed for the MD DFT IP and have superior timing performance. The RDA and CSA flows are mapped onto a unified architecture which is implemented on an FPGA platform. When clocked at 100MHz, the RDA and CSA computations with data size 4096x4096 can be completed in 323ms and 162ms, respectively. This implementation outperforms existing SAR image accelerators based on FPGA and GPU.