Graduate Institute of Electronics Engineering NTU FFT VLSI

Graduate Institute of Electronics Engineering, NTU FFT VLSI Implementation VLSI Signal Processing 台灣大學電機系 吳安宇 1. 2. Shousheng He and Mats Torkelson, A new approach to pipeline FFT processor. IEEE Proc. Of IPPS, P 766 -770, 1996. E. Bidet, D. Castelain, C. Joanblanq, and P. Senn, A fast single-chip implementation of 8192 complex point FFT. IEEE J. Solid-State Circuits, P 300 -305, March 1995 ACCESS IC LAB

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU FFT Review

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Implementation --- Two Extreme Method Slow --------- Speed --------- Fast Small ---------Area---------- Large Complicated ------ Control -------- Simple

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Design Consideration System Requirement e. g. , speed, area, power … Trade-off in these two cases, we need More Processing Elements (PE’s) Better Processing Element Utilization Rate Better Control Scheme

ACCESS IC LAB FFT Processor Graduate Institute of Electronics Engineering, NTU --- Block Diagram

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Some Current Themes Radix-2 Multi-path Delay Commutator. ( N = 16 ) Radix-2 Single-path Delay Feedback. ( N = 16 )

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Some Current Themes (cont. ) Radix-4 Single-path Delay Feedback. ( N = 256 ) Radix-4 Multi-path Delay Commutator. ( N = 256 ) Radix-4 Single-path Delay Commutator. ( N = 256 )

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Distinctive merit of the above The delay-feedback are more efficient than delay-commutator in terms of memory utilization Radix-4 has higher multiplier utilization , however, Radix-2 has simpler BF which are better utilized

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Comparison Radix / Speed Low ------------------ High Control Theme Simple ------------------ Complex Processing Ability / Unit Low ------------------ High Combine the advantages Further decompose high radix PE

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Decompose Method (1) Simply ‘‘reuse’’ the repeated micro unit A radix-4 PE

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Decompose Method (2) From algorithm level Applying 3 index: n=<n 1*N/2 + n 2*N/4 + n 3>N where n 1, n 2={0, 1} ; n 3={0~N/4 -1} k=<k 1 + 2 k 2 + 4 k 3>N Summation of n 1

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Decompose Method (2) cont. Summation of n 2 Only real-imaginary swapping & sign inversion

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Graphical Explanation (N=16) Trivial multiplication

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Graphical Explanation (cont. ) The Eqs are equivalent to the operations below

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Circuit of BF 2 I First N/2 cycles Xr(n) Zr(n+N/2) Xi(n) Zi(n+N/2) Xr(n+N/2) Zr(n) Xi(n+N/2) Zi(n) Second N/2 cycles

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Circuit of BF 2 II Xr(n) Zr(n+N/2) Xi(n) Zi(n+N/2) Xr(n+N/2) Zr(n) Xi(n+N/2) Zi(n) Swap Re&Im and sign inversion

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Radix-22 Single-path Delay Feedback FFT architecture using the above technique, for N=256 Compare with original architecture, for N=256

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Structural advantage Radix-22 has the same complexity as radix-4, but still retain radix-2 BF structure The stage has non-trivial multiplication Control is simple; synchronization controller n address counter for W

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Conclusions 1. FFT Applications: Radar Signal Processing, Fast convolution, Spectrum Estimation, OFDM-based Modulation/demodulations 2. Efficient VLSI architectures (parallel processing) are required for real-time processing. 3. However, most systems still employ DSP processors (e. g. , TI C 3 x/C 5 x) for computations (fast algorithms like DIT and DIF FFT). 4. VLIW (Very Long-length Instruction Word)-based processors (TI C 6 x) need new programming skills to utilize the two parallel MAC units.