近年來，在先進的多輸入多輸出正交分頻多工(MIMO-OFDM)系統中，對於速度的需求巨幅提升，而隨著FFT點數的提升，以及在多輸入多輸出系統中，更高的天線維度之需求，以往tone-by-tone的QR分解所產生的複雜度形成了實作上的瓶頸。為了解決此問題，內插式QR分解演算法已經被證實能有效的降低複雜度。在本論文中，我們提出一種低複雜度內插式QR分解演算法以減少在原始的內插式QR分解演算法的複雜度，除此之外，本論文也提出一種部分層級映射之技術。而我們我提出的低複雜度內插式QR分解演算法亦可和部分層級映射技術搭配，使得整體的複雜度能被更進一步的降低。同時，本論文也設計一種對應於低複雜度內插式QR分解演算法的硬體架構，並提出一種scaling scheme以解決在固定點數的情況下，原始的內插式QR分解演算法中會發生的動態範圍過大之問題。此外，本論文所提出的硬體架構具有適合平行處理之特性，可以適用於任何高傳輸速率的MIMO-OFDM系統中。最後，我們利用90nm UMC CMOS製程與Faraday cell library實現本論文所設計的低複雜度內插式QR分解處理器。透過完整的驗證流程後，在不考慮平行處理的條件下，本論文所設計的內插式QR分解處理器的速度可以達到45.6MQRD/s，而在平行處理的情況下，最高的處理速度則可以提升到182.4MQRD/s。

The throughput requirement of advanced MIMO-OFDM systems increases extremely in recent years. The complexity of traditional tone-by-tone QR decomposition raises along with FFT-point and MIMO dimension, and thus becomes the bottleneck of hardware implementation. The interpolation-based QR decomposition (IQRD) algorithm has been proved that it has lower complexity compared to traditional tone-by-tone QR decomposition algorithm.
In this thesis, a reduced-complexity interpolation-based QR decomposition (RC-IQRD) is proposed to decrease the complexity of original IQRD. Moreover, a low-complexity mapping scheme, called as partial layer-mapping (PLM) scheme, is adopted in RC-IQRD algorithm to further reduce the complexity. For the RC-IQRD algorithm, the corresponding architecture is proposed as well. Besides, we present a scaling scheme to solve the dynamic-range problem in IQRD algorithm. Nevertheless, the proposed architecture can use multiple hardwares easily to achieve higher throughput.
The proposed architecture is implemented by 90nm UMC CMOS technology and Faraday cell library. According to post-layout results, the proposed architecture can achieve 45.6MQRD/s with single QR decomposition unit, and the maximum throughput can be up to 182.4MQRD/s.

[1] E. Viterbo and J. Boutros, “A universal lattice code decoder for fading channels,” Information Theory, IEEE Transactions on, vol. 45, no. 5, pp. 1639 –1642, Jul. 1999.
[2] E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, “Closest point search in lattices,”
IEEE Transactions on Information Theory, vol. 48, no. 8, pp. 2201–2214, Aug. 2002.
[3] K. W. Wong, C. Y. Tsui, R. S. K. Cheng, and W. H. Mow, “A VLSI architecture of a K-best lattice decoding algorithm for MIMO channels,” in Proc. IEEE Int. Symp. On Circuits and Systems, vol. 3, May 2002, pp. 273–276.
[4] Y.-C. Liang, D. Kit, S. Attallah, W. S. Leon, and C. Xu, “Dynamic qrdm receivers
for mimo beamforming systems with imperfect channel state information,” 2005, pp. 801 –805.
[5] IEEE 802.16e-2005–Amendment 2: Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, IEEE Std. 802.16, 2006.
[6] IEEE 802.11n-2009–Amendment 5: Enhancements for Higher Throughput, IEEE Std. 802.11, 2009.
[7] 3GPP TS 36.211–Physical Channels and Modulation, 3GPP Technical Specification, Rev. 8.9.0, 2009.
[8] D. Cescato, M. Borgmann, H. B¨olcskei, J. Hansen, and A. Burg, “Interpolation-
based QR decomposition in MIMO-OFDM systems,” in Proc. IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, Jun. 2005, pp. 945–949.
[9] D. Cescato and H. B¨olcskei, “Algorithms for interpolation-based QR decomposition in MIMO-OFDM systems,” IEEE Transaction on Signal Processing, Oct. 2009. [Online]. Available: http://www.nari.ee.ethz.ch/commth/pubs/p/qrdectsp09
[10] D. W¨ubben and K. D. Kammeyer, “Interpolation-based successive interference cancellation for per-antenna-coded MIMO-OFDM systems using P-SQRD,” in Proc.
IEEE Workshop on Smart Antennas, Mar. 2006.
[11] REV-090003r1 LTE-Advanced Physical Layer, 3GPP Std., Dec. 2009.
[12] P. Wolniansky, G. Foschini, G. Golden, and R. Valenzuela, “V-blast: an architecture for realizing very high data rates over the rich-scattering wireless channel,” in Signals, Systems, and Electronics, 1998. ISSSE 98. 1998 URSI International Symposium on, sep-2 oct 1998, pp. 295 –300.
[13] R. Bohnke, D. Wubben, V. Kuhn, and K.-D. Kammeyer, “Reduced complexity mmse detection for blast architectures,” in Global Telecommunications Conference,
2003. GLOBECOM ’03. IEEE, vol. 4, Dec. 2003, pp. 2258 – 2262 vol.4.
[14] J.-J. van de Beek, O. Edfors, M. Sandell, S. Wilson, and P. Borjesson, “On channel
estimation in ofdm systems,” in Vehicular Technology Conference, 1995 IEEE 45th,
vol. 2, jul. 1995, pp. 815 –819 vol.2.
[15] A. Bj¨orck and C. C. Paige, “Loss and recapture of orthogonality in the modified Gram-Schmidt algorithm,” SIAM J. Matrix Anal. Appl., vol. 13, no. 1, pp. 176–190, 1992.
[16] C. K. Singh, S. H. Prasad, and P. T. Balsara, “A Fixed-Point Implementation for
QR Decomposition,” in Design, Applications, Integration and Software, 2006 IEEE
Dallas/CAS Workshop on, Oct. 2006, pp. 75–78.
[17] G. Lightbody, R. Woods, and R. Walke, “Design of a parameterizable silicon in-tellectual property core for QR-based RLS filtering,” Very Large Scale Integration
(VLSI) Systems, IEEE Transactions on, vol. 11, no. 4, pp. 659–678, Aug. 2003.
[18] 3GPP TS 36.101–User Equipment (UE) radio transmission and reception, 3GPP Technical Specification, Rev. 8.9.0, 2010.
[19] A. Burg, “VLSI circuits for MIMO communication systems,” Ph.D. dissertation, Swiss Federal Institute of Technology Zurich, Zurich, Switzerland, 2006.
[20] S. Haene, A. Burg, N. Felber, and W. Fichtner, “Ofdm channel estimation algorithm and asic implementation,” jul. 2008, pp. 270 –275.
[21] R. Andraka, “A Survey of CORDIC Algorithms for FPGA Based Computers,”
in Sixth International Symposium on Field Programmable Gate Arrays, Monterey, CA, 1998.
[22] L. Azzam and E. Ayanoglu, “Reduced complexity sphere decoding for square qam
via a new lattice representation,” in Global Telecommunications Conference, 2007. GLOBECOM ’07. IEEE, nov. 2007, pp. 4242 –4246.
[23] T.-D. Chiueh and P.-Y. Tsai, OFDM Baseband Receiver Design for Wireless Communications. Wiley Publishing, 2007.
[24] R. C. H. Chang, C. H. Lin, K. H. Lin, C. L. Huang, and F. C. Chen, “Iterative QR decomposition architecture using the modified Gram-Schmidt algorithm for MIMO
systems,” IEEE Transactions on Circuits and Systems—Part I: Regular Papers,
vol. PP, no. 99, pp. 1–8, May 2010.
[25] D. Patel, M. Shabany, and P. G. Gulak, “A low-complexity high-speed QR de-
composition implementation for MIMO receivers,” in Proc. IEEE Int. Symp. on
Circuits and Systems, May 2009, pp. 33–36.
[26] P.-L. Chiu, L.-Z. Huang, L.-W. Chai, and Y.-H. Huang, “Interpolation-based qr decomposition and channel estimation processor for mimo-ofdm system,” Circuits
and Systems I: Regular Papers, IEEE Transactions on, vol. 58, no. 5, pp. 1129–1141, may 2011.
[27] G. J. Foschini, “Layered space-time architecture for wireless communication in a
fading environment when using multiple antennas,” Bell Laboratories Technical Journal, vol. 1, no. 2, pp. 41–59, Autumn 1996.
[28] P. L. Chiu, L. Z. Huang, and Y. H. Huang, “Scalable interpolation-based QRD
architecture for subcarrier-grouped-ordering MIMO-OFDM system,” in Proc. 43th
IEEE Asilomar Conf. on Signals, Systems, and Computers, Nov. 2009, pp. 708–712.
[29] Y. G. Li, J. Cimini, L.J., and N. Sollenberger, “Robust channel estimation for ofdm
systems with rapid dispersive fading channels,” vol. 3, jun. 1998, pp. 1320 –1324 vol.3.
[30] G. H. Golub and C. F. Van Loan, Matrix computations (3rd ed.). Baltimore, MD, USA: Johns Hopkins University Press, 1996.
[31] P. Luethi, C. Studer, S. Duetsch, E. Zgraggen, H. Kaeslin, N. Felber, and W. Fichtner, “Gram-Schmidt-based QR decomposition for MIMO detection: VLSI implementation and comparison,” in Proc. IEEE Asia Pacific Conf. on Circuits and Systems, Nov. 2008, pp. 830–833.
[32] K. H. Lin, C. H. Lin, R. C. H. Chang, C. L. Huang, and F. C. Chen, “Iterative QR decomposition architecture using the modified Gram-Schmidt algorithm,” in Proc. IEEE Int. Symp. on Circuits and Systems, May 2009, pp. 1409–1412.