Decoupling of Broadband Optical MIMO Systems Using the Multiple Shift SBR2 Algorithm

Zeliang Wang, André Sandmann, John G. McWhirter, Andreas Ahrens

Abstract


Polynomial singular value decomposition (PSVD) plays a very important role in broadband multiple-input multiple-output (MIMO) systems. One of its applications lies in the decoupling of MIMO convolutive mixing channel matrix
in order to recover the transmitted signals corrupted by the channel interference (CI) at the receiver. In this paper, a novel algorithm, known as multiple shift second order sequential best rotation (MS-SBR2), is proposed to compute the approximate PSVD of the broadband MIMO channel matrix. Experimental examples, including a measured (2 × 2) optical MIMO channel impulse response using the multi-mode fiber (MMF) testbed, are presented to examine the proposed algorithm. Bit error rate (BER) performances are evaluated among different transmission schemes. In addition, power allocation (PA) schemes are investigated to further optimize the BER performance.


Full Text:

PDF

References


A.C. Singer, N.R. Shanbhag, B. Hyeon-Min, “Electronic Dispersion Compensation – An Overview of Optical Communications Systems,” IEEE Signal Processing Magazine, 25(6):110–130, 2008.

P.J. Winzer, G.J. Foschini, “MIMO Capacities and Outage Probabilities in Spatially Multiplexed Optical Transport Systems,” Optics Express, 19(17):16680–16696, 2011.

G.C. Raleigh, J.M. Cioffi, “Spatio-temporal Coding for Wireless Communication,” IEEE Trans. Communications, 46(3):357–366, Mar 1998.

G.C. Raleigh, V.K. Jones, “Multivariate Modulation and Coding for Wireless Communication,” IEEE Journal on Selected Areas in Communications, 17(5):851–866, Mar 1999.

S.S. Haykin, Adaptive Filter Theory, 2nd ed., Upper Saddle River, NJ: Prentice-Hall, 1991.

A. Scaglione, P. Stoica, S. Barbarossa, G.B. Giannakis, H. Sampath, “Optimal designs for space-time linear precoders and decoders,” IEEE Trans. SP, 50(5):1051–1064, May 2002.

C.H. Ta, S. Weiss, “A Design of Precoding and Equalisation for Broadband MIMO Systems,” in Asilomar Conf. Signals, Systems & Computers, Pacific Grove, CA, pp. 1616–1620, Nov. 2007.

A. Sandmann, A. Ahrens, S. Lochmann, “Resource Allocation in SVDAssisted Optical MIMO Systems using Polynomial Matrix Factorization,” ITG-Fachtagung: Photonische Netze, Leipzig, Germany, 2015.

J.A. Foster, J.G. McWhirter, M.R. Davies, J.A. Chambers, “An Algorithm for Calculating the QR and Singular Value Decompositions of Polynomial Matrices,” IEEE Trans. SP, 58(3):1263–1274, Mar. 2010.

J.G. McWhirter, “An Algorithm for Polynomial Matrix SVD Based on Generalised Kogbetliantz Transformations,” in 18th EUSIPCO, pp. 457–461, Aalborg, Denmark, Aug. 2010.

J.G. McWhirter, P.D. Baxter, “A Novel Technique for Broadband Singular Value Decomposition,” in 12th Annual ASAP Workshop, MA, USA, Mar. 2004.

J.G. McWhirter, P.D. Baxter, T. Cooper, S. Redif, J. Foster, “An EVD Algorithm for Para-Hermitian Polynomial Matrices,” IEEE Trans. SP, 55(5):2158–2169, May 2007.

Z. Wang, J.G. McWhirter, J. Corr, S. Weiss, “Multiple Shift Second Order Sequential Best Rotation Algorithm for Polynomial Matrix EVD,” in 23rd EUSIPCO, pp. 844–848, Nice, France, Aug. 2015.

A. Tarighat, R.C.J. Hsu, A. Shah, A.H. Sayed, B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links,” IEEE Communications Magazine, 45(5):57–63, May 2007.

P.P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice-Hall, 1993.

S. Icart, P. Comon, “Some properties of Laurent polynomial matrices,” in IMA Conference on Mathematics in Signal Processing, Birmingham, UK, Dec. 2012.

S. Redif, S. Weiss, J.G. McWhirter, “Sequential Matrix Diagonalization Algorithms for Polynomial EVD of Parahermitian Matrices,” IEEE Trans. SP, 63(1):81–89, Jan. 2015.

J. Corr, K. Thompson, S. Weiss, J.G. McWhirter, S. Redif, I.K. Proudler, “Multiple Shift Maximum Element Sequential Matrix Diagonalisation for Parahermitian Matrices,” in IEEE SSP Workshop, pp. 312–315, Gold Coast, Australia, Jun. 2014.

Z. Wang, J.G. McWhirter, J. Corr, S. Weiss, “Order-controlled multiple shift SBR2 algorithm for para-Hermitian polynomial matrices,” in IEEE SAM Workshop, pp. 1–5, Rio de Janerio, Brazil, Jul. 2016.

J. Foster, J.G. McWhirter, J. Chambers, “Limiting the Order of Polynomial Matrices Within the SBR2 Algorithm,” in IMA Conference on Mathematics in Signal Processing, Cirencester, UK, Dec. 2006.

C.H. Ta, S. Weiss, “Shortening the Order of Paraunitary Matrices in SBR2 Algorithm,” in Int. Conference on Information, Communications & Signal Processing, pp. 1–5, Singapore, Dec. 2007.

P.P. Vaidyanathan, “Theory of optimal orthonormal subband coders,” IEEE Trans. SP, 46(6):1528–1543, Jun 1998.

A. Sandmann, A. Ahrens, S. Lochmann, “Experimental Description of Multimode MIMO Channels utilizing Optical Couplers,” ITGFachbericht 248, Photonische Netze, pp. 125-130, 2014.

A. Sandmann, A. Ahrens, S. Lochmann, “Performance Analysis of Polynomial Matrix SVD-based Broadband MIMO Systems,” Sensor Signal Processing for Defence Conference (SSPD), pp. 50–54, 2015.

A. Sandmann, A. Ahrens, S. Lochmann, “Zero-Forcing Equalisation of Measured Optical Multimode MIMO Channels,” Communications in Computer and Information Science (CCIS 554), Springer International Publishing, 2015.




DOI: http://dx.doi.org/10.11601/ijates.v6i1.207

Refbacks

  • There are currently no refbacks.