Variable Tap-Length Mixed-Tone RLS-based Per-Tone Equalisation with Adaptive Implementation
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Abstract
In this paper, a methodology of mixed-tone recursive least squares algorithm development based on an orthogonal projection approach and a new variable tap-length mechanism is presented for per-tone equalisation (PTEQ) in discrete multitone systems. A mixed-tone cost function described as the sum of weight estimated errors is minimised to achieve the solutions for different per-tone equalisers simultaneously. We describe about the inverse square-root recursive least squares algorithm based upon the QRdecomposition which preserves the Hermitian symmetry of the inverse autocorrelation matrix by means of the product of square-root matrix and its Hermitian transpose. Such symmetrical property lends the benefit to the parallel implementation. In order to reduce the computational complexity, a new variable tap-length algorithm based on the sense of mean square mixted-tone errors is introduced to search a proper choice of tap-length of PTEQ. Simulation results show the improvement of achievable bit rate and signal to noise ratio performance as compared to the PTEQ exploiting conventional recursive least squares algorithm.
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References
[2] S.Sitjongsataporn, and P.Yuvapoositanon, “An Adaptive Step-size Order Statistic Time Domain Equaliser for Discrete Multitone Systems”, in Proc. of IEEE Int. Symp. on Circuits and Syst. ISCAS’07), New Orleans, USA, pp.1333-1336, May 2007.
[3] T.Pollet, M.Peeters, M.Moonen, and L.Vandendorpe, “Equalization for DMTBased Broadband Modems”, IEEE Commun. Magazine, pp. 106-113, May 2000.
[4] K.V.Acker, G.Leus, M.Moonen, O.van de Wiel, and T.Pollet, “Per Tone Equalization for DMTbased Systems”, IEEE Trans. on Commun., vol. 49, no. 1, pp. 109-119, Jan. 2001.
[5] K.V.Acker, G.Leus, M.Moonen, and T.Pollet, “RLS-Based Initialization for Per-Tone Equalizers in DMT Receivers”, IEEE Trans. on Commun., vol. 51, no. 6, pp. 885-889, Jun. 2003.
[6] S.Sitjongsataporn and P.Yuvapoositanon, “A Mixed-Tone RLS Algorithm with Orthogonal Projection for Per-Tone DMT Equalisation”, in Proc. of IEEE Int. Midwest Symp. on Circuits and Syst. MWSCAS’08), Knoxville, Tennesse, USA,pp. 942-945, Aug. 2008.
[7] F.Yu and M.Bouchard, “Recursive Least-Squares Algorithms with Good Numerical Stability for Multichannel Active Noise Control”, in Proc. of IEEE Int. Conf. Acoust., Speech and Signal Process.
(ICASSP’01), vol. 5, pp. 3221-3224, May 2001.
[8] A.S.Morris, and S.Khemaissia, “A Fast New Algorithm for A Robot Neurocontroller using Inverse QR Decomposition”, UKACC Int. Conf. on Control (CONTROL’98), vol. 1, pp. 751-756, Sep. 1998.
[9] M.Moonen and J.G.McWhirter, “Systolic Array for Recursive Least Squares by Inverse Updating”, Electronics Letters, vol. 29, no. 13, pp. 1217-1218, June 1993.
[10] Z.Pritzker and A.Feuer, “Variable Length Stochastic Gradient Algorithm”, IEEE Trans. on Signal Process., vol. 39, no. 4, pp. 997-1001, Apr. 1991.
[11] Y.Gong and C.F.N.Cowan, “An LMS Style Variable Tap-Length Algorithm for Structure Adaptation”, IEEE Trans. on Signal Process., vol. 53, no. 7, pp. 2400-2407, July 2005.
[12] Y.Zhang, N.Li, J.A.Chambers and A.H.Sayed, “Steady-State Performance Analysis of a Variable Tap-Length LMS Algorithm”, IEEE Trans. on Signal Process., vol. 56, no. 2, pp. 839-845, Feb. 2008.
[13] N.Li, Y.Zhang, Y.Zhao and Y.Hao, “An Improved Variable Tap-Length LMS Algorithm”, Signal Process., vol. 89, pp. 908-912, 2009.
[14] G.Strang, Linear Algebra and its Applications, Harcourt Brace Jovanovich, 1988.
[15] S.Haykin, Adaptive Filter Theory, Prentice Hall, 1996.
[16] S.T.Alexander and A.L.Ghirnikar, “A Method for Recursive Least Squares Filtering Based Upon an Inverse QR Decomposition”, IEEE Trans. on Signal Process., vol. 41, no. 1, Jan. 1993.
[17] A.H.Sayed and T.Kailath, “A State-Space Approach to Adaptive RLS filtering”, IEEE Signal Process. Magazine, vol. 11, pp. 18-60, 1994.
[18] S.Sitjongsataporn and P.Yuvapoositanon, “Adaptive Forgetting-factor Gauss-Newton inverse QR-RLS Per-Tone Equalisaiton for Discrete Multitone Systems”, in Proc. of Int. Conf. on Elect. Eng./Electron., Comput., Telecommun. and Inform. Technology (ECTI-CON’08), Krabi, Thailand, pp. 561-564, May 2008.
[19] S.Sitjongsataporn and P.Yuvapoositanon, “Variable Tap-Length RLS-based Per-Tone Equalisation for DMT-based systems”, in Proc. of 33rd Elect. Eng. Conf. (EECON-33), Chiang Mai, Thailand, pp. 1333-1336, Dec. 2010.
[20] N.Al-Dhahir and J.M.Cioffi, “Optimum Finite-Length Equalization for Multicarrier Transceivers”, IEEE Trans. on Commun., vol. 44, pp. 56-64, Jan. 1996.
[21] International Telecommunications Union (ITU). Recommendation G.996.1, Test Procedures for Asymmetric Digital Subscriber Line (ADSL) Transceivers, Feb. 2001.
[22] P.S.R.Diniz, Adaptive Filtering Algorithms and Practical Implementation, Springer, Boston, MA, 2008.