Abstract
This paper presents a new approach for the design of a set of orthogonal digital filters which can be used as message-carrying waveforms in orthogonality division multiple access (ODMA) communication systems. The filter set design problem is formulated as a constrained L 2 space optimization problem. For bandwidth efficiency, all the digital filters in the set are constrained to have approximately the same desired spectral shapes in a prescribed passband; To minimize intersymbol interference and co-channel interference, all the digital filters in the set are constrained to have low values of auto-correlation at nonzero translates of multiple symbol interval and low values of cross-correlation at all translates of multiple symbol interval. Methods for solving the proposed non-convex optimization problem are outlined. Numerical results are presented to illustrate the usefulness of the proposed method.
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References
Akansu, A.N., P. Duhamel, X. Lin, and M. de Courville. (1998). “Orthogonal Transmultiplexers in Communication: A Review.” IEEE Transactions on Signal Processing 46(4), 979–995.
Burnside, D. and T.W. Parks. (1995). “Optimal Design of FIR Filters with the Complex Chebyshev Error Criteria.” IEEE Transactions on Signal Processing 43(3), 605–616.
Chandran, G. and J.S. Jaffe. (1996). “Signal Set Design with Constrained Amplitude Spectrum and Specified Time-Bandwidth Product.” IEEE Transactions on Communications 44(6), 725–732.
Chang, R.W. (1966). “Synthesis of Band-Limited Orthogonal Signals for Multichannel Data Transmission.” The Bell System Technical Journal 1775–1796.
Davidson, T.N., Z.-Q. Luo, and K.M. Wong. (2000). “Design of Orthogonal Pulse Shapes for Communications via Semidefinite Programming.” IEEE Transactions on Signal Processing 48(5), 1433–1445.
Grace, A. (1993). Optimization Toolbox: for Use with MATLAB. South Natick, MA: The Math Works Inc.
Karam, L.J. and J.H. McClellan. (1995). “Complex Chebyshev Approximation for FIR Filter Design.” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing 42(3), 207–216.
King, R.E. and P.N. Paraskevopoulos. (1977). Digital Laguerre Filters, Circuit Theory and Applications 5 81–91.
Kirjner-Neto, C. and E. Polak. (1998). “On the Conversion of Optimization Problems with Max-Min Constraints to Standard Optimization Problems.” SIAM Journal on Optimization 8(4), 887–915.
Lee, E.A. and D.G. Messerschmitt. (1994). Digital Communication, 2nd ed. Boston: Kluwer Academic.
Li, X., I. Thng, and C.C. Ko. (1999). “An Improved Design of 3-D CAP Signature Waveforms against Quantization Noise.” In Proceedings of IEEE International Symposium on Computers and Communications, pp. 369–374.
Lucky, R.W., J. Salz, and E.J. Weldon Jr. (1968). Principles of Data Communications. New York: McGraw-Hill.
Nordebo, S. and Z. Zang. (1999). “Semi-Infinite Linear Programming: A Unified Approach to Digital Filter Design with Time and Frequency Domain Specifications.” IEEE Transactions on Circuit and Systems-II: Analog and Digital Signal Processing 46(6), 765–775.
Parks, T.W. and C.S. Burrus. (1987). Digital Filter Design. New York: Wiley.
Proakis, J.G. (1989). Digital Communications, 2nd ed. New York: McGraw-Hill.
Shalash, A.F. and K.K. Parhi. (1999). “Multidimensional Carrierless AM/PM Systems for Digital Subscriber Loop.” IEEE Transactions on Communications 47(11), 1655–1667.
Streit, R.L. and A.H. Nuttall. (1982). “A General Chebyshev Complex Function Approximation Procedure and an Application to Beamforming.” Journal of the Acoustical Society of America 72(1), 181–190.
Streit, R.L. and A.H. Nuttall. (1983). “A Note on the Semi-Infinite Programming Approach to Complex Approximation.” Mathematics of Computation 40(162), 599–605.
Thng, I., X. Li, and C.C. Ko. (1999). “A New 3D CAP System.” In Proceedings of the IEEE Region 10 Conference, Cheju, Korea, pp. 309–312.
Tuy, H. (1998). Convex Analysis and Global Optimization. Dordrecht: Kluwer Academic.
Vaidyanathan, P.P. (1993). Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall.
Wahlberg, B. (1991). “System Identification Using Laguerre Models.” IEEE Transactions on Automatic Control 36(5), 551–562.
Zang, Z., S. Nordholm, and S. Nordebo. (2001). “Complex Domain Digital Filter Design with Max-Min Type Amplitude Constraints and Group Delay Specifications.” In Proceedings of IEEE Region 10 Conference, Singapore, pp. 265–269.
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Zang, Z., Nordholm, S. Design of ODMA Digital Waveforms Using Non-Convex Optimization Methods. Ann Oper Res 133, 319–330 (2005). https://doi.org/10.1007/s10479-004-5041-y
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DOI: https://doi.org/10.1007/s10479-004-5041-y