Multiple-Symbol Differential Detection Based on Combinatorial Geometry

In this paper, the application of combinatorial geometry to noncoherent multiple-symbol differential detection (MSDD) is considered. The resulting algorithm is referred to as CG-MSDD. Analytical expressions for both the complexity and the error-rate performance of CG-MSDD are derived and it is shown that its complexity is polynomial in the length N of the MSDD observation window if the rank of the N times N channel autocorrelation matrix is fixed, but in fact exponential in N if standard fading models are considered. Compared to popular sphere-decoder based MSDD, CG-MSDD is superior (i) in low-signal-to-noise power ratio (SNR) slow-fading channels as its complexity is independent of the SNR, (ii) as its complexity is constant, i.e., independent of the particular channel and noise realization, and (iii) asymptotically, as its complexity exponent only scales linearly with the bandwidth of the fading process.

[1]  Lutz H.-J. Lampe,et al.  On the Complexity of Sphere Decoding for Differential Detection , 2007, IEEE Transactions on Information Theory.

[2]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[3]  Dariush Divsalar,et al.  Multiple-symbol differential detection of MPSK , 1990, IEEE Trans. Commun..

[4]  Kenneth M. Mackenthun,et al.  A fast algorithm for multiple-symbol differential detection of MPSK , 1994, IEEE Trans. Commun..

[5]  Wolfgang Rave,et al.  On the Complexity of Sphere Decoding , 2004 .

[6]  Björn E. Ottersten,et al.  On the complexity of sphere decoding in digital communications , 2005, IEEE Transactions on Signal Processing.

[7]  Stephen G. Wilson,et al.  Multi-symbol detection of M-DPSK , 1989, IEEE Global Telecommunications Conference, 1989, and Exhibition. 'Communications Technology for the 1990s and Beyond.

[8]  P. Ho,et al.  Error performance of multiple symbol differential detection of PSK signals transmitted over correlated Rayleigh fading channels , 1991, ICC 91 International Conference on Communications Conference Record.

[9]  Paul K. M. Ho,et al.  The performance of Fano-multiple symbol differential detection , 2005, IEEE International Conference on Communications, 2005. ICC 2005. 2005.

[10]  Dimitrios Makrakis,et al.  Optimal decoding in fading channels: a combined envelope, multiple differential and coherent detection approach , 1989, IEEE Global Telecommunications Conference, 1989, and Exhibition. 'Communications Technology for the 1990s and Beyond.

[11]  Thomas M. Liebling,et al.  Solving the fixed rank convex quadratic maximization in binary variables by a parallel zonotope construction algorithm , 2005, Eur. J. Oper. Res..

[12]  Lutz H.-J. Lampe,et al.  Tree-Search Multiple-Symbol Differential Decoding for Unitary Space-Time Modulation , 2007, IEEE Transactions on Communications.

[13]  Bertrand M. Hochwald,et al.  Differential unitary space-time modulation , 2000, IEEE Trans. Commun..

[14]  Lutz H.-J. Lampe,et al.  Multiple-symbol differential sphere decoding , 2005, IEEE Transactions on Communications.

[15]  Achilleas Anastasopoulos,et al.  Optimal Joint Detection/Estimation in Fading Channels With Polynomial Complexity , 2007, IEEE Transactions on Information Theory.

[16]  Chintha Tellambura,et al.  Bound-intersection detection for multiple-symbol differential unitary space-time modulation , 2005, IEEE Transactions on Communications.

[17]  Ajit Kumar Chaturvedi,et al.  Application of computational geometry to multiuser detection in CDMA , 2006, IEEE Transactions on Communications.

[18]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[19]  Robert Schober,et al.  Multiple-symbol differential sphere decoding , 2005, IEEE Trans. Commun..

[20]  Harry Leib,et al.  Optimal noncoherent block demodulation of differential phase shift keying (DPSK) , 1991 .