Two-dimensional signaling in Ricean fading with imperfect channel estimation
ABSTRACT The analytical framework reported in X. Dong et al. (May 2003) for calculating the symbol error rate (SER) of two-dimensional (2-D) signaling in Rayleigh fading with channel estimation errors is further developed to address the more general case of frequency-flat Ricean fading. We show that in the presence of channel estimation errors, the SER of arbitrary 2-D signaling with polygonal decision regions in Ricean fading can be expressed as a two-fold proper integral with finite integration limits, which is suitable for numerical evaluation. Moreover, this new analysis is general in the sense that it is applicable to any channel estimation scheme where the estimated and the actual channel gains are jointly complex-Gaussian. The effect of static channel estimation errors and dynamic channel estimation errors introduced by pilot symbol assisted modulation (PSAM) and minimum mean square error (MMSE) channel estimations are studied using the newly derived SER formula. The effect of Doppler frequency shift in the line-of-sight (LOS) component of the channel on the error performance is investigated in our analysis. The analytical and numerical results presented in this work provide a useful tool on choosing suitable signaling formats and optimizing parameters in the communication system design.
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ABSTRACT: The method used in Aghamohammadi and Meyr (1990) for finding the error probability of linearly modulated signals on Rayleigh frequency-flat fading channels has been applied to the more general case of Ricean fading. A signal received on a fading channel is subject to a multiplicative distortion (MD) and to the usual additive noise. Following a compensation of the MD, the signal provided to the detector may be thought to include only a single additive distortion term (“final noise”), which comprises the effects of the original additive noise, the MD, and the error in MD compensation. An exact expression for the probability density function of the final noise is derived. This allows calculation of error probability for arbitrary types of linear modulations. Results for many cases of interest are presented. Furthermore, as special cases of Ricean fading, error probability for Rayleigh fading and non-fading channels are obtained which either match the results or complete the approximate derivations formerly known from the literatureIEEE Transactions on Communications 03/1995; · 1.75 Impact Factor
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ABSTRACT: The author presents a simple integral expression for calculating the exact probability of a symbol error for an arbitrary array of signal points. The integrand contains only elementary functions and the range of integration is finite. The approach is introduced by applying it to M -ary phase shift keying (MPSK). The special case of M =2 gives novel and possibly useful expressions for calculating the Gaussian tail probability function and the related complementary error function. The approach is outlined for polygonal decision regions, and results are given for 16-point signal constellations. A method of obtaining, not exact, but even simpler and highly accurate expressions for symbol error probability when the latter is less than a few hundredths is presentedMilitary Communications Conference, 1991. MILCOM '91, Conference Record, 'Military Communications in a Changing World'., IEEE; 12/1991