Two-dimensional signaling in Ricean fading with imperfect channel estimation
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.
[Show abstract] [Hide abstract] ABSTRACT: We derive the symbol error probability (SEP) expressions for orthogonal space-time block codes with any form of generalized complex orthogonal design (GCOD) employing arbitrary rectangular quadratic-amplitude modulation signaling over correlative fading channels. By first decorrelating the physical branches into uncorrelated virtual branches, a general expression for the moment generating function of the received signal-to noise ratio (SNR) is obtained, from which the SEP is derived. The result can be applied to correlative fading channels with any form of Gaussian fading gains. Moreover, channels having joint fading models, as well as mixed channel powers, are considered. We also discover that, for certain GCOD codes, different information symbols may exhibit different SEPs. The above features are demonstrated by two GCOD examples used for simulations. Theoretical performance curves are compared with Monte Carlo simulated results in excellent agreement.
- "Then, we have used m = 2 for the Nakagamim fading and the Ricean factor K R = µ 2 /2σ 2 = 7 dB for the Ricean fading. According to , a Ricean factor of 7 dB is typical of practical microcellular channels. In each figure, we have also included the uncorrelated case of ρ = 0. Monte Carlo simulations are also incorporated for comparison. "
- [Show abstract] [Hide abstract] ABSTRACT: The paper presents a general analysis on the performance of selection combining (SC) systems in Rayleigh fading channels with imperfect channel estimation (ICE). The channel estimate and the actual fading are modeled as complex joint Gaussian random variables. Simple single integral formulas with finite integration limits are derived for the symbol error probability (SER) of an arbitrary two-dimensional (2D) modulation format, and a closed-form expression is obtained for the SER of M<sub>s</sub>-PAM. These error probability expressions are then applied to three types of channel estimation errors possibly encountered in practical systems to study their impact on the performance of selection diversity. Other applications of this general analysis include semi-analytical simulation of practical communication systems.
- [Show abstract] [Hide abstract] ABSTRACT: In this paper, we study the effect of imperfect channel estimation (ICE) on the performance of M-level quadrature amplitude modulation (M-QAM) with maximum ratio combining (MRC) and pilot-symbol assisted modulation (PSAM) in generalized Rician fading channels. By expressing the bit error rate (BER) of MRC diversity M-QAM in terms of the distribution of new decision variables, we derive novel, exact, and easy-to-evaluate BER expressions for diversity M-QAM with channel estimation errors. Our results include versatile system and fading channel parameters (e.g., arbitrary spatial and temporal correlation patterns among the diversity branches), and are valid for arbitrary linear channel estimators and square and rectangular M -QAM with different constellation sizes. In addition, we evaluate the performance of minimum mean-squared error (MMSE)- and sinc-interpolator-based channel estimators with PSAM, and provide some new insights into the performance of M-QAM with PSAM in generalized fading channels