Error Probability Of Space-time Codes Research Articles

Asymptotic analysis of coherent and differential space-time codes in non-gaussian noise and interference

In this paper, we provide a unified framework for the asymptotic performance analysis of space-time codes (STCs) in correlated Ricean fading and non-Gaussian noise and interference. In particular, we derive simple and asymptotically tight expressions for the pairwise error probability (PEP) of coherent and differential STCs which are valid for any type of noise and interference with finite moments and detection with general Mahalonobis distance (MD) metrics including Euclidean distance (ED) and noise decorrelating (ND) metrics. These PEP expressions can be combined with truncated union bounds to obtain accurate asymptotic approximations for the bit, symbol, and frame error probabilities of STCs. We show that while the diversity gain of an STC is independent of the type of noise and the type of MD metric used, the coding gain is not and depends on certain moments of the noise and interference. We provide closed-form expressions for these moments for several practically relevant types of noise and interference. We show that for correlated noise significant performance gains can be achieved with the ND metric compared to the ED metric. While noise correlations are beneficial at high signal-to-noise ratios if they can be exploited by the metric, they are harmful if this is not the case and the simple ED metric is employed. All our analytical findings are confirmed by simulations for various popular STCs and several different types of noise and interference.

New Bounds of Pairwise Error Probability for Space-Time Codes in Rayleigh Fading Channels

In this paper, we present new upper and lower bounds of the pairwise error probabilities (PEP) for space-time codes over Rayleigh channels with independent fading. In support of this, we derive a new expression of the PEP using alternative form of the Gaussian tail function, which is very simple and descriptive. The new bounds are very accurate and suitable for easy estimation and application to the performance analysis based on distance spectrum. According to numerical examples, they turn out to be much closer to the exact PEP than other existing bounds. In addition, they help to envision the behavior of the space-time codes for the cases with more than one receiveing antennas.

New Bounds of Pairwise Error Probability for Space-Time Codes in Rayleigh Fading Channels

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we present new upper and lower bounds of the pairwise error probabilities (PEP) for space-time codes over Rayleigh channels with independent fading. In support of this, we derive a new expression of the PEP using alternative form of the Gaussian tail function, which is very simple and descriptive. The new bounds are very accurate and suitable for easy estimation and application to the performance analysis based on distance spectrum. According to numerical examples, they turn out to be much closer to the exact PEP than other existing bounds. In addition, they help to envision the behavior of the space-time codes for the cases with more than one receiveing antennas. </para>

Generalized Union Bound for Space–Time Codes

Gallager's second bounding technique, also known as the generalized union bound, is employed to derive a new upper bound on the error probability of space-time codes (STCs) with maximum-likelihood (ML) decoding on quasi-static Rayleigh fading channels. The new bound is distinguished by two characteristics: unlike the classical union bound, the new bound is rapidly convergent and is only a few decibels away from simulation results; and compared with Gallager's first bound, it has better computational efficiency and numerical stability. Hence, the new bound is a useful tool for performance analysis and computer search of good STCs. Moreover, the correlation between fading coefficients is easily accommodated by the new bound. The application of the new bound to convolutional coding on block-fading channels is also demonstrated, and an improved version is derived for the bit-error probability of maximum a posteriori probability decoding

Comment on "Pairwise error probability of space-time codes in frequency selective Rician channels"

A simpler explicit expression is derived for pairwise error probability (PEP) considered by Dharmawansa and Rajatheva (IEEE Commun. Lett., vol.9, p.894-6, October 2005). The computational efficiency of this expression is established.

A Data-Bearing Approach for Pilot-Embedding Frameworks in Space-Time Coded MIMO Systems

Space-time (ST) coded MIMO systems employing coherent detectors crucially require channel state information. This paper presents a novel pilot-embedding framework for channel estimation and data detection by exploiting the null-space property and the orthogonality property of the data-bearer and pilot matrices. The ST data matrix is firstly projected onto the data bearer matrix, which is a null-space of the pilot matrix, and the resulting matrix and the pilot matrix are combined for transmitting. The data and pilot extractions are achieved independently through linear transformations by exploiting the null-space property. The unconstrained maximum-likelihood (ML) and linear minimum mean-squared error (lmmse) estimators are explored for channel estimation. Then the ML approach for data detection is developed by exploiting the orthogonality property. The mean-squared error (mse) of channel estimation, Cramer-Rao lower bound (CRLB), and the Chernoff's bound of a pair-wise error probability for ST codes are analyzed for examining the performance of the proposed scheme. The optimum power allocation scheme for data and pilot parts is also considered. Three data-bearer and pilot structures, including time-multiplexing (TM)-based, ST-block-code (STBC)-based, and code-multiplexing (CM)-based, are proposed. Simulation results show that the CM-based structure provides superior performance for nonquasi-static flat Rayleigh fading channels, while these three structures yield similar performances for quasi-static flat Rayleigh fading channels

Pairwise error probability of space-time codes in frequency selective Rician channels

In this letter, we investigate the performance of space-time codes in frequency selective correlated Rician channels. An exact expression has been derived for the pairwise error probability (PEP) of space-time trellis codes over frequency selective Rician fading channel, which is in the form of a single finite range integral. We also obtain a closed form expression for the PEP when the signal matrices are drawn from some special design and the performance upper bound.

Pairwise Error Probability of Space-Time Codes in Rician–Nakagami Channels

In this letter, we investigate the shadowing effect on the performance of space-time codes, using the Rician-Nakagami channel model which has been recently introduced. Specifically, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the Rician-Nakagami channel, which is in the form of a simple single finite-range integral. We also present numerical results how the PEP expressions for the Rician-Nakagami channel can be related to those for the classical Rician-lognormal channel based on the parameter transformation between these two models.

Performance bounds for space-time trellis codes

We derive the union bound for space-time trellis codes over quasi-static fading channels. We first observe that the standard approach for evaluating the union bound yields very loose, in fact divergent, bounds over the quasi-static fading channel. We then develop a method for obtaining a tight bound on the error probability. We derive the union bound by performing expurgation of the standard union bound. In addition, we limit the conditional union bound before averaging over the fading process. We demonstrate that this approach provides a tight bound on the error probability of space-time codes. The bounds can be used for the case when the fading coefficients among different transmit/receive antenna pairs are correlated as well. We present several examples of the bounds to illustrate their usefulness.

Design and performance of space-time trellis codes for rapid Rayleigh fading channels

Space-Time (ST) codes are known to provide high transmission rates, diversity and coding gains. In this paper, a tight upper bound on the error probability of ST codes over rapid fading channels is presented. Moreover, ST codes suitable for rapid fading channels are presented. These codes are designed using the QPSK and 16-QAM signal constellations. The proposed codes are based on two different encoding schemes. The first scheme uses a single trellis encoder, whereas the second scheme uses the I-Q encoding technique. Code design is achieved via partitioning the signal space such that the design criteria are maximized. As a solution for the decoding problem of I-Q ST codes, the paper introduces a low-complexity decoding algorithm. Results show that the I-Q ST codes using the proposed decoding algorithm outperform singleencoder ST codes with equal complexity. The proposed codes are tested over fading channels with different interleaving conditions, where it is shown that the new codes are robust under such imperfect interleaving conditions.

New exponential bounds and approximations for the computation of error probability in fading channels

We present new exponential bounds for the Gaussian Q function (one- and two-dimensional) and its inverse, and for M-ary phase-shift-keying (MPSK), M-ary differential phase-shift-keying (MDPSK) error probabilities over additive white Gaussian noise channels. More precisely, the new bounds are in the form of the sum of exponential functions that, in the limit, approach the exact value. Then, a quite accurate and simple approximate expression given by the sum of two exponential functions is reported. The results are applied to the general problem of evaluating the average error probability in fading channels. Some examples of applications are also presented for the computation of the pairwise error probability of space-time codes and the average error probability of MPSK and MDPSK in fading channels.

Correction to "Exact pairwise error probability of space-time codes"

Correction to "Exact pairwise error probability of space-time codes"