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.     

Convolutionally interleaved PSK and DPSK trellis codes forshadowed, fast fading mobile satellite communication channels

Using a model from the literature, the performance of convolutionally interleaved phase-shift-keying (PSK) and differential phase-shift-keying (DPSK) trellis codes for digital speech transmission over shadowed mobile satellite communication channels is determined by computer simulation. First the characteristics of fading channels are examined and analyzed in terms of the probability distributions of amplitude, phase, and burst errors. A statistical method, using a histogram approach, is utilized along with the simulations of fading channels to generate these probability distributions. A test for channel burst error behavior is presented. A periodic convolutional interleaver/deinterleaver to be used with trellis coding to combat slow fading in digital, shadowed mobile satellite channels is designed. This interleaver ha less than half the time delay for the same bit error performance than a block interleaver. The results show that the periodic convolutional interleaver provides considerable improvement in the error and time delay performance of mobile satellite communication channels for up to average shadowing conditions as compared to other techniques     

Space-time trellis codes over rapid rayleigh fading channels with channel estimation?part ii: performance analysis and code design for non-identical channels

We consider the maximum likelihood (ML) receiver design, performance analysis and code design for space-time trellis codes (STTC) over non-identical, rapid fading channels with imperfect channel state information (CSI). The exact pairwise error probability (PEP) and PEP bounds for the ML receiver are obtained. A new code design criterion exploiting the statistical information of the channel estimates is proposed, which can minimize the performance loss caused by channel estimation error. New codes are obtained via an iterative search algorithm with reduced complexity. Under actual channel estimation conditions, our codes perform better than the existing codes in the literature which are designed on the assumption of identical channels, and perfect CSI at the receiver. More performance gain can be achieved by our codes when the degree of imbalance among the links is higher.     

Diversity analysis of space-time coding in cascaded Rayleigh fading channels

Cascaded Rayleigh distribution is used to model multipath fading in mobile-to-mobile communication scenarios and provides a better fit to experimental data in such scenarios compared to the conventional Rayleigh channel model. In this letter, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the cascaded Rayleigh fading channel, which is in the form of a simple single finite-range integral. Through the derived PEP expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degradation in comparison to conventional Rayleigh channels. Monte-Carlo simulations are further demonstrated to confirm the analytical results.     

Exact BER analysis of OSTBCs in spatially correlated MIMO channels

The bit-error rate (BER) performance of orthogonal space-time block codes (STBCs) in correlated multiple-input multiple-output (MIMO) channels is studied. We first derive closed-form exact BER equations for pulse amplitude modulation, quadrature amplitude modulation, and phase-shift keying constellations in a correlated Rayleigh MIMO channel. The BER expressions can be easily evaluated without any numerical methods. Then we consider correlated MIMO channels where the line of sight components exist and they suffer from shadowing, namely, correlated shadowed Rician MIMO channels. For three practical channel scenarios, the BER is analyzed, and closed-form BER equations are presented.     

On the error performance analysis of space-time trellis codes

We present analytical performance results for space-time trellis codes over spatially correlated Rayleigh fading channels. Bit-error-probability estimates are obtained based on the derivation of an exact pairwise error probability expression using a residue technique combined with a characteristic function approach. We investigate both quasi-static and interleaved channels and demonstrate how the spatial fading correlation affects the performance of space-time codes over these two different channel models. Simulation results are also included to confirm the accuracy of analytical estimates.     

Reed-Solomon codes for land mobile satellite channels

The performance of Reed-Solomon codes is determined for land mobile satellite communications where a shadowed Rician channel model is used. An effective coding/interleaving scheme is proposed which uses the multipath fading and shadowing statistics of the channel.<>     

Concatenated space-time block coding with trellis coded modulation in fading channels

Trellis coded modulation (TCM) is a bandwidth efficient transmission scheme that can achieve high coding gain by integrating coding and modulation. This paper presents an analytical expression for the error event probability of concatenated space-time block coding with TCM which reveals some dominant factors affecting the system performance over slow fading channels when perfect interleavers are used. This leads to establishing the design criteria for constructing the optimal trellis codes of such a concatenated system over slow flat fading channels. Through simulation, significant performance improvement is shown to be obtained by concatenating the interleaved streams of these codes with space-time block codes over fading channels. Simulation results also demonstrate that these trellis codes have better error performance than traditional codes designed for single-antenna Gaussian or fading channels. Performance results over quasi-static fading channels without interleaving are also compared in this paper. Furthermore, it is shown that concatenated space-time block coding with TCM (with/without interleaving) outperforms space-time trellis codes under the same spectral efficiency, trellis complexity, and signal constellation.     

Space-Time Trellis Codes Over Rapid Rayleigh Fading Channels With Channel Estimation---Part I: Receiver Design and Performance Analysis

The performance analysis of space-time trellis codes over rapid nonselective Rayleigh fading channels with imperfect channel state information is considered. A pilot-symbol-assisted-modulation scheme is used for channel estimation. The parameters used in this scheme, i.e., pilot spacing and Wiener filter length are chosen in a tradeoff between estimation accuracy, transmission rate/pilot overhead, and receiver complexity. A simple maximum likelihood receiver for M-ary phase shift keying modulation is derived. An exact closed-form pairwise error probability (PEP) expression and explicit PEP bounds are presented. It is shown that the performance loss caused by channel estimation errors increases mainly with the channel fade rate.     

Performance comparison of different decoding strategies for abandwidth-efficient block-coded scheme on mobile radio channels

The performance of bandwidth-efficient Reed-Solomon (RS)-coded MPSK schemes is evaluated on a shadowed Rician fading channel using different decoding strategies, namely, errors-only, errors-and-erasures, and soft-decision decoding. The lower bounds of the bit error probability are found for errors-only and for errors-and-erasures decoding. For the soft-decision decoding the upper bound of the bit error rate is derived. The error bounds are calculated and examined by simulation for some RS-coded MPSK schemes on a shadowed Rician channel. It is shown that their performance is significantly improved compared to uncoded QPSK. The amount of improvement depends on the signal-to-noise ratio (SNR), the decoding strategy, and the degree of shadowing. A comparison between different decoding techniques, for one of the RS-coded schemes, for different degrees of shadowing shows that the use of channel measurement information in the decoding process is more effective for heavy shadowed channels     

Performance and distance spectrum of space-time codes in fast rayleigh fading channels

In this paper, we analyze the performance of spacetime codes and propose a distance spectrum computation method in fast Rayleigh fading channels. We first derive a new FER upper bound using the union bound and the PEP upper bound in the fast fading environment. The derived FER upper bound is very accurate, requires only the distance spectrum of the spacetime code, and takes a closed-form expression. Then we propose a distance spectrum computation method of space-time codes in fast fading channels, which exploits the symmetric property of the error state diagram in space-time trellis coded MPSK modulation to reduce the computation complexity. Numerical results illustrate that the derived FER bound is tight enough to estimate the performance of space-time codes in fast fading channels with sufficient accuracy.     

Bit-error bounds for trellis-coded MPSK in mixed fading channels

Bit-error probability (BEP) bounds of trellis-coded MPSK systems over two classes of mixed fading channels are studied. These two classes of channels have been proposed as candidate models for mobile satellite communications. The first class consists of slow and frequency-nonselective fading channels whose output field strengths follow a probability law characterized by a convex combination of Rician and Rayleigh/lognormal distributions. For the other class of fading channels, the received signal amplitude has a convex combination of Rician and Rician/lognormal distributions. We analyze performance bounds for trellis codes that belong to the class of either geometrically uniform codes (GUCs) or quasi-regular codes (QRCs). Receivers with either ideal channel state information (CSI) or no CSI at all are considered. We examine asymptotic behaviors of these codes and identify key design parameters. Numerical results are provided to illustrate and compare the BEP performances of various codes and to validate the usefulness of the asymptotic analysis     

TCMP-a modulation and coding strategy for Rician fading channels

The authors describe TCMP, a novel modulation strategy for Rician fading channels that multiplexes a time domain pilot sequence with trellis-coded data to permit coherent detection. This technique is shown to provide remarkably robust performance in the presence of fading. It is also shown that, when choosing trellis codes for fading channels, time diversity is of greater important than asymptotic coding gain. The motivation for studying this strategy is to find signaling schemes for transmitting data at a 4.8 kb/s rate over a mobile satellite channel with 5-kHz channel spacing     

Performance of concatenated channel codes and orthogonal space-time block codes

In this paper we analyze the performance of an important class of MIMO systems that of orthogonal space-time block codes concatenated with channel coding. This system configuration has an attractive combination of simplicity and performance. We study this system under spatially independent fading as well as correlated fading that may arise from the proximity of transmit or receive antennas or unfavorable scattering conditions. We consider the effects of time correlation and present a general analysis for the case where both spatial and temporal correlations exist in the system. We present simulation results for a variety of channel codes, including convolutional codes, turbo codes, trellis coded modulation (TCM), and multiple trellis coded modulation (MTCM), under quasi-static and block-fading Rayleigh as well as Rician fading. Simulations verify the validity of our analysis.     

An efficient space-frequency coded OFDM system for broadband wireless communications

We propose an efficient space-frequency coded orthogonal frequency-division multiplexing (OFDM) system for high-speed transmission over wireless links. The analytical expression for the pairwise probability of the proposed space-frequency coded OFDM system is derived in slow, space- and frequency-selective fading channels. The design criteria of trellis codes used in the proposed system are then developed and discussed. It is shown that the proposed space-frequency coded OFDM can efficiently achieve the full diversity provided by the fading channel with low trellis complexity, while for traditional space-frequency coded OFDM systems, we need to design space-time trellis codes with high trellis complexity to exploit the maximum achievable diversity order. The capacity properties of space-frequency coded OFDM over multipath fading channels are also studied. Numerical results are provided to demonstrate the significant performance improvement obtained by the proposed space-frequency coded OFDM scheme, as well as the excellent outage capacity properties.     

On the Performance of Golden Space-Time Trellis Coded Modulation over MIMO Block Fading Channels

The Golden space-time trellis coded modulation (GST-TCM) scheme was proposed in [1] for a high rate 2 × 2 multiple-input multiple-output (MIMO) system over slow fading channels. In this letter, we present the performance analysis of GST-TCM over block fading channels, where the channel matrix is constant over a fraction of the codeword length and varies from one fraction to another, independently. In practice, it is not useful to design such codes for specific block fading channel parameters and a robust solution is preferable. We then show both analytically and by simulation that the GST-TCM designed for slow fading channels are indeed robust to all block fading channel conditions.     

Performance of trellis coded modulation schemes on shadowed mobilesatellite communication channels

The Canadian mobile satellite (MSAT) channel has been modeled as the sum of lognormal and Rayleigh components to represent foliage attenuation and multipath fading, respectively. Several authors have applied trellis coded modulation (TCM) schemes to this channel, estimating the bit error performance via computer simulation. In the present paper, analytical expressions are derived for the pairwise error probability (PEP) of TCM schemes over this channel under ideal interleaving. The analysis is applied to three detection strategies: ideal coherent detection, pilot-tone aided detection, and differential detection. The results are substantiated by means of computer simulation. In addition, first-order statistics of absolute and differential phases of a shadowed Rician process are examined     

Concatenation of space‐time block codes and turbo trellis coded modulation (ST‐TTCM) over Rician fading channels with imperfect phase

In this paper, the performance of space time‐turbo trellis coded modulation (ST‐TTCM) is evaluated over Rician and Rayleigh fading channels with imperfect phase. We modify Baum–Welch (BW) algorithm to estimate the fading and phase jitter parameters for multi‐antenna configurations. Thus, we assume that the channel parameters change slower than carrier frequency. We know that, at high data rate transmissions over wireless fading channels, space–time block codes (STBC) provide the maximal possible diversity advantage. Here, the combined effects of the amplitude and the phase of the received signal are considered, each one modelled by Rician and Tikhonov distributions, respectively. We investigate space time‐turbo trellis coded modulation (ST‐TTCM) for 8‐PSK for several Rician factor K and phase distortion factor η. Thus, our results reflect the degradations both due to the effects of the fading on the amplitude and phase noise of the received signal while the channel parameters are estimated by BW algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

A performance analysis of trellis-coded modulation schemes overRician fading channels

This paper presents a saddle point approximation (SAP) method to compute the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over Rician fading channels. The approximation is applicable under several conditions, such as finite and ideal interleaving, ideal coherent and pilot-tone aided detection, and differential detection. The accuracy of this approximation is demonstrated by comparison to the results of numerical integration. When ideal interleaving is assumed, an asymptotic approximation for the PEP of ideal coherent, pilot-tone aided or differentially detected TCM is derived. This asymptotic approximation of the PEP is in a product form and much tighter than the ordinary Chernoff bound on the PEP. Also, based on the SAP, the effect of finite interleaving depth on the error performance of TCM schemes over Rician and shadowed Rician channels is studied