Pairwise error probability evaluation of multiple symbol trellis-coded continuous phase frequency shift keying in a slow fading channel

This article evaluates the pairwise error probability (PEP) of multiple symbol trellis-coded modulation applied to continuous phase frequency shift keying (MTCM/CPFSK) in a slow fading environment with and without channel state information (CSI). The fading amplitude is assumed to be constant during an error event and distributed as Rician. For the case with CSI, the PEP is approximated using the Gauss-Chebysev formula and a tight upper bound is presented. For the case without CSI, a simplified upper bound is derived by using the improved Chernoff bound technique. Simulation results are also presented.     

On the performance of rate 1/2 convolutional codes with QPSK onRician fading channels

Consideration is given to the bit error probability performance of rate 1/2 convolutional codes in conjunction with quaternary phase shift keying (QPSK) modulation and maximum-likelihood Viterbi decoding on fully interleaved Rician fading channels. Applying the generating function union bounding approach, an asymptotically tight analytic upper bound on the bit error probability performance is developed under the assumption of using the Viterbi decoder with perfect fading amplitude measurement. Bit error probability performance of constraint length K=3-7 codes with QPSK is numerically evaluated using the developed bound. Tightness of the bound is examined by means of computer simulation. The influence of perfect amplitude measurement on the performance of the Viterbi decoder is observed. A performance comparison with rate 1/2 codes with binary phase shift keying (BPSK) is provided     

Error performance of MPSK trellis-coded modulation overnonindependent Rician fading channels

This paper presents new upper bounds on the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over nonindependent Rician fading channels. Cases considered are coherent and pilot-tone-aided detection and differential detection of trellis-coded multilevel phase-shift keying (TC-MPSK) systems. The average bit-error probability P_b can be approximated by truncating the union bound. This method does not necessarily lead to an upper bound on P_b, and, hence, the approximation must be used with simulation results. In addition, for Rayleigh fading channels with an exponential autocovariance function, bounds resembling those for memoryless channels have been derived. The bounds are substantially more accurate than Chernoff bounds and hence allow for accurate estimation of system performance when the assumption of ideal interleaving is relaxed     

Multiple trellis coded frequency and phase modulation

Multiple trellis coded modulation of constant envelope frequency and phase modulated signal sets (MTCM/FPM) is investigated for performance on the additive white Gaussian noise (AWGN) channel and on the one-sided normal, Rayleigh and Rician fading channels. The Nakagami- m fading model is used as an alternative to the Rician fading model to calculate the error probability upper bound for trellis-coded schemes on the fading channel. The likeliness and the disparity between the upper bounds to the error probability for the two fading models are discussed. The design criteria for the one-sided normal fading channel, modeled by the Nakagami-m distribution, are observed to be the same as those for the Rayleigh-fading channel. For the MTCM/FPM schemes, it is demonstrated that the set partitioning designed to maximize symbol diversity (optimum for fading channels) is optimum for performance on the AWGN channel as well. The MTCM/FPM schemes demonstrate improved performance over MTCM/MPSK schemes and TCM/FPM schemes on the AWGN channel and the fading channel     

Differential Space-Time Modulation Using DAPSK Over Rician Fading Channels

This paper studies differential space-time modulation using diversity-encoded differential amplitude and phase shift keying (DAPSK) for the multiple-input multiple-output (MIMO) system over independent but not identically distributed (inid) time-correlated Rician fading channels. An asymptotic maximum likelihood (AML) receiver is developed for differentially detecting diversity-encoded DAPSK symbol signals by operating on two consecutive received symbol blocks sequentially. Based on Beaulieu’s convergent series, the bit error probability (BEP) upper bound is analyzed for the AML receiver over inid time-correlated Rician fading channels. Particularly, an approximate BEP upper bound of the AML receiver is also derived for inid time-invariant Rayleigh fading channels with large received signal-to-noise power ratios. By virtue of this approximate bound, a design criterion is developed to determine the appropriate diversity encoding coefficients for the proposed DAPSK MIMO system. Numerical and simulation results show that the AML receiver for diversity-encoded DAPSK is nearly optimum when the average received signal-to-noise power ratios are high and the channel is heavily correlated fading and can provide better error performance than conventional noncoherent MIMO systems when the effect of non-ideal transmit power amplification is taken into account.     

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.     

MIMO系统在空时二维相关莱斯快衰落信道下的性能

与准静态独立的瑞利衰落信道模型相比较,在MIMO(Multi-Input Multi-Output)系统中,实际信道更趋向于空时相关莱斯快衰落。考虑到MIMO系统的收发分集优势以及收发两端天线阵列的空时相关性,在简单论述了MIMO系统和信道模型的基础上,该文利用多变量统计学理论,推导出MIMO系统在空时相关莱斯快衰落信道下平均成对差错概率上界的闭合表达式,并探讨了信道特性对系统性能的影响,然后给出相应仿真结果。     

Trellis coded MDPSK in correlated and shadowed Rician fadingchannels

The performance of trellis-coded multilevel differential phase-shift keying (TC-MDPSK) signals in correlated and shadowed Rician fading channels is evaluated. The pairwise error probabilities of the TC-MDPSK signals in the channels are calculated directly and approximated asymptotically. The asymptotic expression can be put into a product form and used in a transfer function approach to estimate the error performance of TC-MDPSK. The bit error rate of TC-MDPSK is estimated by using a truncated form of the union bound and by an asymptotic expression. In the two examples considered, these formulas show fairly good agreement in both correlated and shadowed Rician channels and are at least 2-dB tighter in signal-to-noise ratio than the Chernoff bound in the correlated Rician channels. Asymptotic expressions for the error probability of uncoded MDPSK in both correlated and shadowed Rician channels are also obtained     

Performance of M-PSK in mobile satellite communication over combined ionospheric scintillation and flat fading channels with MRC diversity

Combined scintillation and terrestrial fadings occur in mobile satellite communication channels as the signal passes through the ionosphere and the lower atmosphere. This results in a product fading channel, which negatively affects the performance of the system. The challenge is to evaluate the performance of the system, in terms of the average bit error probability (BEP). In this paper, through the use of the moment generating function, we derive expressions for the average BEP and an upper bound for M-ary phase-shift keying (M-PSK) modulation with maximal-ratio combining (MRC) diversity over the product RicianxRician channel. The results are expressed as double summations in terms of the generalized hypergeometric function, which can be computed using standard commercial software. For a large Rician factor, the expression is simplified to a single summation. Numerical results are obtained from the derived expressions and compared with simulation results. They show very good agreement for various Rician factors and the number of diversity branches. The upper bound is also evaluated and shown to be reasonably tight.     

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     

Probability of error analysis for FHSS/CDMA communications in thepresence of fading

Expressions are found for the probability of error of a slow frequency-hopped spread-spectrum (FHSS) code-division multiple-access (CDMA) system using noncoherent M-ary frequency-shift-keyed (FSK) data modification in the presence of slow-nonselective Rayleigh or single-term Rician fading. The analysis is general enough for the consideration of the near/far problem under the specified channel conditions. Comparisons are made between the error expressions developed here and previously published upper bounds. It is found, under certain conditions, that the previous upper bounds on the probability of error may exceed the true probability of error by an order of magnitude     

Blind equalization of quadrature partial response‐trellis coded modulated signals in Rician fading

In this paper, a blind maximum‐likelihood channel estimation algorithm is developed for quadrature partial response‐trellis coded modulated (QPR‐TCM) signals propagating through a Rician fading environment. A hidden Markov model (HMM) formulation of the problem is introduced and the Baum–Welch parameter estimation algorithm is modified to provide a computationally efficient solution to the resulting optimization problem. Performance analysis of the proposed method is carried out through the evaluation of bit‐error probability upper bound for Rician fading channels. Also, some illustrative simulations are presented. Copyright © 2001 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     

Evaluation of the exact union bound for trellis-coded modulationsover fading channels

An analytical technique is presented for computing the exact union bound on the average bit error probability of trellis coded modulation schemes over Rayleigh, Rician, or shadowed Rician-fading channels. To this end, an integral expression is derived for the pairwise error event probability (PEP). Existing bounds can be obtained as special cases of this expression. It turns out that a Gauss-Chebyshev quadrature rule offers excellent accuracy for this integral. By extension, the exact union bound (i.e., the weighted sum of an exact PEPs of a code) can readily be evaluated. This method has the same complexity as the union-Chernoff bound, and a few examples are given to show its application     

Probability-of-error bounds for binary transmission on the slowly fading Rician channel

Chernoff bounds and tilted distribution arguments are applied to obtain error probability bounds for binary signaling on the slowly-fading Rician channel with L diversity. For the maximum likelihood receiver, the CB-optimum [optimum in the sense of minimizing the Chernoff (upper) bound on error probability] signal correlation is determined and plotted; it is found that antipodal signals should be used ifa > b^{2}(1 + b), where a is the signal-to-noise ratio of the specular components andbis that of the fading components. The CB-optimum number of diversity paths is then obtained. Ifa/b > 0.2, antipodal signaling with unlimited diversity is CB-optimum; whereas, ifa/b < 0.2, orthogonal signaling with properly chosen diversity is very nearly CB-optimum. If restricted to orthogonal signaling, unlimited diversity is CB-optimum whenevera/b > 1.0. Similar results are obtained for the generally nonoptimum square-law-combining receiver. In this case, orthogonal signaling with finite diversity is always CB-optimum.     

Two hop amplify-and-forward transmission in mixed rayleigh and rician fading channels

The performance of a two hop amplify-and-forward relay system, where the source-relay and the relay-destination channels experience Rayleigh and Rician fading respectively, is investigated. We derive exact and lower bound expressions for the outage probability and average bit error probability, where the bounds become tight at high signal-to-noise ratios (SNR). Our results are verified through comparison with Monte Carlo simulations, where we also illustrate the positive impact of the Rician factor on the system performance.     

On the performance evaluation, selection, and design ofunique-words for time-division multiple access systems

The issues of performance evaluation, selection, and design of unique-words for time-division multiple-access systems are addressed for both additive white Gaussian noise and time-varying multipath fading channels. An efficient algorithm is proposed to compute the probability of a missed detection, which serves as the performance index of unique-words. Also, a simple upper bound on the probability of a missed detection is derived. This bound has been shown very tight for a large range of bit error rate. Based on this tight upper bound, a two-step algorithm is proposed for easy selection and design of good unique-words. For time-varying multipath fading channels, the performance of unique-words is evaluated for Rayleigh and Rician fading characteristics, which are suitable models for mobile and personal communication environments. The results show that the degradation caused by the fading effect can be larger than 10 dB for the performance of practical interest     

Tight bounds on Rician-type error probabilities and someapplications

Consider the classic problem of evaluating the probability that one Rician random variable exceeds another, possibly correlated, Rician random variable. This probability is given by Stein (1964) in terms of the Marcum's Q-function, which requires numerical integration on the computer for its evaluation. To facilitate application in many digital communication problems, we derive here tight upper and lower bounds on this probability. The bounds are motivated by a classic result in communication theory, namely, the error probability performance of binary orthogonal signaling over the Gaussian channel with unknown carrier phase. Various applications of the bounds are reported, including the evaluation of the bit error probabilities of MDPSK and MPSK with differential detection and generalized differential detection, respectively. The bounds prove to be tight in all cases. Further applications will be reported in the future     

Improved bounds on the word error probability of RA(2) codes with linear-programming-based decoding

This paper deals with the linear-programming-based decoding algorithm of Feldman and Karger for repeat-accumulate "turbo-like" codes. We present a new structural characterization that captures the event that decoding fails. Based on this structural characterization, we develop polynomial algorithms that, given an RA(2) code, compute upper and lower bounds on the word error probability P/sub w/ for the binary-symmetric and the additive white Gaussian noise (AWGN) channels. Our experiments with an implementation of these algorithms for bounding P/sub w/ demonstrate in many interesting cases an improvement in the upper bound on the word error probability by a factor of over 1000 compared to the bounds by Feldman et al.. The experiments also indicate that the improvement in upper bound increases as the codeword length increases and the channel noise decreases. The computed lower bounds on the word error probability in our experiments are roughly ten times smaller than the upper bound.     

Performance Analysis of the Dual-Hop Asymmetric Fading Channel

In real wireless communication environments, it is highly likely that different channels associated with a relay network could experience different fading phenomena. In this paper, we investigate the end-to-end performance of a dualhop fixed gain relaying system when the source-relay and the relay-destination channels experience Rayleigh/Rician and Rician/Rayleigh fading scenarios respectively. Analytical expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio are derived and used to evaluate the outage probability and the average bit error probability of M-QAM modulations. Numerical and simulation results are presented to illustrate the impact of the Rician factor on the end-toend performance. Furthermore, these results confirm that the system exhibits an improved performance in a Rician/Rayleigh (source-relay link/relay-destination link) environment compared to a Rayleigh/Rician environment.