On multilevel coded MPSK for the Rayleigh fading channel

This paper presents a new upper bound on the pair-wise error probability of MPSK sequences for the Rayleigh fading channel when channel state information (CSI) is unavailable. This bound is derived by adding weight factors in computing symbol metrics. Simulation results show that the weight factors which optimize the upper bound likely optimize the error rate as well. Multilevel coded MPSK schemes for the Rayleigh fading channel are also devised. Results show that the added weight factors improve the error performance of these schemes in the case that CSI is unavailable     

空时码在Nakagami衰落信道下性能分析

基于Alamouti提出的BPSK调制下空时分组码在Rayleigh衰落信道中的简单分集方案。推导出多发射和多接收天线系统中正交空时分组码在Nakagami衰落信道的BPSK调制下的比特差错率的最小距离球界,并推广到在高阶调制下衰落信道中系统符号差错率的性能。仿真分析和比较了空时分组码的多天线系统中发射和接收天线分集增益,以及信道相关参数的变化对系统误比特性能的影响。     

Bit error probability of distributed Turbo coded relay systems over quasi-static Rayleigh fading channels

As is known, distributed Turbo coding (DTC) performs close to the theoretic outage probability bound of a relay channel when correct decoding is assumed at the relay. However, decoding error is inevitable in practical fading channels due to the error-prone feature of radio channels, and the decoding error propagation in DTC scheme will severely degrade the error performance of the relay system. As a result, it is necessary to evaluate the error performance of the DTC scheme in multi-hop relaying wireless systems in practical fading channels. Moreover, the theoretical method of analysis provides an effective tool for obtaining the error performance besides lengthy simulations. In this article, the concept of equivalent signal-to-noise ratio (SNR) of the two-hop relay channel and the method of computing equivalent SNR are developed, and then the upper bound on the bit error probability (BEP) of DTC relay systems is analyzed by use of Turbo code's distance spectrum, the concept of uniform interleaver, the limit-before-averaging technique, and the union bound method. Both theoretical analysis and numerical simulation are implemented for relay systems with DTC scheme over quasi-static Rayleigh fading channels. The results show that the upper bound approaches the simulation results in the medium to high SNR region.     

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     

A new, simple, and exact union bound for reference-basedpredetection and postdetection diversity TCM-MPSK systems in Rayleighfading

Trellis-coded modulation (TCM), when combined with interleaving of sufficient depth, is known to provide some form of time diversity that allows for the achievement of good error performance in fading environments. Also, space diversity reception, in which several signals received at different antennas are combined, is a well-known method that can be used to combat the effects of fading in wireless systems. In this paper, we consider the analysis of the error performance of reference-based predetection and postdetection diversity systems when used in conjunction with trellis-coded modulation techniques. Based on the combination of the transfer function upper bounding technique with the exact calculation of pairwise error event probabilities, we present a new and simple method for exact calculation of the union bound on the average bit error rate (BER) performance of these systems in correlated Rayleigh fading channels. This method has the same complexity as the union-Chernoff bound, and some examples are given to illustrate its application. Monte-Carlo simulation results, which are more indicative of the exact system performance, are also shown     

Rician衰落信道下空时分组码的性能分析

基于Alamouti提出的BPSK调制下空时分组码在Rayleigh衰落信道中的码性能原理,推导出高阶(M ary)调制下Rician衰落信道中空时分组码的符号差错率的最小距离球界,并进行计算机仿真分析了两信道下引入空时分组码的多天线系统中发射和接收天线的分集增益,发射天线数量的“地板效应”以及Rician因子K对符号差错性能的影响。     

Performance of high-diversity multidimensional constellations

Following the approach introduced by Cavers and Ho (1992), the performance of component-interleaved multidimensional constellations over the Rayleigh fading channel is evaluated analytically. The error probabilities are approximated by the union bound using an exact expression of the pairwise error probability. Simulation results show that this bound can be used effectively as a design criterion for the selection of high-diversity multidimensional constellation over the Rayleigh fading channel     

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     

Lower bound on training-based channel estimation error for frequency-selective block-fading Rayleigh MIMO channels

A lower bound on the error correlation matrix of training-based channel estimators is derived for multiple-input multiple-output (MIMO) systems over block-fading frequency-selective channels with symbol-spaced receivers. The bound is obtained in a constructive way by evaluating the asymptotic performance of an estimator that fully exploits the algebraic structure of the multipath channel. In particular, the estimator is assumed to be able to estimate the long-term features of the channel consistently (e.g., second order statistics of fading, delays, angles) while tracking the fast-varying fading fluctuations by Wiener filtering. Known estimators that are able to attain the bound under simplified settings are referred to, and general guidelines for designing novel estimators are discussed. Based on the simple analytical expression of the bound, the impact of channel estimation error on the link capacity is investigated for different system parameters and channel characteristics (e.g., Doppler shift, spatial correlation of fading). Numerical results are provided to corroborate the analysis.     

Cellular channel modeling and the performance of DS-CDMA systemswith antenna arrays

In this paper, a new channel modeling approach incorporating nonuniform propagation environments is introduced, and the bit error rate (BER) of a direct sequence code division multiple access cellular system incorporating antenna arrays for spatial filtering is derived analytically. Specifically, this paper introduces a channel model for, and analyzes the performance of, a system in an environment where the multipath signals on each of the diversity branches of a RAKE receiver have varying fading characteristics. This scenario would typically describe urban environments where a large number of multipath echoes are present, each with different fading statistics resulting from the nonhomogeneous propagation paths seen by each multipath echo. It is shown that nonuniform fading parameters for multipath signals can severely influence the system performance, especially at high E_b /N₀ levels. Furthermore, it is shown that the conventional assumption of identical fading statistics for all RAKE receiver branches provide a lower bound on the system performance     

Performance analysis of space-time MMSE multiuser detection for coded DS-CDMA systems in multipath fading channels

This paper investigates the use of convolutional coding in space-time minimum mean-square-error (MMSE) multiuser-based receivers over asynchronous multipath Rayleigh fading channels. We focus on the performance gain attained through error control coding when used with binary-phase-shift-keyed modulation (BPSK) and multiuser access based on direct sequence-code-division multiple access (DS-CDMA). In our analysis, we derive an approximation for the uncoded probability of bit-error in multipath fading channels. This bit-error rate (BER) approximation is shown to be very accurate when compared to the exact performance. For a convolutionally coded system, we obtain a closed form expression for the bit-error rate upper bound. This error bound is noted to be tight as the number of quantization levels increased beyond eight. Using our theoretical results, we obtain an estimate for the achieved user-capacity that accrues due to error control coding. It is found that using convolutional coding with 3-bit soft-decision decoding, a user-capacity gain as much as 300% can easily be achieved when complete fading state information plus ideal channel interleaving are assumed.     

Error performance of innovations-based MLSE for Rayleigh fadingchannels

Error performance of maximum likelihood sequence estimation (MLSE) of digital signals transmitted over Rayleigh fading channels is studied in this paper. The application of the innovations approach provides us not only with a general MLSE receiver structure, but also with a tool for analyzing the performance of the receiver. We show that the sequence pairwise error probability of the MLSE receiver is determined by the eigenvalues of a matrix generated from the autocorrelation function of the received signal. For any practical applications, the MLSE for Rayleigh fading channels exhibits an irreducible error floor that depends on the channel characteristics such as the Doppler frequency bandwidth and frequency selectivity. An upper bound on bit error probability can be calculated by using the sequence pairwise error probability. Also, it is shown that diversity reception can significantly improve the MLSE error performance     

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.     

BICM-ID with signal space diversity over cascaded rayleigh fading channels [transactions letters]

Bit-interleaved coded modulation with iterative decoding (BICM-ID) using signal space diversity (SSD) is considered for cascaded Rayleigh fading channels. A tight bound on the asymptotic error probability is derived to determine the optimal rotation matrix for SSD design and to identify the key parameters that influence the system performance. It is shown that, for small modulation constellation, a cascaded Rayleigh fading causes a much more severe performance degradation than a conventional Rayleigh fading. However, BICM-ID employing SSD with a sufficiently large constellation can close the performance gap between the conventional and cascaded Rayleigh fading channels, and their performance can closely approach that over an AWGN channel. Illustrative simulation results for various scenarios are in a good agreement with analytical derivations.     

Rice衰落下RS码级联空时分组码系统的性能分析

从理论上给出一种Rice衰落条件下Reed-Solomon码级联空时分组码系统的差错性能分析方法,并推导给出级联码误比特率上界的数学表达式。理论分析和仿真结果表明,随着信噪比的增加,级联码系统的性能曲线迅速变好,获得了很高的编码增益。在误比特率为10-4时,与Reed-Solomon码的级联可以使衰落条件下空时分组码的性能提高大约5 dB。     

Design and analysis of transmitter diversity using intentionalfrequency offset for wireless communications

Coded modulation (usually with interleaving) is used in fading channel communications to achieve a good error performance. The major benefit from using coded modulation in fading channels is achieved if each code symbol of a codeword (or coded sequence) suffers statistically different fading (preferably independent fading). However, in many applications of mobile communications (e.g., in a metropolitan environment), a low vehicle speed (and hence, a small Doppler spread, f _D) is very common. With a small Doppler spread, ideal or close-to-ideal interleaving is no longer feasible and all code symbols of a codeword would suffer highly correlated fading especially in stationary fading (f_D≈0). Coded modulations will thus suffer seriously degraded performance. Previous performance analyses based on ideal interleaving are not accurate when a small Doppler spread is encountered and the much used union bound error probability analysis is loose for small Doppler spreads. To rectify this situation, this paper presents an improved performance analysis of coded modulations with correlated fading and pilot-symbol-assisted modulation (PSAM). Transmitter diversity can generate the necessary time-varying fading to maintain the effectiveness of a coded signaling scheme which this paper examines in detail using an intentional frequency offset between antennas. This work found that proper selections of the intentional frequency offset and interleaving depth can lead to good performance with traditional coded modulations (if enough antennas are used) using essentially the same simple demodulation structure as used in the traditional single-antenna PSAM     

The effects of phase estimation errors on RAKE receiver performance

As larger diversity and coding gains are introduced into spread-spectrum systems to mitigate the effects of multipath fading and thermal noise, system performance is increasingly being limited by channel estimation error. To properly design these systems, performance measures incorporating the effects of estimation errors are needed. A lower bound on the probability of bit error for a RAKE receiver operating with imperfect phase estimates is presented along with a method to obtain a closed-form expression for its evaluation. Further, this lower bound is compared to an upper bound so that an accurate assessment of system performance can be obtained     

移动通信系统中空时格码的改进设计

本文根据空时格玛在快瑞利衰落信道下的成对错误概率上界，得出不同发射天线的码设计具有独立性，进而提出一种改进的快瑞利衰落信下空时格码的设计准则，当信道衰落快慢介于准静态和快瑞利衰落之间时，空时格码的设计方法也可做相应的改进，分析及仿真结果表明，由改进方法设计的空时格码比由传统方法得出的具有更优的性能。     

A Tight BER Upper Bound for Bit-Interleaved Coded Modulation with Square QAM and Gray Labeling

Bit-interleaved coded modulation (BICM) is a bandwidth-efficient coded system with diversity order higher than that of Ungerboeck's trellis-coded modulation on fading channels. In this paper, we investigate the BER (bit error rate) performance of BICM in the additive white Gaussian and Rayleigh fading channels. A new upper bound is given for the square QAM constellation with gray labeling, which constitutes a large portion of practical applications of BICM systems. The new upper bound is tighter than the well-known BICM union bound proposed in G. Caire et al. (1998)     

On the performance of error control coding with diversity formobile channels

Upper bounds on the bit error probability are applied to evaluate the error performance of coded systems over non-interleaved and partially interleaved Rician fading mobile channels. The correlation between successive received symbols is exploited to bound the error performance. The bound allows useful evaluation of coding gains on realistic communication systems without going into lengthy computer simulations. By further defining the maximum energy degradation factors, compact upper bounds are expressed in a similar way as on the fully interleaved or memoryless channels. The maximum energy degradation factors are computed for a wide variety of mobile channel conditions. These factors give an interesting evaluation of the fading conditions and may be used to design coded communication systems on mobile channels. Furthermore, independent space or frequency diversity may be taken into account in these bounds and it is shown that the energy degradation due to correlation is independent of this added independent diversity