Analysis of the pairwise error probability of noninterleaved codeson the Rayleigh-fading channel

The majority of previous analytical studies of signal-space coding techniques (includes trellis and block codes) on the Rayleigh-fading channel have assumed ideal interleaving. The effect of finite interleaving on the performance of different coding schemes has been studied only by simulation In this paper we first derive a maximum likelihood (ML) decoder for codewords transmitted over a noninterleaved Rayleigh flat fading channel, followed by an exact expression for the pairwise error event probability of such a decoder. It includes phase shift keying (PSK), quadrature amplitude modulation (QAM) signal sets, trellis coded modulation (TCM) and block coded modulation (BCM) schemes, as well as coherent (ideal channel state information) and partially coherent (e.g., differential, pilot tone, etc.) detection. We derive an exact expression for the pairwise event probability in the case of very slow fading-i.e., the fading experienced by all the symbols of the codeword is highly correlated. We also show that the interleaving depth required to optimize code performance for a particular minimum fading bandwidth can be approximated by the first zero of the fading channel's auto-correlation function     

Coherent detection of interleaved trellis encoded CPFSK on shadowedmobile satellite channels

A receiver that utilizes trellis coded continuous phase frequency shift keying (CPFSK) with coherent detection and convolutional interleaving of the coded symbols for data transmission is presented. An earlier study considered decoding based solely on the code trellis. A new decoding algorithm that copes with the interleaving is presented and uses information from both the modulation trellis and the code trellis. The performance results are obtained by Monte Carlo simulation and are partially verified through analysis. The fading model is Rician, but the line-of-sight (LOS) component is subjected to a log-normal transformation that represents attenuations due to foliage which is referred to as shadowing. The system studied is not suitable for digital speech applications as the required interleaving depths lad to an unacceptable time delay     

Performance analysis of adaptive interleaving for OFDM systems

We proposed a novel interleaving technique for orthogonal frequency division multiplexing (OFDM), namely adaptive interleaving, which can break the bursty channel errors more effectively than traditional block interleaving. The technique rearranges the symbols according to instantaneous channel state information of the OFDM subcarriers so as to reduce or minimize the bit error rate (BER) of each OFDM frame. It is well suited to OFDM systems because the channel state information (CSI) values of the whole frame could be estimated at once when transmitted symbols are framed in the frequency dimension. Extensive simulations show that the proposed scheme can greatly improve the performance of the coded modulation systems utilizing block interleaving. Furthermore, we show that the adaptive interleaving out performs any other static interleaving schemes, even in the fast fading channel (with independent fading between symbols). We derived a semi-analytical bound for the BER of the adaptive interleaving scheme under correlated Rayleigh fading channels. Furthermore, we discussed the transmitter-receiver (interleaving pattern) synchronization problem     

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     

Effect of Time Diversity on the Forward Link of the DS-CDMA Cellular System

A direct-sequences code division multiple access system has been accepted as a digital cellular standard (IS–95) in North America [1]. This digital cellular standard employs a powerful rate 1/2, constraint length 9, convolutional code in its forward link. It is well-known that in a Rayleigh fading channel the performance of a channel code depends very heavily on the interleaving depth and the relative variations of the channel characteristics. In slow fading channels, since the input symbols to the channel decoder are highly correlated, the bit-error-rate at the output of the channel decoder may be unacceptably high. Interleavers of large dimensions can reduce the correlation of the input signal to the channel decoder at the expense of an intolerable delay. In this paper we examine the performance of the IS–95 system, at the mobile receiver, for different channel fade rates. Also, we present a simple time diversity technique which employs multiple receive antennas. The multiple receive antennas in this case generate a fast fading effect and thus improves the performance of the channel decoder significantly.     

The design of trellis coded MPSK for fading channels: performancecriteria

It has been well established that the appropriate criterion for optimum trellis-coded modulation design on the additive white Gaussian noise channel is maximization of the free Euclidean distance. It is shown that when the trellis-coded modulation is used on a Rician fading channel with interleaving/deinterleaving, the design of the code of optimum performance is guided by other factors, in particular, the length of the shortest error-event path, and the product of branch distances (possibly normalized by the Euclidean distance of the path) along the path. Although maximum free distance (d_free) is still an important consideration, it plays a less significant role the more severe the fading is on the channel. These considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over Rician fading channels. If no interleaving/deinterleaving is used, then once again the design of the trellis code is guided by maximizing d_free      

基于协方差反馈的多天线系统优化发送研究

为了克服多天线信道相关性的影响，提出一种新的自适应发送方案。应用空时分组码特征波束成型技术和格形编码调制（TCM）来获得分集增益和编码增益。针对采用和不采用交织器两种情况，基于成对差错概率（PEP）准则。分析了系统的统计性能，分别得到了使系统编码增益和分集增益最大化的TCM设计准则。根据注水法则和Lagrange乘子法求得波束间功率分配算法最优解。此外，码距作为优化功率加载算法中的权重因子，有效降低了获取波束成形分集的信噪比门限。分析和实验结果表明此方案复杂度低。能有效克服相关衰落。     

Chernoff bound of trellis-coded modulation over correlated fadingchannels

We derive a Chernoff upper bound for the pairwise error probability in the presence of an additive white Gaussian noise and a Rayleigh or Rice correlated fading. The bound is useful for situations where perfect interleaving cannot be achieved. We use it to determine some indications in the design of optimum trellis coded modulation for correlated fading channels     

Multiple symbol differentially detected multilevel codes for theRayleigh-fading channel

Conventional differential detection is known to perform poorly on the fast-fading Rayleigh-fading channel due to the rapid variation of the channel state. The technique of multiple symbol differential detection (MSDD) improves the error performance by detecting over a sequence of symbols and exploiting the inherent correlation of the fading process. To further reduce the error rate, we need to introduce some form of coding. Successful coding for the Rayleigh-fading channel requires interleaving to decorrelate the channel-a conflicting requirement to MSDD. We propose a solution consisting of interleaving blocks of L M-ary phase-shift keying (MPSK) symbols that are multiple symbol differentially detected. The blocks are treated as elements of an M^L symbol alphabet over which a multilevel code based on geometrically uniform partitions is defined     

Coded 64-CAP ADSL in an impulse-noise environment-modeling ofimpulse noise and first simulation results

This paper presents the performance of various coding schemes for the asymmetrical digital subscriber line (ADSL) in an impulse-noise environment. Impulse noise is considered to be one of the most damaging impairments in the ADSL, in which compressed video signals are delivered to residential customers. The impulse noise used in this study was measured and collected in German telephone networks. Based on this measurement and the corresponding statistical modeling, a simulation model for impulse noise is proposed and its properties are outlined. The coding schemes considered here utilize burst-error correcting Reed-Solomon codes and/or random error correcting trellis codes as well as symbol interleaving between the two codes. It has been found through computer simulations that a proper concatenation of the two codes could increase the immunity against impulse noise compared to an uncoded scheme. Specifically, a concatenated code, using a 2-dimensional 8-state trellis code and a 4-error-correcting Reed-Solomon code with an interleaving depth of 18 symbols, was able to eliminate all the errors caused by the impulse noise used in the study. It has also been found that the trellis codes are not very effective against impulse noise, unless they are used in conjunction with Reed-Solomon codes and a proper symbol interleaving. Performance results of other coding configurations using Reed-Solomon codes with different error-correcting capabilities are also presented. In addition, we also show the performance results when simple array codes are used instead of the Reed-Solomon codes     

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.     

Diagonal block space-time code design for diversity and coding advantage over flat fading channels

The potential promised by multiple transmit antennas has raised considerable interest in space-time coding for wireless communications. In this paper, we propose a systematic approach for designing space-time trellis codes over flat fading channels with full antenna diversity and good coding advantage. It is suitable for an arbitrary number of transmit antennas with arbitrary signal constellations. The key to this approach is to separate the traditional space-time trellis code design into two parts. It first encodes the information symbols using a one-dimensional (M,1) nonbinary block code, with M being the number of transmit antennas, and then transmits the coded symbols diagonally across the space-time grid. We show that regardless of channel time-selectivity, this new class of space-time codes always achieves a transmit diversity of order M with a minimum number of trellis states and a coding advantage equal to the minimum product distance of the employed block code. Traditional delay diversity codes can be viewed as a special case of this coding scheme in which the repetition block code is employed. To maximize the coding advantage, we introduce an optimal construction of the nonbinary block code for a given modulation scheme. In particular, an efficient suboptimal solution for multilevel phase-shift-keying (PSK) modulation is proposed. Some code examples with 2-6 bits/s/Hz and two to six transmit antennas are provided, and they demonstrate excellent performance via computer simulations. Although it is proposed for flat fading channels, this coding scheme can be easily extended to frequency-selective fading channels.     

Design of Differential Space-Time Trellis Codes

This paper presents the performance analysis and code design for differential space-time trellis code (DSTTC) when no channel state information (CSI) is available at neither the transmitter nor receiver. Upper bounds on the pairwise error probability of DSTTC over fast fading and quasi-static fading channels are derived and new design criteria are proposed based on these bounds. It is shown that the performance of DSTTC is determined by the minimum weighted square product distance (WSPD) over independent fast fading channels, and by the minimum cross correlation distance (CCD) over quasi-static fading channels. New DSTTCs are found by a systematic code search. Simulation results show that under the same spectral efficiency the proposed coding scheme has a superior performance and lower complexity compared to other existing differential space time coding schemes     

Design of trellis coded QAM for flat fading and AWGN channels

The design of trellis coded modulation (TCM) schemes for QAM constellations to counteract simultaneous flat fading and additive white Gaussian noise (AWGN) is considered. Motivated by the results of Divsalar and Simon (see IEEE Trans. Commun., vol.36, p.1004, 1988), and incorporating some recent ideas from Boulle and Belfiore (1992), we develop novel 2-D TCM schemes that attain diversity of order two even for a trellis structure that includes parallel paths with one symbol per edge. An algorithm is described that transforms codes designed for the AWGN channel into codes that achieve significant gains over flat fading channel, while preserving their coding gain over AWGN channel. Their performance is assessed via computer simulation for some representative TCM-QAM schemes under the assumption of uncorrelated fading and perfect channel state information (CSI). Finally, the effects of finite interleaving as well as imperfect CSI on code performance are investigated     

On the Design of Space–Time Trellis Codes for Transmit-Correlated Fading Channels

The analysis and design of space-time codes for correlated fading channels when the diversity gain is large enough is considered. We derive a simple form for a distance metric that characterizes the code performance in the presence of transmit correlation, and propose some design criteria to build good space-time trellis codes (STTCs) for correlated channels. For the case of two transmit antennas, we show that in strongly correlated channels, performance is governed by the constellation that results from the sum of the constellations associated with the transmit antennas. This suggests the use of new constellations to design better codes for correlated channels. The design criteria are then extended to any number of transmit antennas. Based on these criteria, we derive new STTCs for two and three transmit antennas that perform much better in correlated channels than the STTC optimized for the independent and identically distributed case. We also consider set partitioning applied to the sum constellation as a simple technique to design good codes for correlated channels. The codes derived show performance close to the codes found by an exhaustive search. Finally, we consider antenna selection as an alternative to build good codes for more than two antennas in fading-correlated scenarios     

I-Q TCM: reliable communication over the Rayleigh fading channelclose to the cutoff rate

This paper presents some trellis codes that provide high coding gain to channels with slow, non frequency-selective Rayleigh fading. It is shown that the use of two encoders in parallel-used to specify the in-phase and quadrature components of the transmitted signal-results in greater minimum time diversity than the conventional design in which a single encoder is used. Using this approach-which we label “I-Q TCM”-codes with bandwidth efficiencies of 1, 2, and 3 bits/s/Hz are described for various constraint lengths. The performance of these codes is bounded analytically and approximated via simulation; the results show a large improvement in the bit error rate (BER) when compared with conventional trellis-coded modulation (TCM) schemes when perfect channel state information (CSI) is available to the receiver. Indeed, when this approach is applied to channels with independent Rayleigh fading, the resulting coding gain is close to that implied by the cutoff rate limit, even for only moderately complex systems. The proposed codes are also simulated under less ideal assumptions. For instance, results for a 1-bit/s/Hz IQ-TCM code without CSI show a significant gain over conventional coding. Finally, simulations over channels with correlated fading were undertaken; it is concluded that an interleaver span of 4ν yields performance close to what is achieved with ideal interleaving     

MB-OFDM UWB通信空时网格编码误码率分析

 本文研究多带正交频分复用瑞利衰落信道中,空时网格编码发射天线间空间相关性的分集性能.空时网格编码将单个输出的编码符号转换成多个编码符号,并通过多个发射天线传输,在接收端,Viterbi优化软判决算法用于译码.我们分析了MB-OFDM系统在quasi-static和interleaved两种信道中相关空间衰落对误码率的影响.在空间相关性较小时,分集阶数能得到保持;而在空间相关性较大时,interleaved信道能保持分集阶数,quasi-static信道的分集阶数将减小.空时编码总体上对空间相关性表现出鲁棒性.     

Chip‐interleaving direct sequence spread spectrum system over Rician multipath fading channels

Chip interleaving (CI) is a unique technique to exploit time diversity in direct sequence spread spectrum (DS/SS)‐based systems operating in fading environments. In order to facilitate design of CI systems in various fading situations, we present a performance analysis for CI DS/SS system over Rician multipath time‐varying fading channels. We derive the analytical bit error rate (BER) expression for CI DS/SS to allow fast and accurate evaluation of BER performance based on the interleaving depth selected, spreading codes employed, and the time correlation function of the channel. We then discuss some ideal cases by using the analytical results to reveal some of the insights presented in the performance analysis. For the purpose of comparison, we also obtain the BER expression for conventional DS/SS system as a special case of CI system with an interleaving depth of one. Using numerical examples, we verify the analytical results with computer simulations and illustrate the BER performance behavior of CI DS/SS system with varying interleaving depth for all possible combinations of two sets of spreading codes of different type and two different time correlation functions of the channel. Copyright © 2011 John Wiley & Sons, Ltd.     

Ordered statistics decoding of linear block codes on frequencynonselective multipath channels

This paper investigates the performance of ordered statistics decoding (OSD) of linear block codes with binary differential phase-shift-keying (2DPSK) transmission on frequency nonselective multipath channels. First, the wireless channel is modeled as a frequency nonselective, slow fading environment without intersymbol interference. Second, block interleaving is embedded to decorrelate the successive received symbols so that the performance of OSD, designed essentially for memoryless channels, is retained. Third, we derive the log-likelihood ratio of received symbols based on 2DPSK modulation. Fourth, we derive the statistics of received symbols and the statistics of received symbols after ordering. Further, we analyze the system error performance for sufficient degree of interleaving. Specifically, we derive the asymptotic bit error rate (BER) of OSD at high SNRs using the first-order approximation, finally, we conduct experiments at various channel characteristics and interleaving degrees for (128, 61, 22) extended BCH code and (24, 12, 8) extended Golay code. Results show that the error performance improves tremendously with increased interleaving degree     

Space-time code design for CPFSK modulation over frequency-nonselective fading channels

We derive a novel space-time code (STC) design criterion for continuous-phase frequency-shift keying (CPFSK) over frequency-nonselective fading channels. Our derivation is based on a specific matrix that is related to the input symbols of the CPFSK modulators. With this code-design criterion, we propose a simple interleaved space-time encoding scheme for CPFSK modulation over frequency-nonselective correlated fading channels to exploit potential temporal and spatial diversity advantages. Such an encoding scheme consists of a ring convolutional encoder and a spatial encoder, between which a convolutional interleaver is placed. A decoding algorithm that generates symbol metrics for the Viterbi decoder of convolutional codes from the spatial modulation trellis is examined. Simulation results confirm that the advantages of the combination of the interleaved convolutional encoding (for temporal diversity) and the spatial encoding (for spatial diversity) are promising for various system parameters.