Performance analysis and design of STBCs for frequency-selective fading channels

In this paper, space-time block-coded transmission over frequency-selective fading channels is investigated. A lower bound for the pairwise error probability for optimum detection is given. Also, an approximation for the bit-error rate is derived and compared with simulation results for maximum-likelihood sequence estimation (MLSE) for the GSM/EDGE (Enhanced Data Rates for GSM Evolution) system. Furthermore, a novel design rule for space-time block codes (STBCs) for frequency-selective fading channels is provided. A corresponding code is designed and shown to yield higher performance than Alamouti's code. It is demonstrated that for fading channels with L independent impulse response coefficients, STBCs designed for the flat fading channel can achieve at most a diversity order of (N/sub T/+L-1)N/sub R/ if N/sub T/ transmit antennas and N/sub R/ receive antennas are used. On the other hand, the maximum diversity order employing the proposed code design rule is LN/sub T/N/sub R/.     

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。     

在频率选择性相关信道中的空频分组编码技术

本文提出了频率选择性瑞利衰落信道中的对角空频分组码(DSF)，研究了码的性能。分析表明，在各天线对间的信道相互独立，系统有NT个发射天线，NR个接收天线和信道冲击响应长度是L时，DSF码可实现分集增益NRNTL。此外，相关的发射天线阵列会使DSF码分集增益下降，但是对码的性能影响不大，特别是在较长的多路径信道上。因此，DSF码对于相关的衰落信道显示出优越的鲁棒性能。最终仿真结果证实了本文的分析。     

Single-carrier space-time block-coded transmissions over frequency-selective fading channels

We study space-time block coding for single-carrier block transmissions over frequency-selective multipath fading channels. We propose novel transmission schemes that achieve a maximum diversity of order N/sub t/N/sub r/(L+1) in rich scattering environments, where N/sub t/ (N/sub r/) is the number of transmit (receive) antennas, and L is the order of the finite impulse response (FIR) channels. We show that linear receiver processing collects full antenna diversity, while the overall complexity remains comparable to that of single-antenna transmissions over frequency-selective channels. We develop transmissions enabling maximum-likelihood optimal decoding based on Viterbi's ( 1998) algorithm, as well as turbo decoding. With single receive and two transmit antennas, the proposed transmission format is capacity achieving. Simulation results demonstrate that joint exploitation of space-multipath diversity leads to significantly improved performance in the presence of frequency-selective fading channels.     

Impact of diversity reception on fading channels with codedmodulation. II. Differential block detection

For pt. I see ibid., vol.45, no.6, p.563-572, 1997. We study coded modulation with block differential detection in an arbitrarily correlated Rician fading channel with space diversity. Coded differential q-PSK is included in our analysis as a special case. A metric is chosen that is optimum for perfect interleaving, slow fading, and independent diversity branches. For slow fading, we compare the the cutoff rates of the channels resulting from different choices of block length N and diversity index M. Specifically, we show that block detection with diversity may or may not generate a better coding channel than usual differential detection, according to the code selected and the combination of values of M and N. In particular, for low-diversity orders (M=1,2) and for low-to-medium code rates, differential detection is still an optimal or near-optimal solution, while for high-diversity orders (M⩾2) and medium-to-high code rates (up to uncoded modulation) block detection with N>2 can provide a significant gain. An error floor always exists when fading is fast. It decreases exponentially with the product of code diversity and space diversity, so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading. Performance examples based on actual coding schemes 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。     

Design, analysis, and performance evaluation for BICM-ID withsquare QAM constellations in Rayleigh fading channels

We consider bit-interleaved coded modulation with iterative decoding (BICM-ID) for bandwidth-efficient transmission over Rayleigh fading channels. We propose the design criteria that utilize a large Hamming distance inherited in a low-rate code and a new labeling technique designed specifically for fading channels. This results in a large coding gain over noniterative coded modulation and performance close to that of “turbo” coded modulation with less complexity. We also show that BICM-ID designed for fading channels usually has a very good performance over the additive white Gaussian noise (AWGN) channel while the converse is difficult to achieve. When combined with signal space diversity, diversity order can be improved to twice the diversity order of conventional BICM-ID; therefore, the code complexity can further be reduced while maintaining the same level of performance. Specifically, with the bandwidth efficiency of 2 bits/s/Hz over Rayleigh fading channels, a bit error rate (BER) of 10^-6 can be achieved with 16-QAM, a four-state rate 1/2 code at E_b/N₀ of about seven dB. We also derive performance bounds for BICM-ID with and without signal space diversity over Rayleigh fading channels, which can be easily extended for other types of fading channels     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

Effects of Carrier Frequency Offset and Channel Estimation Errors on the Performance of MIMO-OFDM Systems in Spatially Correlated Channels

As an effective technique for combating multipath fading and for high-bit-rate transmission over wireless channels, orthogonal frequency division multiplexing (OFDM) is extensively used in high-rate wireless communication systems, such as, the wireless local area network (WLAN) and the digital television terrestrial broadcasting (DTTB) systems, to support high performance bandwidth-efficient multimedia services. Multiple antennas and transmit or receive diversity, multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), can be used to improve error performance and capacity of wireless systems. In this paper, we consider the effects of carrier frequency offset and channel estimation errors on the performance of MIMO-OFDM systems in spatially correlated channels. Theoretical calculations and computer simulations are done to analyze the performance degradation of MIMO-OFDM systems in spatially correlated channels due to carrier frequency offset and channel estimation errors, and the theoretical and simulated results match well.     

Space-time block coding for wireless communications: performanceresults

We document the performance of space-time block codes, which provide a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-time block code, and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space-time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver. We review the encoding and decoding algorithms for various codes and provide simulation results demonstrating their performance. It is shown that using multiple transmit antennas and space-time block coding provides remarkable performance at the expense of almost no extra processing     

Performance Analysis of Matched and Partially Matched One-Shot Detectors for Doubly-Selective Rayleigh Fading Channels

In this paper optimum one-shot detection over known and partially known doubly-selective Rayleigh fading channels is investigated. Reduced complexity channel models based on Gauss Quadrature Rules (GQRs) and Taylor power series are derived and are employed to develop novel analytical tools for the performance analysis of one-shot detectors. Numerical results allow to assess the implicit diversity gain provided by both channel multipath and signal fading and the energy loss due to the mismatch of the receiver filter.     

Error probability for orthogonal space-time block code diversity system using rectangular QAM transmission over Rayleigh fading channels

In this paper, theoretical symbol error probability (SEP) expressions are derived for orthogonal space-time block code (OSTBC) diversity systems employing arbitrary rectangular M-QAM transmission over flat Rayleigh fading channels. Independent fading between diversity channels is assumed. Channel average powers may be distinctive, identical, or mixed with both. The rectangular M-QAM results are extended to square M-QAM, M-PAM, and binary antipodal signaling. All derived expressions are in elementary forms without complicated high-order transcendental functions and unevaluated integrals and, hence, are strictly exact and can be readily simulated by the computer. Moreover, it is shown that mixed Rayleigh fading results can be readily extended to various Nakagami-m fading results. A four-transmit-antenna system with a half-rate OSTBC for 16-QAM signaling is used to demonstrate that the theoretical result is in excellent agreement with the Monte Carlo simulated result. From simulation curves, it is shown that, under the independent channel fading condition, channels with identical powers have better error rate performance than channels with distinctive powers.     

Turbo processing in transmit antenna diversity systems

We consider turbo-trellis-coded transmission over fading multiple-input-multiple-output (M1M0) channels with transmit diversity using space-time block codes. We give a new view on space-time block codes as a transformation of the fading MIMO channel towards a Gaussian single-input-single-output (siso) channel and provide analytical results on the BER of space-time block codes. Furthermore, we describe the concatenation of Turbo-TCM with a space-time block code and show that in addition to the transmit diversity substantial benefits can be obtained by turbo iterations as long as the channel is time-varying during transmission of a coded block or frequency hopping is applied. Finally, a double iterative scheme for turbo equalization and turbo decoding of the concatenation of Turbo-TCM and space-time block code in frequency-selective MIMO channels is described.     

OFDM or single-carrier block transmissions?

We compare two block transmission systems over frequency-selective fading channels: orthogonal frequency-division multiplexing (OFDM) versus single-carrier modulated blocks with zero padding (ZP). We first compare their peak-to-average power ratio (PAR) and the corresponding power amplifier backoff for phase-shift keying or quadrature amplitude modulation. Then, we study the effects of carrier frequency offset on their performance and throughput. We further compare the performance and complexity of uncoded and coded transmissions over random dispersive channels, including Rayleigh fading channels, as well as practical HIPERLAN/2 indoor and outdoor channels. We establish that unlike OFDM, uncoded block transmissions with ZP enjoy maximum diversity and coding gains within the class of linearly precoded block transmissions. Analysis and computer simulations confirm the considerable edge of ZP-only in terms of PAR, robustness to carrier frequency offset, and uncoded performance, at the price of slightly increased complexity. In the coded case, ZP is preferable when the code rate is high (e.g., 3/4), while coded OFDM is to be preferred in terms of both performance and complexity when the code rate is low (e.g., 1/2) and the error-correcting capability is enhanced. As ZP block transmissions can approximate serial single-carrier systems as well, the scope of the present comparison is broader.     

Analysis of Differential Orthogonal Space–Time Block Codes Over Semi-Identical MIMO Fading Channels

We study the performance of differential orthogonal space-time block codes (OSTBC) over independent and semi-identically distributed block Rayleigh fading channels. In this semiidentical fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are nonidentically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another are considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit-error probabilities (BEPs) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas, and any number of transmit antennas for which OSTBCs exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. For an arbitrary number of transmit antennas, a Chernoff bound on the BEP for the optimal detector is also derived. Our results show that the semi-identical channel statistics degrade the error performance of differential OSTBC, compared with the identical case. Also, the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly. But in near-static fading channels, the two detectors have similar performances     

Optimum diversity combiner based multiuser detection fortime-dispersive Rician fading CDMA channels

Multiuser detection for asynchronous code division multiple access (CDMA) data transmission over the time-dispersive two-path Rician fading channel is considered. The multiuser maximum likelihood sequence detector (MLSD) is derived, and an equivalence of the fading channel to an asynchronous Gaussian intersymbol interference (AGISI) CDMA channel is established. However, the MLSD is found to be implementationally infeasible and this motivates the derivation of the optimum linear detector with near/far resistance as the performance criterion. The optimally near/far resistant linear time-invariant K-user detector is shown to consist of a cascade of a 2 K input/K output linear multiuser diversity combining filter followed by a K input/K output decorrelator that is designed for the equivalent AGISI/CDMA channel. This detector solves the near/far problem and also supports significantly higher bandwidth efficiencies for CDMA communication over the fading channel than does the conventional near/far limited single-user diversity combiner. The performance penalties incurred by multiuser detectors designed for the Gaussian channel when used over the Rician fading channel are also analytically characterized. It is shown that these penalties can be significant, making the case for the use of multiuser detectors optimized for this fading channel, particularly the optimum linear detector due to its relative implementational simplicity     

MIMO-OFDM系统中的空时/频编码技术

OFDM(正交频分复用)是一种高效的多载波调制技术,可以用来对抗无线环境中的多径衰落,减少码间干扰。空时编码是一种发射分集技术。文中主要研究基于M IMO(多输入多输出)-OFDM的空时分组码和空频分组码的系统结构以及编译码方法。仿真结果表明,将空时编码技术与M IMO-OFDM技术相结合能有效地抵抗频率选择性随机衰落。     

Reed-Solomon error control coding for Rayleigh fading channels withfeedback

The use of nonbinary block error control codes over Rayleigh fading channels with feedback is examined. It is assumed that the fading is slow with respect to the rate of symbol transmission. Expressions are derived for the probabilities of channel symbol error and erasure, which are in turn used to develop expressions for code symbol error and erasure. Two erasure generation mechanisms are considered, one based on the existence of channel amplitude side information, the other not. This analytical framework is used to evaluate the performance of the Reed-Solomon/hybrid-ARQ protocol (RS/HARQ) over fading channels with feedback. The RS/HARQ system uses erasure decoding in a hybrid-ARQ protocol to provide excellent reliability performance at the expense of a reduction in throughput. The RS/HARQ protocol allows for the variation of the erasure threshold and the effective diameter of the decoding operation     

Multilevel block codes for Rayleigh-fading channels

New multilevel block codes for Rayleigh-fading channels are presented. At high signal-to-noise ratios (SNRs), the proposed block codes can achieve better bit error performance over TCM codes, optimum for fading channels, with comparable decoder complexity and bandwidth efficiency. The code construction is based on variant length binary component block codes. As component codes for the 8-PSK multilevel block construction, the authors propose two modified forms of Reed-Muller codes giving a good trade-off between the decoder complexity and the effective code rates. Code design criteria are derived from the error performance analysis. Multistage decoding shows very slight degradation of bit error performance relative to the maximum likelihood algorithm     

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.