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/.     

On the design of space-time and space-frequency codes for MIMO frequency-selective fading channels

The authors introduced an algebraic design framework for space-time coding in flat-fading channels . We extend this framework to design algebraic codes for multiple-input multiple-output (MIMO) frequency-selective fading channels. The proposed codes strive to optimally exploit both the spatial and frequency diversity available in the channel. We consider two design approaches: The first uses space-time coding and maximum likelihood decoding to exploit the multi-path nature of the channel at the expense of increased receiver complexity. Within this time domain framework, we also propose a serially concatenated coding construction which is shown to offer a performance gain with a reasonable complexity iterative receiver in some scenarios. The second approach utilizes the orthogonal frequency division multiplexing technique to transform the MIMO multipath channel into a MIMO flat block fading channel. The algebraic framework is then used to construct space-frequency codes (SFC) that optimally exploit the diversity available in the resulting flat block fading channel. Finally, the two approaches are compared in terms of decoder complexity, maximum achievable diversity advantage, and simulated frame error rate performance in certain representative scenarios.     

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.     

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.     

Obtaining full-diversity space-frequency codes from space-time codes via mapping

This paper considers the problem of space-frequency code design for frequency-selective multiple-input-multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) modulation. We show that space-time codes achieving full diversity in quasistatic flat fading environment can be used to construct space-frequency codes that can achieve the maximum diversity available in frequency-selective MIMO fading channels. Since the codes are constructed via a simple mapping from space-time codes to space-frequency codes, the abundant classes of existing space-time block and trellis codes can be used for full diversity transmission in MIMO-OFDM systems. The proposed mapping provides a tradeoff between the achieved diversity order and the symbol rate. Moreover, we characterize the performance of the space-frequency codes obtained via the mapping by finding lower and upper bounds on their coding advantages as functions of the coding advantages of the underlying space-time codes. This result will allow us to investigate the effects of the delay distribution and the power distribution of the channel impulse responses on the performance of the resulting space-frequency codes. Extensive simulation results are also presented to illustrate and support the theory.     

频率选择性衰落信道下一种空时分组码的直接解码

该文针对 3个发射天线,1个接收天线的空时分组码系统,提出了频率选择性衰落信道下,无需信道估计,直接对空时分组码进行解码的方法,把子空间方法应用于空时编码当中,从信号处理和空时编码两个方面考虑空时分组码的直接解码问题,利用空时分组码所特有的正交设计,较为方便地从子空间中解出信号信息,从单载波的角度,解决了频率选择性衰落下空时分组码的解码问题。Monte-Carlo仿真给出了直接解码算法的性能,并与使用准确信道信息的解码算法做了性能比较。     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.     

Optimal designs for space-time linear precoders and decoders

We introduce a new paradigm for the design of transmitter space-time coding that we refer to as linear precoding. It leads to simple closed-form solutions for transmission over frequency-selective multiple-input multiple-output (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block, and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the subchannels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER, and symbol mean square error     

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.     

Space-time block-coded multiple access through frequency-selectivefading channels

Mitigation of multipath fading effects and suppression of multiuser interference (MUI) constitute major challenges in the design of wide-band third-generation wireless mobile systems. Space-time (ST) coding offers an effective transmit-antenna diversity technique to combat fading, but most existing ST coding schemes assume flat fading channels that may not be valid for wide-band communications. Single-user ST coded orthogonal frequency-division multiplexing transmissions over frequency-selective channels suffer from finite-impulse response channel nulls (fades). Especially multiuser ST block-coded transmissions through (perhaps unknown) multipath present unique challenges in suppressing not only MUI but also intersymbol/chip interference. In this paper, we design ST multiuser transceivers suitable for coping with frequency-selective multipath channels (downlink or uplink). Relying on symbol blocking and a single-receive antenna, ST block codes are derived and MUI is eliminated without destroying the orthogonality of ST block codes. The system is shown capable of providing transmit diversity while guaranteeing symbol recovery in multiuser environments, regardless of unknown multipath. Unlike existing approaches, the mobile does not need to know the channel of other users. In addition to decoding simplicity, analytic evaluation and corroborating simulations reveal its flexibility and performance merits     

基于空时分组编码的MC-CDMA下行链路合并方案

基于空时分组编码的发射分集技术利用空间和时间分集 ,能有效抗多径 ,增强信道可靠性。将空时分组编码应用到MC -CDMA下行链路中 ,构建了一种新的多载波CDMA系统 (ST -MC -CD MA) ,通过在每个子载波信道中获得空间分集增益来提高系统性能。具体实现时 ,依据传统MC -CDMA信号合并方案 ,提出了ST -MC -CDMA空时译码后相应的四种合并方案。仿真结果验证了这 4种合并方案的优、缺点 ;并进一步证明 :在频率选择性瑞利衰落信道中 ,该系统比采用相同合并方案的传统MC -CDMA有明显的性能改善。     

System Performance of Transmit Diversity Methods and a Two Fixed-Beam System in WCDMA

Downlink transmit diversity modes for WCDMA together with a two fixed-beam antenna array system are compared relative to the single antenna sectorized system in a radio network simulator. The transmit diversity methods investigated are: space-time transmit diversity and closed-loop mode I transmit diversity. Frequency selective (COST 259) and flat fading channels are considered and their impact to speech-only and data-only services is evaluated. A third service, which highlights the system performance of the various advanced antennas, is also investigated.The results in this investigation point out that the diversity gain in flat fading channels is substantial. In frequency-selective fading, the benefits of fixed beam systems is encouraging, whereas transmit diversity methods (especially Space-Time Transmit Diversity) is unsatisfactory.     

System Performance of Transmit Diversity Methods and a Two Fixed-Beam System in WCDMA

Downlink transmit diversity modes for WCDMA together with a two fixed-beam antenna array system are compared relative to the single antenna sectorized system in a radio network simulator. The transmit diversity methods investigated are: space-time transmit diversity and closed-loop mode I transmit diversity. Frequency selective (COST 259) and flat fading channels are considered and their impact to speech-only and data-only services is evaluated. A third service, which highlights the system performance of the various advanced antennas, is also investigated.The results in this investigation point out that the diversity gain in flat fading channels is substantial. In frequency-selective fading, the benefits of fixed beam systems is encouraging, whereas transmit diversity methods (especially Space-Time Transmit Diversity) is unsatisfactory.     

频率选择性信道下单载波空时分组编码传输系统中的信道估计技术

在频率选择性信道下给出了单载波频域均衡系统结合空时分组编码传输基于训练序列的最优信道估计算法。由于选取具有恒幅特性的Chu序列作为训练序列,因此这一算法能够实现信道估计的最小均方误差,并作了理论证明。最后,对本方案的性能进行了仿真比较,仿真的结果证实了本方案的优点。     

Decision-feedback detection for block differential space-time modulation

Time variation on fading channels hinders accurate channel estimation in differential space-time modulation and deteriorates the performance. Decision-feedback differential detection is studied for block differential space-time modulation, and compared with conventional differential space-time modulation. It is observed that the proposed scheme does not suffer effective fading bandwidth expansion, as does the conventional scheme. An improved effective signal-to-noise ratio approach is proposed for analyzing the performance of the proposed scheme in time-varying flat Rayleigh fading. Theoretical analysis and simulations show the improved performance of the proposed scheme over the conventional scheme.     

Double differential space-time block coding for time-selectivefading channels

Most existing space-time coding schemes assume time-invariant fading channels and offer antenna diversity gains relying on accurate channel estimates at the receiver. Other single differential space-time block coding schemes forego channel estimation but are less effective in rapidly fading environments. Based on a diagonal unitary matrix group, a novel double differential space-time block coding approach is derived in this paper for time-selective fading channels. Without estimating the channels at the receiver, information symbols are recovered with antenna diversity gains regardless of frequency offsets. The resulting transceiver has very low complexity and is applicable to an arbitrary number of transmit and receive antennas. Approximately optimal space-time codes are also designed to minimize bit error rate. System performance is evaluated both analytically and with simulations     

Space-frequency-Doppler coded OFDM over the time-varying Doppler fading channels

In this paper, space-frequency-Doppler coded OFDM (SFDO-OFDM) scheme over the time-varying Doppler fading channels via the time-frequency duality is proposed. Based on the basis expansion model (BEM) and the time-frequency duality, through the circulant matrix diagonalized processing, the nonlinear time-varying Doppler fading channel is dually converted to the virtual frequency-selective linear channels. With OFDM module, subgrouping the subcarriers in OFDM through the block matrix method and fatherly general complex orthogonal coding (GCOD) on each corresponding block subcarriers, SFDO-OFDM codes for the general multiple input multiple output (MIMO) is thus constructed. And concatenating it with the signal constellation precoding, full maximum diversity gains including the inherent Doppler fading are achieved. Theoretical analysis and corroborating simulation results demonstrate that, comparing with existing Doppler coding alternatives, the proposed scheme can effectively and robustly combat the Doppler fading with high bandwidth efficiency and even lower bit error ratio (BER).     

A New Union Bound on the Error Probability of Binary Coded OFDM Systems in Wireless Environments

Orthogonal Frequency Division Multiplexing (OFDM) systems are commonly used to mitigate frequency-selective multipath fading and provide high-speed data transmission. In this paper, we derive new union bounds on the error probability of a coded OFDM system in wireless environments. In particular, we consider convolutionally coded OFDM systems employing single and multiple transmit antennas over correlated block fading (CBF) channels with perfect channel state information (CSI). Results show that the new union bound is tight to simulation results. In addition, the bound accurately captures the effect of the correlation between sub-carriers channels. It is shown that as the channel becomes more frequency-selective, the performance get better due to the increased frequency diversity. Moreover, the bound also captures the effect of multi-antenna as space diversity. The proposed bounds can be applied for coded OFDM systems employing different coding schemes over different channel models.     

Transmission and Reception Concepts for WLAN IEEE 802.11b

State-of-the-art wireless local area network (WLAN) IEEE 802.11b terminals employ complementary code keying (CCK) as modulation format. In this paper, receiver concepts tailored for CCK transmission over frequency-selective fading channels are presented in a unified and systematic framework. First, optimum maximum-likelihood (ML) detection for CCK signaling is considered. Second, for complexity reduction, minimum mean-squared error block decision-feedback equalization (MMSE-DFE) is investigated and reduced-state sequence estimation (RSSE) is considered on the basis of an Ungerbock-like set partitioning of the multidimensional CCK code wordset. In order to improve the reliability of CCK transmission over fading channels, time-reversal space-time block codes (TR-STBCs) combined with receive diversity are applied. Simulation results of the considered suboptimum receivers are compared with a performance approximation for optimum detection. Our results demonstrate the excellent performance of the advocated equalization schemes and the significant gains that can be achieved with TR-STBCs and receive diversity in typical WLAN environments     

Bit Interleaved Coded Multiple Beamforming

In this paper, we investigate the performance of bit-interleaved coded multiple beamforming (BICMB). We provide interleaver design criteria such that BICMB achieves full spatial multiplexing of min( N, M) and full spatial diversity of NM with N transmit and M receive antennas over quasi-static Rayleigh flat fading channels. If the channel is frequency selective, then BICMB is combined with orthogonal frequency division multiplexing (OFDM) (BICMB-OFDM) in order to combat ISI caused by the frequency-selective channels. BICMB-OFDM achieves full spatial multiplexing of min(N, M), while maintaining full spatial and frequency diversity of NML for an NtimesM system over L-tap frequency-selective channels when an appropriate convolutional code is used. Both systems analyzed in this paper assume perfect channel state information both at the transmitter and the receiver. Simulation results show that, when the perfect channel state information assumption is satisfied, BICMB and BICMB-OFDM provide substantial performance or complexity gains when compared to other spatial multiplexing and diversity systems.