Equalization concepts for Alamouti's space-time block code

In this paper, we develop receiver concepts for transmission with space-time block codes (STBCs) over frequency-selective fading channels. The focus lies on Alamouti's space-time block-coding scheme, but the results may be generalized to other STBCs as well. We show that a straightforward combination of conventional equalizers and a space-time block decoder is only possible if at least as many receive antennas as transmit antennas are employed, but not for the practically interesting case of pure transmit diversity, for which space-time coding had been originally developed. This restriction is circumvented by our approach. Here, the structural properties of the transmit signal of space-time block coding, which is shown to be improper (rotationally variant), are fully used. For this, equalizers with widely linear (WL) processing are designed, such as a WL equalizer, a decision-feedback equalizer with WL feedforward and feedback filtering, and a delayed decision-feedback sequence estimator with WL prefiltering. Simulation results demonstrate that the proposed concepts may be successfully employed in an enhanced data rates for GSM evolution (EDGE) receiver, especially for pure transmit diversity. Here, significant gains can be observed, compared with a conventional single-input single-output transmission.     

Detection schemes for space-time block code and spatial multiplexing combined system

Space-time block code is combined with spatial multiplexing technique over multiple-input multiple-output system to take advantages of both schemes. The transmit antennas are divided into groups and each group transmits space-time coded blocks in parallel. At receiver side, three types of group receivers are proposed to separate the filtered version of the multiplexed space-time coded symbol blocks followed by space-time decoder. Error rate performances of the detection schemes are evaluated in correlated channels. The diversity order of the combined system is compared with that of the SM system and the STBC system.     

Minimum bit-error rate design for space-time equalization-based multiuser detection

A novel minimum bit-error rate (MBER) space-time-equalization (STE)-based multiuser detector (MUD) is proposed for multiple-receive-antenna-assisted space-division multiple-access systems. It is shown that the MBER-STE-aided MUD significantly outperforms the standard minimum mean-square error design in terms of the achievable bit-error rate (BER). Adaptive implementations of the MBER STE are considered, and both the block-data-based and sample-by-sample adaptive MBER algorithms are proposed. The latter, referred to as the least BER (LBER) algorithm, is compared with the most popular adaptive algorithm,known as the least mean square (LMS) algorithm. It is shown that in case of binary phase-shift keying, the computational complexity of the LBER-STE is about half of that required by the classic LMS-STE. Simulation results demonstrate that the LBER algorithm performs consistently better than the classic LM Salgorithm, both in terms of its convergence speed and steady-state BER performance.     

Combining beamforming and orthogonal space-time block coding

Multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication. Efficient space-time codes have been developed that utilize a large portion of the available capacity. These codes are designed under the assumption that the transmitter has no knowledge about the channel. In this work, on the other hand, we consider the case when the transmitter has partial, but not perfect, knowledge about the channel and how to improve a predetermined code so that this fact is taken into account. A performance criterion is derived for a frequency-nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code. The resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods. In addition, a particularly efficient solution method is developed for the special case of independently fading channel coefficients. The proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space-time block coding. Simulation results for a narrow-band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge     

Combining ideal beamforming and Alamouti space-time block codes

The simplest Alamouti space-time block code is coupled with a larger number of transmit antennas via ideal beamforming to achieve higher diversity gain. It is shown that the combined system can remain both full diversity and full code rate without orthogonality loss. Simulation results show a significant performance gain over the conventional space-time block codes.     

Timing error detector design and analysis for orthogonal space-time block code receivers

A general framework for the design of low complexity timing error detectors (TEDs) for orthogonal space-time block code (OSTBC) receivers is proposed. Specifically, we derive sufficient conditions for a difference-of-threshold-crossings timing error estimate to be robust to channel fading. General expressions for the S-curve, estimation error variance and the signal-to-noise ratio are also obtained. As the designed detectors inherently depend on the properties of the OSTBC under consideration, we derive and evaluate the properties of TEDs for a number of known codes. Simulations are used to assess the system performance with the proposed timing detectors incorporated into the receiver timing loop operating in tracking mode. While the theoretical derivations assume a receiver with perfect channel state information and symbol decisions, simulation results include performance for pilot-symbol-based channel estimation and data symbol detection errors. For the case of frequency-flat Rayleigh fading and QPSK modulation, symbol-error-rate results show timing synchronization loss of less than 0.3 dB for practical timing offsets. In addition it is shown that the receiver is able to track timing drift with a normalized bandwidth of up to 0.001.     

Application of quasi-orthogonal space-time block codes in beamforming

It is well known that when channel information is available at the transmitter, transmit beamforming scheme can be employed to enhance the performance of a multiple-antenna system. Recently, Jongren et al. and Zhou-Giannakis proposed a new performance criterion based on partial channel side information at the transmitter. With this criterion, an optimal beamforming matrix was constructed for the orthogonal space-time block codes. However, the same method has not been applied to the recently proposed quasi-orthogonal space-time block codes (QSTBCs) due to the nonorthogonal nature of the quasi-orthogonal designs. In this paper, the issue of combining beamforming with QSTBCs is addressed. Based on our asymptotic analysis, we extend the beamforming scheme from Jongren et al. and construct the beamforming matrices for the quasi-orthogonal designs. The proposed beamforming scheme accomplishes high transmission rate as well as high-order spatial diversity. The new QSTBC beamformer can be presented as a novel four-directional or eight-directional eigen-beamformer that works for systems with four or more transmit antennas. Simulations for systems with multiple transmit antennas demonstrate significant performance improvement over several other widely used beamforming methods at various SNRs and for channels with different quality of feedback.     

A single-symbol-decodable space-time block code with full rate and low peak-to-average power ratio

Three desirable properties of a four-antenna spacetime block code are full rate, full diversity, and single-symbol decodability. Previously reported space-time codes that achieve all three properties do so at the expense of the peak-to-average power ratio (PAPR). A fourth desirable property of a space-time block code is that its PAPR be the same as that of the underlying quadrature-amplitude modulation alphabet. In this letter we introduce space-time codes for three and four transmit antennas that achieve all four properties; these codes use a diversity technique based on constellation stretching. Numerical results for quasistatic Rayleigh-fading channels show that, despite their low PAPR, the proposed codes are comparable in SNR performance to the best-performing single-symbol decodable space-time codes for three and four transmit antennas.     

Low-complexity maximum-likelihood decoder for four-transmit-antenna quasi-orthogonal space-time block code

This letter proposes a very low-complexity maximum-likelihood (ML) detection algorithm based on QR decomposition for the quasi-orthogonal space-time block code (QSTBC) with four transmit antennas, called the LC-ML decoder. The proposed algorithm enables the QSTBC to achieve ML performance with significant reduction in computational load for any high-level modulation scheme.     

High-rate orthogonal space-time block code for four transmit antennas

A high-rate (rate 1.5) nonlinear orthogonal space-time block code for four transmit antennas is presented. It outperforms previous space- time block codes where there are more than two receive antennas. This high-rate code improves on the performance of a recently proposed nonlinear orthogonal space-time block code of the same rate and without any extra constellation expansion.     

A complex orthogonal space-time block code for 8 transmit antennas

We present a new complex orthogonal space-time block code (STBC) for 8 transmit antennas, which is generated simply by padding a transmission vector for the 8th transmit antenna to the transmission matrix of the existing complex orthogonal STBC for 7 transmit antennas. The presented complex orthogonal STBC for 8 transmit antennas achieves the same maximal rate 5/8 as well as the same minimal decoding delay 56 as those of the previously constructed complex orthogonal STBC for 7 transmit antennas.     

Exact symbol-error probability analysis for orthogonal space-time block codes: two- and higher dimensional constellations cases

Exact expressions are obtained for the symbol-error probability of orthogonal space-time block codes at the output of the coherent maximum-likelihood decoder in the general case of arbitrary input signal constellation and code. Such expressions are derived for the cases of both deterministic (fixed) and random Rayleigh/Ricean fading channels, and both the two- and higher dimensional constellations.     

A novel power allocation scheme for orthogonal space-time block code systems

In this letter, we propose a novel power allocation scheme among transmit antennas to combat channel fading in orthogonal space-time block code systems based on the metric, amount of fading, which can be used to evaluate the severity of channel fading. Simulation results show that the proposed method can improve the fading-combating performance of orthogonal space-time block code systems significantly.     

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。     

Computation of the exact bit-error rate of coherent M-ary PSK with Gray code bit mapping

The problem of calculating the average bit-error probability (BEP) of coherent M-ary phase-shift keying (PSK) over a Gaussian channel has been studied previously in the literature. A solution to the problem for systems using a binary reflected Gray code (BRGC) to map bits to symbols was first presented by P.J. Lee (see ibid., vol.COM-34, p.488-91, 1986). We show that the results obtained by Lee are incorrect for M/spl ges/16. We show that the reason for this is an invalid assumption that the bit-error rate (BER) is independent of the transmitted symbols, an assumption which has also propagated to textbooks. We give a new expression for the BER of M-PSK systems using the BRGC and compare this with Lee's results.     

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.     

基于高阶累积量的正交空时分组码盲识别

针对多输入多输出(Multiple-Input-Multiple-Output, MIMO)系统中的空时码盲识别问题,提出一种基于高阶累积量的正交空时分组码(Orthogonal Space-Time Block Code, OSTBC)盲识别方法．推导给出了接收信号的两种高阶累积量公式,该高阶累积量包含发射信号信息,由此提出识别OSTBC信号的两个特征参数;利用MIMO信道估计得到空间信道矩阵,并提出了两种特征参数的估计方法;最后,利用最小距离准则实现对OSTBC信号的分类识别．仿真结果表明：所提出方法的正确识别率高于已有的识别方法,具有良好的识别性能．     

高速铁路无线通信中基于正交空时码的格型正交重构算法

分析了基于正交空时码的开环和闭环MIMO系统,并着重研究了高铁场景下速度对正交空时码的影响：高速移动导致的快时变信道将会破环正交空时码的正交结构,降低由此获得的分集增益,从而引起了误码率性能的降低。提出了格型正交重构算法,通过givens变换对正交空时码进行码内正交重构;算法在恢复码内正交性的同时,也改变了发射端波束成形方向。因此,在高速移动场景下,所提算法使发射端获得了波束成形的阵列增益以及与用户静止时相同的分集增益。从系统性能仿真中看出,所提算法提升了高铁场景下基于正交空时码MIMO系统的误码性能。     

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.