Space-time trellis codes for 4-PSK with three and four transmitantennas in quasi-static flat fading channels

It has been established that the appropriate design parameters for space-time trellis code (STTC) in quasi-static flat Rayleigh fading channels are the rank and determinant criteria or the Euclidean distance criterion, depending on the value of the overall diversity gain. We propose two groups of new STTCs with more than two transmit antennas based on these two design criteria, respectively. These new STTCs are shown to achieve large performance improvements over the ones with two transmit antennas     

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。     

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.     

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。     

An optimal two transmit antenna space-time code and its stacked extensions

A space-time code is proposed that exhibits the highest coding gain among competing full-rate full transmit diversity space-time codes for the two transmit and receive antenna coherent quasi-static fading channel. The proposed code is derived from a layered architecture with real rotation of quadrature amplitude modulation (QAM) information symbols in two dimensions. The existing codes of similar architecture concentrate on application of complex full modulation diversity rotations or asymmetric real rotations. An analytic evaluation illustrates the significant improvement in coding gain achieved with the proposed code. Moreover, the coding gain of the proposed code is independent of its rate. This implies that the proposed code achieves the optimal diversity-multiplexing tradeoff curve for the two transmit antenna system. A stacked extension of the proposed code offers a reduced complexity capacity optimal alternative to the full diversity codes for larger number of transmit antennas. Performance enhancement in several scenarios is verified through simulations.     

Design of concatenated space-time block codes using signal space diversity and the Alamouti scheme

New full-rate space-time block codes achieving full diversity for quadrature amplitude modulation (QAM) using an even number of transmit antennas over quasi-static Rayleigh fading channels are proposed. The proposed codes are constructed by serially concatenating unitary rotating precoders with the Alamouti code. The coding advantage of the proposed code for a codeword pair corresponding to any distinct input pair is shown to be greater than or equal to that of the ST-CR code.     

Space-time overlays for convolutionally coded systems

We consider the design of space-time overlays to upgrade single-antenna wireless communication systems to accommodate multiple transmit antennas efficiently. We define the overlay constraint such that the signal transmitted from the first antenna in the upgraded system is the same as that in the single-antenna system. The signals transmitted from the remaining antennas are designed according to space-time coding principles to achieve full spatial diversity in quasi-static flat fading channels. For both binary phase-shift keying (BPSK) and quaternary phase-shift keying modulation systems, we develop an algebraic design framework that exploits the structure of existing single-dimensional convolutional codes in designing overlays that achieve full spatial diversity with minimum additional decoding complexity at the receiver. We also investigate a concatenated coding approach for a BPSK overlay design in which the inner code is an orthogonal block code. This approach is shown to yield near optimal asymptotic performance for quasi-static fading channels. We conclude by offering a brief discussion outlining the extension of the proposed techniques to time-varying block fading channels.     

Improved space-time trellis coded modulation scheme on slowRayleigh fading channels

It has been established that the appropriate criteria for space-time trellis coded modulation (STTCM) design on slow Rayleigh fading channels are maximisation of the minimum rank and the minimum determinant of the distance matrices. It is demonstrated that when STTCM is used in systems with a large product (>3) of the numbers of transmit and receive antennas, the design of codes with maximum coding gain is governed by the minimum trace of the distance matrices. A number of new codes based on the proposed design criterion have been constructed and shown to be superior to other known codes     

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。     

Trellis-coded differential unitary space-time modulation over flat fading channels

Coding and modulation for multiple-antenna systems have gained much attention in wireless communications. This paper investigates a noncoherent trellis-coded scheme based on differential unitary space-time modulation when neither the transmitter nor the receiver know the channel. In a time-varying flat Rayleigh fading environment, we derive differentially noncoherent decision metrics and obtain performance measures for systems with either an ideal interleaver or no interleaver. We demonstrate that with an ideal interleaver, the system performance is dominated by the minimum Hamming distance of the trellis code, while without an interleaver, the performance is dominated by the minimum free squared determinant distance (a novel generalization of the Euclidean distance) of the code. For both cases, code construction is described for Ungerboeck-type codes. Several examples that are based on diagonal cyclic group constellations and offer a good tradeoff between the coding advantage and trellis complexity are provided. Simulation results show that, by applying the soft-decision Viterbi decoder, the proposed scheme can achieve very good performance even with few receive antennas. Extensions to trellis-coded differential space-time block codes are also discussed.     

Parameterised precoder for differential space-time modulation

A parameterised precoder is presented for differential space-time modulation systems under spatial correlated Rayleigh fading channels. Different from the previous design, it does not restrict the distance matrices of the constellation proportional to the identity matrix. Simulation results confirm the performance of the proposed precoder.     

On the design of algebraic space-time codes for MIMO block-fading channels

The availability of multiple transmit antennas allows for two-dimensional channel codes that exploit the spatial transmit diversity. These codes were referred to as space-time codes by Tarokh et al. (see ibid., vol.44, p.744-765, Mar. 1998) Most prior works on space-time code design have considered quasi-static fading channels. We extend our earlier work on algebraic space-time coding to block-fading channels. First, we present baseband design criteria for space-time codes in multi-input multi-output (MIMO) block-fading channels that encompass as special cases the quasi-static and fast fading design rules. The diversity advantage baseband criterion is then translated into binary rank criteria for phase shift keying (PSK) modulated codes. Based on these binary criteria, we construct algebraic space-time codes that exploit the spatial and temporal diversity available in MIMO block-fading channels. We also introduce the notion of universal space-time codes as a generalization of the smart-greedy design rule. As a part of this work, we establish another result that is important in its own right: we generalize the full diversity space-time code constructions for quasi-static channels to allow for higher rate codes at the expense of minimal reductions in the diversity advantage. Finally, we present simulation results that demonstrate the excellent performance of the proposed codes.     

Some block- and trellis-coded modulations for the Rayleigh fadingchannel

The error performance of a modulation code over a channel depends on several distance parameters and the path multiplicity of the code. For the AWGN channel, the error performance of a modulation code depends mainly on its minimum squared Euclidean distance and path multiplicity. For the Rayleigh fading channel, however, the error performance of a modulation code depends strongly on its minimum symbol distance, minimum product distance, and path multiplicity. It depends on the minimum squared Euclidean distance in a lesser degree. This paper is concerned with the construction of block and trellis MPSK modulation codes for the Rayleigh fading channel. In each construction, the distance parameters are chosen to achieve good error performance with reduced decoding complexity     

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     

Robust full-diversity full-rate quasi-orthogonal STBC for four transmit antennas

A novel quasi-orthogonal space-time block code (QSTBC) with full-diversity full-rate transmission and double-symbol decoding is proposed for a system with four transmit antennas, which is constructed by linearly combining two optimally power-scaled component Alamouti codes. Compared with the existing QSTBC with optimal constellation rotation, the proposed code provides excellent robustness, in terms of bit error rate performance, against spatially correlated and/or time-selective fading channels.     

On the theory of space-time codes for PSK modulation

The design of space-time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas. The lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband differences between modulated codewords, which is difficult to relate to traditional code designs over finite fields and rings. We present general binary design criteria for PSK-modulated space-time codes. For linear BPSK/QPSK codes, the rank of (binary projections of) the unmodulated codewords, as binary matrices over the binary field, is a sufficient design criterion: full binary rank guarantees full spatial diversity. This criterion accounts for much of what is currently known about PSK-modulated space-time codes. We develop new fundamental code constructions for both quasi-static and time-varying channels. These are perhaps the first general constructions-other than delay diversity schemes-that guarantee full spatial diversity for an arbitrary number of transmit antennas     

Serially concatenated space time convolutional codes and continuous phase modulation

This paper addresses space time convolutional code design using continuous phase modulation (CPM). The possibility of constructing full diversity space time codes is investigated. A linear modulation approximation to CPM is done. Using the Gram-Schmidt orthogonalization transform the CPM signal is generated as a vector with finite energy in a different Euclidean space. A serially concatenated CPM construction is considered in searching channel codes which are able to exploit maximum diversity. Design criteria based on the encoding scheme are derived for an arbitrary number of transmit antennas. The investigations are done for a quasi-static Rayleigh fading channel.     

一种新的快衰落信道下的差分Unitary时空编码调制方法

该文提出了一种新的基于循环对角群码的差分Unitary 时空编码调制方法,这种新方法通过改变发送符号的顺序来降低快衰落信道时变对解码造成的影响,从而提高在快衰落信道下的性能。这种性能的提高是以处理时延和额外能量开销的增加为代价的,在实际应用中需要在这两者之间寻求平衡,处理时延越大,额外的能量开销就越小,反之亦然。 与传统的差分Unitary时空编码调制方法比较,理论分析和matlab做的Monte Carlo仿真结果表明,在快衰落信道下,提出的差分Unitary时空编码调制方法可获得明显的性能增益,能够显著降低系统的成对差错概率和误比特率。     

Some Designs of Full Rate Space–Time Codes With Nonvanishing Determinant

In this correspondence, we first present a transformation technique to improve the normalized diversity product for a full rate algebraic space-time block code (STBC) by balancing the signal mean powers at different transmit antennas. After rewriting a cyclic division algebra structure into a multilayer structure for a full rate code, we show that the normalized diversity product of the transformed code with the multilayer structure is better than the one of the transformed code with the cyclic division algebra structure. We then present a new full rate algebraic STBC with multilayer structure with nonvanishing determinant (NVD) for three transmit antennas when signal constellation is carved from QAM. We show that the new code has larger normalized diversity product than the existing 3 times 3 NVD full rate STBC for quadrature amplitude modulation (QAM) signals, and we also show that it has the largest normalized diversity product in a family of full rate STBC.     

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.