Diagonal algebraic space-time block codes

We construct a new family of linear space-time (ST) block codes by the combination of rotated constellations and the Hadamard transform, and we prove them to achieve the full transmit diversity over a quasi-static or fast fading channels. The proposed codes transmit at a normalized rate of 1 symbol/s. When the number of transmit antennas n=1, 2, or n is a multiple of four, we spread a rotated version of the information symbol vector by the Hadamard transform and send it over n transmit antennas and n time periods; for other values of n, we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n × n ST code matrix. The codes maintain their rate, diversity, and coding gains for all real and complex constellations carved from the complex integers ring Z [i], and they outperform the codes from orthogonal design when using complex constellations for n > 2. The maximum-likelihood (ML) decoding of the proposed codes can be implemented by the sphere decoder at a moderate complexity. It is shown that using the proposed codes in a multiantenna system yields good performances with high spectral efficiency and moderate decoding complexity     

Improved signal constellations for differential unitary space-time modulations with more than two transmit antennas

In this paper, we propose new and improved unitary signal constellations for differential unitary space-time modulations utilizing more than two transmit antennas. The proposed unitary designs are constructed from fundamental building blocks which comprise the generator matrices of diagonal cyclic codes, and the 2/spl times/2 and 3/spl times/3 rotational matrices. The performances of the proposed codes are superior to those of previously proposed codes.     

On optimal multilayer cyclotomic space-time code designs

High rate and large diversity product (or coding advantage, or coding gain, or determinant distance, or minimum product distance) are two of the most important criteria often used for good space-time code designs. In recent (linear) lattice-based space-time code designs, more attention is paid to the high rate criterion but less to the large diversity product criterion. In this paper, we consider these two criteria together for multilayer cyclotomic space-time code designs. In a previous paper, we recently proposed a systematic cyclotomic diagonal space-time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas, where diagonal codes correspond to single-layer codes in this paper. In this paper, we first propose a general multilayer cyclotomic space-time codes. We present a general optimality theorem for these infinitely many cyclotomic diagonal (or single-layer) space-time codes over general cyclotomic number rings for a general number of transmit antennas. We then present optimal multilayer (full-rate) cyclotomic space-time code designs for two and three transmit antennas. We also present an optimal two-layer cyclotomic space-time code design for three and four transmit antennas. The optimality here is in the sense that, for a fixed mean transmission signal power, its diversity product is maximized, or equivalently, for a fixed diversity product, its mean transmission signal power is minimized. It should be emphasized that all the optimal multilayer cyclotomic space-time codes presented in this paper have the nonvanishing determinant property.     

空时分组码在CDMA下行链路应用的研究

提出了准正交空时分组码在CDMA系统下行链路的两种应用方法，一种是在发射端对用户信号先扩频后空时编码送至发射天线，另一种是先空时编码后扩频送至发射天线，相应给出了两种方法接收端的译码方法。数据仿真结果表明在CDMA系统下行链路的应用时，准正交空时分组码的误码率低于正交空时分组码的误码率，并且第一种方法的误码率低于第二种方法的误码率。     

多天线对角空频编码传输

将平坦衰落信道的对角代数空时码(DAST)推广到频率选择性衰落信道,提出了对角空频分组码(DSF).基于多输入多输出天线和正交频分复用(OFDM),DSF码将满秩的旋转信号星座和子载波分组结合起来,以对角发送方式(每时刻只有一个天线发射)发射旋转信息符号向量的每个分量.成对错误概率分析表明:在频率选择性信道中,通过选择最佳的旋转矩阵,这种DSF-OFDM系统能实现满分集增益和最大的编码增益.系统采用了球型解码器对DSF码实施最大似然解码,它的解码复杂性是中等的,并且,解码算法的复杂性与信号星座的维数无关.此外,和先前所提出的一些方法相比,提出的空频码还具有频谱效率高(1symbol/s/Hz)的性能特点.     

On the design and performance of algebraic space-time codes forBPSK and QPSK modulation

The authors previously developed an algebraic approach to space-time code design that unifies most of the known results on trellis space-time codes and opens the door for more sophisticated space-time code constructions. We present algebraic constructions for trellis and block space-time codes for BPSK and QPSK modulated systems. The new designs benefit from the algebraic approach and are general for arbitrary number of transmit antennas in quasistatic fading channels. We also provide simulation results comparing the frame error rate performance of various constructions. These simulation results establish the performance advantage achieved by algebraic space-time codes compared to previously known codes in various scenarios     

Semiorthogonal Space–Time Block Codes

In this paper, a new class of full-diversity, rate-one space-time block codes (STBCs) called semiorthogonal algebraic space-time block codes (SAST codes) is proposed. SAST codes are delay optimal when the number of transmit antennas is even. The SAST codeword matrix has a generalized Alamouti structure where the transmitted symbols are replaced by circulant matrices and the commutativity of circulant matrices simplifies the detection of transmit symbols. SAST codes with maximal coding gain are constructed by using rate-one linear threaded algebraic space-time (LTAST) codes. Compared with LTSAT codes, SAST codes not only reduce the complexity of maximum-likelihood detection, but also provide remarkable performance gain. They also outperform other STBC with rate one or less. SAST codes also perform well with suboptimal detectors such as the vertical-Bell Laboratories layered space-time (V-BLAST) nulling and cancellation receiver. Finally, SAST codes attain nearly 100% of the Shannon capacity of open-loop multiple-input-single-output (MISO) channels.     

Efficiently decoded full-rate space-time block codes

Space-time block codes with orthogonal structures typically provide full-diversity reception and simple receiver processing. However, rate-1 orthogonal codes for complex constellations have not been found for more than two transmit antennas. By using a genetic algorithm, rate-1 space-time block codes that accommodate very simple receiver processing at the cost of reduced diversity are designed in this paper for more than two transmit antennas. Simulation results show that evolved codes combined with efficient outer codes provide better performance over fading channels than minimum-decoding-complexity quasiorthogonal codes at typical operating signal-to-noise ratios. When the fading is more severe than Rayleigh fading, the spectral efficiency is specified, and an efficient outer code is used, evolved codes outperform orthogonal space-time block codes.     

Distributed Algebraic Space-Time Codes for Ultra-Wideband Communications

In this paper, we extend the Amplify-and-Forward cooperative diversity scheme to the context of impulse radio ultra-wideband. In particular, we present the construction of two families of distributed algebraic space-time codes. The first family is based on totally real cyclic division algebras. The second family encodes the pulses used to transmit one information symbol and permits to achieve high-performance levels with lower complexity. Both families of codes achieve full rate, full diversity with non-vanishing determinants with various numbers of relays. Simulations performed over realistic indoor UWB channel models show important performance gains.     

基于Grassmann流形的非相干空时码设计

本文研究在Grassmann流形上构造非相干酉空时码的代数方法.首先提出一类发射天线数和相干时间都为任意大小的满速率满分集相干空时码,然后采用非线性指数映射方式,将该相干空时码映射到Grassmann流形上,生成Grassmann非相干酉空时码.新构造的Grassmann酉空时码比其它相同发射天线的酉空时码具有更高的频...     

A high-rate orthogonal space-time block code

We present a space-time block code from complex orthogonal designs for 5 transmit antennas, which can send 10 information symbols in a block of 15 channel uses and hence have rate 2/3. Simulation results show that this orthogonal space-time block code with rate 2/3 for five transmit antennas can achieve diversity gain over those orthogonal space-time block codes with higher rates for less number of transmit antennas.     

MIMO-OFDM for wireless communications: signal detection with enhanced channel estimation

Multiple transmit and receive antennas can be used to form multiple-input multiple-output (MIMO) channels to increase the capacity by a factor of the minimum number of transmit and receive antennas. In this paper, orthogonal frequency division multiplexing (OFDM) for MIMO channels (MIMO-OFDM) is considered for wideband transmission to mitigate intersymbol interference and enhance system capacity. The MIMO-OFDM system uses two independent space-time codes for two sets of two transmit antennas. At the receiver, the independent space-time codes are decoded using prewhitening, followed by minimum-Euclidean-distance decoding based on successive interference cancellation. Computer simulation shows that for four-input and four-output systems transmitting data at 4 Mb/s over a 1.25 MHz channel, the required signal-to-noise ratios (SNRs) for 10% and 1% word error rates (WER) are 10.5 dB and 13.8 dB, respectively, when each codeword contains 500 information bits and the channel's Doppler frequency is 40 Hz (corresponding normalized frequency: 0.9%). Increasing the number of the receive antennas improves the system performance. When the number or receive antennas is increased from four to eight, the required SNRs for 10% and 1% WER are reduced to 4 dB and 6 dB, respectively. Therefore, MIMO-OFDM is a promising technique for highly spectrally efficient wideband transmission.     

Noncoherent space-time coding: An algebraic perspective

The design of space-time signals for noncoherent block-fading channels where the channel state information is not known a priori at the transmitter and the receiver is considered. In particular, a new algebraic formulation for the diversity advantage design criterion is developed. The new criterion encompasses, as a special case, the well-known diversity advantage for unitary space-time signals and, more importantly, applies to arbitrary signaling schemes and arbitrary channel distributions. This criterion is used to establish the optimal diversity-versus-rate tradeoff for training based schemes in block-fading channels. Our results are then specialized to the class of affine space-time signals which allows for a low complexity decoder. Within this class, space-time constellations based on the threaded algebraic space-time (TAST) architecture are considered. These constellations achieve the optimal diversity-versus-rate tradeoff over noncoherent block-fading channels and outperform previously proposed codes in the considered scenarios as demonstrated by the numerical results. Using the analytical and numerical results developed in this paper, nonunitary space-time codes are argued to offer certain advantages in block-fading channels where the appropriate use of coherent space-time codes is shown to offer a very efficient solution to the noncoherent space-time communication paradigm.     

On channel orthogonalization using space-time block coding with partial feedback

Orthogonal space-time block codes (OSTBCs) yield full diversity gain even while requiring only a linear receiver. Such full-rate (rate-one) orthogonal designs are available for complex symbol constellations only for N=2 transmit antennas. In this paper, we propose a new family of full-rate space-time block codes (STBCs) using a single parameter feedback for communication over Rayleigh fading channels for N=3,4 transmit antennas and M receive antennas. The proposed rate-one codes achieve full diversity, and the performance is similar to maximum receiver ratio combining. The decoding complexity of these codes are only linear even while performing maximum-likelihood decoding. The partial channel information is a real phase parameter that is a function of all the channel gains, and has a simple closed-form expression for N=3,4. This feedback information enables us to derive (channel) orthogonal designs starting from quasi-orthogonal STBCs. The feedback complexity is significantly lower than conventional closed-loop transmit beamforming. We compare the proposed codes with the open-loop OSTBCs and also with the closed-loop equal gain transmission (EGT) scheme which uses equal power loading on all antennas. Simulated error-rate performances indicate that the proposed channel orthogonalized STBCs significantly outperform the open-loop orthogonal designs, for the same spectral efficiency. Moreover, even with significantly lower feedback and computational complexity, the proposed scheme outperforms the EGT technique for M>N.     

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.     

A rank criterion for QAM space-time codes

Space-time coding has been studied extensively as a powerful error correction coding for systems with multiple transmit antennas. An important design goal is to maximize the level of space diversity that a code can achieve. Toward this goal, the only systematic algebraic coding theory so far is binary rank theory by Hammons and El Gamal (see ibid. vol. 46, p.524-42, 2000) for binary phase-shift keying (BPSK) modulated codes defined over binary field and quaternary phase-shift keying (QPSK) modulated codes defined over modulo four finite ring. To design codes with higher bandwidth efficiency, we develop an algebraic rank theory to ensure full space diversity for 2/sup 2k/ quadrature and amplitude modulated (QAM) codes for any positive integer k. The theory provides the most general sufficient condition of full space diversity so far. It includes the BPSK binary rank theory as a special case. Since the condition is over the same domain that a code is defined, the full space diversity code design is greatly simplified. The usefulness of the theory is illustrated in examples, such as analyses of existing codes, constructions of new space-time codes with better performance, including the full diversity space-time turbo codes.     

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     

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.     

Design of channel-estimate-dependent space-time block codes

So far, the assumption of no channel knowledge at the transmitter has generally been inherent in the design of space-time codes. This paper, on the other hand, assumes that quantized channel information obtained from a feedback link is available at the transmitter and investigates how such channel information can be incorporated into the design of unstructured space-time block codes. Efficient codes are found by means of a gradient search over a continuous alphabet. Simulation results for an uncorrelated Rayleigh fading scenario using two and four transmit antennas and one receive antenna show the benefits of the code designs.     

Variable-rate space-time block codes in M-ary PSK systems

We consider a multiple antenna system when combined array processing with space-time coding is used. We present variable rate space-time block codes for two, three, and four transmit antennas and optimize the transmit power so that the average bit-error rate (BER) is minimized. Numerical results show that this optimum power allocation scheme provides significant gain over the equal power allocation scheme. We then classify all the variable rate space-time block codes having the same code rates and identify the unique code that achieves the lowest BER. We explicitly compute the performance of the variable rate codes over a Rayleigh-fading channel. The proposed variable rate space-time block codes are useful for unequal error protection in multiple transmit antenna systems.