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     

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     

Low-density parity-check codes for space-time wireless transmission

Irregular low-density parity-check (LDPC) codes have shown exceptionally good performance for single antenna systems over a wide class of channels. In this paper, we investigate their application to multiple antenna systems in flat Rayleigh fading channels. For small transmit arrays, we focus mainly on space-time coding with 2/sup p/-ary LDPC codes, where p equals the number of encoded bits transmitted by the transmit antenna array during each signaling interval. For large transmit arrays, we study a layered space-time architecture using binary LDPC codes as component codes of each layer: We show through simulation that, when applied to multiple antenna systems with high diversity order, LDPC codes of quasi-regular construction are able to achieve higher coding gain and/or diversity gain than previously proposed space-time trellis codes, space-time turbo codes, and convolutional codes in a number of fading conditions. Extending the work of density evolution with Gaussian approximation, we study 2/sup p/-ary LDPC codes on multiple antenna fading channels, and search for the optimum 2/sup p/-ary quasi-regular codes in quasi-static fading. We also show that on fast fading channels, 2/sup p/-ary irregular LDPC codes, though designed for static channels, have superior performance to nonbinary quasiregular codes and binary irregular codes specifically designed for fast fading channels.     

Multiple trellis coded orthogonal transmit scheme for multiple antenna systems

In this paper, a novel multiple trellis coded orthogonal transmit scheme is proposed to exploit transmit diversity in fading channels. In this scheme, a unique vector from a set of orthogonal vectors is assigned to each transmit antenna. Each of the output symbols from the multiple trellis encoder is multiplied with one of these orthogonal vectors and transmitted from corresponding transmit antennas. By correlating with corresponding orthogonal vectors, the receiver separates symbols transmitted from different transmit antennas. This scheme can be adopted in coherent/differential systems with any number of transmit antennas. It is shown that the proposed scheme encompasses the conventional trellis coded unitary space-time modulation based on the optimal cyclic group codes as a special case. We also propose two better designs over the conventional trellis coded unitary space-time modulation. The first design uses 8 Phase Shift Keying （8-PSK） constellations instead of 16 Phase Shift Keying （16-PSK） constellations in the conventional trellis coded unitary space-time modulation. As a result, the product distance of this new design is much larger than that of the conventional trellis coded unitary space-time modulation. The second design introduces constellations with multiple levels of amplitudes into the design of the multiple trellis coded orthogonal transmit scheme. For both designs, simulations show that multiple trellis coded orthogonal transmit schemes can achieve better performance than the conventional trellis coded unitarv space-time schemes.     

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.     

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.     

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.     

Adaptive Channel‐Matched Extended Alamouti Space‐Time Code Exploiting Partial Feedback

Since the publication of Alamouti's famous space‐time block code, various quasi‐orthogonal space‐time block codes (QSTBC) for multi‐input multi‐output (MIMO) fading channels for more than two transmit antennas have been proposed. It has been shown that these codes cannot achieve full diversity at full rate. In this paper, we present a simple feedback scheme for rich scattering (flat Rayleigh fading) MIMO channels that improves the coding gain and diversity of a QSTBC for 2ⁿ (n = 3, 4,…) transmit antennas. The relevant channel state information is sent back from the receiver to the transmitter quantized to one or two bits per code block. In this way, signal transmission with an improved coding gain and diversity near to the maximum diversity order is achieved. Such high diversity can be exploited with either a maximum‐likelihood receiver or low‐complexity zero‐forcing receiver.     

Super-quasi-orthogonal space-time trellis codes for four transmit antennas

We introduce a new family of space-time trellis codes that extends the powerful characteristics of super-orthogonal space-time trellis codes to four transmit antennas. We consider a family of quasi-orthogonal space-time block codes as building blocks in our new trellis codes. These codes combine set partitioning and a super set of quasi-orthogonal space-time block codes in a systematic way to provide full diversity and improved coding gain. The result is a powerful code that provides full rate, full diversity, and high coding gain. It is also possible to maintain a tradeoff between coding gain and rate. Simulation results demonstrate the good performance of our new super-quasi-orthogonal space-time trellis codes.     

Multiuser Interference Cancellation and Detection for Users with More Than Two Transmit Antennas

We consider J transmitter units each equipped with N transmit antennas over wireless Rayleigh fading channels. Previously in [1], it was proved that when each transmitter unit has TV transmit antennas, using (J - 1)N + r receive antennas for any r ges 1, the receiver can completely separate the signals of J users. The provided diversity to each user was shown to be Nr if the units employ space-time trellis codes even if the units transmit asynchronously. Here, we consider the case when all units are synchronized and employ quasi-orthogonal space-time block codes (N > 2). It is proved that in this case a receiver with J + r - 1 antennas with r ges 1 can separate the transmitted signals of all units and provide each unit with a diversity order of Nr. Based on our interference cancellation technique, we then offer an array processing scheme which provides trade-off between diversity and spatial multiplexing. It is shown via simulations that this array processing scheme performs better than well-known modulation schemes, e.g. space-time block codes and BLAST, for a moderate number of receive antennas.     

满速率串行级联空时分组MTCM编码方法研究

该文研究了级联空时编码系统在编码增益,分集增益和传输能量效率的限定下最大化传输速率的问题,提出了一种在保留TCM编码方法校验位冗余的同时,还可获得满速率串行级联空时分组TCM编码方法。新方法通过引入具有不同功率分集因子的正交发射码字矩阵,并给出新的译码算法,从而使得新的编码方法在获得满速率的同时还可以获得满分集增益。分析和MATLAB仿真结果表明,在相同的编码状态数下,新方法在编码增益上比现有的满速率超正交空时分组编码方法提高1dB左右。     

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。     

Space-time block codes from cyclic design

It has been proved that full-rate complex orthogonal space-time block codes do not exist for systems with more than two transmit antennas. In this paper, we present a space-time block coding scheme based on cyclic design. The proposed codes provide full rate and full diversity for quaternary phase shift keying (QPSK) symbols in systems with three or four transmit antennas.     

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.     

Non-full rank space-time trellis codes for serially concatenated system

The feasibility of the non-full rank space-time trellis codes (NFR-STTCs) for the serially concatenated system is described carefully in this letter and a QPSK-based NFR-STTC suitable for the system is proposed. As the simulation results show, over the flat block Rayleigh fading channels, a concatenated system with the proposed NFR-STTC inner code can achieve full diversity, and improve the coding gains compared with other concatenated systems adopting full-rank space-time trellis codes (FR-STTCs) of the same complexity. The introduction of the NFR-STTC to serial concatenation space-time (SCST) system provides a new research community of SCST.     

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static 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.     

Space-time codes for high data rate wireless communication:performance criterion and code construction

We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that 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. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders     

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.     

Constructing Space-Time Trellis Codes Using Orthogonal Designs

In this paper we consider the design of space-time trellis codes usingorthogonal designs. We derive a condition on the codewords to obtainthe maximum received signal energy and show that the codes based onorthogonal designs satisfy this condition.We consider in detail the design of a trellis code for two transmitantennas. The new code we develophas a higher diversity in fast fading and a higher coding gain in quasi-static fading when compared to otherexisting space-time codes. We also consider a turbo implementation ofthe new trellis code which results in very high diversity gains infast fading channels.