Adaptive transmit antenna selection with pragmatic space-time trellis codes

We consider the problem of selecting a subset of transmit antennas in MIMO systems to minimize error probability when only partial channel information is available at the transmitter. An upper bound for error probability of space-time coded transmit antenna selection scheme conditioned on the channel state information is presented. Based on the performance analysis, a criterion of selecting a subset of available transmit antennas to minimize the upper bound on the PEP is proposed. In contrast to other transmit antenna selection schemes for uncoded transmission or with a fixed number of antennas within the selection subset in the literature, the proposed scheme can adaptively select both a variable number of transmit antennas and their corresponding space-time codes for transmission. Furthermore, we present pragmatic space-time trellis coding schemes for slow Rayleigh fading channels. The principal advantage of the schemes is that a single encoder and decoder can be used for systems with a variable number of transmit antennas. The performance of the pragmatic space-time codes with adaptive antenna selection and the effect of the imperfect channel estimation on performance are evaluated by simulations. It is shown that the adaptive selection offers considerable antenna selection gain relative to the antenna selection system with a fixed number of antennas within the selection subset     

Space-time turbo trellis codes for two, three, and four transmit antennas

New space-time turbo trellis codes (ST turbo TCs) with 4-phase-shift keying (PSK) and 8-PSK for two, three, and four transmit antennas in slow and fast fading channels are proposed in this paper. The component codes of the space-time turbo schemes are constructed by choosing the feedforward coefficients to maximize the minimum squared Euclidean distance and the feedback coefficients to minimize the iterative decoding threshold. The performance of the proposed ST turbo TCs with various memory orders, transmit antennas, and interleaver structures is evaluated by simulation. It is shown that the new codes achieve better performance than previously designed codes. The impact of antenna correlation and imperfect channel estimation on the code performance is also discussed.     

Asymptotic performance of space-time block codes with imperfect transmit antenna selection

The asymptotic bit error performance of the Alamouti scheme with transmit antenna selection is investigated for imperfect selection of antenna subset. It is shown that the transmit diversity order is equal to the largest ordinal number of the antenna within the selected antenna subset.     

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.     

Space-time turbo codes with full antenna diversity

In attempting to find a spectrally and power efficient channel code which is able to exploit maximum diversity from a wireless channel whenever available, we investigate the possibility of constructing a full antenna diversity space-time turbo code. As a result, both three-antenna and two-antenna (punctured) constructions are shown to be possible and very easy to find. To check the decodability and performance of the proposed codes, we derive non-binary soft-decoding algorithms. The performance of these codes are then simulated and compared with two existing space-time convolutional codes (one has minimum worst-case symbol-error probability; the other has maximal minimum free distance) having similar decoding complexity. As the simulation results show, the proposed space-time turbo codes give similar or slightly better performance than the convolutional codes under extremely slow fading. When fading is fast, the better distance spectra of the turbo codes help seize the temporal diversity. Thus, the performance advantage of the turbo codes becomes evident. In particular, 10^-5 bit-error rate and 10^-3 frame-error rate can be achieved at less than 6-dB E_b/N₀ with 1 b/s/Hz and binary phase-shift keying modulation. The practical issue of obtaining the critical channel state information (CSI) is also considered by applying an iteratively filtered pilot symbol-assisted modulation technique. The penalty when the CSI is not given a priori is about 2-3 dB     

Space-time codes with full antenna diversity using weighted nonbinary repeat-accumulate codes

Like turbo codes, repeat-accumulate codes have remarkably good performance when r/spl ges/3, where r is the number of repetition times. We present space-time codes with full antenna diversity using "weighted" nonbinary repeat-accumulate codes. Compared with the space-time turbo codes of Y. Liu et al. (see IEEE J. Select. Areas Commun., vol.19, p.969-80, 2001) and of H. Su and E. Geraniotis (see ibid., vol.49, p.47-57, 2001), the main advantage of this new scheme is to construct space-time codes with full diversity for any m/spl les/r and any length of frame without searching for interleavers, where m is the number of transmit antennas. These space-time codes have rate m/r and, so, have full rate when m=r. Furthermore, they have an efficient decoding based on the message passing algorithm.     

Super-quasiorthogonal space-time trellis codes for four transmit antennas with rectangular signal constellations

In this paper, we present the first super-quasiorthogonal space-time trellis codes (SQOSTTCs) for systems with four transmit antennas using various types of rectangular signal constellations to increase the spectral efficiency up to 5 bits/s/Hz. In our wireless communications system, we define an eight-dimensional (8D) signal constellation as Cartesian product of four two-dimensional (2D) rectangular signal sets. The transmission of an 8D point from the first antenna is achieved by transmitting four concatenated 2D points in four consecutive channel uses. The 2D symbols transmitted from the other three antennas are not independent but so chosen as to form, together with the symbols transmitted from the first antenna, the entries of a 4×4 quasiorthogonal transmission matrix. The union of two sets of quasiorthogonal transmission matrices forms a so-called super-quasiorthogonal signal set. With the 4×4 quasiorthogonal transmission matrices, we then label the state transitions of a trellis diagram describing the operation of the encoder. The simulation results of the frame error rate and the bit error rate demonstrate the excellent performance of our proposed SQOSTTCs.     

On the diversity order of space-time trellis codes with receive antenna selection over fast fading channels

In this paper, we study the performance of space-time trellis codes (STTCs) with receive antenna selection over fast fading channels. Specifically, we derive upper bounds on the pairwise-error probability (PEP) with antenna selection. In performing the selection, we adopt a criterion that is based on using L out of the available M receive antennas that result in maximizing the instantaneous signal-to-noise ratio (SNR) at the receiver, where L les M. We show that the diversity order resulting from antenna selection deteriorates significantly and is actually dictated by the number of selected antennas. The implication of this result is that adding more receive antennas, while maintaining the same number of selected ones, will have no impact on the diversity order, but it does, however, provide some additional coding gain. This is unlike the case for quasi-static fading channels in which the diversity order is always preserved with antenna selection when the underlying STTC is full-rank. We present numerical examples that support our analysis     

发射天线选择空时分组码的误符号率分析

研究瑞利衰落信道上使用发射天线选择和空时分组编码的多输入多输出系统的误码性能。使用矩生成函数法和Apell超几何函数、Lauricella多变量超几何函数,推导采用相干检测的M进制相移键控(MPSK)和广义矩形M进制正交幅度调制(GR-MQAM)的平均符号错误概率(SEP)的精确闭合表达式。数值计算结果表明:增加发射天线或/和接收天线数可以改善MIMO瑞利衰落上MPSK和GR-MQAM的平均SEP性能。     

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.     

结合发射天线重分组和接收天线选择的双空时发射分集系统的实现方案

对线性接收双空时发射分集系统提出一种新的接收天线选择方案,通信系统在增加较小的实现复杂度的情况下可以有效的改善系统的信道状态,抑制不同子数据流间的干扰,降低系统的误码率(BER).结合发射天线重分组(TAs)方案,不同子数据流间的干扰可以得到更好的抑制,系统性能得到进一步的提高.仿真表明,在增加较少的反馈信息冗余及系统硬件实现复杂度的情况下,系统的性能得到了很大的改善.     

A cross-layer approach to transmit antenna selection

In this paper, we investigate a cross-layer approach to transmit antenna selection capable of adapting the number of active antennas to varying channel conditions. We address a cross-layer methodology in the sense that the criterion for the selection of antenna subsets is the maximization of link layer throughput which takes into account characteristics both at the physical and link layers. In order to enhance system performance, adaptive modulation is included to jointly perform antenna selection and rate adaptation. Performance assessment is conducted in terms of link layer throughput and transmission delay.     

基于特征波束形成的STBC发射天线选择

相关信道下将特征波束形成(E-BF)与空时分组码(STBC)相结合,在保持分集阶数的同时可以获得阵列增益,但需配置更多的发射天线.根据该系统特点提出了统计的发射天线选择方案,在不增加天线数情况下通过自适应子阵选择来提高系统误码率性能,并给出了平均误码率最小的天线选择准则.天线选择与E-BF共享信道信息,算法也不用频繁更新.仿真结果证明了该天线选择方案可提高系统误码率的性能.     

Low-complexity transmit antenna selection algorithm formassive MIMO

Massive multiple input multiple output (MIMO) systems can increase capacity and reliability greatly. However,extremely high hardware costs and computational complexity lead to the demand for reasonable antenna selection.Aiming at the problem that the traditional antenna selection algorithm based on maximizing sum capacity has largecomplexity and worse bit error rate (BER) performance, a two-step selection algorithm is proposed, which selectsa part of the antennas based on the norm-based antenna selection (NBS) firstly, and then selects the antenna basedon maximizing capacity via convex optimization. The simulation results show that the improved algorithm has betterBER performance than the traditional algorithms. At the same time, it reduces computational complexity greatly.     

混合发射天线选择的闭环发射分集系统的优化设计

研究了混合发射天线选择技术的闭环发射分集系统.针对最大率传输和等增益传输两种传输模式,根据信道矢量衰落损耗系数的排序统计分布特性,分别提出了发射天线数和射频链路数的选择算法.这两个算法可分别使系统所需的发射天线数和射频链路数最小.仿真结果显示合理地选择发射天线数和射频链路数可以大大简化系统的复杂度,减少不必要的开销.针对混合发射天线选择的等增益传输提出了相位扇区化量化算法.这种算法只需少量的量化反馈就可以使系统的性能接近全反馈情况.     

Space-time coding over correlated fading channels with antenna selection

In a previous paper by Bahceci et al., antenna selection ' for multiple-antenna transmission systems under the assumption that the subchannels between antenna pairs fade independently was studied. In this paper, the performance of such systems when the subchannels experience correlated fading is considered. It is assumed that the channel-state information (CSI) is available only at the receiver, the antenna selection is performed only at the receiver, and the selection is based on the instantaneous received signal power. The effects of channel correlations on the diversity and coding gain when the receiver system is a subset of the antennas are quantified. Theoretical results indicate that the correlations in the channel do not degrade the diversity order, provided that the channel is full rank. However, it does result in some performance loss in the coding gain.     

Security enhancement with joint transmit antenna selection and transmit beamforming under energy harvesting constraints

This paper considers a multiuser multiple‐input single‐output (MISO) broadcasting system with simultaneous wireless information and power transfer (SWIPT), which consists of one information receiver (IR) and several energy harvesting receivers (ERs) which are capable of eavesdropping the legitimate signals. For reducing cost and hardware complexity, transmit antenna selection (TAS) is applied in the transmitter. We aim to maximize the achievable secrecy rate under the individual energy harvesting constraint at the ERs and the transmit power constraint at the transmitter by jointly optimizing TAS, transmit beamforming, and artificial noise (AN). The joint optimization problem is a non‐convex mixed integer programming problem. We apply variable replacements to decouple the variable couplings and relax and approach the binary constraint by the difference of two convex constraints. Afterwards, penalty method and constrained concave convex procedure (CCCP) are applied to transform the relaxed problem into a sequence of semi‐definiteness programming (SDP) problems. Simulation results shows that our proposed joint optimization scheme is superior over existing non‐joint optimization schemes. This paper studies the joint transmit antenna selection (TAS), transmit beamforming, and artificial noise (AN) optimization in a multiple‐input multiple‐output (MISO) wiretap system with simultaneous wireless information and power transfer (SWIPT). The joint optimization problem is nonconvex and we propose a penalty method based scheme to solve it. The simulation results show that our joint optimization scheme is superior to other non‐joint optimization schemes.     

Diversity order of decode-and-forward MIMO relaying with transmit antenna selection

This article analyzes the diversity order of several proposed schemes, where the transmit antenna selection (TAS) strategies are combined with low-complexity decode-and-forward (DF) protocols in the multiple-input multiple-output (MIMO) relaying scenario. Although antenna selection is a suboptimal form of beamforming, it enjoys the advantages of tractable optimization and low feedback overhead. Specifically, this article proposes schemes that combine TAS strategies with fixed decode-and-forward (FDF) and selection decode-and-forward (SDF) protocols. Following that, the asymptotic expressions of outage probabilities are derived and the diversity order of the proposed schemes analyzed. These kinds of combination of transmit antenna selection strategies and low-complexity decode-and-forward protocols can achieve partial diversity order in the MIMO relaying scenario. The numerical simulations verify the analysis.     

Analysis of cooperative MIMO transmission system with transmit antenna selection and selection combining

Error performance of a cooperative system can be enhanced by using transmit and receive diversity techniques at transmission links. The number of transmit/receive RF chain pairs required to achieve full diversity can be decreased to one for each link by using transmit antenna selection (TAS) method at the transmitter and selection combining (SC) method at the receiver. Thus, hardware complexity of a multiple input multiple output (MIMO) cooperative scheme can be significantly reduced when compared to systems that use TAS and maximum ratio combining (MRC). In this paper, we investigate the performance of an amplify‐and‐forward cooperative system where TAS/SC is utilized. We derive the probability density function (pdf) of end‐to‐end SNR of the system for Rayleigh fading channels. By using this pdf, we obtain the exact symbol error rate expressions for M‐PSK and M‐QAM modulations and the exact outage probability expression. We also obtain the asymptotical diversity order using upper and lower bounds of the outage probability expression and show that our system provides the same diversity order as the cooperative system where TAS/MRC is utilized. We verify our results via computer simulations. Copyright © 2010 John Wiley & Sons, Ltd.