Joint noncoherent demodulation and decoding for the block fading channel: a practical framework for approaching Shannon capacity

The paper contains a systematic investigation of practical coding strategies for noncoherent communication over fading channels, guided by explicit comparisons with information-theoretic benchmarks. Noncoherent reception is interpreted as joint data and channel estimation, assuming that the channel is time varying and a priori unknown. We consider iterative decoding for a serial concatenation of a standard binary outer channel code with an inner modulation code amenable to noncoherent detection. For an information rate of about 1/2 bit per channel use, the proposed scheme, using a quaternary phase-shift keying (QPSK) alphabet, provides performance within 1.6-1.7 dB of Shannon capacity for the block fading channel, and is about 2.5-3 dB superior to standard differential demodulation in conjunction with an outer channel code. We also provide capacity computations for noncoherent communication using standard phase-shift keying (PSK) and quadrature amplitude modulation (QAM) alphabets; comparing these with the capacity with unconstrained input provides guidance as to the choice of constellation as a function of the signal-to-noise ratio. These results imply that QPSK suffices to approach the unconstrained capacity for the relatively low information and fading rates considered in our performance evaluations, but that QAM is superior to PSK for higher information or fading rates, motivating further research into efficient noncoherent coded modulation with QAM alphabets.     

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.     

Embedded Rank Distance Codes for ISI Channels

Designs for transmit alphabet constrained space–time codes naturally lead to questions about the design of rank distance codes. Recently, diversity embedded multilevel space–time codes for flat-fading channels have been designed from sets of binary matrices with rank distance guarantees over the binary field by mapping them onto quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations. In this paper, we demonstrate that diversity embedded space–time codes for fading intersymbol interference (ISI) channels can be designed with provable rank distance guarantees. As a corollary, we obtain an asymptotic characterization of the fixed transmit alphabet rate–diversity tradeoff for multiple antenna fading ISI channels. The key idea is to construct and analyze properties of binary matrices with a particular structure (Toeplitz structure) induced by ISI channels.      

Design of low-density parity-check codes for modulation and detection

A coding and modulation technique is studied where the coded bits of an irregular low-density parity-check (LDPC) code are passed directly to a modulator. At the receiver, the variable nodes of the LDPC decoder graph are connected to detector nodes, and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder. The code is optimized by performing a curve fitting on extrinsic information transfer charts. Design examples are given for additive white Gaussian noise channels, as well as multiple-input, multiple-output (MIMO) fading channels where the receiver, but not the transmitter, knows the channel. For the MIMO channels, the technique operates within 1.25 dB of capacity for various antenna configurations, and thereby outperforms a scheme employing a parallel concatenated (turbo) code by wide margins when there are more transmit than receive antennas.     

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.     

在频率选择性相关信道中的空频分组编码技术

本文提出了频率选择性瑞利衰落信道中的对角空频分组码(DSF)，研究了码的性能。分析表明，在各天线对间的信道相互独立，系统有NT个发射天线，NR个接收天线和信道冲击响应长度是L时，DSF码可实现分集增益NRNTL。此外，相关的发射天线阵列会使DSF码分集增益下降，但是对码的性能影响不大，特别是在较长的多路径信道上。因此，DSF码对于相关的衰落信道显示出优越的鲁棒性能。最终仿真结果证实了本文的分析。     

Space-Code CS-CDMA Systems over MISO Frequency-Selective Rayleigh Fading Channels

We propose a transmit diversity CDMA scheme which is a combination of convolutional spreading (CS) and space-time spreading (STS) over multiple-input single-output (MISO) multipath Rayleigh fading channels. With our scheme, multiuser detection over an MISO multipath channel is transformed to single-user detection over a single-input single-output (SISO) multipath channel as the scheme by Petre et al. Because of its simple configuration, it is immediate to see that our scheme realizes full transmit- and path-diversity for two transmit antennas. We extend the system to four transmit antennas employing quasi-orthogonal construction and show a necessary and sufficient condition for full transmit- and path-diversity to be realized. The proposed scheme requires less hardware complexity and less latency than the one by Petre et al.     

A novel bit mapping scheme for high-order polar coded modulation systems

In order to improve the spectrum efficiency of the high-order polar coded modulation systems, the polar code is used as the component code of the bit-interleave coded modulation (BICM) system, a novel bit mapping scheme is proposed considering of the channel polarization and successive cancellation (SC) decoding principle of polar codes as well as the unequal protection of equivalent channels by modulator. In this scheme, the frozen bits on the unreliable split channel are allocated to the equivalent channel with the low protection of the modulator, while the equivalent channels with the high protection are used to transmit the information bits. Thus, the error-correcting performance of polar codes is improved. Compared with some bit mapping schemes, the proposed bit mapping scheme only needs to divide and choose the parameters of the split channels reliability measurement, the complexity does not increase obviously, and simulation results show that the proposed scheme has the better performance under the quadrature amplitude modulation (QAM) modulation based on the Gray mapping.     

The Universal Operation of LDPC Codes Over Scalar Fading Channels

Root and Varaiya proved the existence of a code that can communicate reliably over any linear Gaussian channel for which the channel mutual information level exceeds the transmitted rate. This paper provides several examples of scalar (single-input single-output) fading channels and shows that on these channels the performance of low-density parity-check (LDPC) codes lies in close proximity to the performance limits identified by Root and Varaiya. Specifically, we consider periodic fading channels and partial-band jamming (PBJ) channels. A special case of periodic fading is the variation of signal-to-noise ratio across orthogonal frequency division modulation subchannels. The robustness of LDPC codes to periodic fading and PBJ across parameterizations of these different channels is demonstrated through the consistency of the required mutual information to provide a specified bit error rate. For the periodic fading case, the Gaussian approximation to density evolution has been adapted such that asymptotic threshold measures can be compared to simulated code performance in various periodic fading scenarios     

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。     

Bandwidth-Efficient Differential Space–Time Modulation

We propose an extension of differential unitary space–time modulation by an additional differential amplitude modulation for bandwidth-efficient transmission with noncoherent detection in a wireless system with multiple transmit antennas. The input bits are subdivided into two groups. The first group chooses a unitary matrix, whereas the second group determines the amplitude of the transmit matrix. We derive a noncoherent soft-output detector that does not require knowledge of channel state or statistical channel properties. The modulation parameters are optimized based on an analytical bit error rate (BER) analysis and mutual information. Furthermore, we propose a pragmatic scheme for outer forward error control coding and interleaving. Compared to differential unitary space–time modulation, the proposed scheme has lower detection complexity and provides superior performance for bandwidth-efficient transmission, particularly in time-varying channels.      

Coded differential space-time modulation for flat fading channels

In this paper, powerful coding techniques for differential space-time modulation (DSTM) over Rayleigh flat fading channels and noncoherent detection without channel state information at the receiver are investigated. In particular, multilevel coding, bit-interleaved coded modulation, and so-called hybrid coded modulation (HCM) are devised and compared. For improved noncoherent reception multiple-symbol differential detection (MSDD) is adapted to DSTM. In order to reduce the computational effort required for MSDD, a low-complexity version of MSDD is applied. Evaluating the ergodic channel capacity for the different schemes as appropriate performance measure, HCM with simplified MSDD is shown to offer a favorable tradeoff between complexity and achievable power efficiency. Simulation results employing turbo codes in properly designed HCM schemes confirm the predictions from information theory.     

Reduced-Complexity Receiver Structures for Space–Time Bit-Interleaved Coded Modulation Systems

Transmission efficiency in radio channels can be considerably improved by using multiple transmit and receive antennas and employing a family of schemes called space-time (ST) coding. Both extended range and/or improved bandwidth efficiency can be achieved, compared with a radio link with a single transmit and receive antenna. Bit-interleaved coded modulation schemes give diversity gains on fading channels with higher order modulation constellations combined with conventional binary convolutional codes also for the case of a single transmit and receive antenna radio link. In this paper, we study a family of flexible bandwidth-efficient ST coding schemes which combine these two ideas in a narrowband flat-fading channel and single-carrier modems. We address receiver complexity for the case of a large number of transmit antennas and higher order modulation constellations. Especially, we focus on practical configurations, where the number of transmit antennas is greater than that of receive antennas. Simplified receivers using tentative decisions are proposed and evaluated by means of simulations. Tradeoffs between complexity reduction and performance loss are presented. We emphasize systems that are of particular interest in applications where the number of transmit antennas exceeds the number of receive antennas. A system with four transmit antennas with an eight-fold complexity reduction and a performance loss of about 1 dB is demonstrated     

Performance analysis of a rate-adaptive dual-branch switched diversity system

In this letter, a performance analysis of a dualbranch switched diversity system operating on statistically independent and identically distributed Nakagami-m flat-fading channels is presented. An adaptive coded modulation (ACM) scheme is employed to increase the spectral efficiency of the system. The ACM scheme consists of a set of multidimensional trellis codes originally designed for additive white Gaussian noise channels, where the codes are based on quadrature amplitude modulation (QAM) signal constellations of varying size. The performance is evaluated by assuming perfect channel knowledge at both transmitter and receiver and instantaneous feedback of channel state information, conveyed from the receiver to the transmitter on an error-free feedback channel. The optimal switching threshold of the switched diversity combiner, maximizing the average spectral efficiency, is identified for spatially uncorrelated antenna branches.     

Analysis of Differential Orthogonal Space–Time Block Codes Over Semi-Identical MIMO Fading Channels

We study the performance of differential orthogonal space-time block codes (OSTBC) over independent and semi-identically distributed block Rayleigh fading channels. In this semiidentical fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are nonidentically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another are considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit-error probabilities (BEPs) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas, and any number of transmit antennas for which OSTBCs exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. For an arbitrary number of transmit antennas, a Chernoff bound on the BEP for the optimal detector is also derived. Our results show that the semi-identical channel statistics degrade the error performance of differential OSTBC, compared with the identical case. Also, the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly. But in near-static fading channels, the two detectors have similar performances     

Coding approaches for multiple antenna transmission in fast fading and OFDM

Multiple-antenna channel coding for orthogonal frequency-division multiplexing (OFDM) transmission over dispersive channels is reconsidered because with frequency interleaving, the effective channel characteristic across subcarriers is rather fast fading. The channel does not comply with the quasistatic model widely assumed for space-time trellis codes (STCs). For that reason, we first study the ideal fast-fading multiple transmit and receive antenna channel and then compare the performance of STCs with that of bit-interleaved coded modulation in fast fading. Mutual information of the ergodic channel is evaluated for numerous modulation scenarios, and capacity comparisons generate guidelines on how to jointly adjust coding rate and modulation cardinality. Bit-based coding offers large flexibility in rate adaptation, and simulation results show that it outperforms STCs in ideal fast fading and, finally, in a realistic OFDM application as well.     

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     

接近最优的编码MIMO系统的发送天线子集选择算法

多天线无线系统可提供更大的信道容量和更好的抗衰落能力,发送端利用反馈的部分信道状态信息进行发送天线子集选择能够进一步提高信道容量。该文提出了一种MIMO系统的快速的、动态的天线子集选择算法,其提供的信道容量高于已有的静态算法,且接近于最优天线选择算法,而无需计算所有可能的天线子集组合的信道容量,因而具有更低的复杂度。将本文算法与比特交织编码调制(BICM)技术相结合,对各天线速率进行适配,提出了空时自适应比特交织编码调制(ST-ABICM)方案。仿真结果证实了该方案性能的优越性。     

On the capacity of OFDM-based spatial multiplexing systems

This paper deals with the capacity behavior of wireless orthogonal frequency-division multiplexing (OFDM)-based spatial multiplexing systems in broad-band fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Introducing a physically motivated multiple-input multiple-output (MIMO) broad-band fading channel model, we study the influence of physical parameters such as the amount of delay spread, cluster angle spread, and total angle spread, and system parameters such as the number of antennas and antenna spacing on ergodic capacity and outage capacity. We find that, in the MIMO case, unlike the single-input single-output (SISO) case, delay spread channels may provide advantages over flat fading channels not only in terms of outage capacity but also in terms of ergodic capacity. Therefore, MIMO delay spread channels will in general provide both higher diversity gain and higher multiplexing gain than MIMO flat fading channels