Distributed differential space-time coding for wireless relay networks

Distributed space-time coding is a cooperative transmission scheme for wireless relay networks. With this scheme, antennas of the distributive relays work as transmit antennas of the sender and generate a space-time code at the receiver. It achieves the maximum diversity. Although the scheme needs no channel information at relays, it does require full channel information, both the channels from the transmitter to relays and the channels from relays to the receiver, at the receiver. In this paper, we propose a differential transmission scheme, which requires channel information at neither relays nor the receiver, for wireless relay networks. As distributed space-time coding can be seen as the counterpart of space-time coding in the network setting, this scheme is the counterpart of differential space-time coding. Compared to coherent distributed space-time coding, the differential scheme is 3dB worse. In addition, we show that Alamouti, square real orthogonal, and Sp(2) codes can be used differentially in networks with corresponding numbers of relays. We also propose distributed differential space-time codes that work for networks with any number of relays using circulant matrices.     

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 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.     

Cyclic Distributed Space–Time Codes for Wireless Relay Networks With No Channel Information

In this paper, we present a coding strategy for half duplex wireless relay networks, where we assume no channel knowledge at any of the transmitter, receiver, or relays. The coding scheme uses distributed space-time coding, that is, the relay nodes cooperate to encode the transmitted signal so that the receiver senses a space-time codeword. It is inspired by noncoherent differential techniques. The proposed strategy is available for any number of relays nodes. It is analyzed, and shown to yield a diversity linear in the number of relays. We also study the resistance of the scheme to relay node failures, and show that a network with R relay nodes and d of them down behaves, as far as diversity is concerned, as a network with R-d nodes. Finally, our construction can be easily generalized to the case where the transmitter and receiver nodes have several antennas.     

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.     

Cooperative Strategies and Capacity Theorems for Relay Networks

Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decode-and-forward the source message to the destination, or they compress-and-forward their channel outputs to the destination. The decode-and-forward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compress-and-forward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination's channel output. The strategies are applied to wireless channels, and it is shown that decode-and-forward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, single-bounce fading, certain quasi-static fading problems, cases where partial channel knowledge is available at the transmitters, and cases where local user cooperation is permitted. The results further extend to multisource and multidestination networks such as multiaccess and broadcast relay channels.     

Cooperative Space–Time Coding with Amplify-and- Forward Relaying

Cooperative diversity using distributed space-time codes has been recently proposed to form virtual antennas in order to achieve diversity gain. In this paper, we consider a multi-relay network operating in amplify-and-forward (AAF) mode. Motivated by protocol III presented in (Nabar et al. 2004), we propose a cooperative diversity protocol implementing space–time coding for an arbitrary number of relay nodes when the source-destination link contributes in the second phase. We consider the use of real-orthogonal and quasi-orthogonal designs of space–time codes as they give better performance than random linear-dispersion codes. The pairwise error probability (PEP) has been derived and the theoretical analysis demonstrates that the proposed protocol achieves a diversity of order N + 1, where N is the number of relay nodes. No instantaneous channel state information is required at the relay nodes. The optimum power allocation that minimizes the PEP is obtained with numerical and theoretical analysis. The aggregate system power constraint is considered in the optimization. Simulation results demonstrate an improvement over the existing orthogonal protocols for different source-destination channel conditions. The results also show that the proposed scheme is robust to the channel estimation errors     

A simple Cooperative diversity method based on network path selection

Cooperative diversity has been recently proposed as a way to form virtual antenna arrays that provide dramatic gains in slow fading wireless environments. However, most of the proposed solutions require distributed space-time coding algorithms, the careful design of which is left for future investigation if there is more than one cooperative relay. We propose a novel scheme that alleviates these problems and provides diversity gains on the order of the number of relays in the network. Our scheme first selects the best relay from a set of M available relays and then uses this "best" relay for cooperation between the source and the destination. We develop and analyze a distributed method to select the best relay that requires no topology information and is based on local measurements of the instantaneous channel conditions. This method also requires no explicit communication among the relays. The success (or failure) to select the best available path depends on the statistics of the wireless channel, and a methodology to evaluate performance for any kind of wireless channel statistics, is provided. Information theoretic analysis of outage probability shows that our scheme achieves the same diversity-multiplexing tradeoff as achieved by more complex protocols, where coordination and distributed space-time coding for M relay nodes is required, such as those proposed by Laneman and Wornell (2003). The simplicity of the technique allows for immediate implementation in existing radio hardware and its adoption could provide for improved flexibility, reliability, and efficiency in future 4G wireless systems.     

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.     

Partially-coherent distributed space-time codes with differential encoder and decoder

Distributed space-time coding is a mean of achieving diversity through cooperative communication in a wireless relay network. In this paper, we consider a transmission protocol that follows a two-stage model: transmission from source to relays in the first stage, followed by a simple relaying technique from relays to destination. The relays transmit a vector which is a transformation of the received vector by a relay-specific unitary transformation. We assume that the relays do not have any channel information, while the destination has only a partial-channel knowledge, by which we mean that destination knows only the relay-to-destination channel. For such a setup, we derive a Chernoff bound on the pairwise error probability and propose code design criteria. A second contribution is the differential encoding and decoding scheme for this setup, which is different from the existing ones. Furthermore, differential codes from cyclic division algebra are proposed that achieve full diversity. For our setup with two relays, a Generalized PSK code is shown to achieve full diversity, for which the decoding complexity is independent of code size     

Non-coherent distributed space–time coding techniques for two-way wireless relay networks

To overcome the overhead involved with channel estimation, several non-coherent distributed space–time coding (DSTC) strategies for two-way wireless relay networks (TWRNs) using the amplify-and-forward and the decode-and-forward protocol have been recently proposed that do not require channel state information (CSI) at any node to decode the information symbols. In this paper, novel differential DSTC strategies for TWRNs using the two- and three-phase protocol are proposed. In our transmission schemes, the relays do not waste power to transmit information known at the respective destination nodes. This is achieved by combining the symbols from both terminals received at the relays into a single symbol of the unaltered constellation. Furthermore, in our strategies, the direct link between the communicating terminals can be naturally incorporated to further improve the diversity gain. Simulations show a substantially improved performance in terms of bit error rate (BER) of the proposed strategies as compared to the existing strategies.     

Distributed Space-Time Codes Using Constellation Rotation

Rate and diversity impose a fundamental tradeoff in wireless communication. We propose a novel distributed space-time coding (DSTC) scheme based on constellation rotation (DSTC-CR) for Amplify-and-Forward relay networks. The proposed code can achieve full-diversity or full-rate, and also offers a flexibility for a desired rate-diversity tradeoff. This code can work well with arbitrary signal constellation and any number of relays and achieve minimal-delay. Through analysis of pairwise error probability, coding design criteria, Chernoff bound, decoding strategies and optimal power allocation are provided. Simulation results show that DSTC-CR scheme outperforms diagonal DSTC (DDSTC) and distributed linear dispersion (DLD) code at high power. From the comparison with DDSTC, the DSTC-CR scheme can achieve the same information rate using a lower modulation order.     

On the performance of multi‐hop wireless relay networks

User cooperation has evolved as a popular coding technique in wireless relay networks (WRNs). Using the neighboring nodes as relays to establish a communication between a source and a destination achieves an increase of the diversity order. The relay nodes can be seen as a distributed multi‐antenna system, which can be exploited for transmit diversity by using distributed space–time block coding (STBC). In this paper, we investigate the bit error rate (BER) of multi‐hop WRNs employing distributed STBC at the relay nodes. We develop the general model of WRNs using distributed STBC, and we derive the pairwise error probability and an approximation of the BER. We examine the impact of several parameters, such as distributed STBC at the relays, the number of relays, the distances between the nodes, and the channel state information available at the receivers, on the BER performance of the multi‐hop WRN. The obtained results provide guidelines about the expected error performance and the design of channel estimation for these networks. Copyright © 2011 John Wiley & Sons, Ltd.     

Low density parity check codes for the relay channel

We propose Low Density Parity Check (LDPC) code designs for the half-duplex relay channel. Our designs are based on the information theoretic random coding scheme for decode-and-forward relaying. The source transmission is decoded with the help of side information in the form of additional parity bits from the relay. We derive the exact relationships that the component LDPC code profiles in the relay coding scheme must satisfy. These relationships act as constraints for the density evolution algorithm which is used to search for good relay code profiles. To speed up optimization, we outline a Gaussian approximation of density evolution for the relay channel. The asymptotic noise thresholds of the discovered relay code profiles are a fraction of a decibel away from the achievable lower bound for decode-and-forward relaying. With random component LDPC codes, the overall relay coding scheme performs within 1.2 dB of the theoretical limit     

A new full-rate full-diversity orthogonal space-time block coding scheme

In this work, we present a new space-time orthogonal coding scheme with full-rate and full-diversity. The proposed space-time coding scheme can be used on quaternary phase-shift keyed (QPSK) transceiver systems with four transmit antennas and any number of receivers. An additional feature is that the coded signals transmitted through all four transmit antennas do not experience any constellation expansion. The performance of the proposed coding scheme is studied in comparison with that of 1/2-rate full-diversity orthogonal space-time code, quasi-orthogonal code, as well as constellation-rotated quasi-orthogonal code. Our study shows that the proposed coding scheme offers full rate and outperforms the 1/2-rate orthogonal codes as well as full-rate quasi-orthogonal codes when the signal-to-noise increases. Compared to the constellation-rotated quasi-orthogonal codes (the improved QO scheme), the newly proposed code has the advantage of not expanding the signal constellation at each transmit antenna. The performance of the newly proposed code is comparable to that of the improved QO scheme.     

Combined array processing and space-time coding

The information capacity of wireless communication systems may be increased dramatically by employing multiple transmit and receive antennas. The goal of system design is to exploit this capacity in a practical way. An effective approach to increasing data rate over wireless channels is to employ space-time coding techniques appropriate to multiple transmit antennas. These space-time codes introduce temporal and spatial correlation into signals transmitted from different antennas, so as to provide diversity at the receiver, and coding gain over an uncoded system. For large number of transmit antennas and at high bandwidth efficiencies, the receiver may become too complex whenever correlation across transmit antennas is introduced. This paper dramatically reduces encoding and decoding complexity by partitioning antennas at the transmitter into small groups, and using individual space-time codes, called the component codes, to transmit information from each group of antennas. At the receiver, an individual space-time code is decoded by a novel linear processing technique that suppresses signals transmitted by other groups of antennas by treating them as interference. A simple receiver structure is derived that provides diversity and coding gain over uncoded systems. This combination of array processing at the receiver and coding techniques for multiple transmit antennas can provide reliable and very high data rate communication over narrowband wireless channels. A refinement of this basic structure gives rise to a multilayered space-time architecture that both generalizes and improves upon the layered space-time architecture proposed by Foschini (see Bell Labs Tech. J., vol.1, no.2, 1996)     

Stacked OSTBC: Error Performance and Rate Analysis

It is well known that the Alamouti scheme is the only space-time code from orthogonal designs achieving the capacity of a multiple-input multiple-output (MIMO) wireless communication system with n_T=2 transmit antennas and n_R=1 receive antenna. In this paper, we propose the n-times stacked Alamouti scheme for n_T=2n transmit antennas and show that this scheme achieves the capacity in the case of n_R=1 receive antenna. This result may regarded as an extension of the Alamouti case. For the more general case of more than one receive antenna, we show that if the number of transmit antennas is higher than the number of receive antennas, we achieve a high portion of the capacity with this scheme. Further, we show that the MIMO capacity is at most twice the rate achieved with the proposed scheme for all signal-to-noise ratio (SNR). We derive lower and upper bounds for the rate achieved with this scheme and compare it with upper and lower bounds for the capacity. In addition to the capacity analysis based on the assumption of a coherent channel, we analyze the error rate performance of the stacked orthogonal space-time block code (OSTBC) with the optimal maximum-likelihood (ML) detector and with the suboptimal lattice-reduction (LR)-aided zero-forcing detector. We compare the error rate performance of the stacked OSTBC with spatial multiplexing (SM) and full-diversity achieving schemes. Finally, we illustrate the theoretical results by numerical simulations.     

On the nonexistence of rate-one generalized complex orthogonal designs

Orthogonal space-time block coding proposed recently by Alamouti (1998) and Tarokh et al. (1999) is a promising scheme for information transmission over Rayleigh-fading channels using multiple transmit antennas due to its favorable characteristics of having full transmit diversity and a decoupled maximum-likelihood (ML) decoding algorithm. Tarokh et al. extended the theory of classical orthogonal designs to the theory of generalized, real, or complex, linear processing orthogonal designs and then applied the theory of generalized orthogonal designs to construct space-time block codes (STBC) with the maximum possible diversity order while having a simple decoding algorithm for any given number of transmit and receive antennas. It has been known that the STBC constructed in this way can achieve the maximum possible rate of one for every number of transmit antennas using any arbitrary real constellation and for two transmit antennas using any arbitrary complex constellation. Contrary to this, in this correspondence we prove that there does not exist rate-one STBC from generalized complex linear processing orthogonal designs for more than two transmit antennas using any arbitrary complex constellation.     

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.     

无线光通信中的空时编码研究进展（二）

无线光MIMO技术结合了天线发射分集、接收分集与信道编码分集,可以显著提高信道容量。介绍了笔者在分层空时编码方面的若干研究进展,分析了误码率特性与发射/接收天线数目、检测算法之间的关系,比较了水平分层空时码、螺旋分层空时码、对角分层空时码和垂直分层空时码不同的编码方案,以及不同检测算法对不同的湍流强度的抑制作用。经分析得出:三种分层空时编码性能最好的是对角分层空时编码,其次是螺旋分层空时编码,最后是水平分层空时编码。