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)     

A Simple Space-Time-Frequency Block Code Scheme for Four Transmit Antennas

It is well known that the full rate and full diversity complex space-time block code (STBC) is not existed for four transmit antennas. In this letter, we propose a simple quasi-orthogonal space-time-frequency block code (QO-STFBC) scheme with four transmit antennas and n _R receive antennas, where every two transmit antennas constitute one group and each group transmits signals over different subcarriers. The receiver can separate the received signals from each group via odd/even index FFT operation. After recombining the separated received signals with received antennas, an equivalent half rate orthogonal STFBC (O-STFBC) can be used for decoding. Thus, the full rate and full diversity are achieved at the transmitter and receiver, respectively. Simulation result shows that the proposed QO-STFBC scheme has better performance than the other schemes, in rate 2 layered Alamouti scheme is about 4 dB, full rate QO-STBC scheme is about 5 dB and half rate O-STBC scheme is about 7 dB at 10^?3 BER for the transmission of 2 bits/s/Hz.     

Antenna selection for unitary space-time modulation

This correspondence studies receive antenna selection (AS) for multiple-antenna systems that employ unitary space-time (ST) signals, where the channel state information (CSI) is known neither at the transmitter nor at the receiver. Without CSI at the receiver, we perform AS only at the receiver and the selection is based on a maximum-norm criterion, i.e., a subset of receive antennas that have the largest received signal power is chosen. Using a Chernoff bound approach, we present theoretical performance analysis based on the pairwise error probability (PEP) and quantify the asymptotic performance at high signal-to-noise ratio (SNR) by giving the diversity and coding gain expressions. We prove that with no CSI at the receiver, the diversity gain with AS is preserved for unitary ST codes with full spatial diversity, the same as the case with known CSI. As a concrete example, for differential unitary ST modulation with M=2 transmit antennas and N=2 receive antennas, we have devised new excellent-performing parametric codes based on the derived PEP bound. The new codes, which are specifically designed for differential AS systems, outperform known differential codes when AS is employed. Corroborating simulations validate our analysis and code design.     

Antenna selection for multiple-antenna transmission systems: performance analysis and code construction

This correspondence studies antenna selection for wireless communications systems that employ multiple transmit and receive antennas. We assume that (1) the channel is characterized by quasi-static Rayleigh flat fading, and the subchannels fade independently, (2) the channel state information (CSI) is exactly known at the receiver, (3) the selection is available only at the receiver, and it is based on the instantaneous signal-to-noise ratio (SNR) at each receive antenna, and (4) space-time codes are used at the transmitter. We analyze the performance of such systems by deriving explicit upper bounds on the pairwise error probability (PEP). This performance analysis shows that (1) by selecting the set of antennas that observe the largest instantaneous SNR, one can achieve the same diversity gain as the one obtained by using all the receive antennas, provided that the underlying space-time code has full spatial diversity, and (2) in the case of rank-deficient space-time codes, the diversity gain may be dramatically reduced when antenna selection is used. However, we emphasize that in both cases the coding gain is reduced with antenna selection compared to the full complexity system. Based on the upper bounds derived, we describe code design principles suitable for antenna selection. Specifically, for systems with two transmit antennas, we design space-time codes that perform better than the known ones when antenna selection is employed. Finally, we present numerical examples and simulation results that validate our analysis and code design principles.     

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.     

一族满分集度酉空时分组码

对于接收端和发送端均不具备信道状态信息的MIMO系统,本文将Cayley变换与对角块正交空时分组码结合,提出了一种新的酉空时分组码构造方法。新构造的空时分组码适用于任意发送天线数为偶数的MIMO系统,能提供满发送分集度和1.5符号/信道利用的信息传输率,并可采用球检测法等低计算复杂度检测算法得到准最优的检测结果。     

Existence and construction of noncoherent unitary space-time codes

We consider transmission using N transmit and reception using M receive antennas in a wireless environment assuming that neither the transmitter nor the receiver knows the channel coefficients. For the scenario that the transmission employs noncoherent T /spl times/ N unitary space-time codes and for a block-fading channel model where the channel is static during T channel uses and varies from T channel uses to the other, we establish the bound r /spl les/ min(T-N, N) on the diversity advantage rM provided by the code. In order to show that the requirement r /spl les/ min(T-N, N) cannot be relaxed, for any given R, N, T, and r /spl les/ min(T-N, N), we then construct unitary T /spl times/ N space-time codes of rate R that guarantee diversity advantage rM. Two constructions are given that are also amenable to simple encoding and noncoherent maximum-likelihood (ML) decoding algorithms.     

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     

一种未知信道下的发射分集差分检测新方法

本文提出一种收发端均不知道信道状态信息情况下发射分集差分检测新方法。该方法将发射天线分组,对每组进行独立的差分空时分组编码以降低编码复杂度,并对每组天线信号进行正交扩频,以便接收端分离各组天线信号实现解码。这种方法不仅编译码简单、编码速率高,而且仍然保持了差分空时分组码的发射端和接收端不需要知道状态信息的优点,同时由于引入了正交的扩频码,系统可获得扩频增益。     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.     

一种天线分集的多载波CDMA上行链路方案

多载波系统能克服多径信道频率选择性的影响，而应用多天线发射和接收能获得分集增益。本文提出了一种两天线发、多天线收的多载波CDMA上行链路系统方案。在发射端，空时块码被用来进行发射分集。对于多载波CDMA上行链路系统，不同的用户的信号经历了不同的多径衰落，信号间的正交性不再能够保持。本文提出了一种接收机方案，并讨论了几种联合检测方法来恢复所有用户在两个编码时刻发送的信息符号，并给出计算机仿真结果。     

Extending orthogonal block codes with partial feedback

During the last few years a number of space-time block codes have been proposed for use in multiple transmit antennas systems. We propose a method to extend any space-time code constructed for m transmit antennas to m p transmit antennas through group-coherent codes (GCCs). GCCs make use of very limited feedback from the receiver (as low as 1 bit). In particular the scheme can be used to extend any orthogonal code (e.g., Alamouti code) to more than two antennas while preserving low decoding complexity, full diversity benefits, and full data rate.     

Array Processing for Multi-User Multi-Antenna Interference Channels Using Precoders

In this paper, we investigate how to send space-time codes with full diversity and low decoding complexity for interference channels using precoders. We assume that we have two transmitters and two receivers. Each transmitter sends codewords to respective receiver at the same time. We propose an orthogonal transmission scheme that combines space-time codes and array processing to achieve low-complexity decoding and full diversity for transmitted signals. To our best knowledge, this is the first scheme which can achieve low-complexity decoding and full diversity for any transmitted codeword in interference channel when all the users transmit at the same time. Simulation results validate our theoretical analysis.     

Rate-one space-time block codes with full diversity

Orthogonal space-time block codes provide full diversity, and maximum-likelihood (ML) decoding for orthogonal codes can be realized on a symbol-by-symbol basis. It has been shown that rate-one complex orthogonal codes do not exist for systems with more than two transmit antennas. For a general system with N transmit and M receive antennas, it is very desirable to design rate-one complex codes with full diversity. In this letter, we provide a systematic method of designing rate-one codes (real or complex) for a general multiple-input multiple-output system. Full diversity of these codes is then achieved by constellation rotation. A generalized, reduced-complexity decoding method for rate-one codes is also provided.     

Impact of spatial correlation on the performance of orthogonal space-time block codes

We analyze the impact of transmitter and receiver spatial correlation on the performance of a multiple-input multiple-output (MIMO) system which applies an orthogonal space-time block code with no channel state information at the transmitter and perfect channel state information at the receiver. We derive a general formula for the bit error rate of a MIMO system with arbitrary number of transmit and receive antennas as a function of the correlation at the transmitter and the receiver. We prove that the diversity advantage is given by M/spl middot/N if M is the rank of the transmit correlation matrix and N the rank of the receive correlation matrix, respectively.     

Performance bounds for space-time block codes with receive antenna selection

In this correspondence, we present a comprehensive performance analysis of orthogonal space-time block codes (STBCs) with receive antenna selection. For a given number of receive antennas M, we assume that the receiver uses the best L of the available M antennas, where, typically, L/spl les/M. The selected antennas are those that maximize the instantaneous received signal-to-noise ratio (SNR). We derive explicit upper bounds on the bit-error rate (BER) performance of the above system for any M and L, and for any number of transmit antennas. We show that the diversity order, with antenna selection, is maintained as that of the full complexity system, whereas the deterioration in SNR is upper-bounded by 10log/sub 10/(M/L) decibels. Furthermore, we derive a tighter upper bound for the BER performance for any N and M when L=1, and derive an expression for the exact BER performance for the Alamouti scheme when L=1. We also present simulation results that validate our analysis.     

A transmitter diversity scheme for wideband CDMA systems based onspace-time spreading

We present a transmit diversity technique for the downlink of (wideband) direct-sequence (DS) code division multiple access (CDMA) systems. The technique, called space-time spreading (STS), improves the downlink performance by using a small number of antenna elements at the base and one or more antennas at the handset, in conjunction with a novel spreading scheme that is inspired by space-time codes. It spreads each signal in a balanced way over the transmitter antenna elements to provide maximal path diversity at the receiver. In doing so, no extra spreading codes, transmit power or channel information are required at the transmitter and only minimal extra hardware complexity at both sides of the link. Both our analysis and simulation results show significant performance gains over conventional single-antenna systems and other open-loop transmit diversity techniques. Our approach is a practical way to increase the bit rate and/or improve the quality and range in the downlink of either mobile or fixed CDMA systems. A STS-based proposal for the case of two transmitter and single-receiver antennas has been accepted and will be included as an optional diversity mode in release A of the IS-2000 wideband CDMA standard     

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.     

Smart versus dumb antennas-capacities and FEC performance

We compare two approaches to use multiple transmit antennas in an FEC coded wireless system: smart antennas use an antenna array to direct a beam in the direction of the dominant transmission path in order to obtain an antenna gain. Another approach is to use multiple transmit antennas for diversity using space-time block codes. Since no knowledge of the channel is required at the transmitter we denote this approach as dumb antennas. Using equivalent single-input channel models we compare smart and dumb antennas in terms of the BER performance and channel capacity and discuss under which conditions it is preferable to use multiple transmit antennas for transmit diversity or for beamforming     

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.