On the performance of orthogonal space-time block coding with quantized feedback

Orthogonal space-time block coding (OSTBC) is a recent technique that provides maximal diversity gains on a space-time channel at a very modest computational cost. Recently, several authors have suggested to improve the performance of an OSTBC system by using a feedback of channel state information from the receiver to the transmitter. In this letter, we study the performance of an OSTBC system with quantized low-rate feedback. We establish conditions under which the system achieves full diversity and we also analyze the performance of a method that employs a feedback consisting of only one information bit.     

Optimal transmitter eigen-beamforming and space-time block coding based on channel mean feedback

Optimal transmitter designs obeying the water-filling principle are well-documented; they are widely applied when the propagation channel is deterministically known and regularly updated at the transmitter. Because channel state information is impossible to be known perfectly at the transmitter in practical wireless systems, we design, in this paper, an optimal multiantenna transmitter based on the knowledge of mean values of the underlying channels. Our optimal transmitter design turns out to be an eigen-beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the correlation matrix of the estimated channel at the transmitter and with proper power loading across beams. The optimality pertains to minimizing an upper bound on the symbol error rate, which leads to better performance than maximizing the expected signal-to-noise ratio (SNR) at the receiver. Coupled with orthogonal space-time block codes, two-directional eigen-beamforming emerges as a more attractive choice than conventional one-directional beamforming with uniformly improved performance, without rate reduction, and without essential increase in complexity. With multiple receive antennas and reasonably good feedback quality, the two-directional eigen-beamformer is also capable of achieving the best possible performance in a large range of transmit-power-to-noise ratios, without a rate penalty.     

Quantized feedback information in orthogonal space-time block coding

This work considers how the presence of quantized channel information obtained from a feedback link may be utilized for determining a transmit weighting matrix that improves the performance of a predetermined orthogonal space-time block (OSTB) code. To reduce the effects of feedback delay, quantization errors and feedback channel bit errors, methods based on vector quantization for noisy channels are used in the design of the feedback link. The resulting transmission scheme and feedback link take the imperfect nature of the channel information into account while combining the benefits of conventional beamforming with those provided by OSTB coding.     

级联信道编码的多幅值差分空时分组码方案及性能

通过引入多电平振幅调制和变换矩阵方法,提出了一种基于多幅值调制的差分正交空时分组码方案。该方案可克服通常基于PSK调制的单幅值差分空时码(DSTC,differential space-time coding)在高频带利用率下由于星座符号间的最小距离减小所带来的性能下降,而且可用于编码矩阵是非方阵情况,避免了已有方案仅适合于方阵码矩阵。与已有单幅值DSTC相比,所提方案有着高的频谱效率和编码增益,且可实现线性译码复杂度和高的码率。此外,还给出了所提方案级联信道编码时的性能。仿真结果表明所提方案与已有单幅值DSTC方案相比,有着较低的误比特率,而且信道编码后的所提多幅值DSTC也好于相应的单幅值DSTC。     

Frequency domain decision feedback equalizer for time-reversal space-time block coding

In this paper,a frequency domain decision feedback equalizer is proposed for single carrier transmission with time-reversal space-time block coding (TR-STBC).It is shown that the diagonal decision feed...     

基于相关函数的空时块编码系统的信道估计

提出了空时块编码（STBC）系统中基于相关函数的信道估计的方法。当输入符号向量的各个元素互不相关时，接收信号的相关函数有特定的结构，信道矩阵可以从接收信号的相关矩阵的特征向量中得到，信道估计结果和真实值仅相差一个常数。研究还发现当发送信号的相关函数满足特定的条件时，可以直接从接收信号的协方差得到信道参数，而不需要矩阵分解或者求逆运算。     

Distributed space-time block coding

In this paper, a new class of distributed space-time block codes (DSTBCs) is introduced. These DSTBCs are designed for wireless networks which have a large set of single-antenna relay nodes /spl Nscr/, but at any given time only a small, a priori unknown subset of nodes S/spl sube//spl Nscr/ can be active. In the proposed scheme, the signal transmitted by an active relay node is the product of an information-carrying code matrix and a unique node signature vector of length N/sub c/. It is shown that existing STBCs designed for N/sub c/2 co-located antennas are favorable choices for the code matrix, guaranteeing a diversity order of d=min{N/sub S/,N/sub c/} if N/sub S/ nodes are active. For the most interesting case, N/sub S//spl ges/N/sub c/, the performance loss entailed by the distributed implementation is analytically characterized. Furthermore, efficient methods for the optimization of the set of signature vectors are provided. Depending on the chosen design, the proposed DSTBCs allow for low-complexity coherent, differential, and noncoherent detection, respectively. Possible applications include ad hoc and sensor networks employing decode-and-forward relaying.     

Optimal transmitter eigen-beamforming and space-time block coding based on channel correlations

Optimal transmitter designs obeying the water-filling principle are well-documented, and widely applied, when the propagation channel is deterministically known and regularly updated at the transmitter. Because channel state information (CSI) may be costly or impossible to acquire in rapidly varying wireless environments, we develop in this paper statistical water-filling approaches for stationary random fading channels. These approaches require only knowledge of the channel correlations that do not necessitate frequent updates, and can be easily acquired. Applied to a multiple transmit-antenna paradigm, our optimal transmitter design turns out to be an eigen-beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the channel's correlation matrix, and with proper power loading across the beams. The optimality pertains to minimizing a tight bound on the symbol error rate. The resulting loaded eigen-beamforming outperforms not only the equal-power allocation across all antennas, but also the conventional beamformer that transmits the available power along the strongest direction. Coupled with orthogonal space-time block codes, two-dimensional (2-D) eigen-beamforming emerges as a more attractive choice than conventional one-dimensional (1-D) beamforming with uniformly better performance, without rate reduction, and without complexity increase.     

Combined beamforming with space-time block coding using double antenna array group

The performance of the combined beamforming of space-time block coding according to the number of antenna array groups has been analysed. CB/spl I.bar/STBC/spl I.bar/single array and CB/spl I.bar/STBC/spl I.bar/double array were compared under the condition of DOA and SNR. CB/spl I.bar/STBC/spl I.bar/double array is shown to have a stable performance independent of DOA and angular spread.     

交织的空时分组码级联不对称网格编码调制方法

根据交织的空时分组码级联TCM编码设计标准,提出了一种空时分组码级联不对称网格编码调制(A-TCM)的优化设计方案,并得到了在空时分组码级联不对称8PSK调制的TCM情况下最优的星座图旋转角度.仿真和分析结果表明,在相同的频谱效益和译码复杂度的情况下,相比传统空时分组码级联TCM的方法,新方法可进一步提高系统性能.     

Comments on "exact error performance of square orthogonal space-time block coding with channel estimation"

In a recent paper [1], Garg et al. present an expression for the exact decoding error probability (DEP) of square orthogonal space-time block codes (OSTBCs) with imperfect channel estimation. We show that their DEP expression is only asymptotically correct and point out how to obtain the exact result for arbitrary signal-to-noise ratio.     

Diversity performance of precoded orthogonal space-time block codes using limited feedback

Orthogonal space-time block codes (OSTBCs) are simple space-time codes that can be used for open-loop transmit diversity systems. OSTBCs, however, can only be designed for certain numbers of transmit antennas. Channel-dependent linear precoders have been proposed to overcome this deficiency, but it is not clear what conditions the precoder design must satisfy to guarantee full diversity order. In this letter, we show necessary and sufficient conditions for linear precoded OSTBCs to provide full diversity order. We show that limited feedback precoding can achieve full diversity order using fewer bits than limited feedback beamforming. We also present a simplified version of antenna subset selection for OSTBCs that can provide full diversity order with low complexity and only a small amount of feedback.     

A new differential space-time block coding scheme

We present a new differential space-time block code (DSTBC). The scheme can be represented by a trellis and decoded using the Viterbi algorithm. It provides a differential coding gain of 1 dB due to redundancy introduced in the differential encoding and it is only 2 dB away from the corresponding coherent space-time block code (STBC).     

Orthogonal space-time block coded rate-adaptive modulation with outdated feedback

Abstract-Channel state information (CSI) at the transmitter can be used to adapt transmission rate or antenna gains in multi-antenna systems. We propose a rate-adaptive M-QAM scheme equipped with orthogonal space-time block coding with simple outdated, finite-rate feedback over independent flat fading channels. We obtain closed-form expressions for the average BER and throughput for our scheme, and analyze the effects of possibly delayed feedback on the performance gains. We derive optimal switching thresholds maximizing the average throughput under average and outage BER constraints with outdated feedback. Our numerical results illustrate the immunity of our optimal thresholds to delayed feedback.     

Combining beamforming and orthogonal space-time block coding

Multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication. Efficient space-time codes have been developed that utilize a large portion of the available capacity. These codes are designed under the assumption that the transmitter has no knowledge about the channel. In this work, on the other hand, we consider the case when the transmitter has partial, but not perfect, knowledge about the channel and how to improve a predetermined code so that this fact is taken into account. A performance criterion is derived for a frequency-nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code. The resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods. In addition, a particularly efficient solution method is developed for the special case of independently fading channel coefficients. The proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space-time block coding. Simulation results for a narrow-band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge     

Low-rate channel coding with complex-valued block codes

This paper addresses aspects of channel coding in orthogonal frequency-division multiplexing-code-division multiple access (OFDM-CDMA) uplink systems where each user occupies a bandwidth much larger than the information bit rate. This inherent bandwidth expansion allows the application of powerful low-rate codes under the constraint of low decoding costs. Three different coding strategies are considered: the combination of convolutional and repetition codes, the code-spread system consisting of one single very low-rate convolutional code and a serial concatenation of convolutional, Walsh-Hadamard and repetition code. The latter scheme is improved by combining the Walsh-Hadamard codes with an additional M-phase-shift keying modulation resulting in complex-valued Walsh-Hadamard codes (CWCs). Analytical performance evaluations will be given for these codes for the first time. The application of CWCs as inner codes in a serial code concatenation is also addressed. We derive a symbol-by-symbol maximum a posteriori decoding algorithm in the complex signal space in order to enable iterative decoding for the entire code. A comprehensive performance analysis by simulation of all the proposed coding schemes shows that the Walsh-Hadamard-based schemes are the best choice for low-to-medium system load. Note that even for fully loaded OFDM-CDMA systems, the concatenation with an inner complex-valued Walsh-Hadamard code leads to a bit-error rate less than 10/sup -5/ for an E/sub b//N/sub 0/ of about 6 dB.     

Power allocation for multi-antenna systems with space-time block coding in the presence of estimation error and delayed feedback

Based on imperfect channel state information with channel estimation error at the receiver and delayed feedback at the transmitter, a suboptimal power allocation (PA) scheme to minimize bit error rate (BER) under a power constraint is developed for beamforming multi-antenna systems with space-time block coding. The proposed scheme is based on a so-called compressed signal-to-noise ratio criterion, where a single compressed factor is utilized, and it can be used to generalize some existing schemes by setting the compressed factor to different forms. A closed-form compressed factor is derived to minimize the BER, and the resultant close-form expression of power allocation is attained. This closed-form expression is computational efficient and can obtain the BER performance close to the existing optimal approach which requires numerical search. Simulation results show that the proposed scheme can provide BER lower than the equal power allocation scheme. However, due to the impact of both estimation error and delayed feedback, it has performance degradation when compared to the PA scheme with estimation error or delayed feedback only.     

Unit-rate complex orthogonal space-time block code concatenated with turbo coding

Space-Time Block （STB） code has been an effective transmit diversity technique for combating fading due to its orthogonal design, simple decoding and high diversity gains. In this paper, a unit-rate complex orthogonal STB code for multiple antennas in Time Division Duplex （TDD） mode is proposed. Meanwhile, Turbo Coding （TC） is employed to improve the performance of proposed STB code further by utilizing its good ability to combat the burst error of fading channel. Compared with full-diversity multiple antennas STB codes, the proposed code can implement unit rate and partial diversity; and it has much smaller computational complexity under the same system throughput. Moreover, the application of TC can effectively make up for the performance loss due to partial diversity. Simulation results show that on the condition of same system throughput and concatenation of TC, the proposed code has lower Bit Error Rate （BER） than those full-diversity codes.     

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.     

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