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.     

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.     

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.     

空时编码OFDM与多维波束形成组合方案

针对MIMO-OFDM系统提出了一种简单灵活的空时分组码与多维特征波束形成组合方案,以充分利用MIMO信道的二阶统计信息。该方案在保证空时编码分集度的同时能最大化系统的编码增益,空时分组码的选取并不受实际发射天线数的限制,因此可以在分集度、编码增益以及系统码率之间进行灵活的折中。理论分析和仿真结果同时表明,当实际发射天线数大于空时码所需天线数时,系统的编码增益随着实际发射天线数的增加大致呈线性增长,发射天线阵列间相关性越强,增长速度越快。     

Simple MMSE Interference Suppression for Real and Rate-1/2 Complex Orthogonal Space-time Block Codes

Orthogonal Space-Time Block Codes (OSTBCs) are known to provide transmit diversity gain with negligible decoding complexity. In this paper, we present a single-stage MMSE multi-user interference suppression technique that exploits the temporal and spatial structure of OSTBCs, leading to simple linear processing. In particular, we show that MMSE-based detection can be implemented for real OSTBCs as well as the derived rate-1/2 complex OSTBCs, using simple linear processing that avoids computationally intensive matrix inversions.     

Capacity Analysis for Transmit Antenna Selection Using Orthogonal Space-Time Block Codes

Antenna selection for multiple-input multiple-output (MIMO) where only a subset of antennas at the transmitter and/or receiver are activated for signal transmission is a practical technique for the realization of full diversity. Despite extensive research, closed-form capacity expressions for MIMO systems employing transmit antenna selection (TAS) and orthogonal space-time block codes (OSTBCs) are not available. We thus derive the exact closed-form capacity expressions when an OSTBC is employed and N transmit antennas out of total L_t antennas are selected for transmission. The expressions are valid for a frequency-flat Rayleigh fading MIMO channel and avoid numerical integration methods     

带内全双工多用户MIMO系统中的用户选择

考虑一种多用户MIMO的传输设计,配置发射天线阵列和接收天线阵列的蜂窝基站可以工作在带内全双工传输模式。在该全双工通信方案中,基站的下行发射信号对基站的上行接收产生显著的干扰,即自干扰。这里,下行预编码处理和上行发射协方差矩阵处理将被依次进行,以简化全双工的设计。其次,为了进一步改善上、下行信道的和速率性能,我们提出一种尝试性的下行用户选择方案,其基本思想是:当某一个下行用户的信道矩阵的范数较小时,关闭该下行用户的数据流。计算机仿真结果表明,在基站下行总发射功率受限时,在低的和中等的下行信噪比区域,用户选择有助于提高下行和速率;在高的上行信噪比区域,简化的用户选择使得上行和速率明显提高。      

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)     

Robust Transmit Antenna Selection with Phase Feedback Over Correlated Fading Channels

A new transmit antenna selection (TAS) scheme with phase feedback for multiple-input multiple-output systems is proposed in this paper. This scheme allows two or more transmit antennas to simultaneously use one radio frequency chain. By grouping the transmit antennas according to their similarities in instantaneous channel coefficients into two subsets and treating each subset as a single antenna, both hardware complexity reduction and antenna array gain can be achieved. Compared with the transmit antenna selection combined with space-time block code (TAS/STBC) scheme, the proposed TAS scheme provides excellent robustness, in terms of symbol error rate performance, against spatially correlated fading channels. Moreover, the proposed TAS scheme need not use STBC encoder and decoder which used in the TAS/STBC schemes. Therefore, the proposed TAS scheme is simpler than the TAS/STBC schemes in practical hardware implementation.     

Performance analysis of combined transmit-SC/receive-MRC

The average bit-error rate of transmit antenna selection combined with receive maximum-ratio combining is computed as a function of the transmit antenna update rate when using binary phase-shift keying in flat Rayleigh fading channels. This scheme achieves an order of diversity equal to the product of the number of transmit and receive antennas. Therefore, it can gain significant diversity benefits over traditional receive diversity schemes by distributing the antennas over the transmit and receive side     

Peroformance analysis of decode-and-forward MIMO relay channels with OSTBCs

Performance analysis is presented for multiple-input multiple-output(MIMO) relay channels employing transmit antenna diversity with orthogonal space-time block codes(OSTBCs),where the source and the destination are equipped with Ns and Nd antennas,and communicate with each other with the help of a multiple-antenna relay operating in decode-and-forward(DF) mode.Over independent,not necessarily identical Rayleigh fading channels,exact closed-form symbol error rate(SER) expressions are derived for various digi...     

On the Blind Identifiability of Orthogonal Space–Time Block Codes From Second-Order Statistics

In this paper, the conditions for blind identifiability from second-order statistics (SOS) of multiple-input multiple-output (MIMO) channels under orthogonal space-time block coded (OSTBC) transmissions are studied. The main contribution of the paper consists in the proof that, assuming more than one receive antenna, any OSTBC with a transmission rate higher than a given threshold, which is inversely proportional to the number of transmit antennas, permits the blind identification of the MIMO channel from SOS. Additionally, it has been proven that any real OSTBC with an odd number of transmit antennas is identifiable, and that any OSTBC transmitting an odd number of real symbols permits the blind identification of the MIMO channel regardless of the number of receive antennas, which extends previous identifiability results and suggests that any nonidentifiable OSTBC can be made identifiable by slightly reducing its code rate. The implications of these theoretical results include the explanation of previous simulation examples and, from a practical point of view, they show that the only nonidentifiable OSTBCs with practical interest are the Alamouti codes and the real square orthogonal design with four transmit antennas. Simulation examples and further discussion are also provided.     

Transmitter optimization and performance gain for multiple-input single-output systems with finite-rate direction feedback

Consider finite-rate channel-direction feedback in a system with multiple transmit but single receive antennas. We investigate how the transmitter should be optimized for symbol error rate with finite-rate feedback, and how the symbol error rate and outage probability improve as a function of the number of feedback bits. It is found that when the number of feedback directions is equal to or larger than the number of transmit antennas, transmit beamforming is optimal. Otherwise, the antennas should be divided into two groups, where antenna selection is used in the first group to choose the strongest channel, and equal power allocation is used in the second group. At high signal to noise ratio (SNR), the optimal power allocation between these two antenna groups is proportional to the number of antennas in each group. Based on high SNR analysis, we quantify the power gain of each feedback bit. It is shown that the incremental gain increases initially and diminishes when the number of feedback bits surpasses the logarithm (base 2) of the number of transmit antennas.     

On the Design of Space–Time Trellis Codes for Transmit-Correlated Fading Channels

The analysis and design of space-time codes for correlated fading channels when the diversity gain is large enough is considered. We derive a simple form for a distance metric that characterizes the code performance in the presence of transmit correlation, and propose some design criteria to build good space-time trellis codes (STTCs) for correlated channels. For the case of two transmit antennas, we show that in strongly correlated channels, performance is governed by the constellation that results from the sum of the constellations associated with the transmit antennas. This suggests the use of new constellations to design better codes for correlated channels. The design criteria are then extended to any number of transmit antennas. Based on these criteria, we derive new STTCs for two and three transmit antennas that perform much better in correlated channels than the STTC optimized for the independent and identically distributed case. We also consider set partitioning applied to the sum constellation as a simple technique to design good codes for correlated channels. The codes derived show performance close to the codes found by an exhaustive search. Finally, we consider antenna selection as an alternative to build good codes for more than two antennas in fading-correlated scenarios     

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     

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     

Error probability performance for W-CDMA systems with multiple transmit and receive antennas in correlated Nakagami fading channels

The bit error rate (BER) performance of a two-dimensional (2-D) RAKE receiver, in combination with transmit diversity on the downlink of a wide-band CDMA (W-CDMA) system, is presented. The analyses assume correlated fading between receive antenna array elements, and an arbitrary number of independent but nonidentical resolvable multipaths combined by the RAKE receiver in the general Nakagami-m (1960) fading channel framework. The impact of the array configuration (e.g., the number of transmit antennas and receive antennas, the antenna element separation) and the operating environment parameters (such as the fading severity, angular spread and path delay profile) on the overall space-path diversity gain can be directly evaluated. In addition, the exact pairwise error probability of a convolutional coded system is obtained, and the coding gain of a space-path diversity receiver is quantified.     

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     

On the performance of using multiple transmit and receive antennas in pulse-based ultrawideband systems

This paper presents an analytical expression for the signal-to-noise ratio (SNR) of the pulse position modulated (PPM) signal in an ultrawideband (UWB) channel with multiple transmit and receive antennas. A generalized fading channel model that can capture the cluster property and the highly dense multipath effect of the UWB channel is considered. Through simulations, it is demonstrated that the derived analytical model can accurately estimate the mean and variance properties of the pulse-based UWB signals in a frequency-selective fading channel. Furthermore, the authors investigate to what extent the performance of the PPM-based UWB system can be further enhanced by exploiting the advantage of multiple transmit antennas or receive antennas. Numerical results show that using multiple transmit antennas in the UWB channel can improve the system performance in the manner of reducing signal variations. However, because of already possessing rich diversity inherently in the UWB channel, using multiple transmit antennas does not provide diversity gain in the strict sense [i.e., improving the slope of bit error rate (BER) versus SNR] but can possibly reduce the required fingers of the RAKE receiver for the UWB channel. Furthermore, because multiple receive antennas can provide higher antenna array combining gain, the multiple receive antennas technique can be used to improve the coverage performance for the UWB system, which is crucial for a UWB system due to the low transmission power operation.     

Performance Analysis of OSTBC Transmission in Amplify-and-Forward Cooperative Relay Networks

A performance analysis is presented for amplify-and-forward (AF) cooperative relay networks employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where multiple antennas are equipped at the transmitter. We develop a symbol-error-rate (SER) and outage performance analysis for OSTBC transmissions with and without cooperative diversity over flat Rayleigh fading channels. We first derive exact probability density functions (pdf's) and cumulative distribution functions (cdf's) for the system SNR without direct transmission with an arbitrary number of transmit antennas and then present the exact closed-form SER and outage probability expressions. Next, we derive the moment-generating function (MGF) for the overall system SNR with direct transmission and present the exact SER and outage probability with joint transmit antenna diversity and cooperative diversity. The theoretical analysis is validated by simulations, which indicate an exact match between them. The results also show how the transmit antenna diversity and the cooperative diversity affect the overall system performance.