基于码本的有限反馈非酉矩阵预编码多用户MIMO系统

该文提出了一种基于码本的有限反馈非酉矩阵预编码下行多用户MIMO系统。该方案根据用户反馈的信道信息SINR在发送端进行调度和预编码来提高系统容量。预编码的码本设计依据格拉斯曼空间装箱原理,并将码本中的向量按其相关性构成非酉矩阵来提高预编码增益和抑制多用户共道干扰。新方案反馈量少、复杂度低,在相同情况下比传统的单用户MIMO系统和基于码本的酉矩阵预编码多用户MIMO系统都具有更好的性能。     

Quantized Principal Component Selection Precoding for Spatial Multiplexing with Limited Feedback

In this paper, for spatial multiplexing with limited feedback, a quantized principal component selection (QPCS) precoding scheme is proposed that achieves comparable capacity to the closed-loop multiple-input multiple-output (MIMO) and furthermore adapts to various fading channel conditions without any additional feedback bits and transmit channel state information (CSI). We propose a systematic design method for a codebook consisting of a finite number of unitary matrices based on a maximizing minimum distance criterion in the one- dimensional angular domain and show that the method outperforms the Grassmannian subspace packing method in various fading channel conditions. The proposed QPCS precoding scheme allows for adjustment of the precoding matrix based on limited feedback information on the principal vectors approximating a MIMO channel in the angular domain according to various channel conditions. Furthermore, for practical implementation of the QPCS precoding scheme, we propose a structured precoder optimization procedure and show that the proposed procedure induces a negligible capacity loss compared with the exhaustive precoder optimization, even with considerably reduced complexity.     

Grassmannian流形上基于高分辨率动态聚焦码本的MIMO信道预测

针对MIMO时变信道下,有限反馈发射预编码存在反馈延迟的问题,提出将多数据流空间复用传输的MIMO信道的主右奇异矩阵的列空间建模于n维复欧氏空间上p维子空间的集合Grassmannian流形Gn,p上,利用Grassmannian流形的测地线对时变信道进行跟踪预测,以补偿反馈延迟对于系统性能的影响。在此基础上,从Grassmannian流形的几何特性入手,针对Grassmannian流形的切空间提出了一种高分辨率动态聚焦的多维切空间码本。计算机仿真表明,Grassmannian流形上基于高分辨率动态聚焦码本的有限反馈预测预编码的系统性能明显优于存在反馈延迟的无记忆有限反馈预编码和采用固定码本的有限反馈预测预编码。      

预编码的反馈方式的仿真

本文主要对预编码的反馈方式进行研究。首先介绍了预编码技术,然后分别对离散傅里叶变换码本反馈法和格拉斯曼码本反馈方式进行介绍和分析。最后在Mat lab上对系统误码率进行仿真,比较不同反馈方式对于预编码性能的影响。格拉斯曼码本反馈法的性能好于离散傅里叶变换码本的性能,但是格拉斯曼码本反馈更复杂。     

Grassmannian precoding MU-MIMO scheme

In this article, a Grassmannian precoding multiuser multiple-input multiple-output （MU-MIMO） scheme for downlink transmission is proposed. The proposed MU-MIMO scheme will perform scheduling and precoding simultaneously at the base station, to obtain both the multiuser diversity gain and the precoding gain, to maximize the system capacity. The precoding method is related to Grassmannian precoding, which extends the point-to-point single-user Grassmannian precoding to point-to-multipoint multiuser Grassmannian precoding. It provides further significant system capacity enhancement than the single user MIMO （SU-MIMO） system and also outperforms the block dia~onalization （BD） algorithm under the same simulation environment.     

What is the value of limited feedback for MIMO channels?

Feedback in a communications system can enable the transmitter to exploit channel conditions and avoid interference. In the case of a multiple-input multiple-output channel, feedback can be used to specify a precoding matrix at the transmitter, which activates the strongest channel modes. In situations where the feedback is severely limited, important issues are how to quantize the information needed at the transmitter and how much improvement in associated performance can be obtained as a function of the amount of feedback available. We give an overview of some recent work in this area. Methods are presented for constructing a set of possible precoding matrices, from which a particular choice can be relayed to the transmitter. Performance results show that even a few bits of feedback can provide performance close to that with full channel knowledge at the transmitter.     

一种OFDM中继系统的有限反馈预编码方法

基于正交频分复用的放大转发协作中继系统,为了减少系统误比特率、增加信道容量和增强实用性,该文提出一种实用的源节点预编码和中继节点预编码的联合优化有限比特反馈的预编码方法。利用3节点构成的两个下行链路,实现两跳协作通信方式;采用SVD分解和QR(orthogonal triangular)分解相结合设计预编码,其中源节点预编码每帧只要一个;优选量化码本,把预编码矩阵量化后反馈到发射端。仿真结果表明,该方案能提高平均和速率、降低误码率和改善中断概率特性,且反馈比特数较少具有更好的实用价值。     

Geodesical codebook design for precoded MIMO systems

We propose a numerical method for finding packings of multiple-input and multiple-output (MIMO) semi-unitary precoding matrices in Grassmannian manifolds with different metrics. The proposed expansion-compression algorithm (ECA) is practical, simple and produces efficient packings without the need for a sophisticated initialization. With chordal distance metric, the algorithm tends to converge into a degenerated point constellation, where two points contain identical as well as orthogonal columns and distance between them cannot increase further along geodesic. Therefore, we alternate between max-min and min-max clustering parts of ECA algorithm, where the latter prevents degenerated constellations. With Fubini-Study distance metric, the algorithm converges to best known packings without extra min-max processing.     

Adaptive precoding and power allocation in distributed antenna systems with limited feedback

This paper introduces the limited feedback precoding into the distributed antenna system and proposes to adapt the predetermined orthogonal space time block codes to the available channel state information at the transmitter. The optimal representation of precoding information, namely the precoder, with least bits therefore becomes the key problem. Inspired by the characteristics of the distributed antenna system, we focus our work on the precoder construction, adaptable in response to the large and small scale fading, such that the symbol error probability is significantly reduced over that of a fixed, non‐adaptive, independent and identically distributed precoder codebook design. Furthermore, a suboptimal power‐loading strategy is presented by minimizing the derived tight upper bound on the average pairwise error probability of the precoded orthogonal space time block codes, which approaches the optimal performance asymptotically without additional channel knowledge other than the available feedback information. We prove that the proposed precoded orthogonal space time transmission scheme can achieve full diversity order. In particular, the robustness of our proposed transmission scheme to channel estimation error and feedback delay is respectively investigated in some detail, and numerical results show that it obviously improves the link reliability and obtains substantial gains even with few bits of feedback in comparison with conventional antenna selection scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Multimode basis selection for spatial multiplexing with limited feedback

Proposed is multimode basis selection in which the active bases are selected at the receiver from the common unitary basis set known at both receiving and transmitting ends, conveyed to the transmitter using limited feedback, and assembled into a precoding matrix at the transmitter. It is shown that the proposed multimode basis selection scheme outperforms both multimode antenna selection and Grassmannian multimode precoding in capacity in correlated fading channels without additional complexity and feedback.     

Grassmannian beamforming for MIMO amplify-and-forward relaying

We consider the problem of beamforming codebook design for limited feedback half-duplex multiple-input multiple output (MIMO) amplify-and-forward (AF) relay system. In the first part of the paper, the direct link between the source and the destination is ignored. Assuming perfect channel state information (CSI), we show that the source and the relay should map their signals to the dominant right singular vectors of the source-relay and relay-destination channels. For the limited feedback scenario, we prove the appropriateness of Grassmannian codebooks as the source and relay beamforming codebooks based on the distributions of the optimal source and relay beamforming vectors. In the second part of the paper, the direct link is considered in the problem model. Assuming perfect CSI, we derive the optimization problem that identifies the optimal source beamforming vector and show that the solution to this problem is uniformly distributed on the unit sphere for independent and identically distributed (i.i.d) Rayleigh channels. For the limited feedback scenario, we justify the appropriateness of Grassmannian codebooks for quantizing the optimal source beamforming vector based on its distribution. Finally, a modified quantization scheme is presented, which introduces a negligible penalty in the system performance but significantly reduces the required number of feedback bits.     

Interpolation Based Unitary Precoding for Spatial Multiplexing MIMO-OFDM With Limited Feedback

Spatial multiplexing with linear precoding is a simple technique for achieving high spectral efficiency in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Linear precoding requires channel state information for each OFDM subcarrier, which can be achieved using feedback. To reduce the amount of feedback, this paper proposes a limited feedback architecture that combines precoder quantization with a special matrix interpolator. In the proposed system, the receiver sends information about a fraction of the precoding matrices to the transmitter and the transmitter reconstructs the precoding matrices for all the subcarriers. A new interpolator is proposed inspired by spherical interpolation that respects the orthogonal columns of the precoding matrices and the performance invariance to right multiplication by a unitary matrix. The interpolator is parameterized by a set of unitary matrices; a construction of a suitable set is briefly described. Simulations illustrate the performance of limited feedback precoding with coding, estimation or prediction error, and time variation for bit error rate (BER), mutual information, and mean squared error (MSE)     

Optimal precoding for orthogonalized spatial multiplexing in closed-loop MIMO systems

In this paper, we propose a new precoding algorithm for orthogonalized spatial multiplexing (OSM) systems over flat-fading multiple-input multiple-output (MIMO) channels. The OSM scheme was recently introduced for closed-loop MIMO systems which allows single symbol decodable maximum likelihood detection. To further improve the performance of the OSM system, we propose a new precoding method by maximizing the minimum Euclidean distance between constellation points in the effective channel. In order to efficiently identify the parameters of a precoder which maximizes the minimum distance, we introduce a partitioning approach. Through analysis, it is shown that one real value parameter and two bits are required for feedback information for precoding in 16-QAM systems. Simulation results demonstrate that our algorithm provides 9 dB and 7.5 dB gains at a bit error rate (BER) of 10^-4 over the conventional OSM systems for 4-QAM and 16-QAM, respectively. We also confirm that the performance of the proposed scheme is the same as that of the optimum closed-loop MIMO systems in terms of the minimum distance. Consequently, our precoding algorithm significantly improves the system performance with a small increase of feedback amount.     

Adaptive bit allocation scheme in multi-cell cooperative block diagonalization systems with delayed and limited feedback

In multi-cell cooperative multi-input multi-output(MIMO) systems,base station(BS) can exchange and utilize channel state information(CSI) of adjacent cell users to manage co-channel interference.Users quantize the CSIs of desired channel and interference channels using finite-rate feedback links,then BS can generate cooperative block diagonalization(BD) precoding matrices using the obtained quantized CSI at transmitter to supress co-channel interference.In this paper,a novel adaptive bit allocation scheme is proposed to minimize the rate loss due to imperfect CSI.We derive the closed-form expression of rate loss caused by both channel delay and limited feedback.Based on the derived rate loss expression,the proposed scheme can adaptively allocate more bits to quantize the better channels with smaller delays and fewer bits to worse channels with larger delays.Simulation results show that the proposed scheme yields higher performance than other allocation schemes.     

Multiple antenna MMSE based downlink precoding with quantized feedback or channel mismatch

In this paper, we consider the downlink of a multiuser wireless communication system with multiple antennas at the base station and users each with a single receive antenna. It is known that when channel state information (CSI) is available at the transmitter a large performance gain can be achieved. In a system employing time-division duplexing (TDD), CSI can be obtained at the base station if there is reciprocity between the forward and reverse channels. CSI can also be conveyed from the users to the base station via a limited-rate feedback channel in a frequency-division duplexing (FDD) system. In any case, channel estimation errors are inevitable due to the presence of background noise in the estimated signal and due to the finite number of feedback bits used in a limited-rate feedback system model. In this paper, we first consider the general case when partial CSI is available at the transmitter. We derive an MMSE based precoding technique that considers channel estimation errors as an integral part of the system design. Using rate-distortion theory and the generalized Lloyd vector quantization algorithm, we then specialize our results for the more practical limited-rate feedback system model. Compared to previously proposed precoding techniques such as channel inversion and regularized channel inversion, it is shown that the proposed precoding technique significantly improves the average bit error rate (BER) in the system. Furthermore, the performance of the proposed technique is investigated in the high signal-tonoise ratio (SNR) regime, and similar to [1], [2], it is shown that the proposed technique suffers from a ceiling effect that asymptotically limits the system performance.     

基于预编码的双路径中继系统信号传输方案研究

针对转发放大(Amplify-and-Forward, AF)模式下的双路径中继网络,为了降低训练序列设计相互约束关系的复杂度,并提升系统误码性能,本文提出了一种基于预编码的信号传输方案。新方案采用一对相互正交的预编码矩阵,分别在两个中继处对信号进行预编码,在目的点右乘相应的解码矩阵将两路叠加信号分离。新方案能够将两路信号完全分离从而使原本需要考虑三处训练序列设计的问题转化为两处,简化了训练序列设计复杂度。由于预编码方案能够在目的点压缩噪声功率,并且避免两路中继信号的互相干扰,单路径误码性能和双路径分集合并误码性能都得到提升。仿真结果验证了新方案的有效性。      

一种多输入多输出系统中有限反馈预编码的自适应跟踪测度

该文提出一种新的适用于无线相关信道中有限反馈预编码多输入多输出系统的预编码矩阵自适应跟踪测度。由于该测度在统计意义下对信道的相关性与预编码矩阵变化的关系具有更优化的描述,所以基于该测度的方案在保持较低反馈信息量的前提下,能够进一步改善预编码系统性能。文中给出优化自适应跟踪测度的理论推导。系统仿真分别针对无线信道的频域相关和时域相关,并结合空间分集和空间复用两类系统结构予以讨论,并验证了理论分析结果。另外,由于该测度方案算法复杂度更低,所以更具工程实用价值。     

Optimized non-unitary linear precoding for orthogonal space-time block codes

This letter proposes a novel optimized non-unitary linear precoding design for orthogonal space-time block codes (OSTBCs). We dig out the transmission potentials by the analysis from eigen-space point of view according to the unique structure of OSTBCs. The proposed precoding form is proved to be theoretically optimized. Compared with the classical unitary Grassmannian codebook design, in the sense of restriction on the time average power of transmit signal, the proposed non-unitary codebook further improves the overall performance of practical systems. The new constraint on codebook size to guarantee full diversity order is given and proved. The advantages of our proposed design are verified in the numerical simulations.     

Joint interference alignment precoding based on the optimization algorithm on the Grassmannian manifold

To solve the interference problem between users of the multiuser MIMO system, we first transform the system sum rate maximization problem into joint optimization of interference signal power and useful signal power. On this basis, we propose a weighted interference alignment objective function, causing the system to obtain a higher sum rate by adjusting the weight with different signal-to-noise ratios. Then, we model the transmit subspace and the interference subspace on the Grassmannian manifold and propose joint interference alignment precoding based on the Grassmannian conjugacy gradient algorithm (GCGA-JIAP algorithm). In contrast to conventional interference alignment algorithms, our proposed algorithm can reduce the computational cost by transforming the constrained optimization of the complex Euclidean space into unconstrained optimization with the degenerate dimension on the Grassmannian manifold. Computer simulation shows that the proposed algorithm improves the convergence of the iterative optimization of the transmitter precoding matrix and the receiver postprocessing matrix and also improves the sum rate performance of the multiuser MIMO interference system.     

Design of reduced complexity feedback precoding for MIMO‐OFDM

Beamforming technique is applied to significantly increase the performance of a MIMO system, if the channel information (CI) of the communication system is available at the transmitter. For the transmitter to obtain the entire CI, however, a considerable reverse‐link bandwidth is required. To save the bandwidth, a limited‐rate closed‐loop system, therefore, uses a predetermined codebook which is derived from the CI. The codebook consists of a finite number of precoders out of which the index of the best one is transmitted from the receiver to the transmitter using only a few bits saving substantial bandwidth. However, the amount of bits that need to be fed back can still be significantly large for MIMO‐OFDM systems when the precoding matrix index (PMI) for each subcarrier should be transmitted. Such per‐subcarrier precoding scheme has high feedback overhead and also incurs huge computational cost to determine the best PMI for each subcarrier. We, therefore, propose a per‐band precoding scheme that precodes a band (group) of subcarriers by only one precoder. More importantly, we develop, for the proposed per‐band scheme, reduced‐complexity precoding selection methods that lead to the design of efficient receivers. The effectiveness of the proposed scheme is investigated through computer simulations. Copyright © 2014 John Wiley & Sons, Ltd.