Interpolation based transmit beamforming for MIMO-OFDM with limited feedback

Transmit beamforming and receive combining are simple methods for exploiting spatial diversity in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system. Optimal beamforming requires channel state information in the form of the beamforming vectors for each OFDM subcarrier. This paper proposes a limited feedback architecture that combines beamforming vector quantization and smart vector interpolation. In the proposed system, the receiver sends a fraction of information about the optimal beamforming vectors to the transmitter and the transmitter computes the beamforming vectors for all subcarriers through interpolation. A new spherical interpolator is developed that exploits parameters for phase rotation to satisfy the phase invariance and unit norm properties of the transmitted beamforming vectors. The beamforming vectors and phase parameters are quantized at the receiver and the quantized information is provided to the transmitter. The proposed quantization system provides only a moderate increase in complexity versus over comparable approaches. Numerical simulations show that the proposed scheme performs better than existing diversity techniques with the same feedback data rate.     

Performance analysis of scheduled transmit beamforming systems under non-identically delayed feedback channels

Wireless Networks - In this paper, we investigate the performance analysis of a scheduled transmit beamforming system under non-identically delayed feedback channels. This paper derives the exact...     

Analytical performance evaluation of downlink beamforming with power control by transmit power limited channel inversion

We investigate the transmission performance of a downlink BPSK transmission system which uses beamforming combined with cross-polarised antenna arrays and power control in a Rayleigh fading environment to fulfil QoS requirements of real time services. A power control method termed “power control by transmit power limited channel inversion” is applied in the system. Power limitation in the downlink and the effect on the bit error rate performance is especially interesting for mobile stations at the cell borders of a cellular communication system. For this non-linear transmit model we derive analytical formulas for the average transmit power and the bit error rate performance. The exact validity of the results is verified by Monte-Carlo simulations. We also show the interaction of power control and beamforming, and the dependency of the gain in transmit power from the SNR, an effect that is not visible without transmit power limited power control.     

A performance analysis framework for limited feedback beamforming in correlated fading

Limited or finite rate, feedback is an efficient way to implement beamforming in multiple antenna systems using frequency division duplexing. Unfortunately, closed-form performance analysis of limited feedback beamforming has not been investigated. This paper provides an analytical framework for the correlated limited feedback beamforming problem by treating selection of the beamforming vector from the codebook as a multibranch selection problem.     

中继辅助MIMO系统中基于有限反馈的分布式波束成形

对协作式中继辅助的多输入多输出通信系统中基于有限反馈的联合波束成形问题进行了研究.首先推导了接收信噪比的下界,并基于该下界建立联合波束成形的数学模型.其次推导了分布式波束成形的最优方案.最后针对该最优方案,设计了一个迭代算法,优化得到分布式波束成形码本,从而分布式中继站的波束成形可基于码本序号的有限反馈来进行.实验结果仿真表明,所设计的联合波束成形码本在反馈开销很小的情况下获得明显的性能增益.     

Coordinated beamforming with limited feedback in the MIMO broadcast channel

In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multiple-input multiple-output (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which iterative computation is required to design the beamformers, we derive specific formulations for the transmit beamformers for two active users via a power iteration and a generalized eigen analysis. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the structure of the algorithm to avoid full channel quantization. The feedback overhead of the proposed algorithm is independent of the number of receive antennas. Monte Carlo simulations are used to evaluate the bit error rate and the sum rate performances of the proposed algorithm. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.     

On the performance of random vector quantization limited feedback beamforming in a MISO system

In multiple antenna wireless systems, beamforming is a simple technique for guarding against the negative effects of fading. Unfortunately, beamforming requires the transmitter to have knowledge of the forward-link channel which is often not available a priori. One way of overcoming this problem is to design the beamforming vector using a limited number of feedback bits sent from the receiver to the transmitter. In limited feedback beamforming, the beamforming vector is restricted to lie in a codebook that is known to both the transmitter and receiver. Random vector quantization (RVQ) is a simple approach to codebook design that generates the vectors independently from a uniform distribution on the complex unit sphere. This correspondence presents performance analysis results for RVQ limited feedback beamforming     

Performance analysis of OFDM system with transmit antenna selection using delayed feedback

We consider orthogonal frequency division multiplexing (OFDM) in a multiple input single output (MISO) system. In the presence of spatially uncorrelated time-varying frequency selective channel, we use subcarrier by subcarrier antenna selection using delayed feedback. We derive closed-form expressions for the pdf of the received SNR and BER for MQAM constellation. The expressions have been obtained as a function of the correlation (ρ) between perfect channel state information (CSI) and delayed CSI, where 0 ≤ ρ ≤ 1. We have verified our analytical expressions by comparing them with simulation results. We have also reduced the BER expression for some special cases and compared them with the results available in the literature. We conclude that the diversity gain of the considered system is reduced to one for ρ < 1, i.e. not having perfect antenna selection for each subcarrier. However, we get some coding gain compared to single input single output system, the coding gain reduces with decreasing the correlation.     

Analysis of transmit beamforming performance on multiple-transmit binary ZCZ waveforms

The Transmit BeamForming (TBF) technology, applied in a multiple-transmit radar system, is studied in this paper, where multiple elements of antenna array transmit binary Zero Correlation Zones Orthogonal Signals (ZCZ-OS) independently. For each Direction Of Arrival (DOA) with respect to the transmitting array, the analysis on the gain and sidelobe level of TBF output is presented. This paper focuses on the range sidelobes performance within the main beam (in angle domain). For the normal direction, due to the inherent phase property of ZCZ-OS, the TBF output has part zero sidelobes area, of which the distribution is discussed. For the other directions, a systematic search algorithm to optimize the transmission order of signals is proposed for an optimal relationship chart of DOA and transmission order. The range sidelobe performance within the main beam can be improved as the optimal transmission order is adopted.     

MIMO relay wireless networks with scheduling and transmit beamforming

In this paper, we investigate the performance of a multiuser wireless relay network with each of its nodes equipped with N antennas and transmit beamforming at its source and relay, where multiuser diversity (MD) is exploited to further improve the system performance. In the first part of this paper, by deriving the approximate error performance expression for a single‐relay MD system without the direct link, we obtain the maximum diversity order achievable by the CSI‐assisted amplify‐and‐forward (CAF) protocol. Then, by taking the direct link into consideration, we propose a sub‐optimal transmit beamforming scheme and show the performance loss is very small. Copyright © 2010 John Wiley & Sons, Ltd.     

基于信道相关统计及有限反馈的多基站协作波束成型

为减少多基站协作波束成形系统中基站间的信息交换量和用户信道信息反馈量,提出一种基站联合利用有限反馈信道参数和信道空间相关矩阵估计信道矢量函数的方法;基于所估计的信道矢量函数,提出一种多基站协作扩展迫零波束成形算法。相比已有的多基站协作波束成形方案,所提算法能在反馈/回程开销和系统性能之间取得更合理的折中,计算仿真验证了所提算法的有效性。     

Security enhancement with joint transmit antenna selection and transmit beamforming under energy harvesting constraints

This paper considers a multiuser multiple‐input single‐output (MISO) broadcasting system with simultaneous wireless information and power transfer (SWIPT), which consists of one information receiver (IR) and several energy harvesting receivers (ERs) which are capable of eavesdropping the legitimate signals. For reducing cost and hardware complexity, transmit antenna selection (TAS) is applied in the transmitter. We aim to maximize the achievable secrecy rate under the individual energy harvesting constraint at the ERs and the transmit power constraint at the transmitter by jointly optimizing TAS, transmit beamforming, and artificial noise (AN). The joint optimization problem is a non‐convex mixed integer programming problem. We apply variable replacements to decouple the variable couplings and relax and approach the binary constraint by the difference of two convex constraints. Afterwards, penalty method and constrained concave convex procedure (CCCP) are applied to transform the relaxed problem into a sequence of semi‐definiteness programming (SDP) problems. Simulation results shows that our proposed joint optimization scheme is superior over existing non‐joint optimization schemes. This paper studies the joint transmit antenna selection (TAS), transmit beamforming, and artificial noise (AN) optimization in a multiple‐input multiple‐output (MISO) wiretap system with simultaneous wireless information and power transfer (SWIPT). The joint optimization problem is nonconvex and we propose a penalty method based scheme to solve it. The simulation results show that our joint optimization scheme is superior to other non‐joint optimization schemes.     

Adaptive transmitted distributed antenna selection strategy in distributed antenna systems with limited feedback beamforming

An adaptive transmitted distributed antenna (DA) selection strategy in distributed antenna systems (DAS) with limited feedback (LFB) beamforming is proposed. By maximising the upper bound of ergodic capacity in DAS with LFB beamforming, the proposed strategy can adaptively adjust the number of transmitted DAs. Simulation results show that the proposed strategy achieves greater ergodic capacity than the strategy with a fixed number of transmitted DAs.     

Performance of variable-power adaptive MQAM with transmit antenna selection and delayed feedback in Nakagami Fading channel

In this paper, the performance of MIMO systems with variable-power (VP) adaptive MQAM and transmit antenna selection (TAS) over Nakagami-m fading channel is presented. The optimum switching thresholds for attaining maximum spectrum efficiency (SE) subject to a target bit error rate (BER) and an average power constraint are derived. It is shown that the Lagrange multiplier in the constrained SE optimization will be unique if the existence condition for MIMO system with TAS is satisfied. A practical iterative algorithm based on Newton's method for finding the Lagrange multiplier is proposed. By using the switching thresholds, closed-form expressions of the SE and average BER are obtained. Besides, BER expressions with delayed feedback are derived for VP and constant-power (CP) systems, respectively. With these expressions, the impact of feedback delay on the BER performance is effectively assessed. Computer simulation for SE and BER shows that the theoretical analysis and simulation are in good agreement. The results show that the VP adaptive modulation (AM) system with TAS provides better SE than the CP counterpart and VP AM system with space-time coding, and has slight BER performance degradation for the normalized time delay less than 0.01.     

Downlink scheduling of multiuser MIMO systems with transmit beamforming

This article deals with downlink scheduling for multiuser multiple-input multiple-output （MIMO） systems, where the base station communicates with multiple users simultaneously through transmit beamforming. Most of the existing transmission schemes for multiuser MIMO systems focus on optimizing sum rate performance of the system. The individual quality of service （QoS） requirements （such as packet delay and minimum transmission rate for the data traffic） are rarely considered. In this article, a novel scheduling strategy is proposed, where we try to optimize the global system performance under individual QoS constraints. By performing scheduling into two steps, namely successive user selection and power allocation, the scheduler can achieve efficient resource utilization while maintaining the QoS requirements of all users. Extensive simulations and analysis are given to show the effectiveness of the proposed scheduler.     

Channel quality-to-interference ratio quantization criterion for limited feedback beamforming in MIMO systems

The discrete Fourier transform (DFT)-based codebook is employed in this paper to quantize channel state information so that the amount of feedback can be reduced in the multiple input multiple output (MIMO) downlink of long term evolution (LTE) system. And a novel beamforming (BF) scheme based on the proposed channel quality-to-interference (QIR) quantizing criteria is developed, which uses only the index of the optimal codebook for the beamforming at the base station (BS), and dramatically reduces the amount of feedback. The proposed BF scheme jointly considers the influences of the quality of the quantized channels and the mutual interference among the sub-channels. The extensive simulation results verify that throughput of the proposed BF scheme is better than that of the random BF with a little feedback, and that of the eigen-beamforming even under low signal noise ratio (SNR) scenario.     

Sum-rate analysis of multiuser MIMO system with zero-forcing transmit beamforming

In this letter, we present the exact sum-rate analysis of the multiuser multiple-input multiple-output (MIMO) systems with zero-forcing transmit beamforming (ZFBF). We develop the analytical expressions of the ergodic sum-rate for two low-complexity user selection strategies for the dual-transmit-antenna scenario. Based on the analytical results, we examine the parameter optimization problem to properly trade off between channel power gain and directional gain in term of maximizing the ergodic sum rate.     

Distributed transmit beamforming: challenges and recent progress

Distributed transmit beamforming is a form of cooperative communication in which two or more information sources simultaneously transmit a common message and control the phase of their transmissions so that the signals constructively combine at an intended destination. Depending on the design objectives and constraints, the power gains of distributed beamforming can be translated into dramatic increases in range, rate, or energy efficiency. Distributed beamforming may also provide benefits in terms of security and interference reduction since less transmit power is scattered in unintended directions. Key challenges in realizing these benefits, however, include coordinating the sources for information sharing and timing synchronization and, most crucially, distributed carrier synchronization so that the transmissions combine constructively at the destination. This article reviews promising recent results in architectures, algorithms, and working prototypes which indicate that these challenges can be surmounted. Directions for future research needed to translate the potential of distributed beamforming into practice are also discussed.     

Power control and beamforming for systems with multiple transmit and receive antennas

This paper investigates the performance of narrowband, slowly fading, and delay-limited multiple-antenna systems where channel state information (CSI) is available at the transmission end. This situation can arise in time-division duplex (TDD) based two-way systems where channel state estimation can be performed using the signal received from the opposite link. Power control methods which attempt to keep the transmission rate constant at the expense of randomizing the transmit power are considered. It is shown that significant savings in average transmit power (sometimes on the order of tens of decibels) can be expected compared to systems which keep the total transmit power constant. Several practical channel coding examples using are illustrated and their bit and frame error rate performance are discussed.     

一种双天线发射分集方案的性能分析

在平坦的瑞利衰落信道中,通过分析一种简单的双发射天线分集方案(即Alamouti编码方案,简称ACS)接收信号的统计特性和输出信噪比.在多相相移键控调制下,推导了该方案的传输比特误码率的一般理论分析式,证明了采用ACS技术的移动通信系统与采用2分集阶的最大比率合并接收分集技术的误码性能相同.Monte-Carlo仿真结果也验证此结论.这一理论成果可推广到采用正交空时分组码的多天线发射分集系统.