Multiple-input Multiple-output Beamforming Systems Research Articles

Coulomb Gas Analogy: A Statistical Physics Approach to Performance Analysis of MIMO Systems

In this correspondence, by adopting the Coulomb gas analogy that is an analytical approach from statistical physics, we derive a closedform approximation of the cumulative distribution function (CDF) of the largest eigenvalue of a random Gram matrix H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sup> H, where H denotes the channel matrix of a multiple-input multiple-output (MIMO) system. The expression of approximation has a simple structure in terms of several elementary functions, which is derived by assuming that the entries of H have Nakagami-m distributed amplitude with an independent phase. This assumption is made because it applies in two common cases of the Nakagami-m distributions, i.e., with a uniformly distributed phase and a complex signal model. Simulation results indicate that the theoretical expression also provides a good approximation to the CDF for Rice and Hoyt distributions when the CDF is within a near-one range. This range takes the form of (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">no</sub> ,1), where we assume P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">no</sub> = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> by default in this study. The derived approximation can find many uses for the performance analysis of MIMO beamforming and singular value decomposition MIMO systems, e.g., evaluating the outage probability for these systems.

Reducing the Codeword Search Complexity of FDD Moderately Large MIMO Beamforming Systems

It is of great interest to develop larger scale multiple-input multiple-output (MIMO) technology based on frequency division duplexing (FDD) for backward compatibility with existing standards and already deployed cellular networks. One hindrance to the FDD approach is the complexity of the codeword search performed by the receiver, which is known to scale with the number of transmit antennas $N_{t}$ in a system. The codeword search complexity does not scale linearly and soon becomes infeasible even for the not-so-massive MIMO systems expected in the very near future. We address this problem by proposing a natural sequence-based orthogonal codebook and an intra-array interference magnitude (IIM) framework for MIMO beamforming based on quantized equal gain transmission that altogether tremendously simplifies the codeword search problem. We also present an assessment on the quality of the codeword selected by the proposed framework that explains it’s near optimal performance, and, provide detailed codeword search complexity quantification. Finally, we provide simulation analyses of beamforming gain under time selective fading channels and an FDD MIMO system transmit delay model. Our analyses indicate that despite significantly reducing complexity, the proposed IIM framework executed by already commercialized processors is capable of approaching the ideal performance of an static system even in the presence of time-selectivity inherent to high-speed mobile communications. Our analyses also quantify the impact of feedback delay on average beamforming gain of moderately large transmit arrays.

MIMO beamforming system for speech enhancement in realistic environment with multiple noise sources

Multiple noise sources in a realistic environment severely degrade the quality and intelligibility of the desired speech signal, thus posing a severe problem for many speech applications. Several noise reduction algorithms have been proposed with a main goal to solve this problem. However, the good performances of such algorithms are severely impaired in realistic environment under multi-noise sources condition. In this paper, the author treats the noise cancellation system as a multiple-input multiple-output (MIMO) beamformer system. The proposed approach consists of two steps. First, the noise signals are generated by applying the white noise sources to a MIMO AR system. Then, the noisy microphone signals are sequentially processed by employing multi-channel linear prediction error filters (MCLPEFs) and multi-channel adaptive noise estimation filters (MCANEFs) in the lower path of the proposed beamformer. The MCLPEFs are used to whiten the input signals, while the MCANEFs are used as a MIMO system identification to perform the modeling process of the noise signals. Finally, the noise signals in the upper path are subtracted from the estimated noises in the lower path to recover an enhanced speech signal. Moreover, the performance of the proposed MIMO approach was validated under a realistic environment with real noise sources.

On the Throughput of Large MIMO Beamforming Systems With Channel Aging

We study the problem of throughput optimization in large multiple-input multiple-output (MIMO) beamforming systems with channel aging, as the number of transmit and receive antennas is increased. We quantify the effective channel coherence time in terms of the intertraining interval, which is the time after which the channel state information needs to be reestimated to avoid loss in performance due to outdated channel estimates. Conventional wisdom suggests that the coherence time of large MIMO systems should decrease with increasing number of antennas, because the system has a large number of independently varying channel coefficients. On the contrary, we show that the effective channel coherence time increases with the number of antennas. We optimize the throughput with respect to the symbol and pilot energies, the number of antennas, frame duration, and target SNR. This analysis brings out the important fact that the effective channel coherence time critically depends on the underlying signaling scheme, and not only on the temporal correlation coefficient of the wireless channel.

Rate-Adaptive Feedback with Bayesian Compressive Sensing in Multiuser MIMO Beamforming Systems

Multiple-input multiple-output (MIMO) is a promising way to increase link capacity and energy efficiency in the next generation communication systems. However, the benefits of such an approach depend on proper channel state information (CSI) availability at the transmitter. The CSI is usually estimated at the receiver and fed back to the transmitter through a band-limited channel. Thus, an efficient feedback scheme is needed. In this paper, a comprehensive Bayesian compressive sensing (BCS) based feedback mechanism is proposed for time-varying spatially and temporally correlated vector autoregression (VAR) wireless channel, and the feedback rate distortion function is derived in closed form in statistics. The proposed BCS feedback scheme utilizes the sparse CSI features and prior knowledge to significantly compress the dimensionality of the feedback CSI. Furthermore, the relationship between the feedback rate and downlink capacity is derived in closed form in statistics to guide rate-adaptive feedback in MIMO system. We find out that the ergodic downlink capacity of a user is determined only by its own feedback rate in the proposed feedback scheme. Theoretical and simulation results all show that the proposed feedback scheme can realize efficient, rate-adaptive feedback based on downlink capacity requirement, and the proposed feedback performance is superior to other related works.

Optimal designs of collaborative relay-assisted multiuser beamforming for cellular systems

With careful calculation of signal forwarding weights, relay nodes can be used to work collaboratively to enhance downlink transmission performance by forming a virtual multiple-input multiple-output beamforming system. Although collaborative relay beamforming schemes for single user have been widely investigated for cellular systems in previous literatures, there are few studies on the relay beamforming for multiusers. In this paper, we study the collaborative downlink signal transmission with multiple amplify-and-forward relay nodes for multiusers in cellular systems. We propose two new algorithms to determine the beamforming weights with the same objective of minimizing power consumption of the relay nodes. In the first algorithm, we aim to guarantee the received signal-to-noise ratio at multiusers for the relay beamforming with orthogonal channels. We prove that the solution obtained by a semidefinite relaxation technology is optimal. In the second algorithm, we propose an iterative algorithm that jointly selects the base station antennas and optimizes the relay beamforming weights to reach the target signal-to-interference-and-noise ratio at multiusers with nonorthogonal channels. Numerical results validate our theoretical analysis and demonstrate that the proposed optimal schemes can effectively reduce the relay power consumption compared with several other beamforming approaches. Copyright © 2012 John Wiley & Sons, Ltd.

Binary Grassmannian Weightbooks for MIMO Beamforming Systems

Binary weightbooks for multiple-input multiple-output (MIMO) beamforming systems using quantized feedback are designed based on the Grassmannian beamforming criterion. It is shown that the Grassmannian criterion for binary weightbook design is to maximize the minimum Hamming distance of the corresponding block code. Thus, block codes that have large minimum Hamming distance can be used for binary weightbook design for MIMO beamforming systems using quantized feedback. The optimum binary weightbooks when the number of transmit antennas has value from two to six are tabulated.

On MIMO beamforming systems using quantized feedback

We propose the Hadamard matrix as a codebook for multiple-input multiple-output (MIMO) beamforming systems, and show that a quantized equal gain transmission (QEGT) scheme using the Hadamard codebook has the same symbol error probability performance as a receiver selection diversity combining scheme operating in independent generalized Rayleigh fading channels. We show that a MIMO beamforming system using quantized feedback over Rician fading channels can be analyzed by considering a corresponding receiver selection combining scheme operating in single-input multiple-output (SIMO) systems over correlated generalized Rician fading channels. Also, we propose a greedy cophasing scheme for MIMO beamforming systems using quantized feedback. The greedy cophasing scheme provides 3.2 dB power gain over an orthogonal space-time block code when the number of transmit antennas is four, the number of receive antennas is one, and the number of feedback bits is three.

Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design

Channel Adaptive Quantization for Limited Feedback MIMO Beamforming Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining techniques. In the absence of full channel knowledge at the transmitter, the transmit beamforming vector can be quantized at the receiver and sent to the transmitter using a low-rate feedback channel. In the literature, quantization algorithms for the beamforming vector are designed and optimized for a particular channel distribution, commonly the uncorrelated Rayleigh distribution. When the channel is not uncorrelated Rayleigh, however, these quantization strategies result in a degradation of the receive signal-to-noise ratio (SNR). In this paper, switched codebook quantization is proposed where the codebook is dynamically chosen based on the channel distribution. The codebook adaptation enables the quantization to exploit the spatial and temporal correlation inherent in the channel. The convergence properties of the codebook selection algorithm are studied assuming a block-stationary model for the channel. In the case of a nonstationary channel, it is shown using simulations that the selected codebook tracks the distribution of the channel resulting in improvements in SNR. Simulation results show that in the case of correlated channels, the SNR performance of the link can be significantly improved by adaptation, compared with nonadaptive quantization strategies designed for uncorrelated Rayleigh-fading channels