MIMO Broadcast Channels With Finite-Rate Feedback

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well-known zero-forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite-rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signal-to-noise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to point-to-point multiple-input multiple-output (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR     

On the User Selection for MIMO Broadcast Channels

In this paper, a downlink communication system, in which a base station (BS) equipped with $M$ antennas communicates with $N$ users each equipped with $K$ receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum–rate throughput of the system, in a Rayleigh-fading environment. For the asymptotic case when $N$ tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum–rate throughput, such that the difference between the achievable sum–rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the BS, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum–rate capacity, with a very low complexity.      

Multi-Antenna Downlink Channels with Limited Feedback and User Selection

We analyze the sum-rate performance of a multi- antenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sum-rate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load.     

Transmitter Optimization for Correlated MISO Fading Channels with Generic Mean and Covariance Feedback

Transmitter optimization for correlated multipleinput single-output (MISO) channels with average channelinformation feedback is of theoretical and practical importance. It was tackled in the past by mainly focusing on cases with either mean or covariance feedback alone. The difficulty with generic MISO optimization arises from the fact that the treatment of optimal beam directions and power allocation are no longer separable, thereby making the problem nearly impossible to be tackled on the basis of its current formulation. We therefore take a different philosophy by representing the derivative of the ergodic capacity as a single integral and linking it to the channel characteristic function. This new formulation allows us to obtain the sufficient and necessary conditions, simply in the form of two vector equations which can be efficiently solved by a Newton-Raphson type algorithm developed in this paper. Numerical results are presented for illustration.     

Throughput-Optimal Precoding and Rate Allocation for MISO Systems With Noisy Feedback Channels

A throughput metric is considered for a multiple-input single-output (MISO) system with noisy feedback of channel state information (CSI). The goal is to optimize a precoding matrix with a medium-access control layer metric. The problem is a nonlinear multidimensional optimization. Results show that the optimal precoding turns into beamforming when the signal-to-noise ratio (SNR) of CSI feedback is sufficiently large. A necessary condition for the optimality of beamforming under the throughput metric is determined, and the necessary and sufficient condition is numerically found based on the Gauss-Chebyshev Quadrature method. Next, the rate allocation for beamforming and spatial diversity is analyzed. Then, a two-mode transmission scheme is proposed such that the transmitter is engaged in either the beamforming mode or the spatial diversity mode depending on the SNR of the CSI feedback. It is shown that at a fairly high SNR of CSI feedback, the rate allocation needs to be reduced, while at a low SNR of CSI feedback, the allocated rate should be increased. It is shown that when the SNR of CSI feedback is lower than a threshold, there always exists an SNR of the transmitted signal such that the CSI feedback can be viewed as the real CSI solely for the purpose of rate allocation. The result also shows that the throughput of two-mode transmission is almost the same as the throughput of the optimal precoding scheme, even with a low SNR and large feedback delay.     

Analysis of Multiple Antenna Systems With Finite-Rate Channel Information Feedback Over Spatially Correlated Fading Channels

This paper employs a high resolution quantization framework to study the effects of finite-rate quantization of the channel state information (CSI) on the performance of MISO systems over correlated fading channels. The contributions of this paper are twofold. First, as an application of the general distortion analysis, tight lower bounds on the capacity loss of correlated MISO systems due to the finite-rate channel quantization are provided. Closed-form expressions for the capacity loss in high-signal-to-noise ratio (SNR) and low-SNR regimes are also provided, and their analysis reveals that the capacity loss of correlated MISO channels is related to that of i.i.d. fading channels by a simple multiplicative factor which is given by the ratio of the geometric mean to the arithmetic mean of the eigenvalues of the channel covariance matrix. Second, this paper extends the general asymptotic distortion analysis to the important practical problem of suboptimal quantizers resulting from mismatches in the distortion functions, source statistics, and quantization criteria. As a specific application, two types of mismatched MISO CSI quantizers are investigated: quantizers whose codebooks are designed with minimum mean square error (MMSE) criterion but the distortion measure is the ergodic capacity loss (i.e., mismatched design criterion), and quantizers with codebook designed with a mismatched channel covariance matrix (i.e., mismatched statistics). Bounds on the channel capacity loss of the mismatched codebooks are provided and compared to that of the optimal quantizers. Finally, numerical and simulation results are presented and they confirm the tightness of theoretical distortion bounds.     

QoS‐Guaranteed Multiuser Scheduling in MIMO Broadcast Channels

This paper proposes a new multiuser scheduling algorithm that can simultaneously support a variety of different quality‐of‐service (QoS) user groups while satisfying fairness among users in the same QoS group in MIMO broadcast channels. Toward this goal, the proposed algorithm consists of two parts: a QoS‐aware fair (QF) scheduling within a QoS group and an antenna trade‐off scheme between different QoS groups. The proposed QF scheduling algorithm finds a user set from a certain QoS group which can satisfy the fairness among users in terms of throughput or delay. The antenna trade‐off scheme can minimize the QoS violations of a higher priority user group by trading off the number of transmit antennas allocated to different QoS groups. Numerical results demonstrate that the proposed QF scheduling method satisfies different types of fairness among users and can adjust the degree of fairness among them. The antenna trade‐off scheme combined with QF scheduling can improve the probability of QoS‐guaranteed transmission when supporting different QoS groups.     

Queue Proportional Scheduling via Geometric Programming in Fading Broadcast Channels

For fading broadcast channels (BC), a throughput optimal scheduling policy called queue proportional scheduling (QPS) is presented via geometric programming (GP). QPS finds a data rate vector such that the expected rate vector over all fading states is proportional to the current queue state vector and is on the boundary of the ergodic capacity region of a fading BC. Utilizing the degradedness of BC for each fading state, QPS is formulated as a geometric program that can be solved with efficient algorithms. The GP formulation of QPS is also extended to orthogonal frequency-division multiplexing (OFDM) systems in a fading BC. The throughput optimality of QPS is proved, and it is shown that QPS can arbitrarily scale the ratio of each user's average queueing delay. Throughput, delay, and fairness properties of QPS are numerically evaluated in a fading BC and compared with other scheduling policies such as the well-known maximum weight matching scheduling (MWMS). Simulation results for Poisson packet arrivals and exponentially distributed packet lengths demonstrate that compared with MWMS, QPS provides a significant decrease in average queueing delay and has more desirable fairness properties.     

Simulation Models for Investigation of Multiuser Scheduling in MIMO Broadcast Channels

Spatial correlation is a result of insufficient antenna spacing among multiple antenna elements, while temporal correlation is caused by Doppler spread. This paper compares the effect of spatial and temporal correlation in order to investigate the performance of multiuser scheduling algorithms in multiple‐input multiple‐output (MIMO) broadcast channels. This comparison includes the effect on the ergodic capacity, on fairness among users, and on the sum‐rate capacity of a multiuser scheduling algorithm utilizing statistical channel state information in spatio‐temporally correlated MIMO broadcast channels. Numerical results demonstrate that temporal correlation is more meaningful than spatial correlation in view of the multiuser scheduling algorithm in MIMO broadcast channels. Indeed, the multiuser scheduling algorithm can reduce the effect of the Doppler spread if it exploits the information of temporal correlation appropriately. However, the effect of spatial correlation can be minimized if the antenna spacing is sufficient in rich scattering MIMO channels regardless of the multiuser scheduling algorithm used.     

Compression of Feedback for Adaptive Transmission and Scheduling

For wireless systems with adaptive modulation and/or scheduling, feedback of channel quality information is often necessary. It has been questioned whether the increased system performance is worth the additional feedback rate and the increased algorithm complexity. In this paper, we study how the feedback rate can be minimized, without losing the gains due to adaptive modulation and multiuser diversity. We present an in-depth study of the literature in the area, and evaluate the performance of several state-of-the-art channel quality feedback schemes. By illustrating the compromise between system throughput and feedback channel rate for various schemes, we are able to give valuable insight in choice of method for feedback rate reduction. A major conclusion is that for multicarrier systems, a lossy compression scheme is the best choice, while for single-carrier systems, schemes limiting feedback to only high-SNR users show good performance. Another conclusion is that there are still many issues to study before the schemes can be used in practice.     

Coding of Broadcast TV Signals for Transmission Over Satellite Channels

This paper presents the coding algorithms and simulation results of multimode movement-compensated interframe video coders operating at 15 and 20 mbits/s for broadcast applications. The coding algorithms are based on a motion-compensated predictive coding approach. Simulation results using samples of broadcast video sequence indicate that excellent picture quality is obtained at the 20 Mbit/s transmission bit rate. Results of informal subjective evaluation of picture quality are also presented.     

Energy-Efficient Scheduling over Fading Channels with Transmission Modulation and Deadline Constraints

This letter investigates the problem of energy-efficient scheduling over fading channels. Considering the practical constraints of transmission modulation and deadline, a more rigorous system model is described. Furthermore, the scheduling problem is formulated as a stochastic programming problem. Then, the stochastic programming problem can be solved by exploiting the idea of dynamic programming (DP) and two DP-based scheduling schemes are given. The numerical results show that the proposed optimization problem is more efficient at guiding the development of the scheduling schemes for energy-efficient scheduling. Moreover, the proposed scheduling schemes perform quite well in terms of quality and computational complexity.     

Adaptive Beamforming with Dimension Reduction in Spatially Correlated MISO Channels

In this paper, we propose an adaptive beamforming scheme that generates the beam weight using dominant eigenvectors of the spatial covariance matrix. The number of eigenvectors used for the generation of beam weight is determined to maximize the signal-to-noise ratio (SNR) for given feedback constraints (e.g., the amount of feedback information and feedback delay). It is shown that the conventional limited feedback beamforming and eigen-beamforming are special cases of the proposed scheme. Simulation results show that the proposed beamforming scheme can effectively be applied to spatially correlated channels.     

Coordinated User Scheduling Based on Hybrid CSI in Multi-User MIMO Relay System with Limited Feedback

This paper considers coordinated user scheduling in a multi-user two-hop multi-input multi-output relay system with limited feedback. The proposed scheme utilizes a quantized transmit correlation and channel quality information, enabling to achieve both interference mitigation and multi-user diversity (MUD) gain. To this end, we first investigate the effect of quantization error on the statistical characteristics of co-channel interference (CCI) cased by the relay. Then, the coordinated user-scheduling strategy is designed with the use of eigen-beamforming to maximize the desired signal power in an instantaneous manner while minimizing the CCI in an average sense. Analytic and numerical results show that the proposed scheme can maximize the achievable sum-rate by handling a tradeoff between interference mitigation and MUD gain according to the number of quantization bits, providing a large sum-rate performance in the presence of quantization error.     

Optimized Transmission for Fading Multiple-Access and Broadcast Channels With Multiple Antennas

In mobile wireless networks, dynamic allocation of resources such as transmit powers, bit-rates, and antenna beams based on the channel state information of mobile users is known to be the general strategy to explore the time-varying nature of the mobile environment. This paper looks at the problem of optimal resource allocation in wireless networks from different information-theoretic points of view and under the assumption that the channel state is completely known at the transmitter and the receiver. In particular, the fading multiple-access channel (MAC) and the fading broadcast channel (BC) with additive Gaussian noise and multiple transmit and receive antennas are focused. The fading MAC is considered first and a complete characterization of its capacity region and power region are provided under various power and rate constraints. The derived results can be considered as nontrivial extensions of the work done by Tse and Hanly from the case of single transmit and receive antenna to the more general scenario with multiple transmit and receive antennas. Efficient numerical algorithms are proposed, which demonstrate the usefulness of the convex optimization techniques in characterizing the capacity and power regions. Analogous results are also obtained for the fading BC thanks to the duality theory between the Gaussian MAC and the Gaussian BC.     

Tomlinson-Harashima Precoding for Broadcast Channels with Uncertainty

We consider the design of Tomlinson-Harashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplink-downlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: a set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we present a closed-form solution for the robust TH precoder that incurs essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worst-case channel uncertainty subject to both types of power constraints. We also present a conservative robust design for this type of channel uncertainty that has reduced computational complexity for the case of power constraints on individual antennas and leads to a closed-form solution for the total power constraint case. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the rather high sensitivity of broadcast transmissions to errors in channel state information.     

Broadcast Scheduling in Interference Environment

Broadcast is a fundamental operation in wireless networks and naive flooding is not practical because it cannot deal with interference. Scheduling is a good way to avoid interference, but previous studies on broadcast scheduling algorithms all assume highly theoretical models such as the unit disk graph model. In this work, we re-investigate this problem using the 2-Disk and the signal-to-interference-plus-noise-ratio (SINR) model to realize it. We first design a constant approximation algorithm for the 2-Disk model and then extend it to the SINR model. This result is the first result on broadcast scheduling algorithms in SINR model, to the best of our knowledge.     

Capacity of Correlated MISO Channels with Correlated Co-channel Interference and Noise

Exact and general analysis of the capacity for multiple-input single-output (MISO) correlated Rayleigh fading channels in the presence of both correlated Rayleigh co-channel interference and additive Gaussian noise is not available in the literature, although its counterpart with Gaussian noise alone has been thoroughly investigated. The difficulty arises from the quadratic form of interference term. In this paper, we obtain exact solutions to the ergodic and outage capacity for MISO systems with and without channel state information at the transmitter. Numerical results are also presented for illustration.     

Fundamental Limits in MIMO Broadcast Channels

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system parameters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling.     

Feedback Communications in Fading Channels

A modulation scheme for varying the data rate and transmitted power in accordance with received signal strengths in a fading channel is discussed. The system, using ideal feedback, performs better than one using only rate control with the same constraint on bandwidth.