Robert W. Heath

An overview of limited feedback in wireless communication systems

It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.

Shifting the MIMO Paradigm

Multi-user MIMO (MU-MIMO) networks reveal the unique opportunities arising from a joint optimization of antenna combining techniques with resource allocation protocols. Furthermore, it brings robustness with respect to multipath richness, allowing for compact antenna spacing at the BS and, crucially, yielding the diversity and multiplexing gains without the need for multiple antenna user terminals. To realize these gains, however, the BS should be informed with the users channel coefficients, which may limit practical application to TDD or low-mobility settings. To circumvent this problem and reduce feedback load, combining MU-MIMO with opportunistic scheduling seems a promising direction. The success for this type of scheduler is strongly traffic and QoS-dependent, however.

Spatially Sparse Precoding in Millimeter Wave MIMO Systems

Millimeter wave (mmWave) signals experience orders-of-magnitude more pathloss than the microwave signals currently used in most wireless applications and all cellular systems. MmWave systems must therefore leverage large antenna arrays, made possible by the decrease in wavelength, to combat pathloss with beamforming gain. Beamforming with multiple data streams, known as precoding, can be used to further improve mmWave spectral efficiency. Both beamforming and precoding are done digitally at baseband in traditional multi-antenna systems. The high cost and power consumption of mixed-signal devices in mmWave systems, however, make analog processing in the RF domain more attractive. This hardware limitation restricts the feasible set of precoders and combiners that can be applied by practical mmWave transceivers. In this paper, we consider transmit precoding and receiver combining in mmWave systems with large antenna arrays. We exploit the spatial structure of mmWave channels to formulate the precoding/combining problem as a sparse reconstruction problem. Using the principle of basis pursuit, we develop algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware. We present numerical results on the performance of the proposed algorithms and show that they allow mmWave systems to approach their unconstrained performance limits, even when transceiver hardware constraints are considered.

GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION

Abstract For a given class F of unit norm frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation |〈fk,fl〉| among all frames {f k } k∈ I ∈ F . We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These bounds yield a simple condition under which Grassmannian frames coincide with unit norm tight frames. We exploit connections to graph theory, equiangular line sets, and coding theory in order to derive explicit constructions of Grassmannian frames. Our findings extend recent results on unit norm tight frames. We then introduce infinite-dimensional Grassmannian frames and analyze their connection to unit norm tight frames for frames which are generated by group-like unitary systems. We derive an example of a Grassmannian Gabor frame by using connections to sphere packing theory. Finally we discuss the application of Grassmannian frames to wireless communication and to multiple description coding.

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.

Channel Estimation and Hybrid Precoding for Millimeter Wave Cellular Systems

Millimeter wave (mmWave) cellular systems will enable gigabit-per-second data rates thanks to the large bandwidth available at mmWave frequencies. To realize sufficient link margin, mmWave systems will employ directional beamforming with large antenna arrays at both the transmitter and receiver. Due to the high cost and power consumption of gigasample mixed-signal devices, mmWave precoding will likely be divided among the analog and digital domains. The large number of antennas and the presence of analog beamforming requires the development of mmWave-specific channel estimation and precoding algorithms. This paper develops an adaptive algorithm to estimate the mmWave channel parameters that exploits the poor scattering nature of the channel. To enable the efficient operation of this algorithm, a novel hierarchical multi-resolution codebook is designed to construct training beamforming vectors with different beamwidths. For single-path channels, an upper bound on the estimation error probability using the proposed algorithm is derived, and some insights into the efficient allocation of the training power among the adaptive stages of the algorithm are obtained. The adaptive channel estimation algorithm is then extended to the multi-path case relying on the sparse nature of the channel. Using the estimated channel, this paper proposes a new hybrid analog/digital precoding algorithm that overcomes the hardware constraints on the analog-only beamforming, and approaches the performance of digital solutions. Simulation results show that the proposed low-complexity channel estimation algorithm achieves comparable precoding gains compared to exhaustive channel training algorithms. The results illustrate that the proposed channel estimation and precoding algorithms can approach the coverage probability achieved by perfect channel knowledge even in the presence of interference.

Adaptive modulation and MIMO coding for broadband wireless data networks

Link adaptation techniques, where the modulation, coding rate, and/or other signal transmission parameters are dynamically adapted to the changing channel conditions, have emerged as powerful tools for increasing the data rate and spectral efficiency of wireless data-centric networks. While there has been significant progress on understanding the theoretical aspects of time adaptation in LA protocols, new challenges surface when dynamic transmission techniques are employed in broadband wireless networks with multiple signaling dimensions. Those additional dimensions are mainly frequency, especially in multicarrier systems, and space in multiple-antenna systems, particularly multiarray multiple-input multiple-output communication systems. We give an overview of the challenges and promises of link adaptation in future broadband wireless networks. We suggest guidelines to help in the design of robust, complexity/cost-effective algorithms for these future wireless networks.

Networked MIMO with clustered linear precoding

A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination-to enhance the sum rate-and limited inter-cluster coordination-to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.

Transmit selection in spatial multiplexing systems

In this letter we solve the transmit antenna selection problem for a zero forcing spatial multiplexing system with knowledge of the channel statistics at the transmitter. We show through Wishart matrix analysis that the signal-to-noise ratio on the kth stream is a weighted Chi-squared variable with the weight equal to-the kth diagonal entry of the inverted transmit correlation matrix. We use this result to develop selection algorithms for two cases-maximizing ergodic capacity and minimizing the average probability of error. Monte Carlo simulations illustrate potential performance improvements.

Switching between diversity and multiplexing in MIMO systems

Multiple-input multiple-output (MIMO) wireless communication systems can offer high data rates through spatial multiplexing or substantial diversity using transmit diversity. In this letter, switching between spatial multiplexing and transmit diversity is proposed as a simple way to improve the diversity performance of spatial multiplexing. In the proposed approach, for a fixed rate, either multiplexing or diversity is chosen based on the instantaneous channel state and the decision is conveyed to the transmitter via a low-rate feedback channel. The minimum Euclidean distance at the receiver is computed for spatial multiplexing and transmit diversity and is used to derive the selection criterion. Additionally, the Demmel condition number of the matrix channel is shown to provide a sufficient condition for multiplexing to outperform diversity. Monte Carlo simulations demonstrate improvement over either multiplexing or diversity individually in terms of bit error rate.