The interest in MIMO systems has shifted from point-to-point MIMO chan-nels to MIMO broadcast chanchan-nels during the last years. As shown in [10], [11], the capacity can be boosted by exploiting the spatial multiplexing ca-pability of transmit antennas, transmitting to multiple users simultaneously over the same bandwidth by means of SDMA, rather than trying to maximize the capacity of a single-user link. If a base station with M transmit anten-nas communicating withK single-antenna receivers has perfect channel state information (CSIT), a multiplexing gain of min(M, K) can be achieved. In cellular systems, this is a setting of practical interest, since multiple antennas can be easily deployed at the base station.
It has recently been proven [12] that the capacity region of the MIMO broadcast channel is achieved by dirty paper coding (DPC) [1]. The fun-damental idea behind this technique is that when the interference is known non-causally at the transmitter, it is possible to achieve the same capacity
as if there were no interference. However, this technique has two main dis-advantages that limit its applicability: a high computational complexity and the need for full CSIT. Hence, it is of particular interest to identify what kind of partial CSIT can be conveyed to the BS and what type of low-complexity transmission techniques can be used in order to achieve sum rates reasonably close to the optimum.
Lack of perfect CSIT in point-to-point MIMO systems simply translates into an offset in the capacity versus SNR curve. The slope is not affected by imperfect channel knowledge and thus the multiplexing gain does not change.
However, in MIMO broadcast channels, the level of CSIT critically affects the system performance, and thus feedback design has a greater importance in such systems. This is due to the fact that CSI not only provides better SNR at the receiver side, but also reduces the interference from data intended to other users in the cell. Thus, in a multiuser MIMO environment, co-channel interference must be taken into account for throughput maximization. In a system withK users, the capacity region is characterized by aK dimensional volume. The maximum achievable system throughput is the sum capacity, which is the point in the capacity region that maximizes the sum of all users’
information rates. Our goal is to design systems based on partial CSIT that provide sum rates close to the sum capacity while exhibiting reasonable complexity.
A promising low complexity alternative to DPC for the downlink of MIMO systems is linear beamforming. Downlink linear beamforming, al-though suboptimal, has been shown to achieve a large portion of the DPC capacity, exhibiting the best tradeoff between complexity and performance [13], [14], [15], [16]. In order to achieve the optimal capacity growth of Mlog logK for K → ∞ and single antenna receivers, linear beamforming schemes need to be combined with efficient multiuser scheduling algorithms that exploit multiuser diversity [17]. However, finding the optimal beamform-ing vectors is a non-convex optimization problem, and the optimal solution for a downlink channel with K users is given by exhaustive search over all possible combinations. Evidently, the complexity of the above problem be-comes prohibitively high for large K. Thus, we are interested in designing suboptimal linear beamforming techniques that, combined with efficient low-complexity multiuser scheduling algorithms, provide high sum rates.
In realistic scenarios, it is not reasonable to assume that all channel coef-ficients from each user can be perfectly fed back to the transmitter. Accurate CSIT is difficult to realize in practice, especially in frequency-division duplex
1.1 Thesis Overview and Outline 47 (FDD) systems. Training can be used to obtain channel estimates at the re-ceiver side and thus the assumption of perfect CSIR is reasonable. Methods for obtaining instantaneous CSIT can in general be of two types, by exploit-ing channel reciprocity (in TDD systems) or by obtainexploit-ing feedback from the mobile terminals. In reciprocity-based approaches, the CSIT is obtained in the uplink, which in turn is used for downlink transmission. In the latter case, each mobile user obtains estimates of its own channel by using pilot symbols transmitted in the downlink. The users feedback information to the base station by using a dedicated feedback link. Identifying the type of feed-back that has to be made available at the base station in order to achieve high sum rates is a critical issue that is addressed in this dissertation.
Based on the above motivations, the second part of this dissertation fo-cuses on systems with joint linear beamforming and multiuser scheduling with limited feedback. In general, a single-cell setting is considered, in which the base station has multiple antennas and each user terminal is equipped with a single antenna receiver. The goal consists of maximizing the sum-rate performance of such systems, while satisfying an average power constraint at the transmitter. At a PHY/MAC level, we focus on the optimization of the following aspects: feedback strategies, feedback quantization techniques, user scheduling algorithms and linear beamforming techniques. However, a joint optimization of all these elements is rather complicated. When optimizing such networks, we address the following issues:
• What feedback measures are of importance at the base station in order to design spatial transmission filters and exploit the multiuser diversity?
• How should users perform feedback quantization in order to optimize the system performance for a given available feedback rate?
• How should multiuser scheduling algorithms be designed in order to exploit multiuser diversity while exhibiting reasonable complexity?
• How to design robustlinear beamformingtechniques in limited feedback scenarios?
• Can we find joint solutions to these problems?
Chapter 3 provides a general perspective of the challenges in systems with joint linear beamforming and multiuser scheduling. An overview of these systems is provided, introducing some standard linear beamforming
techniques and multiuser scheduling algorithms. The remainder of the chap-ter is devoted to low-complexity solutions to the joint linear beamforming and multiuser scheduling problem. Initially, a scenario with perfect CSIT is considered, in which a simple scheduling algorithm and linear beamforming technique based on orthogonal beams are presented. This leads to a dra-matic complexity reduction in the multiuser scheduling part with respect to exhaustive user search. In the last part of this chapter, an integral low-complexity solution is proposed in a scenario with limited feedback. As we show, simple codebooks adapted to the transmit spatial correlation can yield large performance gains. In addition, a bound on the multiuser interference experienced by each user is derived, based on a geometric interpretation of the problem. This bound is of practical importance since, as we show in the following chapters, since it can be used for the design of feedback metrics for the purpose of user selection.
In Chapter 4, a design framework for scalar feedback in MIMO broadcast channels is proposed. We consider limited feedback scenarios in which each user conveys channel quality information to the base station for the pur-pose of user scheduling along with channel direction information. A family of metrics is presented based on bounds on the individual SINRs, which are computed at the receivers and fed back to the base station as channel quality information. Based on this framework, the sum rate of systems with joint linear beamforming, multiuser scheduling and limited fedback is analyzed, in a variety of asymptotic regimes. Particular importance is given to the comparison between time division multiple access (TDMA) and SDMA tech-niques, due to its timely relevance in the current developments of wireless standards. The effect of quantization on such scalar feedback is also studied, introducing the tradeoff between multiuser diversity and multiplexing gain that arises in scenarios with a finite sum-rate feedback model.
In Chapter 5, an alternative limited feedback model to the one presented in Chapter 4 is considered, in which the users quantize directly their vector channels by using optimized channel quantization codebooks, thus embed-ding channel direction and quality information in a single codebook. We focus on the design of such quantization codebooks for MIMO broadcast channels, adapting them to arbitrary linear beamforming techniques and multiuser scheduling algorithms. The proposed quantization codebooks ex-ploit spatial and temporal correlations in the system, providing performance increases over non optimized channel quantization techniques.
Chapter 6 addresses the design of linear beamforming techniques for
1.2 Contributions 49