Capacity limits of MIMO channels - Selected Areas in ...

1 684 IEEE JOURNAL ON Selected Areas IN COMMUNICATIONS, VOL. 21, NO. 5, JUNE 2003 Capacity limits of mimo ChannelsAndrea Goldsmith, Senior Member, IEEE, Syed Ali Jafar, Student Member, IEEE, Nihar Jindal, Student Member, IEEE,and Sriram Vishwanath, Student Member, IEEEI nvited PaperAbstract We provide an overview of the extensive recentresults on the Shannon Capacity of single-user and multiusermultiple-input multiple-output ( mimo ) channels . Althoughenormous Capacity gains have been predicted for such channels ,these predictions are based on somewhat unrealistic assumptionsabout the underlying time-varying channel model and how wellit can be tracked at the receiver, as well as at the realistic assumptions can dramatically impact the potentialcapacity gains of mimo techniques.

2 For time-varying mimo channels there are multiple Shannon theoretic Capacity definitionsand, for each definition, different correlation models and channelinformation assumptions that we consider. We first provide acomprehensive summary of ergodic and Capacity versus outageresults for single-user mimo channels . These results indicate thatthe Capacity gain obtained from multiple antennas heavily dependson the available channel information at either the receiver ortransmitter, the channel signal-to-noise ratio, and the correlationbetween the channel gains on each antenna element.

3 We then focusattention on the Capacity region of the multiple-access channels (MACs) and the largest known achievable rate region for thebroadcast channel . In contrast to single-user mimo channels , Capacity results for these multiuser mimo channels are quitedifficult to obtain, even for constant channels . We summarizeresults for the mimo broadcast and MAC for channels that areeither constant or fading with perfect instantaneous knowledgeof the antenna gains at both transmitter(s) and receiver(s).

4 Weshow that the Capacity region of the mimo multiple access andthe largest known achievable rate region (called the dirty-paperregion) for the mimo broadcast channel are intimately relatedvia a duality transformation. This transformation facilitatesfinding the transmission strategies that achieve a point on theboundary of the mimo MAC Capacity region in terms of thetransmission strategies of the mimo broadcast dirty-paper regionandvice-versa. Finally, we discuss Capacity results for multicellMIMO channels with base station cooperation.

5 The base stationsthen act as a spatially diverse antenna array and transmissionstrategies that exploit this structure exhibit significant capacitygains. This section also provides a brief discussion of system levelissues associated with mimo cellular. Open problems in this fieldabound and are discussed throughout the Terms Antenna correlation, beamforming, broadcastchannels (BCs), channel distribution information (CDI), channelstate information (CSI), multicell systems, multiple-access chan-nels (MACs), multiple-input multiple-output ( mimo ) channels ,multiuser systems, Shannon received November 8, 2002; revised January 31, 2003.

6 This workwas supported in part by the Office of Naval Research (ONR) under GrantsN00014-99-1-0578 and N00014-02-1-0003. The work of S. Vishwanath wassupported by a Stanford Graduate authors are with the Department of Electrical Engineering, StanfordUniversity, Stanford, CA 94305 USA (e-mail: Object Identifier INTRODUCTIONWIRELESS systems continue to strive for ever higherdata rates. This goal is particularly challenging forsystems that are power, bandwidth, and complexity , another domain can be exploited to significantlyincrease channel Capacity : the use of multiple transmit andreceive antennas.)

7 Pioneering work by Winters [81], Foschini[20], and Telatar [69] ignited much interest in this area bypredicting remarkable spectral efficiencies for wireless systemswith multiple antennas when the channel exhibits rich scat-tering and its variations can be accurately tracked. This initialpromise of exceptional spectral efficiency almost for free resulted in an explosion of research activity to characterize thetheoretical and practical issues associated with multiple-inputmultiple-output ( mimo ) wireless channels and to extend theseconcepts to multiuser systems.

8 This tutorial summarizes thesegment of this recent work focused on the Capacity of mimo systems for both single-users and multiple users under differentassumptions about spatial correlation and channel informationavailable at the transmitter and large spectral efficiencies associated with mimo chan-nels are based on the premise that a rich scattering environmentprovides independent transmission paths from each transmit an-tenna to each receive antenna. Therefore, for single-user sys-tems, a transmission and reception strategy that exploits thisstructure achieves Capacity on approximatelysepa-rate channels , whereis the number of transmit antennas andis the number of receive antennas.

9 Thus, Capacity scales lin-early withrelative to a system with just one transmitand one receive antenna. This Capacity increase requires a scat-tering environment such that the matrix of channel gains be-tween transmit and receive antenna pairs has full rank and in-dependent entries and that perfect estimates of these gains areavailable at the receiver. Perfect estimates of these gains at boththe transmitter and receiver provides an increase in the constantmultiplier associated with the linear scaling. Much subsequentwork has been aimed at characterizing mimo channel capacityunder more realistic assumptions about the underlying channelmodel and the channel estimates available at the transmitter andreceiver.

10 The main question from both a theoretical and prac-tical standpoint is whether the enormous Capacity gains initiallypredicted by Winters, Foschini, and Telatar can be obtained inmore realistic operating scenarios and what specific gains resultfrom adding more antennas and/or a feedback link to feed re-ceiver channel information back to the $ 2003 IEEEGOLDSMITHet al.: Capacity limits OF mimo CHANNELS685 mimo channel Capacity depends heavily on the statis-tical properties and antenna element correlations of thechannel. Recent work has developed both analytical andmeasurement-based mimo channel models along with the cor-responding Capacity calculations for typical indoor and outdoorenvironments [26].