arXiv:1112.3810v1 [cs.IT] 16 Dec 2011 SUBMITTED TO THE IEEE TRANSACTIONS ON COMMUNICATIONS 1 Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems Hien Quoc Ngo, Erik G. Larsson, and Thomas L. Marzetta Abstract A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. A MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system. Index Terms Energy efficiency, spectral efficiency, multiuser MIMO, very large MIMO systems I. I NTRODUCTION In multiuser multiple-input multiple-output (MU-MIMO) systems, a base station (BS) equipped with multiple antennas serves a number of users. Such systems have attracted much attention for some time now [2]. Conventionally, the communication between the BS and the users is performed by orthogonalizing the channel so that the BS communicates with each user in separate time-frequency resources. This is not optimal from an information-theoretic point of view, and higher rates can be achieved if the BS communicates with several users in the same time-frequency resource [3], [4]. However, complex techniques to mitigate inter-user interference must then be used, such as maximum-likelihood multiuser detection on the uplink [5], or “dirty-paper coding” on the downlink [6], [7]. H. Q. Ngo and E. G. Larsson are with the Department of Electrical Engineering (ISY), Link¨ oping University, 581 83 Link¨ oping, Sweden (Email: nqhien@isy.liu.se; egl@isy.liu.se). T. L. Marzetta is with Bell Laboratories, Alcatel-Lucent, 600 Moutain Avenue, Murray Hill, NJ 07974, USA (Email: tom.marzetta@alcatel- lucent.com). This work was supported in part by the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), and ELLIIT. E. Larsson is a Royal Swedish Academy of Sciences (KVA) Research Fellow supported by a grant from the Knut and Alice Wallenberg Foundation. Parts of this work were presented at the 2011 Allerton Conference on Communication, Control and Computing [1].