# Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

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TL;DR: A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval and a complete multi-cellular analysis yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve.

Abstract: A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.

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##### Citations

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^{1}, University of Cassino

^{2}, Macquarie University

^{3}, Pompeu Fabra University

^{4}, Huawei

^{5}, Samsung

^{6}

6,462 citations

### Cites background from "Noncooperative Cellular Wireless wi..."

...• An excellent pairing for MIMO, since OFDM allows for the spatial interference from multiantenna transmission to be dealt with at a subcarrier level, without the added complication of intersymbol interference....

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5,302 citations

### Cites background from "Noncooperative Cellular Wireless wi..."

...In [13], for a typical operating scenario, the maximum number of orthogonal pilot sequences in a one millisecond coherence interval is estimated to be about 200....

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...Pilot contamination as a basic phenomenon is not really specific to massive MIMO, but its effect on massive MIMO appears to be much more profound than in classical MIMO [13,14]....

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...This directed interference grows with the number of service-antennas at the same rate as the desired signal [13]....

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4,913 citations

### Cites background from "Noncooperative Cellular Wireless wi..."

...Our emphasis on TDD rather than FDD is driven by the need to acquire channel state-information between extreme numbers of service antennas and much smaller numbers of terminals....

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...For example, 11 directive antennas pointing in distinct directions tend toexperience a lower correlation than nondirective antennas, since each of these directive antennas“see” signals arriving from a distinct angular sector....

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^{1}, University of Texas at Austin

^{2}, Pompeu Fabra University

^{3}, Bell Labs

^{4}, Aalborg University

^{5}

3,295 citations

2,568 citations

##### References

^{1}

6,728 citations

### "Noncooperative Cellular Wireless wi..." refers background in this paper

...A point-to-point MIMO system [2] requires expensive multiple-antenna terminals....

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*2,540 citations*

*"Noncooperative Cellular Wireless wi..." refers background in this paper*

...An alternative to a point-to-point MIMO system is a multiuser MIMO system [3], [4], [5], [6] in which an antenna array simultaneously serves a multiplicity of autonomous terminals....

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*28 Jun 2004TL;DR: A tutorial on random matrices is provided which provides an overview of the theory and brings together in one source the most significant results recently obtained.Abstract: Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth.*

2,196 citations

### "Noncooperative Cellular Wireless wi..." refers background in this paper

...It can be shown that the vector φkjΦ ∗ l has exactly the same probability distribution as does any row vector of Φl [15], [16]....

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*01 Jan 2004*

2,180 citations

*••*

*TL;DR: It is shown that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper bound on the sum rate.*

*Abstract: We consider a multiuser multiple-input multiple- output (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO BC is in general a nondegraded BC, its capacity region remains an unsolved problem. We establish a duality between what is termed the "dirty paper" achievable region (the Caire-Shamai (see Proc. IEEE Int. Symp. Information Theory, Washington, DC, June 2001, p.322) achievable region) for the MIMO BC and the capacity region of the MIMO multiple-access channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. We also show that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the MIMO BC.*

*1,743 citations*

*"Noncooperative Cellular Wireless wi..." refers background in this paper*

...An alternative to a point-to-point MIMO system is a multiuser MIMO system [3], [4], [5], [6] in which an antenna array simultaneously serves a multiplicity of autonomous terminals....

*[...]*