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Journal ArticleDOI

Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

Thomas L. Marzetta1
01 Nov 2010-IEEE Transactions on Wireless Communications (IEEE)-Vol. 9, Iss: 11, pp 3590-3600
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.
Citations
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Proceedings ArticleDOI
Hong Yang1, Thomas L. Marzetta1
04 Dec 2014
TL;DR: It is shown that by means of its superior beamforming and frequency response flattening capabilities, simple noncooperative uplink and downlink power controls can be devised for an LSAS macro-cellular wireless network to provide intra-cell equalized, multi-Mbps throughputs to all users.
Abstract: Traditional macro-cellular wireless networks are not capable of delivering even throughputs to all the users due to large variations in slow fading and inter-cell and inter-user interferences, and the throughputs for cell edge users are necessarily sacrificed to achieve an acceptable level of cell spectral efficiency. We show that this is not the case for large-scale antenna systems (LSAS, also known as Massive MIMO). Specifically, we show that by means of its superior beamforming and frequency response flattening capabilities, simple noncooperative uplink and downlink power controls can be devised for an LSAS macro-cellular wireless network to provide intra-cell equalized, multi-Mbps throughputs to all users. Compared with current LTE, a 64-antenna LSAS can provide cell edge throughputs with at least a ten-fold increase in the uplink and a significant gain in the downlink, and at the same time provide a total spectral efficiency per cell that quintuples in the uplink and triples in the downlink.

70 citations


Cites background or methods from "Noncooperative Cellular Wireless wi..."

  • ...2: While pilot contamination remains even as the number of service antennas M → ∞ [5], proper reuse of pilots can drastically reduce the pilot contamination to a negligible level [11]....

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  • ...LSAS CAPACITY For the usual LSAS with TDD wide band OFDM operation and with uplink pilots for CSI acquisition [5], referring to the notation at the end of Section I, we have [10] Theorem 2....

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  • ...LSAS, also known as Massive MIMO, with its many service antennas serving a much smaller number of spatially multiplexed single-antenna mobiles, has been shown to be capable of achieving huge spectral efficiency [2] [3] [4] [5] [6] [7] [8]....

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Journal ArticleDOI
TL;DR: Both theoretical and simulation results demonstrate that the SP-aided scheme can effectively reduce the estimation contamination by increasing the data frame size and achieve a significant improvement over the spectral efficiency, in comparison with conventional pilot-based methods.
Abstract: This paper concerns the uplink of multicell multiuser multiple-input multiple-output (MIMO) systems. To tackle the effect of pilot contamination that is generally viewed as a bottleneck in previous work, this paper presents a superimposed pilot (SP)-aided uplink channel estimation scheme and mathematically characterizes the impact that an SP has on the performance of such a very large MIMO system. It is shown that there are two types of interference components that do not vanish, even when the number of antennas $M$ grows to infinity. The first type, which is referred to as cross-contamination, is due to the correlation between the SP and data among different cells. The second type, which is referred to as self-contamination, is due to the dependence between channel estimation and estimation error. Cross-contamination is, in principle, similar to pilot contamination in a conventional pilot-based multicell MIMO system, whereas self-contamination is unique for the SP-aided scheme. Both theoretical and simulation results demonstrate that the SP-aided scheme can effectively reduce the estimation contamination by increasing the data frame size and, in turn, achieve a significant improvement over the spectral efficiency, in comparison with conventional pilot-based methods.

70 citations


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

  • ...2414651 large number of antennas to existing cell sites significantly increases the spectral efficiency of a cellular uplink network [4]–[6]....

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  • ...2The optimal pilot length or the pilot-reuse factor for maximizing the achievable cell throughput may refer to [4] and [18] but will not be addressed here since it is beyond the scope of this paper....

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Journal ArticleDOI
TL;DR: Two approximations of the achievable uplink rate with the perfect/imperfect channel state information (CSI) in cell-free massive multi-input multi-output (MIMO) systems are derived and indicate that the cell- free massive MIMO system has huge potential of spectral efficiency.
Abstract: In this paper, we firstly derive two approximations of the achievable uplink rate with the perfect/imperfect channel state information (CSI) in cell-free massive multi-input multi-output (MIMO) systems, and all these approximations are not only in the simple, but also converge into the classical bounds achieved in conventional massive MIMO systems where the base-station (BS) antennas are co-located. It is worth noting that the obtained two approximations with perfect CSI could be regarded as the special cases of the obtained two approximations with imperfect CSI when the pilot sequence power becomes infinite, respectively. Moreover, the theory analysis shows that all obtained approximations with perfect/imperfect CSI have an asymptotic lower bound $\frac {\alpha }{2}\log _{2} L$ thanks to the extra distance diversity offered by massively distributed antennas, where $L$ is the number of BS antennas and the path-loss factor $\alpha >2$ , except for the free space environment. Obviously, these results indicate that the cell-free massive MIMO system has huge potential of spectral efficiency than the conventional massive MIMO system with the asymptotically tight bound $\log _{2} L$ .

70 citations


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

  • ...In this regard, massive multiple-input multiple-output (MIMO) technology has been at the forefront thanks to its high SE characteristic provided by the massive array [2]–[6]....

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Journal ArticleDOI
TL;DR: In this paper, the authors investigate the applicability of massive MIMO to IoT connectivity and provide insights into the trade-offs that emerge when massive mIMO is applied to mMTC or URLLC and present a number of suitable communication schemes.

70 citations

Proceedings ArticleDOI
02 Jun 2013
TL;DR: This paper focuses on the algorithm which is based on belief propagation and implementable with the second-order calculations and provides very good BER performance in MIMO spatial multiplexing when the number of antenna elements is 100 and reasonably low complexity in comparison to the MMSE spatial filtering.
Abstract: A very large MIMO system has a potential to achieve extremely-high system throughput. In general, however, algorithms detecting spatially-multiplexed signals require the complexity proportional to the cubed number of antenna elements in the least case. Thus, the implementation of an antenna array with an order of 100 elements becomes very difficult. In this paper, we focus on the algorithm which is based on belief propagation and implementable with the second-order calculations. The simulation results show that the algorithm provides very good BER performance in MIMO spatial multiplexing when the number of antenna elements is 100 and reasonably low complexity in comparison to the MMSE spatial filtering.

69 citations


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

  • ...As an extension of this concept, recently, very large (or massive) MIMO systems with an order of 100 antenna elements have been proposed, and there its capability to achieve extremely high capacity is demonstrated [4], [5]....

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References
More filters
Journal ArticleDOI
Gerard J. Foschini1
TL;DR: This paper addresses digital communication in a Rayleigh fading environment when the channel characteristic is unknown at the transmitter but is known (tracked) at the receiver with the aim of leveraging the already highly developed 1-D codec technology.
Abstract: This paper addresses digital communication in a Rayleigh fading environment when the channel characteristic is unknown at the transmitter but is known (tracked) at the receiver. Inventing a codec architecture that can realize a significant portion of the great capacity promised by information theory is essential to a standout long-term position in highly competitive arenas like fixed and indoor wireless. Use (n T , n R ) to express the number of antenna elements at the transmitter and receiver. An (n, n) analysis shows that despite the n received waves interfering randomly, capacity grows linearly with n and is enormous. With n = 8 at 1% outage and 21-dB average SNR at each receiving element, 42 b/s/Hz is achieved. The capacity is more than 40 times that of a (1, 1) system at the same total radiated transmitter power and bandwidth. Moreover, in some applications, n could be much larger than 8. In striving for significant fractions of such huge capacities, the question arises: Can one construct an (n, n) system whose capacity scales linearly with n, using as building blocks n separately coded one-dimensional (1-D) subsystems of equal capacity? With the aim of leveraging the already highly developed 1-D codec technology, this paper reports just such an invention. In this new architecture, signals are layered in space and time as suggested by a tight capacity bound.

6,812 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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Journal ArticleDOI
TL;DR: Under certain mild conditions, this scheme is found to be throughput-wise asymptotically optimal for both high and low signal-to-noise ratio (SNR), and some numerical results are provided for the ergodic throughput of the simplified zero-forcing scheme in independent Rayleigh fading.
Abstract: A Gaussian broadcast channel (GBC) with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite its apparent simplicity, this model is, in general, a nondegraded broadcast channel (BC), for which the capacity region is not fully known. For the two-user case, we find a special case of Marton's (1979) region that achieves optimal sum-rate (throughput). In brief, the transmitter decomposes the channel into two interference channels, where interference is caused by the other user signal. Users are successively encoded, such that encoding of the second user is based on the noncausal knowledge of the interference caused by the first user. The crosstalk parameters are optimized such that the overall throughput is maximum and, surprisingly, this is shown to be optimal over all possible strategies (not only with respect to Marton's achievable region). For the case of r>2 users, we find a somewhat simpler choice of Marton's region based on ordering and successively encoding the users. For each user i in the given ordering, the interference caused by users j>i is eliminated by zero forcing at the transmitter, while interference caused by users j

2,616 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....

    [...]

Book
28 Jun 2004
TL;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.

2,308 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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Journal ArticleDOI
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.

1,802 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....

    [...]