Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas
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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Patent•
AT&T1
TL;DR: In this article, the authors describe a network device of a neighborhood network that determines that data is directed to a group of recipient devices positioned in a service area of the neighborhood network, determines a second network device according to a neighborhood routing scheme that limits delivery of the data to recipient devices within the service area, and transmits the data.
Abstract: Aspects of the subject disclosure may include, for example, a network device of a neighborhood network that determines that data is directed to a group of recipient devices positioned in a service area of the neighborhood network, determines a second network device according to a neighborhood routing scheme that limits delivery of the data to recipient devices within the service area, and transmits the data. Other embodiments are disclosed.
93 citations
TL;DR: It is shown that, using massive MIMO, the uplink SINR in certain urban marcocell scenarios is limited by interference, and the optimal compensation fraction in fractional power control to optimize rate is generally different for MRC and ZF receivers.
Abstract: This paper proposes a stochastic geometry framework to analyze the signal-to-noise-and-interference ratio (SINR) and rate performance in a large-scale uplink massive multiple-input and multiple-output (MIMO) network. Based on the model, expressions are derived for spatial average SINR distributions over user and base station distributions with maximum ratio combining (MRC) and zero-forcing (ZF) receivers. We show that, using massive MIMO, the uplink SINR in certain urban marcocell scenarios is limited by interference. In the interference-limited regime, the results reveal that for MRC receivers, a superlinear (polynomial) scaling law between the number of base station antennas and scheduled users per cell preserves the uplink signal-to-interference ratio (SIR) distribution, while a linear scaling applies to ZF receivers. ZF receivers are shown to outperform MRC receivers in the SIR coverage, and the performance gap is quantified in terms of the difference in the number of antennas to achieve the same SIR distribution. Numerical results verify the analysis. It is found that the optimal compensation fraction in fractional power control to optimize rate is generally different for MRC and ZF receivers. Besides, simulations show that the scaling results derived from the proposed framework apply to the networks, where base stations are distributed according to a hexagonal lattice.
93 citations
Cites background or methods from "Noncooperative Cellular Wireless wi..."
...In this paper, we focus on the defacto massive MIMO systems operated below 6 GHz, where pilot-aided channel estimation is performed in the uplink, and pilots are reused across cells to reduce the training overhead [2]–[5]....
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...By deploying large-scale antenna arrays, base stations can use multi-user MIMO to serve a large number of users and provide high cell throughput [2]–[5]....
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...Note that the system model assumption applies to general uplink multi-user MIMO networks with pilot-aided channel estimation in the uplink, including but not limited to the time-division duplex (TDD) massive MIMO [2]....
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...(i) they did not take account for the effects of pilot contamination, which becomes a limiting factor with large numbers of antennas [2]; (ii) the analysis in [15]–[20] was intended for downlink performance, which follows different distributions from the uplink network; and (iii) the results in [16]–[19] were intended for MIMO networks with a few antennas, where the computational complexity for the analytical expressions grows with the number of antennas, and hinders their direct applications to the massive MIMO scenarios....
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...MASSIVE multiple-input and multiple-output (MIMO) is an approach to increase the area spectrum efficiency in 5G cellular systems [2]–[5]....
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TL;DR: Simulation results show that the proposed signal detection algorithm converges fast, and achieves the near-optimal performance of the classical MMSE algorithm.
Abstract: The minimum mean square error (MMSE) signal detection algorithm is near-optimal for uplink multi-user large-scale multiple-input-multiple-output (MIMO) systems, but involves matrix inversion with high complexity. It is firstly proved that the MMSE filtering matrix for large-scale MIMO is symmetric positive definite, based on which a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method to avoid the matrix inversion is proposed. The complexity can be reduced from O(K 3 ) to O(K 2 ), where K is the number of users. The convergence proof of the proposed algorithm is also provided. Simulation results show that the proposed signal detection algorithm converges fast, and achieves the near-optimal performance of the classical MMSE algorithm.
93 citations
TL;DR: A single-cell analysis discloses that Massive MIMO with max-min power control performs comparably underLoS and iid Rayleigh, when a simple algorithm is applied under LoS to drop a small number of high-correlation users from service.
Abstract: Massive MIMO relies on the asymptotic orthogonality of channel vectors to different users. For $M$ service antennas, the expected correlation between a pair of channel vectors under line-of-sight (LoS) conditions decreases at least as fast as $\log (M)/M$ , while in independent and identically distributed (iid) Rayleigh fading, it decreases much slower at $1/\sqrt {M}$ , but the variance is higher under LoS. This signifies that typically channel vectors are more nearly orthogonal under LoS, but with a non-negligible probability, they can have an anomalously large correlation. A single-cell analysis discloses that Massive MIMO with max-min power control performs comparably under LoS and iid Rayleigh, when a simple algorithm is applied under LoS to drop a small number of high-correlation users from service.
93 citations
Cites background or methods from "Noncooperative Cellular Wireless wi..."
...THE analysis of Massive MIMO (multi-input multioutput) [1] systems is greatly facilitated by assuming a rich scattering, iid (independent and identically distributed) Rayleigh fading environment [2], and experiments have established conditions under which this model is approximately valid [3]....
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...The notion of ergodic capacity is associated with coding over many independent realizations of all sources of randomness, and it permits us to average over the channel matrix to obtain capacity expressions [1], [2]....
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TL;DR: A new approach to constant-envelope precoding (CEP) based on an interference-driven optimization region for generic phase-shift-keying modulations in the multi-user (MU) multiple-input-multiple-output downlink is introduced.
Abstract: We introduce a new approach to constant-envelope precoding (CEP) based on an interference-driven optimization region for generic phase-shift-keying modulations in the multi-user (MU) multiple-input-multiple-output downlink. While conventional precoding approaches aim to minimize the multi-user interference (MUI) with a total sum-power constraint at the transmitter, in the proposed scheme we consider MUI as a source of additional energy to increase the signal-to-interference-and-noise-ratio at the receiver. In our studies, we focus on two different CEP approaches: a first technique, where the power at each antenna is fixed to a specific value, and a two-step approach, where we first relax the power constraints to be lower than a defined parameter and then enforce CEP transmission. The algorithms are studied in terms of computational costs, with a detailed comparison between the proposed approach and the classical interference suppression schemes from the literature. Moreover, we analytically derive a robust optimization region to counteract the effects of channel-state estimation errors. The presented schemes are evaluated in terms of achievable symbol error rate in a perfect and imperfect channel-state information scenario for different modulation orders. Our results show that the proposed techniques further extend the benefits of classical CEP by judiciously relaxing the optimization region.
93 citations
Cites background or methods from "Noncooperative Cellular Wireless wi..."
...The pioneering work from [1] proved that a base station (BS) equipped with high dimensional antenna arrays can achieve high throughput values by exploiting the innate high degrees of freedom offered by a large number of antennas at the transmitter....
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...Complex channel gains hm,n in M-MIMO are modeled to include both the complex small scale fading gm,n between the n-th antenna and the m-th user and the real large scale fading coefficient βm experienced by the m-th user [1], leading to the following analytical definition...
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...MASSIVE Multiple-Input-Multiple-Output (M-MIMO) communication systems have experienced an increasing growth of interest from the scientific community, because of the significant benefits they provide in terms of spectral efficiency when compared to classical MIMO approaches [1], [2]....
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References
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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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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....
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Book•
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.
2,308 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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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.
1,802 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....
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