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.
Citations
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10 Jun 2014
TL;DR: The lower bound on the average post-processing uplink signal to interference-plus-noise ratio (SINR) is derived with individual power assignment between pilot and data transmissions for each user, which facilitates a joint iterative uplink pilot andData power control strategy that minimizes the sum transmit power of all users subject to the per-user SINR and per- user power constraints.
Abstract: In the current literature considering multi-cell multi-user massive multiple-input multiple-output (MU-Massive-MIMO) systems, equal uplink power allocation among users is typically assumed, which does not exploit the potential of peruser power control. By contrast, in this paper we apply multi-cell uplink power control, assuming the minimum mean-square-error receiver based on the pilot contaminated channel estimation and a very large but finite number of antennas at the base station. We derive the lower bound on the average post-processing uplink signal to interference-plus-noise ratio (SINR) with individual power assignment between pilot and data transmissions for each user, which facilitates a joint iterative uplink pilot and data power control strategy that minimizes the sum transmit power of all users subject to the per-user SINR and per-user power constraints. The convergence of the proposed algorithm to a unique fixed point optimal solution is discussed for both single- and multi-user scenarios. Numerical results indicate the significance of uplink power control which further improves the energy efficiency in MU-Massive-MIMO systems.
105 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...The breakthrough work in [1] has stimulated substantial research activities investigating various aspects of multi-user massive multiple-input multiple-output (MU-Massive-MIMO) systems, where hundreds of antennas are deployed at the base station (BS) serving a much smaller number of singleantenna users at the same time-frequency resource....
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...Unlike the equal power allocation in [1]-[7], the diagonal matrix Pr,i = diag {[pr,i1, ....
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...However, these advantages of uplink power control have not been addressed in previous massive MIMO work [1]-[7], since equal uplink power allocation among users has always been assumed....
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...Based on the favorable propagation [2], where any pair of distinct channel vectors to a given BS tends to become orthogonal as the number of BS antennas increases, the results in [1]-[3] have demonstrated that simple linear receivers with infinite number of BS antennas completely eliminate the intra-cell interference and noise....
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Posted Content•
TL;DR: In this article, the performance of randomly-directional beamforming (RDB) and the MU gain in mm-wave MISO downlink systems were analyzed based on the uniform random line-of-sight (UR-LoS) channel model suitable for highly directional mmWave radio propagation channels.
Abstract: In this paper, randomly-directional beamforming (RDB) is considered for millimeter-wave (mmwave) multi-user (MU) multiple-input single-output (MISO) downlink systems. By using asymptotic techniques, the performance of RDB and the MU gain in mm-wave MISO are analyzed based on the uniform random line-of-sight (UR-LoS) channel model suitable for highly directional mm-wave radio propagation channels. It is shown that there exists a transition point on the number of users relative to the number of antenna elements for non-trivial performance of the RDB scheme, and furthermore sum rate scaling arbitrarily close to linear scaling with respect to the number of antenna elements can be achieved under the UR-LoS channel model by opportunistic random beamforming with proper user scheduling if the number of users increases linearly with respect to the number of antenna elements. The provided results yield insights into the most effective beamforming and scheduling choices for mm-wave MU-MISO in various operating conditions. Simulation results validate our analysis based on asymptotic techniques for finite cases.
104 citations
01 Dec 2014
TL;DR: This work investigates the properties of measured Massive MIMO channels in a large indoor venue and finds that performance is improved as the aperture increases, with an impact mostly visible in crowded scenarios where the users are closely spaced.
Abstract: Massive MIMO is a new technique for wireless communications that claims to offer very high system throughput and energy efficiency in multi-user scenarios. The cost is to add a very large number of antennas at the base station. Theoretical research has probed these benefits, but very few measurements have showed the potential of Massive MIMO in practice. We investigate the properties of measured Massive MIMO channels in a large indoor venue. We describe a measurement campaign using 3 arrays having different shape and aperture, with 64 antennas and 8 users with 2 antennas each. We focus on the impact of the array aperture which is the main limiting factor in the degrees of freedom available in the multiple antenna channel. We find that performance is improved as the aperture increases, with an impact mostly visible in crowded scenarios where the users are closely spaced. We also test MIMO capability within a same user device with user proximity effect. We see a good channel resolvability with confirmation of the strong effect of the user hand grip. At last, we highlight that propagation conditions where line-of-sight is dominant can be favourable.
104 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...Our vision is that the theoretical benefits described in [1] can be achieved in those large infrastructure deployment, while cellular deployment with BS located in high towers would benefit from the capability of massive MIMO for sharp beams....
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...In the seminal work of Marzetta [1], a massive MIMO (Multiple-Input Multiple-Output) system refers to a multi-user MIMO communication system where a base station comprises a very large number of antennas, much larger than the number of served users....
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...I. INTRODUCTION In the seminal work of Marzetta [1], a massive MIMO (Multiple-Input Multiple-Output) system refers to a multi-user MIMO communication system where a base station comprises a very large number of antennas, much larger than the number of served users....
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TL;DR: Numerical results depict that the proposed achievable SINRs (MMSE/RZF) are more efficient than simpler solutions (MRC/MRT) in delayed CSIT conditions, and yield a higher prediction at no special computational cost due to their deterministic nature.
Abstract: Delayed channel state information at the transmitter (CSIT) due to time variation of the channel, coming from the users' relative movement with regard to the BS antennas, is an inevitable degrading performance factor in practical systems Despite its importance, little attention has been paid to the literature of multi-cellular multiple-input massive multiple-output (MIMO) system by investigating only the maximal ratio combining (MRC) receiver and the maximum ratio transmission (MRT) precoder Hence, the contribution of this work is designated by the performance analysis/comparison of/with more sophisticated linear techniques, ie, a minimum-mean-square-error (MMSE) detector for the uplink and a regularized zero-forcing (RZF) precoder for the downlink are assessed In particular, we derive the deterministic equivalents of the signal-to-interference-plus-noise ratios (SINRs), which capture the effect of delayed CSIT, and make the use of lengthy Monte Carlo simulations unnecessary Furthermore, prediction of the current CSIT after applying a Wiener filter allows to evaluate the mitigation capabilities of MMSE and RZF Numerical results depict that the proposed achievable SINRs (MMSE/RZF) are more efficient than simpler solutions (MRC/MRT) in delayed CSIT conditions, and yield a higher prediction at no special computational cost due to their deterministic nature Nevertheless, it is shown that massive MIMO are preferable even in time-varying channel conditions
104 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...Along these lines, given a multi-cellular scenario, linear detectors and precoders behave nearly optimal as the number of BS antennas goes to infinity, taking into account that channel vectors tend to be orthogonal when the number of antennas is large [7]....
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...In this section, we present certain basic impairments that limit the performance by starting with the pilot contamination due to the interference from adjacent cells [7]....
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TL;DR: In this paper, the problem of determining the optimal downtilt weight vector for antenna ports, which maximizes the minimum signal-to-interference ratio of a multi-user multiple-input-single-output (MISO) system, is formulated as a fractional optimization problem.
Abstract: This paper discusses full-dimension multiple-input-multiple-output (FD-MIMO) technology, which is currently an active area of research and standardization in wireless communications for evolution toward Fifth Generation (5G) cellular systems. FD-MIMO utilizes an active antenna system (AAS) with a 2-D planar array structure that not only allows a large number of antenna elements to be packed within feasible base station form factors, but also provides the ability of adaptive electronic beamforming in the 3-D space. However, the compact structure of large-scale planar arrays drastically increases the spatial correlation in FD-MIMO systems. In order to account for its effects, the generalized spatial correlation functions for channels constituted by individual elements and overall antenna ports in the AAS are derived. Exploiting the quasi-static channel covariance matrices of users, the problem of determining the optimal downtilt weight vector for antenna ports, which maximizes the minimum signal-to-interference ratio of a multi-user multiple-input-single-output system, is formulated as a fractional optimization problem. A quasi-optimal solution is obtained through the application of semi-definite relaxation and Dinkelbach’s method. Finally, the user-group specific elevation beamforming scenario is devised, which offers significant performance gains as confirmed through simulations. These results have direct application in the analysis of 5G FD-MIMO systems.
104 citations
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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