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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04 Dec 2014
TL;DR: It is proved that the filtering matrix of the MMSE algorithm in large-scale MIMO is symmetric positive definite, based on which a low-complexity signal detection algorithm is proposed by exploiting the Richardson method to avoid the complicated matrix inversion.
Abstract: Minimum mean square error (MMSE) signal detection is near-optimal for uplink multi-user large-scale MIMO systems with hundreds of antennas at the base station, but involves matrix inversion with high complexity. In this paper, we first prove that the filtering matrix of the MMSE algorithm in large-scale MIMO is symmetric positive definite, based on which we propose a low-complexity signal detection algorithm by exploiting the Richardson method to avoid the complicated matrix inversion. The proof of the convergence of the proposed scheme is also provided. We then propose a zone-based initial solution by simply checking the values of the received signals, which can accelerate the convergence rate of the Richardson method for high-order modulations to reduce the complexity further. The analysis shows that the complexity can be reduced from O(K3) to O(K2) by the proposed signal detection algorithm, where K is the number of users. Simulation results indicate that the proposed algorithm outperforms the recently proposed Neumann series approximation algorithm and achieves the near-optimal performance of the classical MMSE algorithm.
62 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...serve K single-antenna UEs [2], [3], [5]....
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...Unlike the conventional MIMO with small number of antennas (e.g., at most 4 for uplink in LTE-A), large-scale MIMO, where the base station (BS) is equipped with a very large number of antennas (e.g., 128 antennas or even more) to simultaneously serve multiple user equipments (UEs), is recently proposed [2]....
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..., 128 antennas or even more) to simultaneously serve multiple user equipments (UEs), is recently proposed [2]....
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...Consider a uplink large-scale multi-user MIMO system which employs N antennas at the BS to simultaneously 978-1-4799-4449-1/14/$31.00 ©2014 IEEE serve K single-antenna UEs [2], [3], [5]....
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Posted Content•
TL;DR: This paper proposes a frequency synchronization scheme for multiuser orthogonal frequency division multiplexing uplink with a large-scale uniform linear array at base station (BS) by exploiting the angle information of users to perform carrier frequency offset estimation for each user individually through a joint spatial-frequency alignment procedure.
Abstract: In this paper, we propose a frequency synchronization scheme for multiuser orthogonal frequency division multiplexing (OFDM) uplink with a large-scale uniform linear array (ULA) at base station (BS) by exploiting the angle information of users. Considering that the incident signal at BS from each user can be restricted within a certain angular spread, the proposed scheme could perform carrier frequency offset (CFO) estimation for each user individually through a \textit{joint spatial-frequency alignment} procedure and can be completed efficiently with the aided of fast Fourier transform (FFT). A multi-branch receive beamforming is further designed to yield an equivalent single user transmission model for which the conventional single-user channel estimation and data detection can be carried out. To make the study complete, the theoretical performance analysis of the CFO estimation is also conducted. We further develop a user grouping scheme to deal with the unexpected scenarios that some users may not be separated well from the spatial domain. Finally, various numerical results are provided to verify the proposed studies.
62 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...LARGE-SCALE multiple-input multiple-output (MIMO) or “massive MIMO” systems have drawn considerable interests from both academia and industry [1]–[4]....
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TL;DR: A novel and comprehensive optimization problem for the maximization of SE and EE in which power control, access point-UE (AP-UE) association and AP selection are jointly optimized under a realistic power consumption model, resulting in a difficult class of mixed-integer nonconvex programming.
Abstract: In-band full-duplex (FD) operation is practically more suited for short-range communications such as WiFi and small-cell networks, due to its current practical limitations on the self-interference cancellation. In addition, cell-free massive multiple-input multiple-output (CF-mMIMO) is a new and scalable version of MIMO networks, which is designed to bring service antennas closer to end user equipments (UEs). To achieve higher spectral and energy efficiencies (SE-EE) of a wireless network, it is of practical interest to incorporate FD capability into CF-mMIMO systems to utilize their combined benefits. We formulate a novel and comprehensive optimization problem for the maximization of SE and EE in which power control, access point-UE (AP-UE) association and AP selection are jointly optimized under a realistic power consumption model, resulting in a difficult class of mixed-integer nonconvex programming. To tackle the binary nature of the formulated problem, we propose an efficient approach by exploiting a strong coupling between binary and continuous variables, leading to a more tractable problem. In this regard, two low-complexity transmission designs based on zero-forcing (ZF) are proposed. Combining tools from inner approximation framework and Dinkelbach method, we develop simple iterative algorithms with polynomial computational complexity in each iteration and strong theoretical performance guaranteed. Furthermore, towards a robust design for FD CF-mMIMO, a novel heap-based pilot assignment algorithm is proposed to mitigate effects of pilot contamination. Numerical results show that our proposed designs with realistic parameters significantly outperform the well-known approaches (i.e., small-cell and collocated mMIMO) in terms of the SE and EE. Notably, the proposed ZF designs require much less execution time than the simple maximum ratio transmission/combining.
62 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...The coherence interval is short, and thus, each UE should practically be assigned a non-orthogonal pilot sequence, resulting in the well-known pilot contamination problem [29]....
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...As being collocated massive MIMO networks (Co-mMIMO) [28], [29], CF-mMIMO also inherits the properties of favorable propagation and channel hardening to multiplex a large number of UEs....
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TL;DR: An additive quantization noise model and an extended error vector magnitude model are utilized to analyze the impacts of low-resolution analog-to-digital converters (ADCs) and RF impairments, respectively and support the feasibility of equipping economical coarse ADCs and economical imperfect RF components in practical massive MIMO systems.
Abstract: This letter considers channel estimation and uplink achievable rate of the coarsely quantized massive multiple-input multiple-output (MIMO) system with radio frequency (RF) impairments. We utilize an additive quantization noise model and an extended error vector magnitude model to analyze the impacts of low-resolution analog-to-digital converters (ADCs) and RF impairments, respectively. We show that hardware impairments cause a nonzero floor on the channel estimation error, which contraries to the conventional case with ideal hardware. The maximal-ratio combining technique is then used at the receiver, and an approximate tractable expression for the uplink achievable rate is derived. The simulation results illustrate the appreciable compensations between ADCs’ resolution and RF impairments. The proposed studies support the feasibility of equipping economical coarse ADCs and economical imperfect RF components in practical massive MIMO systems.
62 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...Introduction M ASSIVE multi-input multi-output (MIMO), a promising technology for 5G mobile network, deploys a large number of radio frequency (RF) chains and analog-to-digital converters (ADCs) at the base station (BS) [1]....
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...where hmk ∼ CN(0, 1) is the fast-fading coefficient, and βk presents both geometric attenuation and shadow fading of the kth user to the whole antenna array [1]....
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...The geometric attenuation and shadow fading are defined as βk = zk/(rk/rh), where zk is a log-normal variable with 10 log10(zk) ∼ N(0, σ2 shadow) [1], and rk is the distance between the kth user and the BS....
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TL;DR: Numerical results demonstrate that the two-tier precoding with the proposed iterative compensation algorithm can achieve a good performance with a significant complexity reduction compared with the conventional two- tier precoding techniques in the literature.
Abstract: Massive MIMO is a promising technology in future wireless communication networks. However, it raises a lot of implementation challenges, for example, the huge pilot symbols and feedback overhead, requirement of real-time global CSI, large number of RF chains needed and high computational complexity. We consider a two-tier precoding strategy for multi-cell massive MIMO interference networks, with an outer precoder for inter-cell/inter-cluster interference cancellation, and an inner precoder for intra-cell multiplexing. In particular, to combat with the computational complexity issue of the outer precoding, we propose a low complexity online iterative algorithm to track the outer precoder under time-varying channels. We follow an optimization technique and formulate the problem on the Grassmann manifold. We develop a low complexity iterative algorithm, which converges to the global optimal solution under static channels. In time-varying channels, we propose a compensation technique to offset the variation of the time-varying optimal solution. We show with our theoretical result that, under some mild conditions, perfect tracking of the target outer precoder using the proposed algorithm is possible. Numerical results demonstrate that the two-tier precoding with the proposed iterative compensation algorithm can achieve a good performance with a significant complexity reduction compared with the conventional two-tier precoding techniques in the literature.
61 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...eases the signaling latency. Remark 1 (Inter-cell Interference in Massive MIMO): It is reported that the inter-cell interference (ICI) of multi-cell massive MIMO systems can be asymptotically ignored [26] using simple per-cell zero-forcing. One key assumption is that the direct links and interference links are spatially uncorrelated. However, such uncorrelation may not hold under local scattering (suc...
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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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