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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TL;DR: This paper provides an overview on the rationales in incorporating massive multiple-input multiple-output (MIMO), non-orthogonal multiple access (NOMA), and interleave division multipleAccess (IDMA) in a unified framework based on IDMA and iterative data-aided channel estimation (DACE).
Abstract: This paper provides an overview on the rationales in incorporating massive multiple-input multiple-output (MIMO), non-orthogonal multiple access (NOMA), and interleave division multiple access (IDMA) in a unified framework. Our emphasis is on multi-user gain that refers to the advantage of allowing multi-user transmission in massive MIMO. Such a gain can potentially offer tens or even hundreds of times of rate increase. The main difficulty in achieving multi-user gain is the reliance on accurate channel state information (CSI) in the existing schemes. With accurate CSI, both OMA and NOMA can deliver performance not far away from capacity. Without accurate CSI, however, most of the existing schemes do not work well. We outline a solution to this difficulty based on IDMA and iterative data-aided channel estimation (DACE). This scheme can offer very high throughput and is robust against the pilot contamination problem. The receiver cost is low, since only maximum ratio combining (MRC) is involved and there is no matrix inversion or decomposition. Under time division duplex, accurate CSI acquired in the up-link can be used to support low-cost down-link solutions, such as zero forcing. These findings offer useful design considerations for future systems.
55 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...Pilot contamination is an open problem in this case [12]....
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...Massive MIMO refers to the situation when the number of antennas involved is very large [12]–[18]....
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...CHANNEL MODEL Massive MIMO systems can be divided into millimeterwave [80]–[86] and sub-millimeter wave ones [12]–[18]....
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...The correlation among different pilots also results in the so-called pilot contamination problem [12], [13], [21], [22]....
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08 Jun 2015
TL;DR: In this paper, the effects of the ratio of the number of massive MIMO antennas to the total number of users on the performance of NS-based matrix inversion approximations were analyzed.
Abstract: Zero-Forcing (ZF) has been considered as one of the potential practical precoding and detection method for massive MIMO systems. One of the most important advantages of massive MIMO is the capability of supporting a large number of users in the same time-frequency resource, which requires much larger dimensions of matrix inversion for ZF than conventional multi-user MIMO systems. In this case, Neumann Series (NS) has been considered for the Matrix Inversion Approximation (MIA), because of its suitability for massive MIMO systems and its advantages in hardware implementation. The performancecomplexity trade-off and the hardware implementation of NSbasedMIA in massive MIMO systems have been discussed. In this paper, we analyze the effects of the ratio of the number of massive MIMO antennas to the number of users on the performance of NS-based MIA. In addition, we derive the approximation error estimation formulas for different practical numbers of terms of NS-based MIA. These results could offer useful guidelines for practical massive MIMO systems.
55 citations
TL;DR: In this paper, the authors considered a cell-free massive multiple-input multiple-output (MIMO) system where access points and users are equipped with multiple antennas and derived a general spectral efficiency formula with arbitrary side information at the users.
Abstract: This paper studies a cell-free massive multiple-input multiple-output (MIMO) system where its access points (APs) and users are equipped with multiple antennas. Two transmission protocols are considered. In the first transmission protocol, there are no downlink pilots, while in the second transmission protocol, downlink pilots are proposed in order to improve the system performance. In both transmission protocols, the users use the minimum mean-squared error-based successive interference cancellation (MMSE-SIC) scheme to detect the desired signals. For the analysis, we first derive a general spectral efficiency formula with arbitrary side information at the users. Then analytical expressions for the spectral efficiency of different transmission protocols are derived. To improve the spectral efficiency (SE) of the system, max-min fairness power control (PC) is applied for the first protocol by using the closed-form expression of its SE. Due to the computation complexity of deriving the closed-form performance expression of SE for the second protocol, we apply the optimal power coefficients of the first protocol to the second protocol. Numerical results show that two protocols combining with multi-antenna users are prerequisites to achieve the sub-optimal SE regardless of the number of user in the system.
55 citations
TL;DR: A comprehensive survey of MIMO detectors ranging from hard decision to soft decision can be found in this paper, where the authors provide reduced-complexity design guidelines for a wide range of soft-decision detectors.
Abstract: A pair of salient tradeoffs have driven the multiple-input multiple-output (MIMO) systems developments. More explicitly, the early era of MIMO developments was predominantly motivated by the multiplexing-diversity tradeoff between the Bell Laboratories layered space-time and space-time block coding. Later, the linear dispersion code concept was introduced to strike a flexible tradeoff. The more recent MIMO system designs were motivated by the performance-complexity tradeoff, where the spatial modulation and space-time shift keying concepts eliminate the problem of inter-antenna interference and perform well with the aid of low-complexity linear receivers without imposing a substantial performance loss on generic maximum-likelihood/max a posteriori -aided MIMO detection. Against the background of the MIMO design tradeoffs in both uncoded and coded MIMO systems, in this treatise, we offer a comprehensive survey of MIMO detectors ranging from hard decision to soft decision. The soft-decision MIMO detectors play a pivotal role in approaching to the full-performance potential promised by the MIMO capacity theorem. In the near-capacity system design, the soft-decision MIMO detection dominates the total complexity, because all the MIMO signal combinations have to be examined, when both the channel’s output signal and the a priori log-likelihood ratios gleaned from the channel decoder are taken into account. Against this background, we provide reduced-complexity design guidelines, which are conceived for a wide-range of soft-decision MIMO detectors.
55 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....
[...]