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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01 Dec 2012
TL;DR: In this article, the authors proposed a massive MIMO system where three radio units (RUs) connected via one digital unit (DU) support multiple user equipments (UEs) at a cell-boundary through the same radio resource, i.e., the same frequency/time band.
Abstract: In this paper, we propose network massive multiple-input multiple-output (MIMO) systems, where three radio units (RUs) connected via one digital unit (DU) support multiple user equipments (UEs) at a cell-boundary through the same radio resource, i.e., the same frequency/time band. For precoding designs, zero-forcing (ZF) and matched filter (MF) with vector or matrix normalization are considered. We also derive the formulae of the lower and upper bounds of the achievable sum rate for each precoding. Based on our analytical results, we observe that vector normalization is better for ZF while matrix normalization is better for MF. Given antenna configurations, we also derive the optimal switching point as a function of the number of active users in a network. Numerical simulations confirm our analytical results.
48 citations
TL;DR: This paper derives an exact analytical closed-form expression for the achievable ergodic rate and presents tractable tight upper and lower bounds, and reveals that the rate gap tends to zero in the high Rician $K$-factor regime.
Abstract: In this paper, we study the achievable ergodic sum-rate of multiuser multiple-input multiple-output downlink systems in Rician fading channels. We first derive a lower bound on the average signal-to-leakage-and-noise ratio by using the Mullen's inequality, and then use it to analyze the effect of channel mean information on the achievable ergodic sum-rate. A novel statistical-eigenmode space-division multiple-access (SE-SDMA) downlink transmission scheme is then proposed. For this scheme, we derive an exact analytical closed-form expression for the achievable ergodic rate and present tractable tight upper and lower bounds. Based on our analysis, we gain valuable insights into the impact of the system parameters, such as the number of transmit antennas, the signal-to-noise ratio (SNR) and Rician $K$ -factor, on the system sum-rate. Results show that the sum-rate converges to a saturation value in the high SNR regime and tends to a lower limit for the low Rician $K$ -factor case. In addition, we compare the achievable ergodic sum-rate between SE-SDMA and zero-forcing beamforming with perfect channel state information at the base station. Our results reveal that the rate gap tends to zero in the high Rician $K$ -factor regime.
48 citations
Cites background or result from "Noncooperative Cellular Wireless wi..."
...In [7], it was found that the effect of fast fading will vanish when the BS deploys very large antenna arrays while simultaneously serving multiple users....
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..., hundreds of antennas), has the advantage of providing both higher spectral efficiency and energy efficiency [6], [7]....
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...This is because as Nt → ∞, the random channel vectors between the BS and the users become orthogonal, which is consistent with the conclusion in [7]....
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...This observation means that all leakage to other users can be eliminated by deploying a large number of antennas at the BS, which is in good agreement with the conclusion in [7]....
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TL;DR: The results show that the transmit power allocated to the users should be nonoverlapping across beams defined by the channel transmit covariance matrices, and two algorithms to optimize power allocation in the beam space are presented.
Abstract: We investigate power allocation strategies for beam division multiple access transmission in multicell massive multiple-input-multiple-output (MIMO) communications. Focusing on massive MIMO downlink with only statistical channel state information at serving base stations and multiantenna terminals, the eigenmatrices of channel transmit covariance matrices become identical and independent of terminals. Utilizing these eigenmatrices as precoding matrices, we consider power allocation of beam domain transmission. By treating cochannel user interferences as noises, the objective function of achievable ergodic sum-rate of the multicell massive MIMO downlink reduces to a difference of concave functions. We identify the orthogonality conditions for optimal power allocation. The results show that the transmit power allocated to the users should be nonoverlapping across beams defined by the channel transmit covariance matrices. We present two algorithms to optimize power allocation in the beam space. We also prove the convergence of the algorithms and show that the solution obtained by the algorithms satisfies the orthogonality conditions. Numerical results confirm the efficiency and the improved performance of the proposed algorithms.
48 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...2675862 channels, such a massive MIMO configuration has several attractive features [1] including: 1) downlink channel vectors for different users become asymptotically orthogonal with growing number of transmit antennas at the BS; 2) independent user beamforming can mitigate intra-cell interferences and uncorrelated noises; and 3) transmit power can be asymptotically low....
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...IN developing next generation wireless networks, massive multiple-input multiple-output (MIMO) is a promising technology to deliver high spectral and power efficiencies and has attracted much interest from both academia and industry [1]–[4]....
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TL;DR: A special property that the filtering matrix of the linear MMSE algorithm is symmetric positive definite for indoor optical MIMO systems is proved, and a low-complexity signal detection algorithm based on the successive overrelaxation (SOR) method can achieve a faster convergence rate than the recently proposed Neumann-based algorithm.
Abstract: Optical wireless communication (OWC) has been a rapidly growing research area in recent years. Applying multiple-input multiple-output (MIMO), particularly large-scale MIMO, into OWC is very promising to substantially increase spectrum efficiency. However, one challenging problem to realize such an attractive goal is the practical signal detection algorithm for optical MIMO systems, whereby the linear signal detection algorithm like minimum mean square error (MMSE) can achieve satisfying performance but involves complicated matrix inversion of large size. In this paper, we first prove a special property that the filtering matrix of the linear MMSE algorithm is symmetric positive definite for indoor optical MIMO systems. Based on this property, a low-complexity signal detection algorithm based on the successive overrelaxation (SOR) method is proposed to reduce the overall complexity by one order of magnitude with a negligible performance loss. The performance guarantee of the proposed SOR-based algorithm is analyzed from the following three aspects. First, we prove that the SOR-based algorithm is convergent for indoor large-scale optical MIMO systems. Second, we prove that the SOR-based algorithm with the optimal relaxation parameter can achieve a faster convergence rate than the recently proposed Neumann-based algorithm. Finally, a simple quantified relaxation parameter, which is independent of the receiver location and signal-to-noise ratio, is proposed to guarantee the performance of the SOR-based algorithm in practice. Simulation results verify that the proposed SOR-based algorithm can achieve the exact performance of the classical MMSE algorithm with a small number of iterations.
48 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...proposed large-scale MIMO using tens or hundreds of antennas [6], into indoor OWC to simultaneously increase the spectrum efficiency and energy efficiency by orders of magnitude [7]....
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...Additionally, as it has been verified that MMSE algorithm can approach the performance of the optimal ML algorithm in large-scale MIMO systems [6], while the simulation results demonstrate that the proposed SOR-based algorithm can achieve the exact performance of MMSE algorithm with a small number of iterations, i....
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TL;DR: Simulation results demonstrate the effectiveness of the proposed information-theoretic pilot design for the downlink channel estimation in FDD massive MIMO systems.
Abstract: Massive multiple-input multiple-output (MIMO) is one of the most promising techniques for next generation wireless communications due to its superior capability to provide high spectrum and energy efficiency. Considering the very large number of antennas employed at the base station, however, the pilot overhead for downlink channel estimation becomes unaffordable in frequency division duplex (FDD) multiuser massive MIMO systems. In this paper, we propose an information-theoretic metric to design the pilot for downlink channel estimation in FDD multiuser massive MIMO systems. By exploiting the low-rank nature of the channel covariance matrix, we first derive the minimum number of pilot symbols required to ensure perfect channel recovery, which is much less than the number of antennas at the base station. Further, under a general channel model that the channel vector of each user follows a Gaussian mixture distribution, the pilot symbols are designed by maximizing the weighted sum of the Shannon mutual information between the measurements of the users and their corresponding channel vectors on the complex Grassmannian manifold. Simulation results demonstrate the effectiveness of the proposed information-theoretic pilot design for the downlink channel estimation in FDD massive MIMO systems.
48 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...Among them, the TDD is popular for massive MIMO [2], [15]–[18], where the principle of reciprocity can be leveraged, that is, the downlink channel vector (or matrix) is simply the transpose of the uplink channel vector (or matrix)....
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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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