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 considers a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter, and derives an asymptotic achievable secrecy rate when the number of transmit antennas approaches infinity.
Abstract: In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multiple-input multiple-output systems with a multi-antenna active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform toward the eavesdropper, thus increasing its received signal power. Assuming matched filter precoding and artificial noise (AN) generation at the transmitter, we derive an asymptotic achievable secrecy rate when the number of transmit antennas approaches infinity. For the case of a single-antenna active eavesdropper, we obtain a closed-form expression for the optimal power allocation policy for the transmit signal and the AN, and find the minimum transmit power required to ensure reliable secure communication. Furthermore, we show that the transmit antenna correlation diversity of the intended users and the eavesdropper can be exploited in order to improve the secrecy rate. In fact, under certain orthogonality conditions of the channel covariance matrices, the secrecy rate loss introduced by the eavesdropper can be completely mitigated.
272 citations
Cites methods from "Noncooperative Cellular Wireless wi..."
...Then, rlE,RR l E,T can be obtained by subtracting the correlation matrices of the legitimate users and the noise from E [ ỹlmỹ H lm ] ....
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...(1) can be rewritten as y0 = K∑ k=1 √ P0k (ω0k ⊗ INt) h00k + L∑ l=1 K∑ k=1 √ Plk (ωlk ⊗ INt) h0lk + √ PE Ne (ω0m ⊗ INt) Ne∑ r=1 h0eff,r + n, (2) where y0 = vec (Y0), n = vec (N), and hleff,r denotes the rth column of matrix HlEPe, l = 0, 1, · · · , L....
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...(8)] R0m = E [log2 (1 + SINR0m)] (19) where SINR0m is given by SINR0m = pγ ∣∣∣(h00m)Hw0m∣∣∣2 A (20) A = pγ K∑ k=1,k 6=m ∣∣∣(h00m)Hw0k∣∣∣2 + qγ∣∣∣(h00m)HUnull, 0∣∣∣2 +pγ L∑ l=1 K∑ k=1 ∣∣∣(hl0m)Hwlk∣∣∣2+qγ L∑ l=1 ∣∣∣(hl0m)HUnull, l∣∣∣2+1....
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TL;DR: An accurate and tractable model is proposed to characterize the uplink SINR and rate distribution in a multi-tier HCN as a function of the association rules and power control parameters and it is shown that the optimal degree of channel inversion increases with load imbalance in the network.
Abstract: Load balancing by proactively offloading users onto small and otherwise lightly-loaded cells is critical for tapping the potential of dense heterogeneous cellular networks (HCNs). Offloading has mostly been studied for the downlink, where it is generally assumed that a user offloaded to a small cell will communicate with it on the uplink as well. The impact of coupled downlink-uplink offloading is not well understood. Uplink power control and spatial interference correlation further complicate the mathematical analysis as compared to the downlink. We propose an accurate and tractable model to characterize the uplink $\textnormal{\texttt{SINR}}$ and rate distribution in a multi-tier HCN as a function of the association rules and power control parameters. Joint uplink-downlink rate coverage is also characterized. Using the developed analysis, it is shown that the optimal degree of channel inversion (for uplink power control) increases with load imbalance in the network. In sharp contrast to the downlink, minimum path loss association is shown to be optimal for uplink rate. Moreover, with minimum path loss association and full channel inversion, uplink $\textnormal{\texttt{SIR}}$ is shown to be invariant of infrastructure density. It is further shown that a decoupled association —employing differing association strategies for uplink and downlink—leads to significant improvement in joint uplink-downlink rate coverage over the standard coupled association in HCNs.
271 citations
Cites methods from "Noncooperative Cellular Wireless wi..."
... 25 on the presented insights could be considered in the future. The proposed uplink interference characterization can also be used to analyze systems like massive MIMO, where it plays a crucial role [30]. Performance analysis for decoupled association incorporating the cost of possible architectural changes [20] could also be one area of future investigation. ACKNOWLEDGMENT The authors appreciate hel...
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Patent•
AT&T1
TL;DR: In this paper, a dielectric antenna array is configured to receive the first guided electromagnetic waves and to transmit a controllable beam in response thereto, and other aspects of the subject disclosure are disclosed.
Abstract: Aspects of the subject disclosure may include, for example, an antenna system that includes a plurality of dielectric members configured to propagate first guided electromagnetic waves. A dielectric antenna array is configured to receive the first guided electromagnetic waves and to transmit a controllable beam in response thereto. Other embodiments are disclosed.
269 citations
Patent•
AT&T1
TL;DR: In this paper, a conductive layer forms an uninsulated outer surface of the transmission medium and is configured to impede accumulation of water to support propagation of first electromagnetic waves guided by the conductive outer surface.
Abstract: Aspects of the subject disclosure may include, for example, a transmission medium having a core. A conductive layer forms an uninsulated outer surface of the transmission medium. The conductive layer is configured to impede accumulation of water to support propagation of first electromagnetic waves guided by the uninsulated outer surface. Other embodiments are disclosed.
268 citations
TL;DR: A general overview of the current low-rank channel estimation approaches is provided, including their basic assumptions, key results, as well as pros and cons on addressing the aforementioned tricky challenges.
Abstract: Massive multiple-input multiple-output is a promising physical layer technology for 5G wireless communications due to its capability of high spectrum and energy efficiency, high spatial resolution, and simple transceiver design. To embrace its potential gains, the acquisition of channel state information is crucial, which unfortunately faces a number of challenges, such as the uplink pilot contamination, the overhead of downlink training and feedback, and the computational complexity. In order to reduce the effective channel dimensions, researchers have been investigating the low-rank (sparse) properties of channel environments from different viewpoints. This paper then provides a general overview of the current low-rank channel estimation approaches, including their basic assumptions, key results, as well as pros and cons on addressing the aforementioned tricky challenges. Comparisons among all these methods are provided for better understanding and some future research prospects for these low-rank approaches are also forecasted.
265 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...If the same training sequences are reused or non-orthogonal training sequences are adopted, then the inter-user interference will arise during the channel estimation stage, which is known as pilot contamination [1]....
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...Unfortunately, channel reciprocity is not applicable for frequency division duplexing (FDD) systems, which is still a dominant transmission mode in most communications systems [1]....
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...INTRODUCTION Large-scale multiple-input multiple-output (MIMO) or ‘‘massive MIMO’’, a new technique that employs hundreds or even thousands of antennas at base station (BS) to simultaneously serve multiple users, has been widely investigated for its numerous merits, such as high spectrum and energy efficiency, high spatial resolution, and simple transceiver design [1]....
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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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