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
More filters
TL;DR: Practical open-loop and closed-loop training frameworks are proposed that offer better performance in the data communication phase, especially when the signal-to-noise ratio is low, the number of transmit antennas is large, or prior channel estimates are not accurate at the beginning of the communication setup, all of which would be mostly beneficial for massive MIMO systems.
Abstract: The concept of deploying a large number of antennas at the base station, often called massive multiple-input multiple-output (MIMO), has drawn considerable interest because of its potential ability to revolutionize current wireless communication systems. Most literature on massive MIMO systems assumes time division duplexing (TDD), although frequency division duplexing (FDD) dominates current cellular systems. Due to the large number of transmit antennas at the base station, currently standardized approaches would require a large percentage of the precious downlink and uplink resources in FDD massive MIMO be used for training signal transmissions and channel state information (CSI) feedback. To reduce the overhead of the downlink training phase, we propose practical open-loop and closed-loop training frameworks in this paper. We assume the base station and the user share a common set of training signals in advance. In open-loop training, the base station transmits training signals in a round-robin manner, and the user successively estimates the current channel using long-term channel statistics such as temporal and spatial correlations and previous channel estimates. In closed-loop training, the user feeds back the best training signal to be sent in the future based on channel prediction and the previously received training signals. With a small amount of feedback from the user to the base station, closed-loop training offers better performance in the data communication phase, especially when the signal-to-noise ratio is low, the number of transmit antennas is large, or prior channel estimates are not accurate at the beginning of the communication setup, all of which would be mostly beneficial for massive MIMO systems.
464 citations
Cites background or methods from "Noncooperative Cellular Wireless wi..."
...Moreover, the user is not able to learn the instantaneous downlink channel (because there isno downlink training for CSI estimation in TDD massive MIMO) [7], which might cause a significant error in data decoding at the user....
[...]
...Most of the massive MIMO research assumes TDD systems that rely on channel reciprocity for the base station to acquire CSI....
[...]
...Theoretic ally, massive MIMO systems can almost perfectly alleviate the inter-user interference that occurs in downlink and uplink multiuser MIMO (MU-MIMO) systems with a simple linear precoder and receive combiner [2]....
[...]
...[10] J. Guey and L. D. Larsson, “Modeling and evaluation of MIMO systems exploiting channel reciprocity in TDD mode,”Proceedings of IEEE Vehicular Technology Conference, Sep. 2004....
[...]
...Ideally, pilot contamination, which is caused by using non-orthogonal uplink pilot signals in neighbouring cells , i the only factor that limits TDD massive MIMO system performance [2], [7]....
[...]
Book•
31 Jan 2013TL;DR: The use of multiple antennas at base stations is a key component in the design of cellular communication systems that can meet high-capacity demands in the downlink.
Abstract: The use of multiple antennas at base stations is a key component in the design of cellular communication systems that can meet high-capacity demands in the downlink. Under ideal conditions, the gai ...
456 citations
TL;DR: In this paper, the authors proposed an approach for channel estimation that is applicable for both flat and frequency-selective fading, based on the Bussgang decomposition that reformulates the nonlinear quantizer as a linear function with identical first and second-order statistics.
Abstract: This paper considers channel estimation and system performance for the uplink of a single-cell massive multiple-input multiple-output system. Each receiver antenna of the base station is assumed to be equipped with a pair of one-bit analog-to-digital converters to quantize the real and imaginary part of the received signal. We first propose an approach for channel estimation that is applicable for both flat and frequency-selective fading, based on the Bussgang decomposition that reformulates the nonlinear quantizer as a linear function with identical first- and second-order statistics. The resulting channel estimator outperforms previously proposed approaches across all SNRs. We then derive closed-form expressions for the achievable rate in flat fading channels assuming low SNR and a large number of users for the maximal ratio and zero forcing receivers that takes channel estimation error due to both noise and one-bit quantization into account. The closed-form expressions, in turn, allow us to obtain insight into important system design issues such as optimal resource allocation, maximal sum spectral efficiency, overall energy efficiency, and number of antennas. Numerical results are presented to verify our analytical results and demonstrate the benefit of optimizing system performance accordingly.
452 citations
TL;DR: Future mobile broadband technologies and standards as well as evolutions of the 3GPP's existing LTE standard and IEEE 802.11 standards are targeted, providing subscribers with the type of responsive Internet browsing experience that previously was only possible on wired broadband connections.
Abstract: Mobile services based on 4G LTE services are steadily expanding across global markets, providing subscribers with the type of responsive Internet browsing experience that previously was only possible on wired broadband connections. With more than 200 commercial LTE networks in operation as of August 2013 [1], LTE subscriptions are expected to exceed 1.3 billion by the end of 2018 [2]. LTE's rapid uptake, based on exponential growth in network data traffic, has opened the industry's eyes to an important reality: the mobile industry must deliver an economically sustainable capacity and performance growth strategy; one that offers increasingly better coverage and a superior user experience at lower cost than existing wireless systems, including LTE. This strategy will be based on a combination of network topology innovations and new terminal capabilities. Simple network economics also require that the industry's strategy enable new services, new applications, and ultimately new opportunities to monetize the user experience. To address these pressing requirements, many expert prognosticators are turning their attention to future mobile broadband technologies and standards (i.e., 5G) as well as evolutions of the 3GPP's existing LTE standard and IEEE 802.11 standards.
440 citations
TL;DR: This paper proposes an improved Network-MIMO TDD architecture achieving spectral efficiencies comparable with "Massive MIMO", with one order of magnitude fewer antennas per active user per cell (roughly, from 500 to 50 antennas).
Abstract: Time-Division Duplexing (TDD) allows to estimate the downlink channels for an arbitrarily large number of base station antennas from a finite number of orthogonal uplink pilot signals, by exploiting channel reciprocity. Based on this observation, a recently proposed "Massive MIMO" scheme was shown to achieve unprecedented spectral efficiency in realistic conditions of distance-dependent pathloss and channel coherence time and bandwidth. The main focus and contribution of this paper is an improved Network-MIMO TDD architecture achieving spectral efficiencies comparable with "Massive MIMO", with one order of magnitude fewer antennas per active user per cell (roughly, from 500 to 50 antennas). The proposed architecture is based on a family of Network-MIMO schemes defined by small clusters of cooperating base stations, zero-forcing multiuser MIMO precoding with suitable inter-cluster interference mitigation constraints, uplink pilot signals allocation and frequency reuse across cells. The key idea consists of partitioning the users into equivalence classes, optimizing the Network-MIMO scheme for each equivalence class, and letting a scheduler allocate the channel time-frequency dimensions to the different classes in order to maximize a suitable network utility function that captures a desired notion of fairness. This results in a mixed-mode Network-MIMO architecture, where different schemes, each of which is optimized for the served user equivalence class, are multiplexed in time-frequency. In order to carry out the performance analysis and the optimization of the proposed architecture in a systematic and computationally efficient way, we consider the large-system regime where the number of users, the number of antennas, and the channel coherence block length go to infinity with fixed ratios.
438 citations
Cites background or methods from "Noncooperative Cellular Wireless wi..."
...For Time Division Duplexing (TDD) systems, exploiting channel reciprocity [16], [17], the CSIT can be obtained from the uplink pilot signals....
[...]
...As in [17], we also analyze the performance of the proposed system in the limit of a large number of antennas....
[...]
...In this regime we find that the LSUBF scheme advocated in [17] performs very poorly....
[...]
...Following this idea, Marzetta [17] showed that simple Linear Single-User BeamForming (LSUBF) and random user scheduling, without any BS joint processing, yields very high spectral efficiency in TDD cellular systems, provided that a sufficiently large number of transmit antennas per active...
[...]
...With LSUBF, as in [17], cluster C + c serves user k at location x + c with beamforming vector ĥk,c,c(f ;x)/‖ĥk,c,c(f ;x)‖, which is strongly correlated with the vector hk,c′,c(f ;x) of the channel from cluster C+ c to the unintended user k at location x+ c′, sharing the same pilot signal....
[...]
References
More filters
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....
[...]
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....
[...]
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]....
[...]
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....
[...]