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.
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TL;DR: In this paper, a low-complexity hybrid block diagonalization (Hy-BD) scheme is proposed to harvest the large array gain through phase-only RF precoding and combining and then digital BD processing is performed on the equivalent baseband channel.
Abstract: For a massive multiple-input multiple-output (MIMO) system, restricting the number of RF chains to far less than the number of antenna elements can significantly reduce the implementation cost compared to the full complexity RF chain configuration. In this paper, we consider the downlink communication of a massive multiuser MIMO (MU-MIMO) system and propose a low-complexity hybrid block diagonalization (Hy-BD) scheme to approach the capacity performance of the traditional BD processing method. We aim to harvest the large array gain through the phase-only RF precoding and combining and then digital BD processing is performed on the equivalent baseband channel. The proposed Hy-BD scheme is examined in both the large Rayleigh fading channels and millimeter wave (mmWave) channels. A performance analysis is further conducted for single-path channels and large number of transmit and receive antennas. Finally, simulation results demonstrate that our Hy-BD scheme, with a lower implementation and computational complexity, achieves a capacity performance that is close to (sometimes even higher than) that of the traditional high-dimensional BD processing.
49 citations
TL;DR: This work proves that, under a total power constraint on the beamformer, the maximum-SNR joint beamforming transmit AS problem with two receive antennas and an arbitrary number of transmit antennas N is polynomially solvable and develops an algorithm that solves it with quartic complexity, independently of the number of selected antennas.
Abstract: The recent increased interest in large-scale multiple- input multiple-output systems, combined with the cost of analog radio-frequency (RF) chains, necessitates the use of efficient antenna selection (AS) schemes. Capacity or signal-to-noise ratio (SNR) optimal AS has been considered to require an exhaustive search among all possible antenna subsets. In this work, we prove that, under a total power constraint on the beamformer, the maximum-SNR joint beamforming transmit AS problem with two receive antennas and an arbitrary number of transmit antennas N is polynomially solvable and develop an algorithm that solves it with quartic complexity, independently of the number of selected antennas. The algorithm identifies with complexity O(N
4
) a cubic-size collection of antenna subsets that contains the one that maximizes the post-processing receiver SNR. From a different perspective, for any given two-row complex matrix, our algorithm computes with quartic complexity its two-row submatrix with the maximum principal singular value, for any number of selected columns. In addition, our method also applies to receive AS with two transmit antennas. Finally, if we enforce a per-antenna-element power constraint on the beamformer (i.e., constant-envelope transmission), then the set of transmit AS subsets that contains the optimal one is the same as in the total power constraint case. Therefore, our algorithm offers a practical solution to the maximum-SNR antenna selection problem when either the transmitter or the receiver consists of a large number of antennas.
49 citations
17 May 2015
TL;DR: An overview on the drivers behind the 5G evolution is presented and the disruptive architectures and technologies that are creating the backbone for the5G transition envisioned beyond 2020 are presented.
Abstract: Current wireless communication networks and technologies are being pushed to their limits by the massive growth in demands for mobile wireless data services. We now stand at a turning point in the wireless communication domain where the technologies are being driven by applications and expected use cases. This paper presents an overview on the drivers behind the 5G evolution and presents the disruptive architectures and technologies that are creating the backbone for the 5G transition envisioned beyond 2020.
49 citations
TL;DR: It is concluded that in MaMI, intermediate ADC resolutions are optimal in energy efficiency sense, and, except in some special cases, scaling up the antennas to very large numbers does not change this conclusion.
Abstract: Massive MIMO (MaMI) is often promoted as a technology that will enable the use of low-quality, cheap hardware. One particular component that has been in the focus of MaMI-related research is the analog-to-digital converter (ADC), and use of very low-resolution ADCs has been proposed. However, studies about whether this strategy is justified from an energy-efficiency point of view have largely been inconclusive. In this paper, we choose system setup and models that reflect the hardware implementation reality as close as possible and perform a parametric analysis of uplink energy efficiency as a function of ADC resolution. If antenna scaling and decrease of ADC resolution are considered independently, the energy efficiency is shown to be maximized at intermediate ADC resolutions, typically in the range of 4–8 bits. Moreover, optimal ADC resolution does not decrease when more antennas are used except in some specific cases, and when it does, the decrease is approximately logarithmic in the number of antennas. In the case when antenna scaling and ADC degradation are coupled through a constant-performance constraint, it is shown that energy efficiency cannot improve with reduced bit resolution unless the power consumption of blocks other than ADCs scales down with the upscaling of antennas at a fast enough rate. Altogether it is concluded that in MaMI, intermediate ADC resolutions are optimal in energy efficiency sense, and, except in some special cases, scaling up the antennas to very large numbers does not change this conclusion.
48 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...b ∈ [1, 25] and μ∗l (b) and target δσ 2 PQN of −13 dB....
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...Introduced in [1] andmost often referred to as Massive MIMO (MaMI), this technique promises substantial increase in system throughput while simultaneously allowing for reduced radiated power both at the base station and at user terminals [2]....
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25 Nov 2013
TL;DR: This paper investigates how much standard linear precoders help the ISI mitigation by shortening the rms delay spread, and measures a massive MIMO channel with 128 antennas at the base station and 36 users, including 26 line-of-sight and 10 non line- of-sight.
Abstract: Massive multiple-input multiple-output (MIMO) systems, where the base station (BS) is equipped with a large number of antennas and the mobile devices have a single antenna, can significantly enhance the system performance. In many wireless systems inter symbol interference (ISI) due to delay dispersion of the channel can dramatically affect the demodulation process of the received signals. Precoding in massive MIMO can reduce or eliminate ISI, while still exploiting the spatial diversity. In this paper, we investigate how much standard linear precoders help the ISI mitigation by shortening the rms delay spread. In order to evaluate the system performance, we measured a massive MIMO channel with 128 antennas at the base station and 36 users, including 26 line-of-sight and 10 non line-of-sight, each equipped with a single antenna. We also compare the results from the measurements with an independent identically distributed Gaussian channel with an exponentially decaying average power delay profile.
48 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....
[...]
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....
[...]