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, the authors considered a heterogeneous cellular network with densely underlaid small cell access points (SAPs), and proposed an iterative algorithm for the ''ell_1'' -relaxed problem.
Abstract: We consider a heterogeneous cellular network with densely underlaid small cell access points (SAPs). Wireless backhaul provides the data connection from the core network to SAPs. To serve as many SAPs and their corresponding users as possible with guaranteed data rates, admission control of SAPs needs to be performed in wireless backhaul. Such a problem involves joint design of transmit beamformers, power control, and selection of SAPs. In order to tackle such a difficult problem, we apply $\ell_1$ -relaxation and propose an iterative algorithm for the $\ell_1$ -relaxed problem. The selection of SAPs is made based on the outputs of the iterative algorithm, and we prove such an algorithm converges locally. Furthermore, this algorithm is fast and enjoys low complexity for small-to-medium sized systems. However, its solution depends on the actual channel state information, and resuming the algorithm for each new channel realization may be unrealistic for large systems. Therefore, we make use of the random matrix theory and also propose an iterative algorithm for large systems. Such a large-system iterative algorithm can produce the asymptotically optimum solution for the $\ell_1$ -relaxed problem, which only requires large-scale channel coefficients irrespective of the actual channel realization. Near optimum results are achieved by our proposed algorithms in simulations.
50 citations
08 Jun 2015
TL;DR: The analysis and simulation results show that the asymptotic signal-plus-interference-to-noise ratio (SINR) of hybrid beamforming is reduced by a factor of π/4 compared to conventional beamforming methods, and the resulting achievable sum-rate degradation can be compensated by simply employing 27% more transmit antennas.
Abstract: Massive multiple-input multiple-output (MIMO) systems can attain a high channel capacity and spectral efficiency by using a very large antenna array at the base station (BS) However, the cost of having one radio frequency (RF) chain behind every antenna element can be prohibitive In addition, the overall power consumption of the RF hardware can be excessively high A hybrid analog-digital structure can be utilized to reduce the required number of RF chains at the BS In this paper, we present achievable rates of hybrid beamforming in multi-user MIMO (MU-MIMO) when employing only one RF chain per user The analysis and simulation results show that the asymptotic signal-plus-interference-to-noise ratio (SINR) of hybrid beamforming is reduced by a factor of π/4 compared to conventional beamforming methods, and the resulting achievable sum-rate degradation can be compensated by simply employing 27% more transmit antennas
50 citations
Patent•
14 Sep 2011
TL;DR: In this article, non-linear or linear precoding is used to create separate areas of coherence to different users and limited feedback techniques are employed to send channel state information (CSI) from the plurality of users to the MU-MAS.
Abstract: Non-linear or linear precoding is used to create separate areas of coherence to different users. Limited feedback techniques may also be employed to send channel state information (CSI) from the plurality of users to the MU-MAS. In some embodiments, a codebook is built based on basis functions that span the radiated field of a transmit array. Additionally, the precoding may be continuously updated to create non-interfering areas of coherence to the users as the wireless channel changes due to Doppler effect. Moreover, the size of the areas of coherence may be dynamically adjusted depending on the distribution of users.
50 citations
TL;DR: A hybrid modeling approach of 3-D ray-tracing simulations in a realistic office room is developed to obtain estimates of the impact of surface roughness on the channel capacity which depends on generic channel characteristics and the scattering properties of materials can favorably be exploited to maximize spatial multiplexing gains, especially in LoS scenarios.
Abstract: The use of massive multiple-input multiple-output (MIMO) systems is becoming progressively feasible, as well as progressively important, as the carrier frequency increases. Terahertz (THz) frequencies lead to smaller-sized RF components including antennas, so that even antenna arrays with a large number of antennas have a reasonable form factor while providing large beamforming gain and multi-user MIMO (MU-MIMO) capability. However, the THz propagation mechanisms differ in various ways from previously explored channels. In fact, reflections by a rough surface and diffuse scattering mechanisms are the most critical features contributing to spatial and temporal dispersion at THz frequencies. For this article, first, we develop a hybrid modeling approach of 3-D ray-tracing simulations in a realistic office room at 300 and 350 GHz to obtain estimates of the impact of surface roughness on the channel capacity which depends on generic channel characteristics. Then, the indoor multipath propagation and its impact on massive MIMO channels considering smooth and rough surfaces are investigated by employing the Beckmann-Kirchhoff (B-K) model. Finally, channel capacities of indoor THz massive MIMO channels with different surface roughnesses for both line-of-sight (LoS) and non-LoS (NLoS) scenarios are calculated. Though based on modeling results, the scattering properties of materials can favorably be exploited to maximize spatial multiplexing gains, especially in LoS scenarios.
50 citations
Additional excerpts
...robust signal-processing techniques [2]–[5]....
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01 Aug 2019
TL;DR: This paper focuses on the task of recovering a desired signal statistically related to the high-dimensional input, and analyzes two quantization approaches, and considers vector quantization, which is typically computationally infeasible, and the optimal performance achievable with this approach.
Abstract: Quantizers take part in nearly every digital signal processing system that operates on physical signals. They are commonly designed to accurately represent the underlying signal, regardless of the specific task to be performed on the quantized data. In systems working with high-dimensional signals, such as massive multiple-input multiple-output (MIMO) systems, it is beneficial to utilize low-resolution quantizers, due to cost, power, and memory constraints. In this paper, we study quantization of high-dimensional inputs, aiming at improving performance under resolution constraints by accounting for the system task in the quantizers design. We focus on the task of recovering a desired signal statistically related to the high-dimensional input, and analyze two quantization approaches. We, first, consider vector quantization, which is typically computationally infeasible, and characterize the optimal performance achievable with this approach. Next, we focus on practical systems that utilize hardware-limited scalar uniform analog-to-digital converters (ADCs), and design a task-based quantizer under this model. The resulting system accounts for the task by linearly combining the observed signal into a lower dimension prior to quantization. We then apply our proposed technique to channel estimation in massive MIMO networks. Our results demonstrate that a system utilizing low-resolution scalar ADCs can approach the optimal channel estimation performance by properly accounting for the task in the system design.
50 citations
Cites background or methods from "Noncooperative Cellular Wireless wi..."
...The massive MIMO channel follows a block-fading model [20]....
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..., [20]–[22], we assume that the BS knows: 1) the pilot symbols; 2) the channel input-output relationship, i....
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...Here, we extend the study of [28] to account for asymptotically large data, developing a framework for task-based quantization with high-dimensional inputs, and then apply the resulting analysis to massive MIMO systems, which are commonly studied in the asymptotic number of antennas regime [20], [21]....
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...In particular, we focus on massive MIMO channel estimation, carried out in a time-division duplex (TDD) manner [20]–[22]....
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...In such systems, a wireless base station (BS) is equipped with a large number of antennas [20]–[22]....
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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....
[...]