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: The proposed outer beamformer design method has the capability of optimally controlling the weighting factor between the signal power to the desired user and the interference leakage power to undesired users according to different channel statistics.
Abstract: In this paper, the problem of outer beamformer design based only on channel statistic information is considered for two-stage beamforming for multi-user massive MIMO downlink, and the problem is approached based on signal-to-leakage-plus-noise ratio (SLNR). To eliminate the dependence on the instantaneous channel state information, a lower bound on the average SLNR is derived by assuming zero-forcing (ZF) inner beamforming, and an outer beamformer design method that maximizes the lower bound on the average SLNR is proposed. It is shown that the proposed SLNR-based outer beamformer design problem reduces to a trace quotient problem (TQP), which is often encountered in the field of machine learning. An iterative algorithm is presented to obtain an optimal solution to the proposed TQP. The proposed method has the capability of optimally controlling the weighting factor between the signal power to the desired user and the interference leakage power to undesired users according to different channel statistics. Numerical results show that the proposed outer beamformer design method yields significant performance gain over existing methods.
99 citations
Additional excerpts
...November 27, 2014 DRAFT...
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TL;DR: A unified framework is presented to develop a family of detectors on a massive MIMO uplink system through probabilistic Bayesian inference, which comprises an optimal detector, which is developed to provide a minimum mean-squared-error estimate on data symbols.
Abstract: Using a very low-resolution analog-to-digital convertor (ADC) unit at each antenna can remarkably reduce the hardware cost and power consumption of a massive multiple-input multiple-output (MIMO) system. However, such a pure low-resolution ADC architecture also complicates parameter estimation problems such as time/frequency synchronization and channel estimation. A mixed-ADC architecture, where most of the antennas are equipped with low-precision ADCs while a few antennas have full-precision ADCs, can solve these issues and actualize the potential of the pure low-resolution ADC architecture. In this paper, we present a unified framework to develop a family of detectors over the massive MIMO uplink system with the mixed-ADC receiver architecture by exploiting probabilistic Bayesian inference. As a basic setup, an optimal detector is developed to provide a minimum mean-squared-error (MMSE) estimate on data symbols. Considering the highly nonlinear steps involved in the quantization process, we also investigate the potential for complexity reduction on the optimal detector by postulating the common \emph{pseudo-quantization noise} (PQN) model. In particular, we provide asymptotic performance expressions including the MSE and bit error rate for the optimal and suboptimal MIMO detectors. The asymptotic performance expressions can be evaluated quickly and efficiently; thus, they are useful in system design optimization. We show that in the low signal-to-noise ratio (SNR) regime, the distortion caused by the PQN model can be ignored, whereas in the high-SNR regime, such distortion may cause 1-bit detection performance loss. The performance gap resulting from the PQN model can be narrowed by a small fraction of high-precision ADCs in the mixed-ADC architecture.
98 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...2606592 Such systems can substantially reduce cell interference via simple signal processing by equipping a base station (BS) with hundreds or thousands of antennas in a centralized [4], [5] or distributed [6] manner because a channel vector between users and a BS becomes quasi-orthogonal....
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TL;DR: In this article, a low-complexity precoding algorithm is proposed, which generates constant-envelope (CE) signals at each BS antenna to achieve a desired per-user information rate, the extra total transmit power required under the per-antenna CE constraint when compared to the commonly used less stringent total average transmit power constraint, is small.
Abstract: We consider downlink precoding in a frequency-selective multi-user Massive MIMO system with highly efficient but non-linear power amplifiers at the base station (BS). A low-complexity precoding algorithm is proposed, which generates constant-envelope (CE) signals at each BS antenna. To achieve a desired per-user information rate, the extra total transmit power required under the per-antenna CE constraint when compared to the commonly used less stringent total average transmit power constraint, is small.
98 citations
TL;DR: A mutual coupling-based calibration method for time-division-duplex massive MIMO systems, which enables downlink precoding based on uplink channel estimates and proposes an estimator which exploits the structure of the process in order to reduce the calibration error across frequency.
Abstract: This paper presents a mutual coupling-based calibration method for time-division-duplex massive MIMO systems, which enables downlink precoding based on uplink channel estimates. The entire calibration procedure is carried out solely at the base station (BS) side by sounding all BS antenna pairs. An expectation-maximization (EM) algorithm is derived, which processes the measured channels in order to estimate calibration coefficients. The EM algorithm outperforms the current state-of-the-art narrow-band calibration schemes in a mean squared error and sum-rate capacity sense. Like its predecessors, the EM algorithm is general in the sense that it is not only suitable to calibrate a co-located massive MIMO BS, but also very suitable for calibrating multiple BSs in distributed MIMO systems. The proposed method is validated with experimental evidence obtained from a massive MIMO testbed. In addition, we address the estimated narrow-band calibration coefficients as a stochastic process across frequency, and study the subspace of this process based on measurement data. With the insights of this study, we propose an estimator which exploits the structure of the process in order to reduce the calibration error across frequency. A model for the calibration error is also proposed based on the asymptotic properties of the estimator, and is validated with measurement results.
98 citations
Cites methods from "Noncooperative Cellular Wireless wi..."
...To deal with this challenge, the approach adopted is to operate in time-division-duplex (TDD) mode, rely on channel reciprocity, and use uplink channel state information (CSI) for downlink precoding purposes [4]....
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Posted Content•
TL;DR: In this article, the authors proposed a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method to avoid the matrix inversion in uplink multi-user large-scale multiple input multiple output (MIMO) systems.
Abstract: Minimum mean square error (MMSE) signal detection algorithm is near- optimal for uplink multi-user large-scale multiple input multiple output (MIMO) systems, but involves matrix inversion with high complexity. In this letter, we firstly prove that the MMSE filtering matrix for large- scale MIMO is symmetric positive definite, based on which we propose a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method to avoid the matrix inversion. The complexity can be reduced from O(K3) to O(K2), where K is the number of users. We also provide the convergence proof of the proposed algorithm. Simulation results show that the proposed signal detection algorithm converges fast, and achieves the near-optimal performance of the classical MMSE algorithm.
98 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....
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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....
[...]