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: In this article, an overhead-aware resource allocation framework for wireless networks where reconfigurable intelligent surfaces are used to improve the communication performance is proposed and incorporated in the expressions of the system rate and energy efficiency.
Abstract: Reconfigurable intelligent surfaces have emerged as a promising technology for future wireless networks. Given that a large number of reflecting elements is typically used and that the surface has no signal processing capabilities, a major challenge is to cope with the overhead that is required to estimate the channel state information and to report the optimized phase shifts to the surface. This issue has not been addressed by previous works, which do not explicitly consider the overhead during the resource allocation phase. This work aims at filling this gap, by developing an overhead-aware resource allocation framework for wireless networks where reconfigurable intelligent surfaces are used to improve the communication performance. An overhead model is proposed and incorporated in the expressions of the system rate and energy efficiency, which are then optimized with respect to the phase shifts of the reconfigurable intelligent surface, the transmit and receive filters, the power and bandwidth used for the communication and feedback phases. The bi-objective maximization of the rate and energy efficiency is investigated, too. The proposed framework characterizes the trade-off between optimized radio resource allocation policies and the related overhead in networks with reconfigurable intelligent surfaces.
112 citations
TL;DR: A novel hybrid channel estimation is proposed by separately estimating the angle information and the gain matrix, which could significantly save the training overhead and substantially improve the channel estimation accuracy compared with the conventional beamspace approach.
Abstract: This paper presents a new view of multi-user (MU) hybrid massive multiple-input and multiple-output (MIMO) systems from array signal processing perspective. We first show that the instantaneous channel vectors corresponding to different users are asymptotically orthogonal if the angles of arrival of users are different. We then decompose the channel matrix into an angle domain basis matrix and a gain matrix. The former can be formulated by steering vectors and the latter has the same size as the number of RF chains, which perfectly matches the structure of hybrid precoding. A novel hybrid channel estimation is proposed by separately estimating the angle information and the gain matrix, which could significantly save the training overhead and substantially improve the channel estimation accuracy compared with the conventional beamspace approach. Moreover, with the aid of the angle domain matrix, the MU massive MIMO system can be viewed as a type of non-orthogonal angle division multiple access to simultaneously serve multiple users at the same frequency band. Finally, the performance of the proposed scheme is validated by computer simulation results.
112 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...On the other hand, when there are common paths between two instantaneous channels, the orthogonality depends on their instantaneous fading coefficients [6], [28]....
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...In time division duplex (TDD) systems where channel reciprocity holds, the channel state information (CSI) required by DL precoding can be obtained via uplink (UL) pilots to avoid the significant training overhead [6]....
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TL;DR: In this article, a fast root multiple signal classification HDAPA (root-MUSIC-HDAPA) method is proposed specially for this hybrid structure to implement an approximately analytical solution.
Abstract: A large-scale fully digital receive antenna array can provide very high-resolution direction of arrival (DOA) estimation, but resulting in a significantly high RF-chain circuit cost. Thus, a hybrid analog and digital (HAD) structure is preferred. Two phase alignment (PA) methods, HAD PA (HADPA) and hybrid digital and analog PA (HDAPA), are proposed to estimate DOA based on the parametric method. Compared to analog PA (APA), they can significantly reduce the complexity in the PA phases. Subsequently, a fast root multiple signal classification HDAPA (root-MUSIC-HDAPA) method is proposed specially for this hybrid structure to implement an approximately analytical solution. Due to the HAD structure, there exists the effect of direction-finding ambiguity. A smart strategy of maximizing the average receive power is adopted to delete those spurious solutions and preserve the true optimal solution by linear searching over a set of limited finite candidate directions. This results in a significant reduction in computational complexity. Eventually, the Cramer–Rao lower bound (CRLB) of finding emitter direction using the HAD structure is derived. Simulation results show that our proposed methods, root-MUSIC-HDAPA and HDAPA, can achieve the hybrid CRLB with their complexities being significantly lower than those of pure linear searching-based methods, such as APA.
112 citations
TL;DR: Simulation results show the advantage of optimizing the power control over both pilot and data power, as compared to the cases of using full power and of only optimizing the data powers as done in previous work.
Abstract: This paper considers the jointly optimal pilot and data power allocation in single-cell uplink massive multiple-input-multiple-output systems. Using the spectral efficiency (SE) as performance metric and setting a total energy budget per coherence interval, the power control is formulated as optimization problems for two different objective functions: the weighted minimum SE among the users and the weighted sum SE. A closed form solution for the optimal length of the pilot sequence is derived. The optimal power control policy for the former problem is found by solving a simple equation with a single variable. Utilizing the special structure arising from imperfect channel estimation, a convex reformulation is found to solve the latter problem to global optimality in polynomial time. The gain of the optimal joint power control is theoretically justified, and is proved to be large in the low-SNR regime. Simulation results also show the advantage of optimizing the power control over both pilot and data power, as compared to the cases of using full power and of only optimizing the data powers as done in previous work.
111 citations
TL;DR: A practical channel estimation for 60-GHz indoor systems with the massive uniform rectangular array at base station that does not require any knowledge of channel statistics and can be efficiently deployed by the 2-D fast Fourier transform.
Abstract: This paper proposes a practical channel estimation for 60-GHz indoor systems with the massive uniform rectangular array at base station. Through antenna array theory, the parameters of each channel path can be decomposed into the angular information and the channel gain information. We first prove that the true direction of arrivals of each uplink path can be extracted via an efficient array signal processing method. Then, the channel gain information could be obtained linearly with small amount of training resources, which significantly reduces the training overhead and the feedback cost. More importantly, the proposed scheme unifies the uplink/downlink channel estimations for both the time duplex division and frequency duplex division systems, making itself particularly suitable for protocol design. Compared with the existing channel estimation algorithms, the newly proposed one does not require any knowledge of channel statistics and can be efficiently deployed by the 2-D fast Fourier transform. Meanwhile, the number of user terminals simultaneously served can be increased from a sophisticatedly designed angle division multiple access scheme. Simulation results are provided to corroborate the proposed studies.
111 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...However, all the potential gains of massive MIMO systems rely heavily on the accurate channel estimation at BS, which formulates a great challenge for millimeter-wave indoor scenario [11]....
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...Index Terms— Massive MIMO, angle domain signal processing, DOA estimation, angle division multiple access (ADMA), angle reciprocity....
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...Hence, downlink training in massive MIMO systems needs extremely large number of OT sequences....
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...For time division duplexing (TDD) massive MIMO systems, downlink channel state information (CSI) could be obtained via the channel reciprocity [13] from uplink channel estimation [14]–[16]....
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...We showed that the channel estimation can be decomposed into angular estimation and gain estimation, which is a unique property for massive MIMO systems....
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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....
[...]