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: Simulation and analytical results show that the performance of the proposed IQI aware WLMMSE (IQA-WLMM SE) receiver in a system with IQI is close to that of the MMSE receiver in an ideal system without IQI.
Abstract: In-phase/quadrature-phase imbalance (IQI) is one of the most important hardware impairments in communication systems. It arises in the analogue parts of direct conversion transceivers and can cause severe performance losses. In this paper, IQI aware widely-linear (WL) channel estimation and data detection schemes for uplink multicell massive multiple-input multiple-output (MIMO) systems are proposed. The resulting receiver is a WL extension of the minimum mean-square-error (MMSE) receiver and jointly mitigates multiuser interference and IQI by processing the real and the imaginary parts of the received signal separately. Thereby, the IQI arising at both the base station and the user terminals is taken into account. The considered channel state information acquisition model includes the effect of pilot contamination, which is caused by the reuse of the same training sequences in neighbouring cells. We apply results from random matrix theory to derive analytical expressions for the asymptotic achievable sum rates of the proposed IQI aware and conventional IQI unaware (IQU) receivers in the large system limit. Our simulation and analytical results show that the performance of the proposed IQI aware WLMMSE (IQA-WLMMSE) receiver in a system with IQI is close to that of the MMSE receiver in an ideal system without IQI.
61 citations
Cites background from "Noncooperative Cellular Wireless wi..."
...A newly emerging research area in wireless communications are so-called massive MIMO systems [1], [2]....
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TL;DR: 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.
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. 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 random matrix theory and also propose an iterative algorithm for large systems. Such a large system iterative algorithm produces 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.
61 citations
Cites methods from "Noncooperative Cellular Wireless wi..."
...In order to achieve enormous enhancement in spectral efficiency, the technique of “massive multiple-input multipleoutput (MIMO)” is envisioned to be an important ingredient in 5G communication systems [23], [24]....
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TL;DR: This paper derives bounds on the mean squared channel estimation error to derive deterministic equivalents of the receive SINRs and yields a lower bound on the achievable uplink and downlink spectral efficiencies and shows that the effect of channel aging can be mitigated by optimally choosing the frame duration.
Abstract: In this paper, we study the effect of channel aging on the uplink and downlink performance of an FDD massive MIMO system, as the system dimension increases. Since the training duration scales linearly with the number of transmit dimensions, channel estimates become increasingly outdated in the communication phase, leading to performance degradation. To quantify this degradation, we first derive bounds on the mean squared channel estimation error. We use the bounds to derive deterministic equivalents of the receive SINRs, which yields a lower bound on the achievable uplink and downlink spectral efficiencies. For the uplink, we consider maximal ratio combining and MMSE detectors, while for the downlink, we consider matched filter and regularized zero forcing precoders. We show that the effect of channel aging can be mitigated by optimally choosing the frame duration. It is found that using all the base station antennas can lead to negligibly small achievable rates in high user mobility scenarios. Finally, numerical results are presented to validate the accuracy of our expressions and illustrate the dependence of the performance on the system dimension and channel aging parameters.
61 citations
02 Jun 2013
TL;DR: This paper derives the transmission conditions for subspace separability based on free probability and perturbation theory and shows that it does not occur in cellular systems with power control and power-controlled handoff when the nonlinear channel estimation method is used.
Abstract: A subspace method for channel estimation is proposed for asymmetric antenna array systems. The so-called pilot contamination problem reported in [1] is found to be due to the linearity of channel estimation in [2]. We show that it does not occur in cellular systems with power control and power-controlled handoff when the nonlinear channel estimation method proposed in this paper is used. Power-control hand-off is needed to guarantee separability between signal and interference subspaces. We derive the transmission conditions for subspace separability based on free probability and perturbation theory.
61 citations
Cites background or methods from "Noncooperative Cellular Wireless wi..."
...The proposed algorithm widely outperforms the receiver based on linear channel estimation in [2] (conventional receiver)....
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...5 pilot symbols in total, and an identical set of orthogonal training sequences is adopted by all the access points as proposed in [2]....
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...According to the results in [2], the only impairment that does not vanish in asymptotic conditions is the inter-cell interference due to the re-use of orthogonal pilot sequences in other cells....
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...In all the simulations we adopt as performance metric the uncoded bit error rate (BER) and compare the proposed algorithm with the linear channel and data estimation proposed in [2]....
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...Two pioneering works [1], [2] introduced the concept of large antenna array networks, commonly referred to as massive MIMO, and showed that the use of very large antenna arrays in multiuser networks is even more appealing than the use of single user MIMO systems....
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10 Jun 2014
TL;DR: It is shown that there are two types of interference components in this scheme that do not vanish even when the number of antennas grows to infinity, and self-contamination can be effectively suppressed by iterative processing.
Abstract: This paper is concerned with the uplink in a multi-cell large antenna system. We study a channel estimation scheme where partially decoded data is used to estimate the channel. We show that there are two types of interference components in this scheme that do not vanish even when the number of antennas grows to infinity: cross-contamination and self-contamination. Cross contamination is in principle similar to pilot contamination in a conventional pilot-based channel estimation scheme, while self-contamination is unique for the data-aided scheme. The data-aided scheme can effectively suppress the contamination effect by increasing the data frame length without causing rate loss. This is confirmed by both analysis and simulation results.
61 citations
Cites background or methods or result from "Noncooperative Cellular Wireless wi..."
..., around 200 for a typical scenario in LTE [1], [11]), resulting in effective suppression of cross-contamination....
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...This phenomenon is referred to as “pilot contamination” [1]–[11]....
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...This fact motivates the research activities on large (or massive) antenna systems [1]–[12]....
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...For example, one millisecond coherence interval corresponds to roughly 200 symbols in a typical LTE (Long Term Evolution) communication scenario [1], [11]....
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...In this system, orthogonal pilots are adopted for the intra-cell users and the same orthogonal pilots are reused for different cells [1]....
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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....
[...]