Recent Advances in Acquiring Channel State Information in Cellular MIMO Systems

In cellular multi-user multiple input multiple output (MU-MIMO) systems the quality of the available channel state information (CSI) has a large impact on the system performance. Specifically, reliable CSI at the transmitter is required to determine the appropriate modulation and coding scheme, transmit power and the precoder vector, while CSI at the receiver is needed to decode the received data symbols. Therefore, cellular MUMIMO systems employ predefined pilot sequences and configure associated time, frequency, code and power resources to facilitate the acquisition of high quality CSI for data transmission and reception. Although the trade-off between the resources used user data transmission has been known for long, the near-optimal configuration of the vailable system resources for pilot and data transmission is a topic of current research efforts. Indeed, since the fifth generation of cellular systems utilizes heterogeneous networks in which base stations are equipped with a large number of transmit and receive antennas, the appropriate configuration of pilot-data resources becomes a critical design aspect. In this article, we review recent advances in system design approaches that are designed for the acquisition of CSI and discuss some of the recent results that help to dimension the pilot and data resources specifically in cellular MU-MIMO systems

Massive MIMO with Non-Ideal Arbitrary Arrays: Hardware Scaling Laws and Circuit-Aware Design

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas $N$. Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today's conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phase-drifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with $N$ while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make the circuit power increase as $\sqrt{N}$, instead of linearly, by careful circuit-aware system design.Comment: Accepted for publication in IEEE Transactions on Wireless Communications, 16 pages, 8 figures. The results can be reproduced using the following Matlab code: https://github.com/emilbjornson/hardware-scaling-law

Massive MIMO Multicasting in Noncooperative Cellular Networks

We study the massive multiple-input multiple-output (MIMO) multicast transmission in cellular networks where each base station (BS) is equipped with a large-scale antenna array and transmits a common message using a single beamformer to multiple mobile users. We first show that when each BS knows the perfect channel state information (CSI) of its own served users, the asymptotically optimal beamformer at each BS is a linear combination of the channel vectors of its multicast users. Moreover, the optimal combining coefficients are obtained in closed form. Then we consider the imperfect CSI scenario where the CSI is obtained through uplink channel estimation in timedivision duplex systems. We propose a new pilot scheme that estimates the composite channel which is a linear combination of the individual channels of multicast users in each cell. This scheme is able to completely eliminate pilot contamination. The pilot power control for optimizing the multicast beamformer at each BS is also derived. Numerical results show that the asymptotic performance of the proposed scheme is close to the ideal case with perfect CSI. Simulation also verifies the effectiveness of the proposed scheme with finite number of antennas at each BS.Comment: to appear in IEEE JSAC Special Issue on 5G Wireless Communication System

Analysis and Design of Channel Estimation in Multicell Multiuser MIMO OFDM Systems

This paper investigates the uplink transmission in multicell multiuser multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. The system model considers imperfect channel estimation, pilot contamination (PC), and multicarrier and multipath channels. Analytical expressions are first presented on the mean square error (MSE) of two classical channel estimation algorithms [i.e., least squares (LS) and minimum mean square error (MMSE)] in the presence of PC. Then, a simple H-infinity (H-inf) channel estimation approach is proposed to have good suppression to PC. This approach exploits the space-alternating generalized expectation–maximization (SAGE) iterative process to decompose the multicell multiuser MIMO (MU-MIMO) problem into a series of single-cell single-user single-input single-output (SISO) problems, which reduces the complexity significantly. According to the analytic results given herein, increasing the number of pilot subcarriers cannot mitigate PC, and a clue for suppressing PC is obtained. It is shown from the results that the H-inf has better suppression capability to PC than classical estimation algorithms. Its performance is close to that of the optimal MMSE as the length of channel impulse response (CIR) is increased. By using the SAGE process, the performance of the H-inf does not degrade when the number of antennas is large at the base station (BS)

Massive MIMO has Unlimited Capacity

The capacity of cellular networks can be improved by the unprecedented array gain and spatial multiplexing offered by Massive MIMO. Since its inception, the coherent interference caused by pilot contamination has been believed to create a finite capacity limit, as the number of antennas goes to infinity. In this paper, we prove that this is incorrect and an artifact from using simplistic channel models and suboptimal precoding/combining schemes. We show that with multicell MMSE precoding/combining and a tiny amount of spatial channel correlation or large-scale fading variations over the array, the capacity increases without bound as the number of antennas increases, even under pilot contamination. More precisely, the result holds when the channel covariance matrices of the contaminating users are asymptotically linearly independent, which is generally the case. If also the diagonals of the covariance matrices are linearly independent, it is sufficient to know these diagonals (and not the full covariance matrices) to achieve an unlimited asymptotic capacity.Comment: To appear in IEEE Transactions on Wireless Communications, 17 pages, 7 figure

Channel estimation in massive MIMO systems

Last years were characterized by a great demand for high data throughput, good quality and spectral efficiency in wireless communication systems. Consequently, a revolution in cellular networks has been set in motion towards to 5G. Massive multiple-input multiple-output (MIMO) is one of the new concepts in 5G and the idea is to scale up the known MIMO systems in unprecedented proportions, by deploying hundreds of antennas at base stations. Although, perfect channel knowledge is crucial in these systems for user and data stream separation in order to cancel interference. The most common way to estimate the channel is based on pilots. However, problems such as interference and pilot contamination (PC) can arise due to the multiplicity of channels in the wireless link. Therefore, it is crucial to define techniques for channel estimation that together with pilot contamination mitigation allow best system performance and at same time low complexity. This work introduces a low-complexity channel estimation technique based on Zadoff-Chu training sequences. In addition, different approaches were studied towards pilot contamination mitigation and low complexity schemes, with resort to iterative channel estimation methods, semi-blind subspace tracking techniques and matrix inversion substitutes. System performance simulations were performed for the several proposed techniques in order to identify the best tradeoff between complexity, spectral efficiency and system performance