Pilot Contamination and Precoding in Multi-Cell TDD Systems

By Jubin Jose, Alexei E. Ashikhmin, T. Marzetta, Sriram Vishwanath. IEEE Transactions on Wireless Communications, 2009

1,312 citations recorded by the source corpus.

This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for obtaining this CSI is time-division duplex (TDD) operation where uplink training in conjunction with reciprocity simultaneously provides the base stations with downlink as well as uplink channel estimates. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closed-form expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular single-cell precoding methods.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/a6291b47fac10becfbede645ac6cfa6170a272ec

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Electrical and Electronic Engineering

Citations in the corpus

A Coordinated Approach to Channel Estimation in Large-Scale Multiple-Antenna Systems (2012, background): “In particular, it has been shown that pilot contamination effects [2], [3], [4] (i.e., the reuse of non-orthogonal pilot sequences across interfering cells) cause the interference rejection performance to quickly saturate with the number of antennas, thereby undermining the value of MIMO systems in…”
Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems (2011, background): “This is not optimal from an information-theoretic point of view, and higher rates can be achieved if the BS communicates with several users in the same time-frequency resource [3], [4].”
Effects of channel aging in massive MIMO systems (2013, methodology): “Applying the method commonly used in prior work [8, 11, 12, 24], we derive a standard bound on the ergodic achievable uplink rates based on the worst-case uncorrelated additive noise.”
Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need? (2013, methodology): “During a dedicated uplink training phase, the UTs in each cell transmit mutually orthogonal pilot sequences which allow the BSs to compute estimates ^ H jj of their local channels H jj .”
The Multicell Multiuser MIMO Uplink with Very Large Antenna Arrays and a Finite-Dimensional Channel (2013, background): “Most of the studies referred to above assume that the channels are independent [5], [6], [8] or that the channel vectors for different users are asymptotically orthogonal [9], [11].”
Massive MIMO is a Reality - What is Next? Five Promising Research Directions for Antenna Arrays (2019, background): “Some of the key research directions that are now approaching the ﬁnish lines are the spectral efﬁciency analysis [17]–[20], system design for high energy efﬁciency [21]–[23], pilot contamination and decontamination [24]–[27], and power optimization [28]–[30].”
Multipair Full-Duplex Relaying With Massive Arrays and Linear Processing (2014, neutral): “This technique is widely used in the analysi s of massive MIMO systems since: i) it yields a simplified insightful rate expression, which is basically a lower boun d of what can be achieved in practice; and ii) it does not requir e instantaneous CSI at the destination [23], [25], [26].”
Power Scaling Laws and Near-Field Behaviors of Massive MIMO and Intelligent Reflecting Surfaces (2020, background): “is that the linear scaling holds true even in the asymptotic regime where N → ∞ [3], [11], [12], [34]–[37], which has been utilized to define properties such as channel hardening and favorable propagation, as well as studying the fundamental impact of pilot contamination.”
Massive MIMO Systems for 5G and beyond Networks—Overview, Recent Trends, Challenges, and Future Research Direction (2020, background): “This phenomenon is known as pilot contamination, and it limits achievable throughput, as shown in Figure 14 [55].”
Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated? (2014, background): “Similar bounds are found in [6]–[8] and the bounding technique interacts with the Rayleigh fading, which is why its expectations end up inside the logarithm while the user positions are averaged at the outside.”
OFDM Inspired Waveforms for 5G (2016, background): “In particular, in some recent works [70], [71], we have shown that the blind equalization capability of CMT which has been introduced in [72] may prove very useful in overcoming the problem of pilot contamination (a serious problem [73]) in massive MIMO systems.”
A Comprehensive Survey of Pilot Contamination in Massive MIMO—5G System (2016, methodology): “literature [11], [13], [26], [27], [32], [74], [75], [92], [93].”
Pilot Reuse for Massive MIMO Transmission over Spatially Correlated Rayleigh Fading Channels (2015, methodology): “It has been shown that pilot contamination [10] caused by inter-cell pilot reuse can degrade the performance of massive MIMO transmission.”
Beam Division Multiple Access Transmission for Massive MIMO Communications (2015, methodology): “Without CSI at the users’ side, the achievable sum-rate of the WMMSE algorithm can be calculated following [8].”