How much training is needed in multiple-antenna wireless links?

By Babak Hassibi, Bertrand M. Hochwald. IEEE Transactions on Information Theory, 2003

2,428 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/5190f12fbd92898a853477824ea7b8b388c98d13

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Citations in the corpus

Secure Transmission With Artificial Noise Over Fading Channels: Achievable Rate and Optimal Power Allocation (2010, background): “Therefore, the beamforming vector becomes w 1 = ˆ h † / k ˆ h k , and the received symbol at Bob is given by A capacity lower bound for the channel between Alice and Bob can be obtained by considering ˜ hW [ u v T ] T + n as the worst case Gaussian noise [31].”
Sum-Rate Maximization for Linearly Precoded Downlink Multiuser MISO Systems With Partial CSIT: A Rate-Splitting Approach (2016, methodology): “This is typically obtained through Uplink (UL) training in Time Division Duplex (TDD) systems [32] or quantized feedback in Frequency Division Duplex (FDD) systems [33].”
Compressed Channel Sensing: A New Approach to Estimating Sparse Multipath Channels (2010, methodology): “In order to estimate non selective MIMO channels, traditional trainingbased methods such as those in [9], [10] therefore require th atMtr = Ω(NT ) so as to ensure that X has full column rank and produce an estimate that satisfies E[∆(H v )] = Ω(NRN 2 T /E).”
Challenges and enabling technologies for energy aware mobile radio networks (2010, background): “At full load the energy consumed to transmit this overhead is overcompensated by the enhanced spectral efficiency; in fact, in theory, up to 50 percent of reference signal overhead is acceptable to still see capacity gains by adding transmit and receive antennas at fixed total power [8].”
Multipair Full-Duplex Relaying With Massive Arrays and Linear Processing (2014, positive): “This observation can be interpreted as, when we cut the transmitted power of each source, both the data signal and the pilot signal suffer from power reduction, which leads to the so-called “squaring effect” on the spectral efficiency [24].”
What Will 5G Be? (2014, background): “[100] B.”
Uplink Achievable Rate for Massive MIMO Systems With Low-Resolution ADC (2015, methodology): “Following the assumption in [10], we model this term as additive Gaussian noise independent of xn and derive the ergodic achievable uplink rate of the nth user as”
Training-based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals (2006, background): “In [11], the problem of training sequence design for MIMO channels has been linked with the channel capacity.”
MIMO Configurations for Relay Channels: Theory and Practice (2007, background): “Some examples for the impact of training on MIMO capacity performance can be found in [34] and [35].”
Multi-Cell MIMO Cooperative Networks: A New Look at Interference (2010, background): “Its importance can be seen from the point to point MIMO channel where it is known that the number of transmit antennas should not exceed the number of symbols in the coherence block [57].”
Virtual MIMO-based cooperative communication for energy-constrained wireless sensor networks (2006, background): “For example, [3] suggests that in general we may need the number of training symbols greater than or equal to the number of transmit antennas if both training and data symbols were to use the same transmit energy.”
Pilot Reuse for Massive MIMO Transmission over Spatially Correlated Rayleigh Fading Channels (2015, background): “The UL sum achievable rate R u,sum [9], [32] is given by (50), shown at the top of the next page, where w k is the k th column of the UL receiver matrix W given in (27).”
Channel Estimation and Performance Analysis of One-Bit Massive MIMO Systems (2016, background): “Furthermore, while the quantizer noise qd is non-Gaussian, we can obtain a lower bound on the achievable rate by making the worst-case assumption [41], [42] that in fact it is Gaussian with the same covariance matrix in (41).”
A Unified Transmission Strategy for TDD/FDD Massive MIMO Systems With Spatial Basis Expansion Model (2017, background): “From the conventional orthogonal training strategy [5], the optimal number of training streams should be the same as the number of transmit antennas, and the length of the training should be no less than the number of transmit antennas.”