Performance of massive MIMO uplink with zero-forcing receivers under delayed channels

Anastasios K. Papazafeiropoulos, Hien Quoc Ngo, Tharmalingam Ratnarajah

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22 Citations (Scopus)
34 Downloads (Pure)


In this paper, we analyze the performance of the uplink communication of massive multicell multiple-input multiple-output (MIMO) systems under the effects of pilot contamination and delayed channels because of terminal mobility. The base stations (BSS) estimate the channels through the uplink training and then use zero-forcing (ZF) processing to decode the transmit signals from the users. The probability density function (pdf) of the signal-to-interference-plus-noise ratio (SINR) is derived for any finite number of antennas. From this pdf, we derive an achievable ergodic rate with a finite number of BS antennas in closed form. Insights into the impact of the Doppler shift (due to terminal mobility) at the low signal-to-noise ratio (SNR) regimes are exposed. In addition, the effects on the outage probability are investigated. Furthermore, the power scaling law and the asymptotic performance result by infinitely increasing the numbers of antennas and terminals (while their ratio is fixed) are provided. The numerical results demonstrate the performance loss for various Doppler shifts. Among the interesting observations revealed is that massive MIMO is favorable even under channel aging conditions.

Original languageEnglish
Article number7519076
Pages (from-to)3158-3169
Number of pages12
JournalIEEE Transactions on Vehicular Technology
Issue number4
Early online date22 Jul 2016
Publication statusPublished - 1 Apr 2017


  • Delayed channels
  • Massive multiple-input multiple-output (MIMO)
  • Multiuser MIMO system
  • Zero-forcing (ZF) processing


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