Power allocation for artificial-noise secure MIMO precoding systems

Shang-Ho Tsai, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

103 Scopus citations


This paper investigates the power allocation problem for artificial noise (AN) secure precoding systems, and proposes closed-form solutions for maximizing the achievable secrecy rate. It is assumed that the transmitter knows the full channel information at the legitimate receiver, and knows only the statistics of the channel information at the eavesdropper. Lower bounds are derived for the secrecy rates in multiple-input single-output channels with single or multiple eavesdroppers and multiple-input multiple-output channels with multiple eavesdroppers. When the number of transmit antennas is sufficiently large, the bounds are tight, and closed-form solutions can be derived from these bounds. The analytical results suggest simple and yet informative solutions as follows: Let the numbers of receive antennas at the legitimate receiver and at the eavesdropper be Nr and Nr,e, respectively. The system should distribute Nr,e (Nr+Nr,e of the power to AN in the high SNR regime, and distribute zero power to AN in the low SNR regime; the rate loss due to the eavesdropper is -Nr log N r (Nr+Nr,e-Nr,e log Nr,e (Nr+Nr,e bits/sec/Hz in the high SNR regime and nearly negligible in the low SNR regime. The derived results also show that equal power and water-filling power allocations lead to similar solutions and rate loss. Simulation results corroborate the theoretical results.

Original languageEnglish
Article number6826572
Pages (from-to)3479-3493
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number13
StatePublished - 1 Jul 2014


  • Artificial noise
  • beamforming
  • physical layer security
  • power distribution
  • precoding
  • secrecy capacity
  • wire-tap channel


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