Optimal Transmit Strategy for MISO Channels with Joint Sum and Per-Antenna Power Constraints

Phuong Le Cao, Tobias J. Oechtering, Rafael F. Schaefer, Mikael Skoglund

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


In this paper, we study an optimal transmit strategy for multiple-input single-output (MISO) Gaussian channels with joint sum and per-antenna power constraints. We study in detail the interesting case where the sum of the per-antenna power constraints is larger than sum power constraint. A closed-form characterization of an optimal beamforming strategy is derived. It is shown that we can always find an optimal beamforming transmit strategy that allocates the maximal sum power with phases matched to the complex channel coefficients. The main result is a simple recursive algorithm to compute the optimal power allocation. Whenever the optimal power allocation of the corresponding problem with sum power constraint only exceeds per-antenna power constraints, it is optimal to allocate maximal per-antenna power to those antennas to satisfy the per-antenna power constraints. The remaining power is divided amongst the other antennas whose optimal allocation follows from a reduced joint sum and per-antenna power constraints problem of smaller channel coefficient dimension and reduced sum power constraint. Finally, the theoretical results are illustrated by numerical examples.

Original languageEnglish
Article number7465807
Pages (from-to)4296-4306
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number16
StatePublished - 15 Aug 2016
Externally publishedYes


  • MISO
  • Sum power constraint
  • beamforming
  • per-antenna power constraint
  • transmission rate
  • transmit strategy


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