Optimal signal design for coherent detection of binary signals in Gaussian noise under power and secrecy constraints

DÜLEK B., Gezici S.

Signal Processing, cilt.210, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 210
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.sigpro.2023.109052
  • Dergi Adı: Signal Processing
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, zbMATH
  • Anahtar Kelimeler: Hypothesis testing, Probability of error, Secrecy, Signal design
  • Hacettepe Üniversitesi Adresli: Evet

Özet

The problem of optimal signal design for coherent detection of binary signals in Gaussian noise is revisited under power and secrecy constraints. In particular, the aim is to select the binary transmitted signals in an optimal manner so that the probability of error is minimized at an intended receiver while the probability of error at an eavesdropper is maintained above a threshold value and the signal powers are limited. It is shown that an optimal solution exists in the form of antipodal signaling along the eigenvector corresponding to the solution of a maximum (possibly generalized) eigenvalue problem, which is specified explicitly based on the channel coefficient matrices and the noise covariance matrices at the intended receiver and the eavesdropper. Furthermore, optimal signal design can be performed in an efficient manner by solving a semidefinite programming (SDP) relaxation followed by a matrix rank-one decomposition. Numerical examples are provided to illustrate optimal solutions for three different but exhaustive cases.