cov_secrecy_capacity_loyka

secrecy_capacity.cov_secrecy_capacity_loyka(mat_bob, mat_eve, power: float = 10, t: float = 1000.0, alpha: float = 0.3, beta: float = 0.5, mu: float = 2, eps: float = 1e-10, dirname: Optional[str] = None, return_interm_results: bool = False)

Optimal covariance matrix (Loyka’s algorithm)

Calculate the optimal covariance matrix for a fading wiretap channel using the algorithm from [1].

Parameters

  • mat_bob (numpy.array) – Matrix with the channel realizations of Bob’s channels.

  • mat_eve (numpy.array) – Matrix with the channel realizations of Eve’s channels.

  • power (float) – Power contraint at the transmitter.

  • alpha (float) – Parameter \(\alpha\) with \(0<\alpha<0.5\) is a percent of the linear decrease in the residual one is prepared to accept at each step, cf. Algorithm 1 in [1].

  • beta (float) – Parameter \(\beta\) with \(0 < \beta < 1\) is a parameter controlling the reduction in step size at each iteration of the algorithm, cf. Algorithm 1 in [1].

  • mu (float) – Parameter \(\mu\) with \(\mu > 1\) defines the multiplicator in the barrier method, cf. Algorithm 3 in [1].

  • eps (float) – Tolerance level for the outer barrier algorithm, cf. Algorithm 3 in [1].

  • dirname (str) – Path of the directory in which checkpoints and log should be saved. If None, no intermediate results will be saved.

  • return_interm_results (bool) – If True, the history/intermediate results of the algorithm will be return together with the optimal covariance matrix. This changes the return structure of the function!

Returns

  • cov (numpy.array) – Optimal covariance matrix which maximizes the secrecy rate.

  • (interm_res_norm, interm_sec_rate) (tuple of list of float) – Only returned, when return_interm_results == True! Tuple that represents the history of the algorithm. The norm of the residual is stored in interm_res_norm, while the intermediate secrecy rates are in interm_sec_rate.

References

1

S. Loyka and C. D. Charalambous, “An Algorithm for Global Maximization of Secrecy Rates in Gaussian MIMO Wiretap Channels,” IEEE Trans. Commun., vol. 63, no. 6, pp. 2288–2299, Jun. 2015.