Estimation of the number of orthogonal signals with unknown parameters

Determining the Number of Sinusoids Measured with Errors

“…Some practical applications may require reducing the computational complexity of the result (13). An asymptotically exact approximation for (13) can be written as follow…”

“…The approximate formula ( 14) can be used instead of the exact formula (13) for the next parameters ranges min(Q, R) > 3, and |ρ| < 0.9. Now let us describe how the result (13) can help to make the choice between the QL algorithm and any other algorithms.…”

“…This is a typical case for measurements with errors. The result (13) can help one to choose between the quasi-likelihood algorithm and any other algorithms for estimating the number of signals, the following should be made:…”

“…Let us list the settings for Fig 1 ., Fig 2 .: δ a = 0.25, ∆ ϕ = 0.1, δ ω = 0.02. The following notations are used: the solid curve is the theoretical curve predicted by (13), the circles mark simulation results for ν max = 3 and ν 0 = 2, and the squares mark simulation results for ν max = 5 and ν 0 = 3.…”

“…(ii) the error probability can be sufficiently approximated by the abridged error probability (13) starting with a particular SNR, for example: if N s = 128, ν max = 5 and ν 0 = 3, then starting with z = −11 dB;…”