Estimation of the Number of Radio Signals with Unknown Amplitudes and Phases

Abstract

621.391Some algorithms for estimating the number of radio signals with known and unknown amplitudes and phases are synthesized and analyzed. Modified maximum-likelihood algorithms are used to obtain consistent algorithms for estimating the number of radio signals in the case of unknown amplitudes and phases. Efficiency of the estimation algorithms is quantitatively characterized by the abridged probability of the signal-number estimation error. The studied-algorithm parameters are optimized according to the analysis results.

Determining the Number of Sinusoids Measured with Errors

“…The representations (10) are useful for the further calculations of the coefficients K * * i,j (5) and K * i,j (9). In this paper, we use an error probability, i.e., Pr(ν = ν 0 ) as a measure of performance of the algorithm for estimating the number of signals and an abridged error probability [10]- [14] as a universal approximation to the error probability.…”

“…The representations (10) are useful for the further calculations of the coefficients K * * i,j (5) and K * i,j (9). In this paper, we use an error probability, i.e., Pr(ν = ν 0 ) as a measure of performance of the algorithm for estimating the number of signals and an abridged error probability [10]- [14] as a universal approximation to the error probability. Let us write down a definition of the abridged error probability that can be found in [10]- [14]…”

“…The problems that are described there cannot be solved by the classical maximum likelihood method, that is why many different approaches to modify the maximum likelihood method have been proposed. However, as it is shown in [10] and [11], in some cases the maximum likelihood method can be applied directly without any modification. One of these cases is a problem of determining the number of signals with known parameters, but it is a very rare one in practice.…”

Model selection for the robust efficient signal processing observed with small Lévy noise

“…As a result, the effective detection algorithms can significantly improve the noise immunity in data transmission over a multi-path channel (see, for example, the papers of Flaksman, Manelis, El-BeMac, Trifonov, Kharin, and Chernoyarov [7,23,5,30,29,28,31,32]). These problems for signals with unknown amplitudes are discussed by Trifonov and Kharin in [30]. The signal amplitude is an energy parameter because it affects the signal energy.…”

“…At the same time, quite often, such as in radars studied by El-BeMac in [5], it is necessary to detect the number of signals, which besides an unknown amplitude, it contains non-energy parameters such as the time and directions of the signal arrival, its frequency and initial phase. Moreover, Trifonov, Kharin, Chernoyarov and Kalashnikov in [28] considered this problem with unknown initial phases, in [31] with unknown amplitudes and phases and in [32] the detection signal number problem is considered for orthogonal signals with arbitrary non-energy parameters. In all these papers the signals number detection problems are considered only for observation with Gaussian white nose.…”