The issues of signal processing and noise suppression in receiving systems with spatially distributed elements are considered. Processing algorithms are based on the theory of Markovian processes. The processing takes into account the broadband nature of the observable spatial-temporal signals. The signal with linear frequency modulation was taken as the useful signal. Spatial Time Process Model The task of detecting a wideband signal (in terms of space-time) by spatially distributed elements seems to be laborious, since only in some cases can be divided temporal and spatial filtering [1]. Also, applying the Bayesian optimal signal detection criterion requires reversing the correlation noise matrices of order corresponding to the square of the product of the number of receiving spatially distributed elements moments . This requires laborious calculations, leads to errors, and at small angles of arrival of the noise, the correlation matrix is close to a degenerate matrix. These problems can be solved by using the Markovian random process model to describe the noise on spatially distributed receiving elements.
(
Thus, Figure 2 shows a graph of spatial fluctuations on the elements of a linear antenna without taking into account fluctuations caused by modulations Ξ( − ( − 1) 0) and Ψ( − ( − 1) 0).
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In this case, when different sections of the broadband signal are sequentially hit the line of spatially distributed
elements, only one frequency is visible in the discrete spectrum of the spatial signal, regardless of the presence of
modulation. This property is convenient when there are several noise signals with different directions of arrival. This
character is continued when considering the spatial-temporal fluctuations. Figure 3 presents the spatial-temporal
spectrum of one interfering fluctuation after it passes through a matched filter with a complex frequency response
corresponding to (
As an indicator of the correspondence of the noise of the Markovian model, Figure 4 shows the temporary
implementation of the noise before and after the decorrelation procedure (
) ∏ =3 ( | −1, −2), ( ) = 22 2 −1 22 + ∑ =3[ 3 3
−1 3 − 2 2
−1 2 ],
where 2 , 3 , 2 , 3 are the shortened vectors from the samples of the signal and noise oscillations at fixed and
и Θ , 2 and 3 are the correlation matrices of the shortened vectors. In a theoretical study, the quality criterion of
the proposed method was to improve the signal-to-noise ratio (SNR) after spatial processing to the input
signal-tonoise ratio. In Figure 7 is shown the improvement of the SNR depending on the direction of arrival of one noise
fluctuation and with a fixed direction to the useful signal.
(
We turn to the spatial-temporal detection algorithm, provided that the set of samples at the given time is independent, that is, we have the vector:
The decisive statistics according to (6) and (7) has the form:
( ) = ∑ =1 〈 〉( 〈 〉), ( ) = ∑ =1 { 22〈 〉 2−1 22〈 〉 + ∑ =3 [ 3 〈 〉 3−1 3 〈 〉 − 2 〈 〉 2−1 2 〈 〉]}.
Thus, temporary accumulation of the above-described spatial processing occurs.
Signal processing in the presence of several noise requires a larger number of prediction coefficients in (
The paper considers the issues of signal processing against the background of noise in reception systems with spatially distributed antenna elements. Processing algorithms are built on the model of Markovian random processes, which makes it possible to factorize spatial-temporal processing, and, therefore, leads to a simplification of the implementation of the algorithm. Using the spatial spectrum allows to determine the amount and direction of arrival of active interference.