Orthogonal PCM signal processing algorithm

At present, the resolution problem remains relevant in radar, and in the transmission of information - the task of distinguishing signals.

To solve these problems, one can use PCM signals encoded by ensembles of orthogonal functions, which, as is known, have zero cross-correlation.

To resolve signals in radar, a burst signal can be used, each pulse of which is encoded by one of the rows of the orthogonal matrix, for example, the Vilenkin-Chrestenson or Walsh-Hadamard matrices. These signals have good correlation characteristics, which allows them to be used for the aforementioned tasks. To distinguish between signals in data transmission systems, you can use the same signal with a duty cycle equal to one.

In this case, the Vilenkin-Chrestenson matrix can be used to form a polyphase ( p- phase) PCM signal, and the Walsh-Hadamard matrix, as a special case of the Vilenkin-Chrestenson matrix for the number of phases equal to two, for the formation of a biphasic signal.

Polyphase signals are known to have high noise immunity, structural stealth and a relatively low level of side lobes of the autocorrelation function. However, to process such signals, it is necessary to spend more algebraic operations of addition and multiplication due to the presence of the real and imaginary parts of the signal samples, which leads to an increase in processing time.

The problems of discrimination and resolution can be aggravated by a priori unknown Doppler shift of the carrier frequency due to the relative motion of the information source and the subscriber or radar and the target, which also complicates the processing of signals in real time due to the presence of additional Doppler processing channels.

To process the aforementioned signals having a Doppler frequency addition, it is proposed to use a device that consists of an input register, a discrete conversion processor, a cross-link unit, and a set of identical ACF signal generation units, which are series-connected shift registers.

If we take the Vilenkin-Chrestenson orthogonal matrix for processing a polyphase burst signal as the basis matrix, then the discrete transformation will go over to the discrete Vilenkin-Chrestenson-Fourier transform.

Because the Vilenkin-Chrestenson matrix can be factorized using the Good algorithm, then the discrete Vilenkin-Chrestenson-Fourier transform can be reduced to the fast Vilenkin-Chrestenson-Fourier transform.

If we take the orthogonal Walsh-Hadamard matrix as a basis matrix, a special case of the Vilenkin-Chrestenson matrix for processing a biphasic burst signal, then the discrete transformation will go over to the discrete Walsh-Fourier transform, which can be reduced to the fast Walsh-Fourier transform by factorization.

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