Algorithm for processing orthogonal FCM signals
At present, the problem of resolution remains relevant in radar, and the problem of distinguishing signals in information transmission systems.
To solve these problems, one can use FCM signals encoded by ensembles of orthogonal functions, which, as is well known, have zero cross-correlation.
To resolve signals in radar, you can use a burst signal, each pulse of which is encoded by one of the rows of an 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 above tasks. To distinguish between signals in data transmission systems, you can use the same signal with a duty cycle equal to one.
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In this case, the Vilenkin-Chrestenson matrix can be used to form a polyphase ( p- phase) FCM signal, and the Walsh-Hadamard matrix, as a special case of the Vilenkin-Chrestenson matrix for the number of phases, is equal to two, to form a bi-phase signal.
Polyphase signals are known to have high noise immunity, structural secrecy and a relatively low level of side lobes of the autocorrelation function. However, to process such signals, it is necessary to expend more algebraic addition and multiplication operations due to the presence of the real and imaginary parts of the signal samples, which leads to an increase in processing time.
The tasks of discrimination and resolution can be aggravated by a priori unknown Doppler shift of the carrier frequency due to the relative movement of the information source and the subscriber or the radar and the target, which also makes it difficult to process signals in real time due to the presence of additional Doppler processing channels.
To process the above-mentioned 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-linking unit, and a set of identical ACF signal generation units, which are serially connected shift registers.
If we take the Vilenkin-Chrestenson orthogonal matrix for processing a polyphase burst signal as a matrix basis, then the discrete transform will turn into the discrete Vilenkin-Chrestenson-Fourier transform.
Since the Vilenkin-Chrestenson matrix can be factorized using the Good algorithm, then the Vilenkin-Chrestenson-Fourier transform can be reduced to the fast Vilenkin-Chrestenson-Fourier transform.
If the Walsh – Hadamard orthogonal matrix — a special case of the Vilenkin – Chrestenson matrix for processing a biphasic burst signal — is taken as the matrix basis, then the discrete transform will turn into the discrete Walsh – Fourier transform, which can be reduced to a fast Walsh – Fourier transform by factorization.
To solve these problems, one can use FCM signals encoded by ensembles of orthogonal functions, which, as is well known, have zero cross-correlation.
To resolve signals in radar, you can use a burst signal, each pulse of which is encoded by one of the rows of an 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 above 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) FCM signal, and the Walsh-Hadamard matrix, as a special case of the Vilenkin-Chrestenson matrix for the number of phases, is equal to two, to form a bi-phase signal.
Polyphase signals are known to have high noise immunity, structural secrecy and a relatively low level of side lobes of the autocorrelation function. However, to process such signals, it is necessary to expend more algebraic addition and multiplication operations due to the presence of the real and imaginary parts of the signal samples, which leads to an increase in processing time.
The tasks of discrimination and resolution can be aggravated by a priori unknown Doppler shift of the carrier frequency due to the relative movement of the information source and the subscriber or the radar and the target, which also makes it difficult to process signals in real time due to the presence of additional Doppler processing channels.
To process the above-mentioned 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-linking unit, and a set of identical ACF signal generation units, which are serially connected shift registers.
If we take the Vilenkin-Chrestenson orthogonal matrix for processing a polyphase burst signal as a matrix basis, then the discrete transform will turn into the discrete Vilenkin-Chrestenson-Fourier transform.
Since the Vilenkin-Chrestenson matrix can be factorized using the Good algorithm, then the Vilenkin-Chrestenson-Fourier transform can be reduced to the fast Vilenkin-Chrestenson-Fourier transform.
If the Walsh – Hadamard orthogonal matrix — a special case of the Vilenkin – Chrestenson matrix for processing a biphasic burst signal — is taken as the matrix basis, then the discrete transform will turn into the discrete Walsh – Fourier transform, which can be reduced to a fast Walsh – Fourier transform by factorization.
Source: https://habr.com/ru/post/249191/
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