V.V. Pyatkov – Dr. Sc. (Eng.), Professor, Mozhaysky Military Space Academy (Saint Petersburg)
A.Yu. Onufrei – Dr. Sc. (Eng.), Professor, Leading Research Scientist, Mozhaysky Military Space Academy (Saint Petersburg)
A.V. Meleshko – Ph. D. (Eng.), Leading Specialist, JSC «RPC «Radar mms»
M.S. Vorona – Engineer, Laboratory, Mozhaysky Military Space Academy (Saint Petersburg)
The paper considers three- and four-channel digital angular discriminators as a part of angular coordinate measurement systems, that are based on the prediction-correction method applied to phased array radar characterized by monopulse coordinate measurement method. When monopulse coordinate measurement method is used, the signal reflected from a target is transformed within four blocks of quadrants of the radar’s antenna and waveguide system into corresponding output signals that are carried onto the sum and difference converter that creates one sum and two difference signals of high frequency. After the sum and difference converter, the signals are carried to corresponding three identical receivers; the signals from their outputs are carried to corresponding intermediate frequency amplifiers, and their outputs are connected to the analogue-to-digital converter (ADC) of signal processor. In each channel continuous-time intermediate frequency input signals in the ADC undergo time discretization and amplitude quantization. Model of the input ADC signal is presented in a vector form as an additive function of desired signal and noise.
With given statistical properties of signals and interferences that are formed at the ADC inputs and outputs, the task is to synthesize an optimal structure of the digital angular discriminator based on the statistical decision theory. The synthesis of the discriminator is performed using Markov chains. In order to choose the decision rule, discrete multivariate distributions of desired signal and interference are set. In that case the decision rule is derived using likelihood equation, on condition of quadratic penalty function, uniform prior probability distribution and symmetric posterior probability distribution. The equation for the optimal two-dimensional discriminator can be derived through expanding the logarithm of the conditional likelihood factor into the Taylor series around extrapolated object position, restricting to the addent with the second derivative, differentiating the resulting expressions and setting them to zero. The structure of the optimal discriminator is provided. In case of unknown distributions it is suggested to substitute them with informational equivalents. The expression for the quasi-optimal angular coordinate discriminator is provided. A factor in a form of fraction sets steepness of discriminator characteristic to one. Independence of steepness of discriminator characteristic from the input signal amplitude is achieved due to valuation of the difference signal on the sum signal (the second factor in a form of fraction). The parameters of the steepness of discriminator characteristic can be set through approximation at the radar design stage and further specified at the stage of the radar pre-production model development when ground and flight tests are conducted.
The drawback of the three-channel scheme of building an angular discriminator is very stringent requirements to receivers of sum and difference signals in ensuring equal coefficients of power gain and phase angles. This drawback can be eliminated by switching to a four-channel receiver of monopulse radars which excludes the sum and difference converter. All the radiators of phased array radar are divided into several sub-arrays with separate receivers, and for each sub-array a separate signal processor is used. In that case the ADC is installed closer to the outcome of low-noise amplifiers that are connected directly to antenna and waveguide system of partial channels in transmit/receive modules. In the latter case the synthesis of an optimal digital discriminator will be performed in the same way as described above, and sum and difference signals in that case will be formed in a digital form. The structure of the digital angular discriminator built for the four-channel angular coordinate measurement system, is provided. The increased accuracy of measurement of angular coordinates is achieved in that case through digitalization of receivers’ analogue signals directly in transmit/receive modules which increases the signal-to-noise ratio. In that case further signal processing is performed in a digital form.
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