# DIGITAL BEAM-FORMING ANTENNA OPTIMIZATION FOR REFLECTOR BASED SPACE DEBRIS RADAR SYSTEM

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4 Pulse Repetition Frequency (PRF) and v is the velocity of the object. Since the HPBW, Θ 3dB, is proportional to the diameter of the reflector antenna via: [4] is shown in Fig. 6 as a function of number of integrated pulses and compared to the coherent case when n E(n) = n. Θ 3dB = ɛ λ D (5) where ɛ is the function of shape and illumination of the reflector surface, one can relate the number of received echoes to the antenna aperture size. The number of received echo pulses for a single beam as a function of antenna diameter is shown in Fig. 5. The results are obtained for a target orbiting the Earth at the height of 1000 km illuminated in the beam-park mode with a fixed antenna elevation angle of 25 at L-Band by a pulse train at a PRF rate, f P RF, of 10 Hz, 50 Hz and 100 Hz. Figure 6. Decrease in the required SNR for one pulse with a non-coherent (solid line) and coherent (dashed line) integration of n pulses relative to the single pulse operation as a function of number of integrated pulses. Linear detector, p d = 0.9 %, p fa = Figure 5. Number of received echo pulses for a single beam as a function of a reflector diameter: f P RF = 10 Hz (solid line), f P RF = 50 Hz (dotted line), f P RF = 100 Hz (dashed line). Using equations (4), (5) and (6) one can relate the required decrease in SNR for one pulse (relative to the single pulse operation) with the aperture diameter assuming that all returned echo pulses, n, are non-coherently integrated. The given dependence for a single beam without taking into account the gain increase is shown in Fig. 7 by black lines for different values of PRF, f P RF Integration of the returned echoes per beam In practice the pulse integration effect in the multi-pulse mode is achieved using energy storage elements. Due to a non-constant phase between transmitted and received pulses the pulses are integrated non-coherently. The improvement achieved by this integration is identified as an integration efficiency expressed by [4]: E(n) = SNR 1 n SNR n (6) where SNR 1 is the SNR for a single pulse operation and SNR n is the SNR for a single pulse with the integration of n pulses resulting in the same probability of detection and a false alarm rate. The parameter n E(n) representing the decrease in the required SNR for one pulse with non-coherent integration of n pulses relative to the single pulse operation Figure 7. Required SNR decrease for one pulse as a function of aperture diameter relative to the single pulse operation for different values of f P RF without taking into account the increase in gain (black lines). Red line represents the total required decrease in SNR for one pulse for the system with 34 digital channels operated in a multipulse mode with f P RF = 50 Hz relative to the singlepulse reference system with D = 5 m.

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