Fast Pulse Doppler Radar Processing Accounting for Range Bin Migration

An airborne pulse Doppler radar depends on a combination of range selectivity and velocity selectivity to detect targets in ground cluttsr. In principle clutter sensitivity can be reduced by employing higher bandwidths for greater range resolution. However at a sufficiently high bandwidth the phenomenon of range bin migration occurs which precludes the use of conventional Doppler processing. Here: the product of the range-rate and the coherent integration pericd exceeds the range resolution. We introduce a fast algorithm which performs coherent integrationDoppler filtering while explicitly accounting for range bin migration. The fast algorithm is based on an integration along a slanted line in the 2-D frequency domain. INTRODUCTION A pulse-Doppler radar transmits a sequence of phasecoherent pulses. The radar return is a function of transmit time, t , and delay-time (i.e. the time since the pulse was transmitted), T. Conventional Doppler processing consists of taking onedimensional Fourier transforms overt, for constant values of 7, with two beneficial effects: first, it improves the signal-to-noise ratio by virtue of the coherent integration, and second it imparts velocity (e.g. range-rate) selectivity of moving targets on the basis of differing Doppler frequencies. Velocity selectivity is particularly important in an airborne radar for detecting targets in ground clutter Ill. There are two well-known constraints on the applicability of conventional Doppler processing. The first constraint, related to target acceleration, is that the maximum possible change in Doppler freqiiency over the integration period must be smaller than the frequency resolution. If a is the target acceleration, T is the integration period, and li is the wavelength then the maximum change in Doppler frequency over the integration period is equal to 2aT/L. This must be smaller than the frequency resolution, In, yielding the requirement that T < G a . The second constraint is that the return must remain in a single range cell during the integration period, or equivalently that the product of the integration period and the maximum range-rate must be smaller than the range resolution. For example an X-band radar (1 = .03 m), viewing a target having an acceleration of 10 g's (98. m/s2) is limited to an integration period of .012 seconds. With this same integration period a 300 m/s target would move 3.7 meters during the integration period, so range bin migration would occur if the range resolution were less than 3.7 meters, or equivalently if the bandwidth were greater than 40 Mhz. The new algorithm deals with the second of the above consmaints by performing coherent integrationDoppler filtering while explicitly accounting for the movement of the target through multiple range bins during the integration period. The key connibutim of this paper is to show that this processing can be performeu eiiiciently in the 2-D frequency domain. The problem of range bin migration has previously been addmsed in the context of SAR and rotational Doppler imaging [2] 151. In contrast this paper is focussed on nonimaging pulse Doppler radar. The fast algorithm is based on a rather general signal model that accounts for pulse dilation. In fact it is straightforward to extend the fast algorithm to "carrier free" pulses where the bandwidth is comparable to the center frequency. SIGNAL MODEL We denote the demodulated complex-valued radar return by r(t.7) where t is the time at which the radar transmitted the pulse, and 7 is delay time, i.e. the time since the pulse was transmitted. In reality of course, the radar receiver measures only a single complex function of time that is mapped into a two-variable signal by the transformation, r(t+7) + r(t,r), where 7 ranges between zero and the pulse repetition period. Let a(.) be the complex envelope of the transmitted pulse. Here we discuss a sequence of models for the received signal of increasing complexity. It what follows fo is the canier frequency, c is the speed of light, and k=c/fo is the wavelength. Stationan, Tar@ If the target were stationary the radar return would merely be a delayed version of the transmitted pulse with a phase shift corresponding to the phase delay of the camer. We denote the signal model by s(t.7). where R is the target range. Moving Target Conventional Pulse Douuler Model Assume now that the target is moving with a constant rangerate, v , and that Ro is the range at a reference time, to. Then the instantaneous range is s(t,T) = a(7 2FUc)exp { -i2m2RA) , ( 1 ) R = % + v.(t-tO) . (2) Within a sufficiently short interval of time that is centered on the reference time, the target motion causes a progressive phase shift in the received signal but the target movement is small compared with the range resolution. These assumptions yield the signal model on which conventional pulse-Doppler processing is based: s(t,f) = a(o 2Rdc)eexp [ -i2n2v.(t-t0)A) .exp [ -iQ0) , (3)