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Range and velocity estimation of moving targets using conventional stepped-frequency pulse radar may suffer from the range-Doppler coupling and the phase wrapping. To overcome these problems, this paper presents a new radar waveform named multiple stepped-frequency pulse trains and proposes a new algorithm. It is shown that by using multiple stepped-frequency pulse trains and the robust phase unwrapping theorem (RPUT), both of the range-Doppler coupling and the phase wrapping can be robustly resolved, and accordingly, the range and the velocity of a moving target can be accurately estimated.

Range and velocity estimation of moving targets using high range resolution radar is a topic of great interest. To achieve this goal, there are two problems to be considered. The

In this paper, we propose a new algorithm to robustly resolve both of the range-Doppler coupling and the phase wrapping. The radar transmits and receives multiple stepped-frequency pulse trains with different carrier frequencies, and IDFT is operated on every pulse train. It will be shown that, using the difference information among multiple IDFT results and the robust phase unwrapping theorem (RPUT) [

This paper is organized as follows. In Section 2, the range-Doppler coupling and the phase wrapping is reviewed in conventional stepped-frequency pulse train processing. In Section 3, the multiple stepped-frequency pulse trains are introduced and an algorithm is proposed to resolve both of the range-Doppler coupling and the phase wrapping. In Section 4, some numerical examples are given to demonstrate the proposed algorithm.

In this section, we review the single stepped-frequency pulse train processing and introduce the range-Doppler coupling and the phase wrapping. Like most studies on stepped-frequency pulse train processing, we take the following assumptions: 1) the target moves with constant velocity

The received baseband echo can be expressed as
_{p}_{c}_{0} − _{0} is the initial range position of the target, and _{0}

After the range compression in every pulse, _{0} − (_{c} M

In this section, we present a new waveform named multiple stepped-frequency pulse trains and describe how to resolve both range-Doppler coupling and phase wrapping using this waveform.

We replace the single stepped-frequency pulse train by multiple stepped-frequency pulse trains. This new waveform is shown in _{c1}, _{c2} and _{c3} and transmitted by three antennas, respectively, and then the different echoes on_{c}_{1}, _{c2} and _{c3} are collected and demodulated by three antennas, respectively. Without loss of generality, we assume _{c1} < f_{c2} < f_{c3}_{c2} − f_{c1}_{c3} − f_{c1}

Now we perform the processing described in the previous section on three stepped-frequency pulse trains. By performing _{i}_{ci}_{i}_{i}_{i}_{i}

We first estimate _{1} and _{2}_{i}_{i}_{i}_{i}_{1} < 0, the first equation of _{1} is replaced by determining (_{1} -1). Thus, without loss of generality, we assume
_{1} ≜ Γ/(_{c2} − f_{c1}_{2}=Γ/(_{c3} − f_{c1}_{c2}−_{c1}) and (_{c3} − _{c1}) are not integer multiples of each other, and _{ci}_{1} and Γ_{2} to the two equations in _{1} and _{2} can be correctly determined as

Submitting _{0}

In this section, some numerical examples are given to show the effectiveness of the proposed algorithm. Assume that the observation range is about 20km, the pulse repetition interval _{c1}, _{c2} and _{c3} are 7GHz, 9GHz and 10GHz, respectively, a target is moving toward the radar with speed 100m/s, and the initial distance between the radar and the target is _{0}=19885m. In each pulse, the low range resolution is _{0}

According to the derivation in the previous section, one can calculate that Γ = 6x10^{9}, Γ_{1} =3 and Γ_{2} =2. The maximal determinable speed is | _{max} | =120m/s according to

In this paper, a new radar waveform is designed and a new algorithm is proposed to estimate the range and velocity of a moving target. In order to resolve both range-Doppler coupling and phase unwrapping, three (or multiple) stepped–frequency pulse trains and the RPUT are used. Theoretical analysis and the simulation results show that the proposed algorithm can accurately estimate the range and the velocity of the moving target. As a remark, the proposed algorithm relies on the detectability of the moving targets. About the moving target detection using stepped-frequency pulse train, we would like to refer the readers to [

This work was supported by the Chuanxin Foundation from the Department of Electronic Engineering, Tsinghua University. Xia's work was partially supported by the Air Force Office of Scientific Research (AFOSR) under Grant No. FA 9550-05-1-0161 and a DEPSCoR Grant W911NF-07-1-0422 through ARO.

Multiple stepped-frequency pulse trains with different base carrier frequencies.

The estimation error of speed

The estimation error of range r versus various maximal remainder error level