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RESEARCH PAPERS

SCIENCE CHINA

Information Sciences

December 2010 Vol. 53 No. 12: 2664–2674

doi: 10.1007/s11432-010-4110-x

 Science China Press and Springer-Verlag Berlin Heidelberg 2010 info.scichina.com www.springerlink.com

The impact of time synchronization error on passive

coherent pulsed radar system

HE You

, ZHANG CaiSheng

1,2 ∗

,DINGJiaHui

& TANG XiaoMing

Research Institute of Information Fusion, Naval A eronautical and Astronautical University,

Yantai 264001,China;

Nanjing Research Institute of Electronics Technology, Nanjing 210039,China

Received May 18, 2010; accepted August 9, 2010

Abstract Passive bistatic coherent radar system operates with distinct non-cooperative transmitter and re-

ceiver located at diﬀerent sites. In such spatial separation, the receiving system needs to independently solve

the problem of time and phase synchronization via direct-path signal. The impact of time synchronization error

was explored and solved in passive bistatic coherent radar. The common model of digital sampling process is

introduced to illustrate the eﬀect of time synchronization error (TSE). The periodicity of relative sample instant

variation of each pulse is deduced. Then, normalized interference power (NIP) is deﬁned to evaluate the poten-

tial impact of TSE. The NIP expressions are derived when the diﬀerence between the adjacent relative sample

instant is uniform distribution or Gaussian distribution. It is found that there are new spurious frequency com-

ponents and the detection performance is decreased in the case of asynchronous sampling. At the same time,

the analytical Doppler frequency bias expression caused by TSE is presented. Theoretical results are conﬁrmed

by simulation in the cases of diﬀerent periods of relative sampling instant.

Keywords passive coherent radar (PCR), time synchronization error (TSE), normalized interference power

(NIP)

Citation He Y, Zhang C S, Ding J H, et al. The impact of time synchronization error on passive coherent pulsed

radar system. Sci China Inf Sci, 2010, 53: 2664–2674, doi: 10.1007/s11432-010-4110-x

1 Introduct ion

One premise of digital coherent signal processing for Doppler radar is keeping the coherence between

pulses after data sampling. Several restrictions on digital sampling parameters are proposed in [1, 2]. In

order to guarantee the coherence between pulses, the sampling clock and trigger signal must synchronize

to the pulse repetition frequency (PRF) of non-cooperative transmitting signal. The performance of time

synchronization will directly aﬀect the coherent signal processing gain [3].

One of the most critical issues for coherent detection in passive coherent pulsed radar is time synchro-

nization. The only technique of time synchronization for passive coherent pulsed radar, however, is to

synchronize the sampling clock by direct-path signal in the passive receiving system [4–7]. In practice,

even if the direct-path signal can be received successively during the scanning of the transmitter’s an-

tenna, the signal-to-noise ratio of direct-path signal will aﬀect the accuracy of PRF estimation. As a

∗

Corresponding author (email: caifbi2008@yahoo.com.cn)

HE You, et al. Sci China Inf Sci Decemb er 2010 Vol. 53 No. 12 2665

result, there is TSE between the time-base of sampling clock and target echo. The number of samples

per PRF may be not an integer, and the relative sample instant will drift, too. In the process of digital

signal processing, however, the independent variable in the sampling sequence has no information about

the jitter of timing clock.

Jenq [8, 9] ﬁrst described and analyzed the spectrum of ideal sine wave in the case of non-uniformly

sampling. Its original idea is decomposing the non-uniformly sampled sequence into M subsequences,

which are subsequently treated as uniformly sampled data. The digital spectral representation of a non-

uniformly sampled sequence data is proposed in terms of its analog spectrum. Based on this research,

ref. [10] explored a more generalized digital spectral expression for non-uniformly sampled signal. Perfect

reconstruction algorithm of digital spectrum from non-uniformly sampled signals is proposed if timing

error in the receiving system is known [11]. Some special cases on the spectrum reconstruction algorithm

are presented in [3, 12].

In this paper, we concentrate on the impact of TSE on coherent detection and Doppler shift estimation

in passive coherent pulsed radar system. The common model of digital sampling process is described in

section 2. The period of relative sample instant variation of each pulse is explored via modeling in

section 3. In section 4, NIP is deﬁned to assess the potential impact of the TSE on coherent detection

and Doppler shift estimation. The NIP expressions are derived when the diﬀerence between the adjacent

relative sample instant is uniform distribution or Gaussian distribution. Finally, conclusions are presented

in section 5.

2 Problem description

A scenario with non-cooperative radar illuminator considered in this paper is illustrated in Figure 1.

Assume that the transmitter is mechanically scanned in azimuth, and the receiver is stationary while the

target is moving. Both the transmitter and receiver are focusing on the moving target. The receiving

system intercepts the direct-path waveform transmission through a reference antenna when it tunes to

the transmitting frequency, and target reﬂection echoes are intercepted by the target antenna. Time

and phase synchronization need to be completed via direct-path signal. Then, optimum detection and

parameters estimation are commonly involved in passive coherent processing. Surveillance and early-

warning may be achieved in the area of interest [13, 14].

According to the Nyquist sampling theorem, the sampling frequency F

must not be less than 2F

where F

is the carrier frequency of transmitting signal. In practice, however, in coherent pulse radar,

the coherence is required among pulses after data sampling process. Generally speaking, the common

sampling process can be described as Figure 2. For convenience, the rising edge of each pulse is deﬁned

as the starting instant of the corresponding PRF. Here, δt

denotes the interval between the ﬁrst sample

instant of the ith pulse, and 0  δt

 T

,whereT

is sampling interval. Then, δt

is ﬁxed time delay

between the sampling clock and the rising edge of the ﬁrst pulse caused by signal transmission. For the

purpose of coherent processing, it is desired that δt

= δt

= ···= δt

. In this way, we should guarantee

that F

= pf

, p =1, 2, 3,...,wheref

is the value of PRF.

In the passive coherent radar system, however, we need to estimate the PRF of the transmitting

signal via direct-path pulses. In theory, the direct-path signal is modulated by the rotating transmitter’s

antenna pattern, which will reduce the estimation accuracy of PRF, and hence TSE between the sample

frequency and PRF is introduced unconsciously.

Assume that the range sweep is initiated by a threshold detection of the direct-path pulse. In a passive

bistatic receiving system, we designate the ﬁrst sample of each direct-path pulse crossed the threshold as

the trigger of sampling clock. There is a series of data samples in every pulse repetition interval (PRI).

With no loss of generality, the sampling process of target reﬂection echoes in the target dwell time can

be illustrated as Figure 3. It can be found that the ﬁrst sample instant of each pulse is drifting relative

to the start of the direct pulse. Note that sample 1 is the ﬁrst sample of direct-path pulse from PRI 1

to PRI 4. However, sample 4 will be the ﬁrst sample of direct-path pulse from PRI 5 to PRI 8 and the

process will be repeated. For the case of a general direct path pulse shape, the net result of this asynch-

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