new antivelocity deception jamming technique using pulses with adaptive initial phases

New Antivelocity Deception

Jamming Technique using

Pulses with Adaptive Initial

Phases

JINDONG ZHANG

DAIYIN ZHU, Member, IEEE

GONG ZHANG, Member, IEEE

Nanjing University of Aeronautics and Astronautics

An effective electronic counter-countermeasures (ECCM)

technique for a moving target indication/pulsed Doppler

(MTI/PD) radar system against velocity deception jamming is

proposed. A novel radar signaling strategy is outlined based

on variations of the initial phases of the transmitted pulses in

pulse repetition interval (PRI) domain. It makes the Doppler

spectrum of the false targets, created by a digital radio frequency

memory (DRFM) repeat-back jammer, form a notch around the

Doppler frequency of the true one. The penalty function and

corresponding algorithm for designing adaptive initial phases

are given. We also present an approach of the multi-channel

matched filter processing to estimate the manner, by which a

DRFM repeat jammer operates, and the parameters of the false

targets. The working flow of an MTI/PD radar for countering

velocity deception jamming is investigated. Simulation results

show the effectiveness of the above methods.

Manuscript received April 30, 2011; revised October 23, 2011 and

May 15, 2011; released for publication October 9, 2012.

IEEE Log No. T-AES/49/2/944536.

Refereeing of this contribution was handled by S. Hary.

This work was supported by the Chinese National Natural Science

Foundation under Contracts 61201367, 61071163, 61071165, and

61100195, the Natural Science Foundation of Jiangsu Province

under Contract BK2012382, and the Defense Industrial Technology

Development Program under Contract B2520110008.

Authors’ address: College of Electronic and Information

Engineering, Nanjing University of Aeronautics and Astronautics,

29 Yudao Street, 210016 Nanjing, China, E-mail: ([email protected]).

0018-9251/13/$26.00 c° 2013 IEEE

I. INTRODUCTION

Moving target indication (MTI) and pulsed

Doppler (PD) radars are two classes of radar systems

designed with coherent processing for detecting

targets in the midst of noise, clutter, and jamming,

which could be stronger than the target signal by

several orders of magnitude. With the capability of

separating moving targets from relatively stationary

clutter, MTI and PD techniques are widely used in

modern radar systems, and are playing an important

role in air surveillance of civilian systems and the

detection of low flying aircraft or missiles [1].

The electronic countermeasures (ECM) has

undergone rapid development with the military radar

over the past two decades [2—3]. The countermeasures

mainly intend to mask useful information, create

deceptive targets more attractive than the true ones,

or aim at saturating the target extraction and tracking

algorithms. The emergence of digital radio frequency

memory (DRFM) makes the jammer, which is referred

to as the repeat-back jammer, capable of listening,

storing, and repeating back the radar’s transmitted

signal to deceive hostile radar systems [4]. In MTI

and PD radar systems, the user relies on multiple

radar signal transmissions for coherent detection.

Based on this property, a DRFM repeat jammer

constructs a series of replicas of the transmitted radar

signal multiplied by a certain Doppler frequency to

deceive the radar system. Therefore DRFM induces

serious threats to the survival of the MTI and PD

radars in the modern battlefield [5].

The most

effective electronic counter-countermeasures (ECCM)

scheme for a radar system against the DRFM repeat

jammer-type systems is pulse diversity [6—9]. The

pulse-diversifying method being considered currently

is to transmit orthogonal pulses from one pulse

repetition interval (PRI) to another. Since the pulse is

varying in the PRI domain, the jammer cannot adapt

easily and the signal transmitted by the DRFM repeat

jammer is approximately orthogonal to the signal that

the radar system is transmitting at the current PRI;

a matched filter with the transmitted radar signal

of the current PRI would weaken the DRFM repeat

jammer signal. Random signal radar (RSR) has been

demonstrated to be quite effective in this application.

Liu and Gu have studied and implemented the random

binary phase-coded pulse radar [10], the random pulse

radar [11], the random position pulse radar [12], and

etc.

The pulse diversifying method has been proved

to be useful for target detection without Doppler

processing. However during MTI filtering in MTI

radar or range-Doppler processing in PD radar,

pulse diversity leads to range sidelobe variation,

severely degrading the integrated signal-to-jammer

ratio (SJR) and therefore limiting the ability to

1290 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 49, NO. 2 APRIL 2013

suppress interference for the radar system. In [8]

several methods have been proposed to mitigate this

performance loss. Code selection of the pseudonoise

(PN) codes with the capability of forming matched

filter output with minimal sidelobe variation improved

the performance by approximately 7 dB. The pulse

compression filter could succeeded in eliminating

sidelobe energy in the filtered output, but suffer

from a 2.5 dB signal-to-noise ratio (SNR) loss

when compared with the matched filter. Combing

the advantages of the matched filter and pulse

compression filter, the digital equalization filtering

method was successful in equalizing differences

created by variable PN codes.

To overcome the demerit of pulse diversity

and reserve the original coherent two-dimensional

processing in range-Doppler domain, pulses with

different initial phases can be utilized. We begin by

examining the merit of pulses with random initial

phases for countering the DRFM repeat-back jammer.

SJR gain obtained by Doppler processing is studied.

Although the Doppler spectrum of the false targets is

suppressed, it will be evenly spread over all Doppler

cells and will affect the true target detection.

In this presentation a novel radar signaling strategy

is outlined based on pulses with adaptive initial

phases. The Doppler spectrum of the false targets

could form a notch around the Doppler frequency of

the true target after Doppler processing. The adaptive

initial phases whose spectrum forms a notch in a

certain band are designed by an iterative algorithm.

The penalty function of a weighted integral of spectral

energy in this band is constructed. The algorithm

applied to compute the adaptive initial phases is to

minimize the penalty function with the phase-only

vector. This constrained optimization problem can be

successfully solved by the phase-only version of the

conjugate gradient and Newton’s method [13]. The

presented technique requires that the manner by which

a DRFM repeat jammer operates (i.e., at the current

PRI, it transmits the radar signal used for the certain

previous or some other past PRI) and parameters of

the false targets for adaptive initial phases design

are both available to the radar. For this purpose we

propose a scheme of multi-channel processing. We

also design a working flow for countering three kinds

of velocity deception jamming, including velocity gate

pull off, multiple false targets, and two blinking false

targets [14, 15]. The detailed introduction of these

deception jammings is given.

Section II introduces the received signal model

under the DRFM repeat-type velocity deception

jamming. Section III evaluates the performance of

pulses with random initial phases. Section IV proposes

a new signaling method using pulses with adaptive

initial phases. The phase-only conjugate gradient

method is introduced in optimizing the penalty

function. A scheme of the multi-channel processing

is proposed to estimate the jammer operation manner

and the parameters of the false targets. The flow

diagram of an MTI/PD radar for countering velocity

deception jamming is given. Section V shows the

simulation results. Section VI is the concluding

remarks.

II. ECHO SIGNAL MODEL UNDER VELOCITYDECEPTION JAMMING

An MTI/PD radar transmits a coherent signal that

is produced by modulating a sinusoid with a pulsed

waveform. Assuming that the signal is composed

of N pulses during coherent processing interval

(CPI). The target in the antenna beam is created as

a point scatter with the specified constant radar cross

section (RCS), and located at a given range with some

Doppler component to simulate velocity from one PRI

to the next. The Doppler frequency of the target is

fd = 2v=¸, where v is its relative velocity to the radar

system and ¸ is the signal wavelength. The signal

returned from a moving target with such Doppler

frequency can be represented as

sn(t) = ¾Tej2¼fdnTr¹(t¡ ¿d ¡nTr) (1)

where ¾T, ¹(t) and Tr denote the target reflectivity

coefficient, complex envelope of the transmitted pulse

and PRI, respectively, ¿d is the delay time, and n

is the pulse number. If the radar system transmits

pulses with a high repetition frequency, there are only

minor changes in the overall operating environment

during the CPI, and the target could be considered

stationary. Therefore we assume that ¾T, ¿d, and fdremain constant over the N slow-time intervals.

The DRFM repeat jammer requires several PRIs

to recognize the radar transmitted pulses, and then

utilizes the captured pulses of the previous PRIs to

replicate multiple false targets. The pulse generated

by the DRFM repeat jammer for deceiving the radar

system at the nth PRI can be expressed as

qn(t) =

PXp=1

¾pe2¼f

p

fnTr¹(t¡ ¿pf ¡nTr) (2)

where P is the number of false targets, and ¾p, ¿pf ,

and fpf denote the amplitude, delay time, and Doppler

frequency of the pth false target, respectively.

The signal received by the radar system can be

written as

rn(t) =qn(t)+ sn(t) + nn(t)

=

PXp=1

¾pe2¼f

p

fnTr¹(t¡ ¿pf ¡nTr)

+¾Tej2¼fdnTr¹(t¡ ¿d¡ nTr) + nn(t) (3)

where nn(t) is the additive white noise at the nth PRI.

ZHANG, ET AL.: NEW ANTIVELOCITY DECEPTION JAMMING TECHNIQUE 1291

Matched filtering is a signal processing strategy for

detecting target, and improving range resolution and

SNR, when using waveforms such as binary phase

encoded PN codes. The M sequence is a typical PN

code and its waveform correlation function can be

given by

ÂM(¿) =

Z¹¤M(t)¹M(t¡ ¿)dt

=1

L

L¡1Xl=¡(L¡1)

Âsub(¿ ¡ lT)Âcode(l) (4)

where

¹M(t) =1pL

L¡1Xk=0

ckrect

μt¡ kTT

¶

Âcode(l) =

L¡1¡kXk=0

c¤kck+l =½L, l = 0

·pL, l 6= 0

Âsub(¿) =T¡ j¿ jT

, j¿ j · T

and T is the subpulse duration, ck is the kth code, and

L is the code length.

The matched filter output, which represents the

correlation function between the received signal and

transmitted pulse, can separate the targets in different

range cells. For simplicity only the case that the

true and false targets are in the same range cell, i.e.,

¿pf ¼ ¿d, is considered, and the noise effect is alsoignored here. The matched filter output at the delay

time ¿d of the nth PRI can be written as

y(n) =

Z¹¤M(t¡ ¿d ¡ nTr)rn(t)dt

=

PXp=1

¾pej2¼f

p

fnTr +¾Te

j2¼fdnTr : (5)

To discriminate the targets with different velocities

in the same range cell, Doppler processing based

on the discrete Fourier transform (DFT) can then be

applied. The DFT result is given by

Y(k) = DFT[y(n)]

=

PXp=1

¾pej(¼=N)(N¡1)(k¡Nfp

fTr)sin¼(k¡Nfpf Tr)sin

¼

N(k¡Nfpf Tr)

+¾Tej(¼=N)(N¡1)(k¡NfdTr) sin¼(k¡NfdTr)

sin¼

N(k¡NfdTr)

: (6)

We can observe that the true and false targets appear

at the same time in Y(k), and cannot be distinguished

from each other. Obviously the enemy could easily

use a DRFM repeat jammer to jam the MTI/PD radar

systems with erroneous replicas of the transmitted

radar pulses.

Fig. 1. Scheme for transmitting pulses with random initial phases

in CPI with lag 2.

III. ECCM USING PULSES WITH RANDOM INITIALPHASES

Now we consider that the radar system is to

transmit a new or modified pulse with a random initial

phase at each PRI. According to (3) the received

signal of the radar system at the nth PRI can be

expressed as

rn(t) =

PXp=1

¾pejÁn¡i e

j2¼fp

fnTr¹(t¡ ¿d ¡ nTr)

+¾TejÁnej2¼fdnTr¹(t¡ ¿d¡ nTr) (7)

where Án, which is the initial phase of the nth

transmitted pulse, is assumed to be uniformly

distributed in [¡¼,¼] and statistically independent ofthat of the other pulses.

The pulse emitted by the jammer is assumed to

lag i PRI behind the pulse transmitted by the radar. It

means that at the nth PRI the DRFM repeat jammer

replicates the pulse that the radar has transmitted

at the (n¡ i)th PRI. For n· i the initial phase ofthe pulse transmitted by the jammer may be that of

the pulse transmitted by the radar during pervious

CPI, or randomly generated. For ease of treatment

extra i pulses with initial phases Á1¡i,Á2¡i, : : : ,Á0 aretransmitted during a CPI and we use the next N pulses

for processing. Figure 1 illustrates the scheme for

transmitting pulses with random initial phases in a

CPI.

For pulses with random initial phases, the matched

filter output at the delay time ¿d of the nth PRI can be

expressed as

y(n) =

PXp=1

¾pej(Án¡i¡Án)ej2¼f

p

fnTr +¾Te

j2¼fdnTr : (8)

In the above equation the initial phase of the

true target Án is canceled by the matched filter of

the current PRI and the residual phase Án¡i¡Ánis induced to the false targets. In the following

description this characteristic can be used to

discriminate the true and false targets in Doppler


spectrum for countering velocity deception jamming.

Considering that the received pulse can be modeled

as the sum of two orthogonal blocks in the

range deception jamming environment in [6], the

matched-filtering operation with regard to the received

pulse of the current PRI brings the possibility of

separating the true target from the false ones in range

domain.

After matched filtering DFT processing is then

applied and the corresponding Doppler spectrum is

given by

P(k) = EfY(k)Y¤(k)g

=

N¡1Xn=0

N¡1Xm=0

E

(¾T exp[j(2¼=N)(NfdTr ¡ k)(n¡m)]

+

PXp=1

¾pej(Án¡i¡Án)e¡j(Ám¡i¡Ám)

¢ exp[j(2¼=N)(Nfpf Tr ¡ k)(n¡m)])

+crossterms

¼N¡1Xn=0

N¡1Xm=0

¾T exp[j(2¼=N)(NfdTr ¡ k)(n¡m)] +PXp=1

¾p

¢(N¡1Xn=0

N¡1Xm=0

exp[j(2¼=N)(Nfp

f Tr ¡ k)(n¡m)]

¢ E[ej(Án¡i¡Án)e¡j(Ám¡i¡Ám)])

(9)

where

Y(k) = DFT[y(n)]

=

N¡1Xn=0

"PXp=1

¾pej(Án¡i¡Án)ej2¼f

p

fnTr +¾Te

j2¼fdnTr

#

¢ e¡j(2¼=N)kn (10)

crossterms

= 2Re

(E

"ÃN¡1Xn=0

¾Tej2¼fdnTr e¡j(2¼=N)kn

!

¢ÃN¡1Xm=0

PXp=1

¾pej(Ám¡i¡Ám)ej2¼f

p

fmTr e¡j(2¼=N)km

!¤#)

= 2Re

(N¡1Xn=0

N¡1Xm=0

PXp=1

¾T¾pej2¼fdnTrE[ej(Ám¡Ám¡i)]

¢ e¡j2¼fp

fmTr exp[¡j(2¼=N)k(n¡m)]

)= 0: (11)

With conclusions in the Appendix, the expectation is 0in the crossterms of (11), which can be neglected.The phase Án introduced by the transmitted pulse

of the current PRI in (8) is canceled out, and theDoppler spectrum P(k) focuses towards the true target.The random phase Án¡i caused by the DRFM repeatjammer cannot cancel out Án, and the energy of thefalse targets will be spread over all Doppler cells.Therefore random initial phases result in the focusedtrue target and suppressed false targets. However in[8], when using variable pulses, changing sidelobemagnitude and phase generated after matched filteringleads to a spreading effect, thereby creating falsesignals in the Doppler spectrum.According to properties in the Appendix, (9) can

be simplified to

P(k) =

N¡1Xn=0

N¡1Xm=0

¾T exp[j(2¼=N)(NfdTr¡ k)(n¡m)]

+

PXp=1

¾p

ÃN¡1Xn=0

ej0

!(12)

where

N¡1Xn=0

N¡1Xm=0

¾T exp[j(2¼=N)(NfdTr¡ k)(n¡m)]¯̄̄̄¯k=NfdTr

=N2¾T (13)

is the power of the true target in the Doppler cellk =NfdTr, and

¾p

ÃN¡1Xn=0

ej0

!¯̄̄̄¯k½[1,N]

=N¾p (14)

is the pth false target power level in any Doppler cellk ½ [1,N]. We find that the energy of the false targetis evenly spread over all Doppler cells.From (13) and (14) the SJR after Doppler

processing can be obtained by

SJRp =N2¾TN¾p

=N¾T¾p=N ¢SJR0,p (15)

whereSJR0,p =

¾T¾p

is the SJR of the true and pth false target beforeDoppler processing. By using pulses with randominitial phases, the power of the false target can besuppressed 10log10N dB in the Doppler spectrum,where N denotes the number of the pulses in a CPI.For 10 pulses the Doppler processing gain is 10 dB.Although the false target is considerably suppressed,the energy of the false targets will be spread overthe entire Doppler spectrum. In the circumstance ofa high-power jammer or the jamming signal enteringvia antenna mainlobe, significantly degraded SJR willaffect the true target detection performance.


Fig. 2. Doppler spectrum of true and false targets formed by

pulses with adaptive initial phases.

IV. ECCM USING PULSES WITH ADAPTIVE INITIALPHASES

A. Adaptive Initial Phases Design

To further improve the target detection

performance in velocity deception jamming

environment, we present a new signaling strategy

and the jamming pulses generated by the DRFM

repeat jammer will adaptively form a notch around

the Doppler frequency of the true target. The width

and depth of this notch can be adjusted adaptively

according to the requirement of target detection. The

Doppler spectrum of the true and false targets formed

by the pulses with adaptive initial phases is sketeched

in Fig. 2.

According to (2) and (8) the matched filter output

of the pth false target created by the DRFM repeat

jammer can be rewritten as

ypn (n) = ¾pej2¼f

p

fnTr ej(Án¡i¡Án) (16)

and the Doppler spectrum of the pth false target can

be expressed as

Pp(k) =

ÃN¡1Xn=0

ypn (n)e¡j(2¼=N)kn

!¢ÃN¡1Xm=0

ypn (n)e¡j(2¼=N)km

!¤

=

N¡1Xn=0

N¡1Xm=0

gng¤m exp[j(2¼=N)(Nf

p

f Tr ¡ k)(m¡ n)]

(17)

where gn = ej(Án¡i¡Án) = ejÃn .

A penalty function is constructed to penalize

the Doppler spectrum Pp(k) of the pth false target

in certain Doppler frequency band where the true

target exists. Assuming the true target’s Doppler

frequency is between f1 and f2 and the weight of the

pth false target is ´p > 0, the penalty function can be

written as

J(g) =

PXp=1

´p

0@ k2Xk=k1

Pp(k)

1A= gHRPg (18)

where

g= [g1,g2, : : : ,gN]T = (ejÃ1 ,ejÃ2 , : : : ,ejÃN )T

is the residual phase vector, (¢)T and (¢)H denotethe transposition and conjugate transposition, k1 =

round(Nf1Tr)¡ 1, k2 = round(Nf2Tr)+1, the round(¢)operation returns a number rounded to a specified

number of decimal places, and

RPmn =

PXp=1

´p

0@ k2Xk=k1

exp[j2¼((m¡ n)=N)(Nfpf Tr¡ k)]1A(19)

is Hermitian Toeplitz [16]. The weight ´p may be

adjusted arbitrarily in accordance with the power of

the false target.

The minimization problem of the Doppler

spectrum of the false targets in certain frequency band

can be summarized as follows:

min J(g) = gHRPg

s.t. gn = ejÃn :

(20)

This optimization problem of minimizing J as a

function of residual phase vector g can be solved bythe new phase-only version of the conjugate gradient

method with quadratic convergence [13]. The gradient

of J is given by the expression

rJ = 2Im[diag(RPggH)] (21)

where diag(¢) denotes diagonal entries of the squarematrix.

Therefore, with the phase-only conjugate gradient

method proposed in [13] and the phase-only gradient

in (21), the optimized value g̃ of the penalty function

can be first derived. Then we can revert to calculate

the adaptive initial phases of pulses fÁngNn=1. Basedon the above description, the adaptive initial phases

design method can be summarized as follows.

Step 1: According to the Doppler frequency

of the true target fd, the false targets fpf , set the

frequency border f1 and f2.

Step 2: Set the weight ´p and calculate the

matrix RP .

Step 3: The phase-only conjugate gradient

algorithm is applied to optimize the problem in (20)

and g̃ is obtained.Step 4: Setting random phases Á¡i,Á¡i+1, : : : ,Á¡1,

the adaptive initial phase fÁng can be calculated byÁn = Án¡i+argfg̃ng:

By using pulses with adaptive initial phases, the

operation of matched filtering and Doppler processing


makes the radar system capable of extracting the

true target while suppressing the false targets in the

Doppler frequency band of the true one.

B. Information Extraction by Multi-Channel Processing

Note that the adaptive initial phases design method

requires that the MTI/PD radar system know how a

DRFM repeat jammer is operating. Moreover, the

radar should have the information on ranges and

velocities of the false targets. In this section, we

discuss the multi-channel processing approach for

prior information extraction. The corresponding

scheme of the multi-channel processing is plotted in

Fig. 3.

We assume that a radar system transmits

pulses with random initial phases and employs the

multi-channel matched filtering for preprocessing.

When the ratio of the power of the jammer signal and

that of the target signal is less than 10log10N dB, the

true and false targets will be detected at the same time

in the two matched filter channels with regard to the

current and previous i PRI. However, if the power

of the jammer signal is very high, the true target

will be buried in the Doppler spectrum of the false

targets. Therefore, the radar system cannot determine

if a true target exists at that moment. Fortunately,

in the matched filter channel of the previous i PRI,

the false targets will not be buried in the Doppler

spectrum of the true one, and the manner by which

a DRFM repeat jammer operates and the parameters

of the false targets can be easily estimated. With these

prior information, the radar system can determine the

frequency border f1 and f2, and the lag PRI i.

In the above section the multi-channel processing

approach for pulses with random initial phases can be

used for prior information extraction. In this section

the multi-channel processing scheme for pulses with

adaptive initial phases is further discussed and the

information extraction capability of the true and false

targets by this method is also evaluated.

The matched filter output of the n¡ l PRI can bewritten as

yl(n) = ¾Tej(Án¡Án¡l)ej2¼fdnTr +

PXp=1

¾pej(Án¡i¡Án¡l)ej2¼f

p

fnTr

(22)

where l = 0,1, : : : ,M, M denotes the maximum

possible lag PRI number. The corresponding Doppler

spectrum can be expressed as

Pl(k) =

N¡1Xn=0

N¡1Xm=0

E

8<:¾Tej(Án¡Án¡l)e¡j(Ám¡Ám¡l) exp[j(2¼=N)(NfdTr¡ k)(n¡m)]+

PXp=1

¾pej(Án¡i¡Án¡l)e¡j(Ám¡i¡Ám¡l) exp[j(2¼=N)(Nfpf Tr¡ k)(n¡m)]

9=; (23)

Fig. 3. Multi-channel processing scheme for pulses with adaptive

initial phases.

where

Pl(k)jl 6=i =N¾T+PXp=1

¾p (24)

means that the Doppler energy of the true and false

targets is evenly spread over all Doppler cells and no

target will be detected in the l 6= ith channel, andPl(k)jl=i = PiT(k) +PiF(k)

=

N¡1Xn=0

N¡1Xm=0

¾Tej(Án¡Án¡i) exp[¡j(Ám¡Ám¡i)]

¢ exp[j(2¼=N)(NfdTr¡ k)(n¡m)]

+N2

0@ PXp=1

¾p±(k¡Nfpf Tr)1A (25)

indicates that the false target energy will be

accumulated by Doppler processing while the energy

of the true target will be disturbed by the phase

ej(Án¡Án¡i) in the ith channel.A Doppler energy function ET is constructed to

evaluate the Doppler spectrum of the true target in

the Doppler frequency band where the false targets

exist. For the true target, a set of P Doppler frequency

bands where the false targets exist are identified,

where the pth band is between kp1 and kp2, with a

correspondence weight ´p, and the Doppler energy

ET generated by the true target in P bands is

ET =

PXp=1

´p

0@ kp2Xk=kp1

PiT(k)

1A : (26)

It is assumed that NfdTr¡ kp1 =Nfpf ¡ k1 and NfdTr¡kp2 =Nf

pf ¡ k2; the above equation can be written as

ET = J(g): (27)


The above equation shows that by using the pulses

with adaptive initial phases, matched filtering

operation with regard to the previous PRI makes

it capable of extracting the false targets while

suppressing the true target in the Doppler spectrum.

This enables the radar to measure the parameters

of the true and false targets simultaneously, and to

monitor the DRFM repeat jammer operation at the

true time.

C. Antivelocity Deception Jamming Working Flow

As aforementioned, three types of velocity

deception jamming usually appear in modern jamming

techniques.

Velocity gate pull off (VGPO): The VGPO

jammer initially creates a false target with the same

Doppler frequency as the true target. The magnitude

of the false target is much higher than that of the

true target and the radar receiver’s automatic gain

control is forced to reduce the gain. The jammer then

increases the Doppler frequency, making the target

seem even farther out of the Doppler cell where the

true target exists. Finally the jammer switches off,

leaving the radar with a broken lock.

Multiple false targets (MFT): Multiple targets

are created simultaneously with different Doppler

frequencies.

Two blinking false targets (TBFT): In blinking

jamming mode, two jammers of the same operation

mode are switched on and off according to a

prescribed patten or almost randomly.

In Fig. 4 the working flow of the MTI/PD radar

for countering velocity deception jamming is given.

When the MTI/PD radar begins to work, it continues

to transmit pulses with random initial phases and

to utilize the multi-channel matched filters for

processing. According to the multi-channel processing

result with regard to the current and previous PRI, the

radar system will judge if the DRFM repeat jammer

exists. If the target is only detected in the matched

filter channel with regard to the current PRI, and no

false targets are detected, then the existence of the

true target can be confirmed. If the false targets are

detected in the channels matched with the previous

PRI, the radar system has to design adaptive initial

phases by using the information of the false targets,

and transmits pulses with them. The multi-channel

processing will also be applied for the true and false

targets information extraction simultaneously. With

this information the jamming mode can be identified

and the radar system will choose the corresponding

antijamming means.

For VPGO if a false target begins to move out

of the Doppler cell of the true target in the matched

filter channel with regard to the previous PRI, the

false target could be identified and recorded by the

radar system. In the following process constant pulses

are transmitted until the jammer shuts down, and the

Fig. 4. Working flow of MTI/PD radar for countering velocity

deception jamming.

pulses with adaptive initial phases are retransmittedfor the next VGPO process.For MFT and TBFT the false targets are very close

to the true one in the Doppler spectrum. Therefore,the pulses with adaptive initial phases which form anotch around the true target in the Doppler spectrumare continuously transmitted and the detection of thetrue target will not be affected.

V. SIMULATION RESULTS

The radar system simulated in this work is basedon modern MTI/PD radars. The carrier frequency is3.3 GHz, the pulse repetition frequency is 40 kHz,and the number of pulses in a CPI is 512. A targetwith specified RCS exists at a given range withthe Doppler frequency of 5 kHz. A false target iscreated by the DRFM repeat-back jammer at thesame range with the Doppler frequency of 5.2 kHzto pull the velocity gate off. The Doppler spectrumof pulses with fixed initial phases in the case ofjammer-to-signal ratio (JSR) of 7 dB and 14 dB areshown in Figs. 5(a) and (b). Both the true and thefalse targets appear in the Doppler spectrum and theycannot be distinguished. The Doppler spectrum iscalculated using fast Fourier transformation (FFT)with length 8192, and SNR is 20 dB.The Doppler spectrum of the pulses with random

initial phases in the case of JSR 7 dB and 14 dBis shown in Figs. 5(c) and (d). Because the powerof jamming signal in the Doppler spectrum canbe suppressed 10log10 512 = 27 dB in theory, thetrue target can be detected in the case of JSR 7 dB,


Fig. 5. Doppler spectrum of pulses with fixed and adaptive initial

phases. (a) Doppler spectrum in case of JSR = 7 dB. (b) Doppler

spectrum in case of JSR = 14 dB. (c) Doppler spectrum of pulses

with random initial phases in case of JSR = 7 dB. (d) Doppler

spectrum of pulses with random initial phases in case of

JSR = 14 dB.

however in the case of JSR 14 dB, the energy ofjamming signal is spread over all Doppler cells andthe true target is buried.The adaptive initial phases are calculated using the

phase-only conjugate gradient method and diagonalloading equal to 10¡5 of the identical diagonal matrixelement of RP . The Doppler spectrum in the caseof JSR 14 dB, 20 dB, and 40 dB is shown by usingthe pulses with adaptive initial phases in Fig. 6(c). Anotch from 3 kHz to 7 kHz in the Doppler spectrum isformed and the true target which does not get buriedcan be detected. The average spectrum outside thenotch is 29.0 dB, 34.5 dB and 46.9 dB higher thanthat in the notch, respectively, in three cases. Theconvergence of the phase-only conjugate gradientmethod used to calculate the adaptive initial phases isplotted in Fig. 6(d). The quadratic convergence of thepenalty function versus the iteration number is evidentin this figure. After 40 iterations, approximatelyoptimal phases are derived.The other methods for countering repeat radar

jammers are applied here to compare with ourmethod in this paper. In Soumekh’s work in [6],a manipulation of the transmitted signal or itsparameters in the fast-time domain was given. Themodulation and/or the rate of the linear frequencymodulated (LFM) signal are varied from one PRIto another. Both the multi-tone phase-modulated(MT-PH) LFM signal and slope-varying (SV) LFMsignal are considered and comparative results ofthese signals are given in Figs. 6(a) and (b). In thecase of JSR 14 dB and 20 dB, the true target can bedetected in the Doppler spectrum. However, the truetarget will be buried in the Doppler spectrum withincreased JSR. Therefore, our conclusion here is that

Fig. 6. Doppler processing output using (a) MT-PM LFM signal,

(b) SV LFM signal, (c) pulses with adaptive initial phases in case

of JSR 14 dB, 20 dB, and 40 dB, (d) convergence of phase-only

conjugate gradient algorithm.

Fig. 7. Multi-channel processing output using pulse with adaptive

initial phases. (a) Channel 1. (b) Channel 2. (c) Channel 3.

(d) Channel 4.

our method circumvents the pulse diversity method inhigh jamming power environment.To measure ranges and velocities of the true

and false targets simultaneously, the multi-channelprocessing approach which utilizes the received signalto correlate with the transmitted pulses of the currentand previous PRIs is used. At the current PRI, theDRFM repeat-back jammer transmits the pulse thatthe radar used 2 PRI before. The Doppler spectrumof the four processing channels is shown in Fig. 7. Inchannel 1 the Doppler spectrum of the true target canbe detected with a surrounding notch. In channel 3 theDoppler spectrum of the jammer signal can also bedetected with a surrounding notch. In other channels,no obvious notches appear and no target can bedetected.


Fig. 8. (a) Doppler spectrum of true and multiple false targets.

(b) Doppler spectrum of MT-PM LFM Signal and SV LFM

signal. (c) Doppler spectrum of true and multiple false targets

using pulses with adaptive initial phases. (d) Detection probability

of true target versus SJR.

Considering the jamming mode of multiple false

targets, 6 false targets appear in 4» 6 kHz in theDoppler spectrum in Fig. 8(a). We design the initial

phases which form a notch in 4» 6 kHz and transmitthe pulses with them. The Doppler spectrum of the

true and multiple false targets using pulses with

adaptive initial phases, MT-PM LFM signal and SV

LFM signal is shown in Figs. 8(b) and (c). A notch

is formed and the true target can be detected by

using pulses with adaptive initial phases. However,

the true target is buried in the Doppler spectrum by

using MT-PM LFM signal and SV LFM signal. The

detection probability of the true target versus SJR

is plotted in Fig. 8(d). Obviously the performance

for pulses with adaptive initial phases is stable with

increased SJR.

VI. CONCLUSIONS

An effective scheme has been presented for MTI

and PD radars for countering DRFM repeat-type

jammers. Although the phase-only conjugate gradient

method has been presented by Smith in [13], this

scheme has novel features. The most obvious

advantage is that the MTI/PD radar can sense the

jammer signal and then change its transmitted pulses

with adaptive initial phases to adapt to the varying

interference. The jammer signal and target signal

can be focused, respectively, in different correlation

channels. According to the ranges and velocities

of the false targets and the manner the DRFM

repeat-back jammer operates, the receiver calculates

the adaptive initial phases and then sends it to the

transmitter. In [16] it is referred to as “cognitive

radar,” originally proposed by Professor Haykin [17].

Another advantage is that original range-Dopplerprocessing for PD radar and MTI filtering for MTIradar can be reserved. Multiple processing channelsare used to replace the original single channel.Although this will increase the system complexity forradar, with the high speed digital signal processorsnow used, the receiver can succeed in finishingthe work easily. The receiver is also required tocalculate the initial phases. It has been verifiedthat computational and memory requirements areboth linear in the number of the pulses, and theconvergence of the phase-only conjugate gradientmethod is quadratic. As a result the initial phases arerapidly calculated, permitting the real-time adaptationto dynamic jamming environment.

APPENDIX

If f'n,n= 1,2, : : : ,Ng is the random variableuniformly distributed in [¡¼,¼] and statisticallyindependent, the random variable ½n = e

j'n will alsobe statistically independent and satisfy

E[½n] =1

2¼

Z ¼

¡¼ej½nd½n = 0

E[j½nj2] =1

2¼

Z ¼

¡¼ej½ne¡j½nd½n = 1

E[½n½¤m] =

½E[½n]E[½

¤m] = 0, n 6=m

E[j½nj2] = 1, n=m

= ±(n¡m):Therefore the variable gn = e

j½n¡m¡½n = ½n¡M½¤n has the

following properties:

E[gn] = E[½n¡M]E[½¤n] = 0

E[jgnj2] = E[j½n¡M j2]E[j½¤nj2] = 1E[gng

¤l ] = E[½n¡M½

¤n½l¡M½

¤l ] = ±(n¡ l):

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Jindong Zhang was born in Nantong, China, in 1981. He received his B.S,M.S., and Ph.D. degrees from the Nanjing University of Science and Technology

(NJUST), Nanjing, China, in 2004, 2006, and 2010, respectively, all in electronic

engineering.

In 2010, he joined the College of Electronic and Information Engineering,

Nanjing University of Aeronautics and Astronautics (NUAA), where he is now an

assistant professor. His current research interests include radar signal a processing

and adaptive radar waveform design.

Daiyin Zhu (M’04) was born in Wuxi, China, in 1974. He received his B.S.degree in electronic engineering from Southeast University, Nanjing, China, in

1996 and his M.S. and Ph.D. degrees in electronic engineering from Nanjing

University of Aeronautics and Astronautics (NUAA), Nanjing, in 1998 and 2002,

respectively.

From 1998 to 1999, he was a guest scientist with the Institute of Radio

Frequency Technology, German Aerospace Center, Oberphaffenhofen, where he

worked in the field of SAR interferometry. In 1998, he joined the Department

of Electronic Engineering, NUAA, where he is currently a professor. He has

developed algorithms for several operational airborne SAR systems. His current

research interests include radar imaging algorithms, SAR/ISAR autofocus

techniques, SAR ground moving target indication (SAR/GMTI), and SAR

interferometry.

Gong Zhang (M’07) received his Ph.D. degree in electronic engineering from the

Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in

2002.

From 1990 to 1998, he was a member of technical staff at No724 Institute

China Shipbuilding Industry Corporation (CSIC), Nanjing, China. Since 1998, he

has been with the College of Electronic and Information Engineering at NUAA,

where he is currently a professor. His research interests include radar signal

processing and classification recognition.

Dr. Zhang is a member of Committee of Electromagnetic Information,

Chinese Society of Astronautics (CEI-CSA) and a Senior Member of the Chinese

Institute of Electronics (CIE).


new antivelocity deception jamming technique using pulses with adaptive initial phases

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