# HRR Profiling on Integrated Radar-Communication Systems Using OFDM-PCSF Signals

Authors: Xuanxuan Tian; Tingting Zhang; Qinyu Zhang; Zhaohui Song
Journal: Mathematical Problems in Engineering
 (2017)

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## Abstract

In order to improve both the transmission data rate and the range resolution simultaneously in integrated radar-communication (RadCom) systems, orthogonal frequency-division multiplexing with phase-coded and stepped-frequency (OFDM-PCSF) waveform is proposed. A corresponding high resolution range (HRR) profile generation method is also presented. We first perform OFDM-PCSF waveform design by combining the intrapulse phase coding with the interpulse stepped-frequency modulation. We then give the ambiguity function (AF) based on the presented waveforms. Then, the synthetic range profile (SRP) processing to achieve HRR performance is analyzed. Theoretical analysis and simulation results show that the proposed methods can achieve HRR profiles of the targets and high data rate transmissions, while a relative low computational complexity can be achieved.


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## Body

## 1. Introduction

Recently, the integrated radar-communication systems using orthogonal frequency division multiplexing (OFDM) signals have been popular [1, 2], where communication and radar functionalities are operated simultaneously on a single platform to improve the spectrum efficiency and cost-effectiveness. There is a large area of applications that would possibly benefit from such systems. One typical example is the intelligent transportation system, which requires both communication links among vehicles and active environment sensing capabilities. With a unified platform, all vehicles on the road could interact as a cooperative radar sensor network, which provides unique safety features and intelligent traffic routing [1]. Another example would be related to ultrawideband (UWB) radar systems for reconnaissance and navigation purposes [2]. In such networks, each sensor can perform synthetic aperture radar (SAR) imaging and ground moving target indication (GMTI) and then share it with other sensor nodes through its own communication links.Orthogonal frequency division multiplex (OFDM) waveforms, along with coding schemes, are called multicarrier complementary phase-coded (MCPC) signals [3, 4] to enhance radar capabilities. A UWB digital system to measure the radar cross section (RCS) of targets has been proposed in [5], where the transmitted waveform is called OFDM phase-coded (OFDM-PC) signal. The OFDM-PC signals are able to minimize the peak-to-mean envelope power ratio (PMEPR). Due to the advantages on the high spectral efficiency, thumbtack-like ambiguity function (AF) [3], good Doppler tolerance [6], and flexible waveform characteristics and easy implementations [7], OFDM and its variations [7] are attractive to both academic and industrial researchers.When considering the presented investigations related to range processing approaches in the integrated systems using traditional OFDM signals, a typical approach of direct match filtering has been presented in [2], where one-bit data is carried on each subcarrier, which results in a low data rate and high range sidelobes. An adaptive pulse compression approach to improve the detection performance has been exploited in [8]. However, a high computational effort will be introduced on the cyclic iterative algorithm. A subspace-based approach based on rotation invariance [9] and a modulation symbol-based processing approach based on element-wise division technique [1] are presented to perform range estimation, which also require high computational complexity due to the high resolution range (HRR) performance.To improve the transmission data rate, a subspace projection approach using the multi-OFDM chirps-based transmit pulses has been appeared in [10]. However, the approach is based on a two-dimensional parameter-searching method, which suffers from a high computational burden. To improve the data rate and range resolution, OFDM linear frequency modulation (LFM) signals based on fractional Fourier transform (FRFT) [11] and a random stepped-frequency (SF) OFDM signal based on correlation processing [12] have been given. However, both signals are prone to the range-Doppler coupling, which may lead to HRR performance degradation. An OFDM-PC strategy along with the discrete Fourier transform (DFT) and correlation processing [13] has been developed to perform range and velocity estimation. However, one of the main drawbacks for OFDM-PC signals in the radar context is that the larger instantaneous bandwidth usually follows higher sampling rate requirements, resulting in higher computational complexity.In view of the above, we give an OFDM phase-coded stepped-frequency (OFDM-PCSF) based strategy as an improvement to [13] by combining the intrapulse (within the pulse) phase coding and interpulse (among different pulses) SF modulation. OFDM-PCSF signals can essentially synthesize the instant narrow bandwidth into effective large bandwidth, which provides improved data rate and range resolution, with low Doppler sensitivity and computational complexity. The proposed scheme, taking full advantage of the signal structure to achieve HRR performance with low computational complexity, is also provided on the receiver end.The rest of this paper is organized as follows. The signal model of OFDM-PCSF integrated system is given in Section2. The analysis of AF for OFDM-PCSF pulse train is presented in Section 3. The principle of SRP processing approach is explained in Section 4. The simulation results are presented in Section 5. Conclusion of the paper is given in Section 6.


## 2. Signal Model

### 2.1. Transmitted Signals

We assume that the OFDM-PCSF signals consist of a coherent burst ofP pulses. The pulse repetition period is Tr. Each pulse is realized by OFDM-PC signals, which transmit on N subcarriers simultaneously. The communication messages on each subcarrier are mapped onto a sequence of M bits. Then the transmitted signals can be described as(1)xt=∑p=0P-1st-pTrej2πfpt,where s(t) is the complex envelope of OFDM-PC single pulse [13] given by(2)st=∑n=0N-1untej2πfnt,where(3)unt=∑m=0M-1apnmrectt-mtb,where un(t) is the envelope of the phase-coded signal on the nth subcarrier, N and M are the numbers of subcarriers and chips, respectively, tb is the chip duration, Δf=1/tb is the subcarrier separation, fn=nΔf, {apnm}m=0M-1 is the transmitted PC sequence on the nth subcarrier and the pth pulse, and rect(t) is given by(4)rectt=10≤t≤tb0otherwise.In (1), fp=fc+pB represents the carrier frequency of the pth pulse, where fc is the radio frequency (RF) carrier frequency and B=NΔf is the bandwidth of the individual pulse. Therefore, the effective bandwidth of the OFDM-PCSF pulse train is Be=PNΔf. The structure of the pulse train can be seen in Figure 1, where T=Mtb is the pulse width.Figure 1
The structure of OFDM-PCSF pulse train.


### 2.2. Intrapulse Phase Coding

Intrapulse phase coding begins by appropriately selecting a phase sequence of lengthM. An uncoded pulse width T is then divided into M equal-length intervals of tb (chips), such that T=Mtb, providing an improved range resolution.The phase coding scheme for the construction of PC sequences is based on cyclic shifts of a phase sequence, where the transmitted messages control the cyclic-shift value. Specific construction steps are summarized as follows:(1)
Select an initial phase sequenceS of length M with a good periodic autocorrelation function (ACF).(2)
The transmitted binary data bits(0,+1) of size (P×N×K) are generated randomly, and K is set as 2K≤M. The K bits data on the nth subcarrier and the pth pulse convert into the decimal form dpn, which represents the time shift on the nth subcarrier and the pth pulse. The time shifts for all subcarriers and pulses are represented as d=dpn,p=0,…,P-1,n=0,…,N-1.(3)
Cyclic shift of the initial phase sequence{apnm}m=0M-1=S→dpn, where S→dpn represents cyclically shifted S by dpn.In order to show how the above construction works, a simple example forP=2,N=4,M=5,K=2 is shown in Table 1. The transmitted data bits are generated randomly, 5-bit Barker code is selected as the initial phase sequence, and + and − denote 1 and -1, respectively.Table 1
An example of the constructed PC sequences forP=2,N=4,M=5,K=2 and 5-bit Barker code.
Pulse
Data bits
PC sequences
1
0
0
+
+
+
-
+
0
1
+
+
-
+
+
1
1
-
+
+
+
+
0
0
+
+
+
-
+
2
1
1
-
+
+
+
+
0
0
+
+
+
-
+
1
0
+
-
+
+
+
0
1
+
+
-
+
+From Table1, we can get that the phase coding scheme allows each subcarrier to carry K bits data and provides a signal protection mechanism, where the receiver has to know the appropriate decoding scheme to recover the transmitted data. Hence, the phase coding scheme enhances the data rate and transmission of confidentiality.


## 2.1. Transmitted Signals

We assume that the OFDM-PCSF signals consist of a coherent burst ofP pulses. The pulse repetition period is Tr. Each pulse is realized by OFDM-PC signals, which transmit on N subcarriers simultaneously. The communication messages on each subcarrier are mapped onto a sequence of M bits. Then the transmitted signals can be described as(1)xt=∑p=0P-1st-pTrej2πfpt,where s(t) is the complex envelope of OFDM-PC single pulse [13] given by(2)st=∑n=0N-1untej2πfnt,where(3)unt=∑m=0M-1apnmrectt-mtb,where un(t) is the envelope of the phase-coded signal on the nth subcarrier, N and M are the numbers of subcarriers and chips, respectively, tb is the chip duration, Δf=1/tb is the subcarrier separation, fn=nΔf, {apnm}m=0M-1 is the transmitted PC sequence on the nth subcarrier and the pth pulse, and rect(t) is given by(4)rectt=10≤t≤tb0otherwise.In (1), fp=fc+pB represents the carrier frequency of the pth pulse, where fc is the radio frequency (RF) carrier frequency and B=NΔf is the bandwidth of the individual pulse. Therefore, the effective bandwidth of the OFDM-PCSF pulse train is Be=PNΔf. The structure of the pulse train can be seen in Figure 1, where T=Mtb is the pulse width.Figure 1
The structure of OFDM-PCSF pulse train.


## 2.2. Intrapulse Phase Coding

Intrapulse phase coding begins by appropriately selecting a phase sequence of lengthM. An uncoded pulse width T is then divided into M equal-length intervals of tb (chips), such that T=Mtb, providing an improved range resolution.The phase coding scheme for the construction of PC sequences is based on cyclic shifts of a phase sequence, where the transmitted messages control the cyclic-shift value. Specific construction steps are summarized as follows:(1)
Select an initial phase sequenceS of length M with a good periodic autocorrelation function (ACF).(2)
The transmitted binary data bits(0,+1) of size (P×N×K) are generated randomly, and K is set as 2K≤M. The K bits data on the nth subcarrier and the pth pulse convert into the decimal form dpn, which represents the time shift on the nth subcarrier and the pth pulse. The time shifts for all subcarriers and pulses are represented as d=dpn,p=0,…,P-1,n=0,…,N-1.(3)
Cyclic shift of the initial phase sequence{apnm}m=0M-1=S→dpn, where S→dpn represents cyclically shifted S by dpn.In order to show how the above construction works, a simple example forP=2,N=4,M=5,K=2 is shown in Table 1. The transmitted data bits are generated randomly, 5-bit Barker code is selected as the initial phase sequence, and + and − denote 1 and -1, respectively.Table 1
An example of the constructed PC sequences forP=2,N=4,M=5,K=2 and 5-bit Barker code.
Pulse
Data bits
PC sequences
1
0
0
+
+
+
-
+
0
1
+
+
-
+
+
1
1
-
+
+
+
+
0
0
+
+
+
-
+
2
1
1
-
+
+
+
+
0
0
+
+
+
-
+
1
0
+
-
+
+
+
0
1
+
+
-
+
+From Table1, we can get that the phase coding scheme allows each subcarrier to carry K bits data and provides a signal protection mechanism, where the receiver has to know the appropriate decoding scheme to recover the transmitted data. Hence, the phase coding scheme enhances the data rate and transmission of confidentiality.


## 3. Ambiguity Function

In this section, we discuss the AF of the proposed OFDM-PCSF signals. The equivalence of the pulse compression processing output to the AF expression is frequently used to evaluate the performance of radar signals [14]. As a consequence, the analysis on the AF of the OFDM-PCSF signals is helpful to understand how the features affect the design of the radar processing.


### 3.1. AF of the OFDM-PCSF Pulse Train

AF is a basic and widely applied performance metric of waveform designing and analysis in radar systems. AF is usually implemented by a matched filter bank for the detection of targets and the estimation of their ranges and velocities. It is defined as [15](5)χτ,fd=∫-∞∞xtx∗t+τej2πfdtdt,where ∗ denotes the complex conjugate, τ and fd represent the relative time delay and Doppler frequency of the received signal, respectively, and x(t) is the reference signal for matched filtering in the receiver.Proposition 1.
The AF of the single-pulse waveform for the OFDM-PCSF pulse train can be represented as(6)χpcτ,fd=∑n=0N-1∑q=-M+1M-1∑m=0M-q-1apnmapnm+q∗×χrτ-qtb,fdej2πfdmtb-nΔfτ,where(7)χrτ,fd=tb-τsincfdtb-τejπfdtb-ττ≤tb0otherwise.Proof.
See AppendixA.Remark 2.
We consider the range AF in this paper. Hence, substitutingfd=0 in (6), the range AF of the single-pulse waveform can be expressed as(8)χpcitb+κ,0=tb-κ∑n=0N-1∑m=0M-i-1apnmapnm+i∗+κ∑n=0N-1∑m=0M-i-2apnmapnm+i+1∗,where τ=itb+κ, i is an integer, and 0≤κ<tb.From (6) and (8), we can see that the AF of the single-pulse waveform for OFDM-PCSF pulse train depends on the ACF of the PC sequences. The thumbtack shape is assumed to be the desirable shape of the AF. PC sequence on each subcarrier with a good periodic ACF can improve the AF performance; this also has been shown in [3]. Besides, the PC sequences with a good periodic ACF also enable us to design the radar signal processing to improve the HRR performance, which will be discussed in Section 4.Proposition 3.
The AF of the OFDM-PCSF pulse train can be expressed as(9)χτ,fd=∑k=-P+1P-1ej2πkB-fcτ+P+k-1kBTr+fdTr-Bτ/2×sin⁡πP-kkBTr+fdTr-Bτsin⁡πkBTr+fdTr-Bτ×χpcτ+kTr,fd+kB,where χpc(·) has a similar form to (6) when apn(m+|q|) is replaced with a(p+|k|)n(m+|q|).Proof.
See AppendixB.From Proposition3, it can be seen that the AF of the OFDM-PCSF pulse train combines the properties of the AF from the OFDM-PC and SF signals. Thus, the range-Doppler coupling problem still exists due to the interpulse SF modulation.


### 3.2. AF Analysis

Performance analysis of the AF is evaluated by comparisons with the existing PCSF [16] and OFDM-PC signals [17]. The PCSF signals have a similar form to (1) when fp is replaced with fp=fc+pΔf, and s(t)=∑m=0M-1‍apmrect(t-mtb).The waveform parameters of the OFDM-PCSF, PCSF, and OFDM-PC signals are shown in Table2; the 5-bit Barker code is selected as the initial phase sequence. We limit the volume computations over a subregion R={|τ|≤tb,0≤fd≤1/Tr}; the corresponding ambiguity diagram is shown in Figure 2. Note the following observations from Figures 2(a)–2(f):(1)
The AFs of the first two signals exhibit the diagonal ridge, where a delay-Doppler coupling appears. However, the former has a relatively smaller tilt, which shows that the OFDM-PCSF signals provide reduced Doppler sensitivity compared to the PCSF signals. Besides, the simulation also demonstrates the feasibility of the OFDM-PCSF signals to realize radar-communication integration.(2)
The AF of the third signal exhibits a thumbtack, while the main-lobe width along the delay axis is much larger than the first two signals. The result demonstrates that the range resolution of the OFDM-PC signals is lower than the other two schemes, due to the fact that the bandwidth is1/8 of the first two signals.Table 2
Waveform parameters for the OFDM-PCSF, PCSF, and OFDM-PC signals.
Symbol
Parameter
OFDM-PCSF
PCSF
OFDM-PC
fc
RF carrier frequency
10 GHz
10 GHz
10 GHz
P
Number of pulses
8
32
8
N
Number of subcarriers
4
0
4
M
Number of chips
5
5
5
tb
Chip duration
1 us
1 us
1 us
Tr
Pulse repetition period
20 us
20 us
20 us
Be
Total signal bandwidth
32 MHz
32 MHz
4 MHz
D
The size of the data
8
×
4
×
2
32
×
2
8
×
4
×
2Figure 2
The ambiguity diagram for the different signals. (a)χ(τ,fd) of OFDM-PCSF; (b) χ(τ,fd) of PCSF; (c) χ(τ,fd) of OFDM-PC; (d) χ(τ,0) of OFDM-PCSF; (e) χ(τ,0) of PCSF; (f) χ(τ,0) of OFDM-PC.
(a)
(b)
(c)
(d)
(e)
(f)Hence, the OFDM-PCSF signals can provide a better HRR performance compared to the OFDM-PC signals, and the Doppler sensitivity is between the OFDM-PC and PCSF signals.


## 3.1. AF of the OFDM-PCSF Pulse Train

AF is a basic and widely applied performance metric of waveform designing and analysis in radar systems. AF is usually implemented by a matched filter bank for the detection of targets and the estimation of their ranges and velocities. It is defined as [15](5)χτ,fd=∫-∞∞xtx∗t+τej2πfdtdt,where ∗ denotes the complex conjugate, τ and fd represent the relative time delay and Doppler frequency of the received signal, respectively, and x(t) is the reference signal for matched filtering in the receiver.Proposition 1.
The AF of the single-pulse waveform for the OFDM-PCSF pulse train can be represented as(6)χpcτ,fd=∑n=0N-1∑q=-M+1M-1∑m=0M-q-1apnmapnm+q∗×χrτ-qtb,fdej2πfdmtb-nΔfτ,where(7)χrτ,fd=tb-τsincfdtb-τejπfdtb-ττ≤tb0otherwise.Proof.
See AppendixA.Remark 2.
We consider the range AF in this paper. Hence, substitutingfd=0 in (6), the range AF of the single-pulse waveform can be expressed as(8)χpcitb+κ,0=tb-κ∑n=0N-1∑m=0M-i-1apnmapnm+i∗+κ∑n=0N-1∑m=0M-i-2apnmapnm+i+1∗,where τ=itb+κ, i is an integer, and 0≤κ<tb.From (6) and (8), we can see that the AF of the single-pulse waveform for OFDM-PCSF pulse train depends on the ACF of the PC sequences. The thumbtack shape is assumed to be the desirable shape of the AF. PC sequence on each subcarrier with a good periodic ACF can improve the AF performance; this also has been shown in [3]. Besides, the PC sequences with a good periodic ACF also enable us to design the radar signal processing to improve the HRR performance, which will be discussed in Section 4.Proposition 3.
The AF of the OFDM-PCSF pulse train can be expressed as(9)χτ,fd=∑k=-P+1P-1ej2πkB-fcτ+P+k-1kBTr+fdTr-Bτ/2×sin⁡πP-kkBTr+fdTr-Bτsin⁡πkBTr+fdTr-Bτ×χpcτ+kTr,fd+kB,where χpc(·) has a similar form to (6) when apn(m+|q|) is replaced with a(p+|k|)n(m+|q|).Proof.
See AppendixB.From Proposition3, it can be seen that the AF of the OFDM-PCSF pulse train combines the properties of the AF from the OFDM-PC and SF signals. Thus, the range-Doppler coupling problem still exists due to the interpulse SF modulation.


## 3.2. AF Analysis

Performance analysis of the AF is evaluated by comparisons with the existing PCSF [16] and OFDM-PC signals [17]. The PCSF signals have a similar form to (1) when fp is replaced with fp=fc+pΔf, and s(t)=∑m=0M-1‍apmrect(t-mtb).The waveform parameters of the OFDM-PCSF, PCSF, and OFDM-PC signals are shown in Table2; the 5-bit Barker code is selected as the initial phase sequence. We limit the volume computations over a subregion R={|τ|≤tb,0≤fd≤1/Tr}; the corresponding ambiguity diagram is shown in Figure 2. Note the following observations from Figures 2(a)–2(f):(1)
The AFs of the first two signals exhibit the diagonal ridge, where a delay-Doppler coupling appears. However, the former has a relatively smaller tilt, which shows that the OFDM-PCSF signals provide reduced Doppler sensitivity compared to the PCSF signals. Besides, the simulation also demonstrates the feasibility of the OFDM-PCSF signals to realize radar-communication integration.(2)
The AF of the third signal exhibits a thumbtack, while the main-lobe width along the delay axis is much larger than the first two signals. The result demonstrates that the range resolution of the OFDM-PC signals is lower than the other two schemes, due to the fact that the bandwidth is1/8 of the first two signals.Table 2
Waveform parameters for the OFDM-PCSF, PCSF, and OFDM-PC signals.
Symbol
Parameter
OFDM-PCSF
PCSF
OFDM-PC
fc
RF carrier frequency
10 GHz
10 GHz
10 GHz
P
Number of pulses
8
32
8
N
Number of subcarriers
4
0
4
M
Number of chips
5
5
5
tb
Chip duration
1 us
1 us
1 us
Tr
Pulse repetition period
20 us
20 us
20 us
Be
Total signal bandwidth
32 MHz
32 MHz
4 MHz
D
The size of the data
8
×
4
×
2
32
×
2
8
×
4
×
2Figure 2
The ambiguity diagram for the different signals. (a)χ(τ,fd) of OFDM-PCSF; (b) χ(τ,fd) of PCSF; (c) χ(τ,fd) of OFDM-PC; (d) χ(τ,0) of OFDM-PCSF; (e) χ(τ,0) of PCSF; (f) χ(τ,0) of OFDM-PC.
(a)
(b)
(c)
(d)
(e)
(f)Hence, the OFDM-PCSF signals can provide a better HRR performance compared to the OFDM-PC signals, and the Doppler sensitivity is between the OFDM-PC and PCSF signals.


## 4. Synthetic Range Profile Processing

In this section, the synthetic range profile (SRP) processing approach taking full usage of the structure of the OFDM-PCSF signals is presented to achieve HRR profile. This approach is similar to the approach described in [16–18]. However, the transmitted communication messages are not considered in previous investigations.The entire processing approach is shown in Figure3, where the correlation processing can reduce the effects of the transmitted data on the HRR performance. Moreover, it directly operates on the transmitted and received phase codes instead of the baseband signals, providing a much lower computational complexity.Figure 3
The flow chart of SRP processing approach.Consider a point target at distanceR and relative velocity v with respect to the radar. Assume that v means that the target is fleeing away from the radar and satisfies 2v/c≪1, where c is the speed of light. The received echo signals in a noise-free scenario can be expressed as(10)yrt=xt-τ,where τ=2(R-vt)/c.Step 1 (demodulation).
The received echo signal of thepth pulse is to be demodulated by multiplying e-j2πfpt; we have(11)yt=∑p=0P-1st-τ-pTre-j2πfpτ.Step 2 (sampling).
The demodulated signals are to be processed in the digital domain. Therefore, we assume that the sampling frequency of the D/A converter isfs=N/tb and sampling time is t=pTr+mtb+itb/N, where p=0,…,P-1,m=0,…,M-1,i=0,…,N-1. Then the discrete form of y(t) can be written as(12)yp,m,i=∑n=0N-1apnmej2πFnitb/N×e-j2πfp+fn2R-vpTr+mtb/c,where Fn=(fp+fn)2v/c+fn.Step 3 (DFT).
Apply DFT ofy(p,m,i) concerning i to acquire the spectrum components of the received echo, which can be expressed as(13)Yfp,m,q=∑i=0N-1yp,m,ie-j2πiq/N=Dp,m,q+εp,m,qq=0,…,N-1,where(14)Dp,m,q=apqmCombη×e-j2πfp+fq2R-vpTr+mtb/c,(15)εp,m,q=∑n=0n≠qN-1apnmCombη+n-q×e-j2πfp+fn2R-vpTr+mtb/c,where(16)Combη=sinπηsinπη/NeπηN-1/N,η=fptb2vc.
From (15), ε(p,m,q) means the intersubcarrier interference, which destroys the orthogonality of subcarriers. It can be negligible for the low speed targets [17]. Hence, (13) can be rewritten as(17)Yfp,m,q=Dp,m,q,which denotes the mth phased code on the nth subcarrier and the pth pulse.Step 4 (correlation processing).
To reduce the effects of the transmitted data on radar performance, performing the correlation processing betweenYf(p,m,q) and {apnm} concerning m, the resulting signal can be written as(18)Ycp,w,q=CombηApqwe-j2πfp+fq2R-vpTr/cw=0,…,M-1,where(19)Apqw=∑m=0M-w-1apmqapm+wq∗ej2πfp+fq2vmtb/c,which contains the ACF of the PC sequence {apnm}m=0M-1, resulting in a single peak. Hence, the peak value of Yc(p,w,q) with respect to w can be expressed as(20)Ycp,q=ApqCombηe-j2πfp+fq2R-vpTr/c,where Apq=maxwApq(w); this is known after PC sequence is chosen. Hence, removing Apq, we get(21)Yp,q=Ycp,qApq=Combηe-j2πfc+pN+qΔf2R-vpTr/c.
Settingg=pN+q gives(22)Yp,g=Combηe-j2πfc+gΔf2R-vpTr/cg=0,…,PN-1.Step 5 (IDFT).
By performing the inverse discrete Fourier transform (IDFT) ofY(p,g) concerning g, the HRR profile can be expressed as(23)yp,l=1PN∑g=0PN-1Yp,gej2πgl/Nl=0,…,PN-1,which can be simplified to(24)yp,l=1PNCombηe-j2πfcτ+Δfτ-l/PNPN-1/2×sinPNπΔfτ-l/PNsinπΔfτ-l/PN,where τ=2(R-vpTr)/c, y(p,l) represents the HRR profile of the pth pulse, and l=0,…,PN-1 is the correspondingrange bin of the IDFT output.
From (24), |y(p,l)| takes maximal value at Δfτ-l/PN=h, where h is an integer. If accumulating time is short, namely, R≫vpTr, we can get (25)R≈h+l/PNc2Δf.From the above analysis, it can be seen that the complete processing approach can be implemented by means of DFT and IDFT operations, which makes it efficient in real time.


## 5. Simulation and Analysis

Simulations are carried out to demonstrate the performance of the SRP processing approach using the OFDM-PCSF signals. The details of the system parameters are summarized in Table3. We use 13-bit Barker code and randomly generated communication data of size (64×32×3) to construct PC sequences, with additive white Gaussian noise (AWGN). The range resolution is ΔR=c/2Be=0.1465m, which is 1/64 of the range resolution for the OFDM-PC signals (9.3760m).Table 3
OFDM-PCSF system parameters.
Symbol
Parameter
Value
fc
RF carrier frequency
10 GHz
P
Number of pulses
64
N
Number of subcarriers
32
M
Number of chips
13
tb
Chip duration
2 us
T
Pulse width
26 us
Tr
Pulse repetition period
104 us
δ
Pulse duty cycle
0.25
Δf
Subcarrier separation
0.5 MHz
Be
Total signal bandwidth
1.024 GHz
SNR
Signal-to-Noise ratio
10 dBAccording to Table3, each subcarrier carries K=3 bits data; the data rate can reach 0.9231Mbps.Firstly, simulated HRR profiles of the OFDM-PCSF signals are provided with the SRP processing and the direct match filtering [2]. We consider the two targets with R=25002500.3 m and v=1010 m/s, and the corresponding HRR profile resulting from the two approaches is shown in Figure 4.Figure 4
HRR profile of the two targets resulting from the two approaches. (a) SRP processing; (b) direct match filtering.
(a)
(b)As shown in Figure4(a), the two targets can be separated successfully and the corresponding estimated ranges are R~=2499.912500.23 m. As shown in Figure 4(b), there exists one single peak that cannot identify the two targets.Secondly, the Doppler sensitivity characterization of the OFDM-PCSF and OFDM-PC signals using SRP processing approach is investigated. For the OFDM-PC signals, the number of subcarriers is2048; other parameters settings are the same as in Table 3. Hence, the range resolution for both signals is the same. We consider a target with R=2500m at the different velocity v=0m/s, v=100m/s, and v=1000m/s; the corresponding HRR profile using the SRP processing approach for the different waveforms is shown in Figure 5.Figure 5
HRR profile of a target at the different velocity using SRP processing for the different waveforms. (a) OFDM-PCSF; (b) OFDM-PC.
(a)
(b)As shown in Figure5, it can be seen that velocity of the target brings the effect of HRR degradation. For v=100m/s, HRR profiles of both signals show little change that takes some translation with amplitude decline. For v=1000m/s, HRR profile of the former slips more range cells and distorts badly. After many simulations, it can be concluded that the effect of the distortion is very low for v=100m/s using both signals. However, the OFDM-PCSF signals are much more sensitive to the Doppler effects for v=1000m/s.Hence, the OFDM-PCSF SRP processing results show that interpulse SF modulation to synthesize larger bandwidth obtains the better HRR performance. However, a cost on the Doppler sensitivity on the high speed target has to be paid. Note that, in most applications, the target speed is not so high, which makes the cost acceptable.


## 6. Conclusion

This paper investigates an integrated radar-communication system using OFDM-PCSF signals. The integrated waveform and associated HRR processing approach are presented to improve the transmission data rate and corresponding HRR performance. From theoretical analysis and simulation results, we can get the following observations: (i) AF demonstrates the feasibility of OFDM-PCSF signals to realize radar-communication integration and shows that the waveform can achieve HRR performance. The achieved Doppler sensitivity is between the OFDM-PC and PCSF signals. (ii) The OFDM-PCSF signals combining intrapulse phase coding scheme use the carried communication messages to control the cyclic-shift value of a phase sequence, which enables a high transmission data rate. Interpulse SF modulation can synthesize instant narrow bandwidth into effective large bandwidth, which provides improved range resolution with relatively low computation load. (iii) The SRP processing approach, taking advantage of the OFDM-PCSF signals structure, provides HRR profile of the target compared to the direct match filtering. These conclusions and presented methods can provide insights into the design and operation of typical applications of integrated radar-communication systems.



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*Source: 5357187-2017-10-22.xml*