Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 9840172, 10 pages

https://doi.org/10.1155/2017/9840172

## Radar Communication Integrated Waveform Design Based on OFDM and Circular Shift Sequence

School of Aerospace Science and Technology, Xidian University, Xi’an 710126, China

Correspondence should be addressed to Luping Xu; moc.621@udegniplx

Received 10 February 2017; Revised 22 May 2017; Accepted 25 May 2017; Published 13 July 2017

Academic Editor: Alessandro Lo Schiavo

Copyright © 2017 Cong Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Based on the orthogonal frequency division multiplexing (OFDM) technique, an intelligent waveform is designed, which is suitable for simultaneously performing data transmission and radar sensing. In view of the inherent high peak-to-mean envelope power ratio (PMERP) and poor peak-to-side-lobe ratio (PSLR) problems in the OFDM based radar and communication (RadCom) waveform design, we propose two technologies to deal with that. To be specific, we adopt Gray code technology to reduce the PMERP and simultaneously choose an optimal cyclic sequence to improve the PSLR of RadCom waveform. In our method, the optimal cyclic sequence is dynamically generated to continuously provide the best waveform according to the change of communication data. In addition, to meet the requirements of different radar detection tasks, two simple methods are utilized to adjust the bandwidth of RadCom waveform. To verify the advantages of the designed waveform, we conduct several simulation experiments to compare with some existing RadCom waveforms. The results show that our designed RadCom waveform can simultaneously achieve lower PMERP and higher PSLR. In addition, our designed RadCom waveform has a thumbtack type fuzzy function and shows the good ability to do multitarget detection.

#### 1. Introduction

The demand for radio-frequency bandwidth is rising, driven by the increasing requirements of consumers for high quality communications and radar detection ability. By using a joint radio-frequency hardware platform for communications and radar applications [1–9], the occupied spectrum can be used very efficiently, which helps to partially overcome the limited availability of spectral resources. There is a large area of applications which possibly benefit from the availability of radar and communication (RadCom) systems, such as intelligent transportation network, radar ad hoc network, and deep space network. Intelligent transportation system [10], for instance, require intelligent vehicles to have the ability to work in an autonomous manner to sense the driving environment and provide unique safety features and intelligent traffic routing. The main challenge in RadCom development lies in finding suitable waveforms that can be simultaneously employed for information transmission and radar sensing.

For communications, data rate and bit error rate are the most important parameters. In order to achieve better communications performance in terms of data rate, continuous waveforms have to be applied. As for the radar function, dynamic range and resolution are critical requirements for object detection. To guarantee the high dynamic range of the measurements, radar waveform designers aim at creating waveforms with optimum autocorrelation properties. A typical continuous waveform with good autocorrelation properties is single-carrier based RadCom waveform combined with code-domain (spread spectrum) scheme [11–14]. In addition, advanced concepts based on multicarrier communication waveforms, also often denoted as orthogonal frequency division multiplexing (OFDM), are proposed [8, 15–18]. Compared with single-carrier waveform, OFDM waveforms offer a number of advantages, such as the availability of processing gain at the receiver, high spectrum efficiency, and good antimultipath performance. However, OFDM based RadCom waveform design also faces some challenging problems, such as a relatively high PMERP and undesirable autocorrelation properties or peak-to-side-lobe ratio (PSLR).

To reduce the PMERP of RadCom waveform, one popular method is to design different subcarrier complex weights [15, 17] and the other method is utilizing phase code technique [19, 20]. These two methods can also be adopted to improve the PSLR of RadCom waveform. Nevertheless, a lower PMERP and higher PSLR of RadCom waveform cannot be achieved simultaneously by using either of these two methods. The reason may be that a lower PMERP always means a poor side lobe level (SLL) suppression when subcarrier complex weight or phase code technique is adopted to reduce the PMERP. In [15], the authors use direct spread spectrum sequence (DSSS) to improve the PSLR of RadCom waveform but ignore the PMERP problem. In [17], chaos-based phase code sequence is utilized to get a good autocorrelation property and the PMERP is suppressed by adding window function. But these two issues are processed separately; in other words, the effects of chaos-based sequence on the PMERP and window function on the PSLR are not taken into account. To address these issues, we present a new designed OFDM based RadCom waveform. For the PMERP problem, a Gray code coding technique is adopted to reduce the PMERP. To improve the PSLR of RadCom waveform, a cyclic shift sequence is proposed, which has no effect on the PMERP but plays an important role in the SLL suppression. Thus, in this paper, a lower PMERP and desired PSLR can be achieved simultaneously by adopting the Gray code technology and choosing an optimal cyclic shift sequence. In addition, taking into account the different detection precision requirements of various radar tasks, two convenient ways are adopted to dynamically adjust the bandwidth of RadCom waveform.

The rest of the paper is organized as follows. The RadCom signal model is presented in Section 2 and the structure of RadCom waveform is described in Section 3. Then the performance analysis and simulation results analysis of RadCom waveform follow in Sections 4 and 5. Finally, conclusions are drawn in Section 6.

#### 2. RadCom Signal Model

Multicarrier Phase Coded (MCPC) signals featured by low SLL, high spectrum efficiency, and an ideal pin-type ambiguity function have been widely adopted in radar waveform design. The complex envelope of a single MCPC waveform is given by [20].where is the complex weight of the th subcarrier, satisfying , is the th element of the sequence which modulates the th subcarrier, is the gate function, is subpulse width, is the th subcarrier, is frequency space, is the number of subcarriers, and is the number of OFDM symbols. Based on the MCPC technology, especially OFDM technology, two RadCom waveforms are presented [15, 17], which can be written as where is communication data within a subpulse, is the complex weight, is the amplitude, and is the phase. is usually used for adjusting the PMERP of RadCom waveform. is the phase sequence, which greatly affects the performance of RadCom waveform and different RadCom waveform designing approaches focus on the phase sequence designs. In literature [15], is designed as direct spread spectrum sequence, while, in [17], is designed as chaos-based phase code sequence. Similar to these two methods, in this paper, is designed as a circular shift sequence within the subpulse . A time-domain circular shift for any arbitrary of the th pulse of RadCom is represented aswhere . Then the proposed RadCom waveform can be finally expressed as

As we all know, OFDM signal is sensitive to Doppler spread and some Doppler processing methods are proposed [21, 22]. In this paper, we assume that the Doppler has been complemented and do not consider the impact of Doppler. Thus, if an OFDM based RadCom signal is reflected at objects, the received signal can be described aswhere ; is the distance from the th target to the radar. For a radar signal, the high resolution range profile (HRRP) can be achieved by pulse compression. In this paper, the pulse compression is realized through a time-domain matched filter. The impulse response of time-domain matched filter is given aswhere represents the complex conjugate. Then the matched filter output of RadCom echo is expressed aswhere is convolution computation. Time-domain convolution takes a large amount of calculation. In order to reduce calculation amount, the convolution is realized by an FFT in frequency domain. Assuming the Fourier transform of is , then the Fourier transform of and can be achieved, respectively, asMaking an IFFT conversion for (9) will yield the HRRP.where is an IFFT version of and also an autocorrelation function of . Equation (10) denotes that in each inverse Fourier transform the signals obtain a total power gain of , whereas noise, as a stochastic quantity, only experiences a power gain of . Hence, the total processing gain of proposed RadCom waveform is

#### 3. Structure of RadCom Waveform

In order to better understand the structure of RadCom, an application scenario is illustrated in Figure 1. The RadCom signal (colored in blue) is transmitted from car 1 on the left. This signal transports communication information to a distant receiver, for example, car 2. At the same time, this RadCom signal is reflected from car 2 and car 3 (reflected signal depicted in red). The RadCom system receives the echoes of its own transmit signal and detects the presence of reflecting objects. For radar processing, it can be assumed that the transmitted signal is known at the radar receiver. For communication processing, the modulation type is perfectly known to the communication terminal. The whole process or structure of the RadCom waveform is shown in Figure 2.