A Novel OFDM Chirp Waveform Scheme for Use of Multiple Transmitters In

568 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 3, MAY 2013 A Novel OFDM Chirp Waveform Scheme for Use of Multiple Transmitters in SAR Jung-Hyo Kim, Member, IEEE, Marwan Younis, Senior Member, IEEE, Alberto Moreira, Fellow, IEEE, and Werner Wiesbeck, Fellow, IEEE Abstract—In this letter, we present a new waveform technique channel coherence bandwidth, in order to avoid the frequency- for the use of multiple transmitters in synthetic aperture radar selective channel effect [4]. The OFDM signaling is also paid (SAR) data acquisition. This approach is based on the principle of attention for SAR applications, and recently, SAR processing the orthogonal-frequency-division-multiplexing technique. Unlike techniques for OFDM waveforms were introduced in [5] and multiple subband approaches, the proposed scheme allows the generation of multiple orthogonal waveforms on common spectral [6]. A major problem of the typical OFDM signal (mainly in support and thereby enables to exploit the full bandwidth for spaceborne SAR) is the fast variation of the signal envelope. each waveform. This letter introduces the modulation and the We resolve the problem by combining the OFDM principle demodulation processing in regard to typical spaceborne SAR with chirp waveforms. Therefore, the basic idea behind the receive signals. The proposed processing techniques are verified proposed waveform scheme is to exploit both the orthogonality by a simulation for the case of pointlike targets. of subcarriers and intrinsic characteristics of traditional chirp Index Terms—Digital beamforming (DBF), multiple-input waveforms. multiple-output (MIMO) synthetic aperture radar (SAR), orthog- The importance of using chirp waveform in the proposed onal frequency division multiplexing (OFDM), orthogonal wave- scheme is emphasized in the following issues: First, one can form, SAR. easily achieve the constant envelope of time domain waveforms aforementioned, which leads to a maximum efficiency I. INTRODUCTION of the transmitter modules of a phased-array antenna. Second, the chirp spectrum approaches a rectangular shape as the HE USE of multiple transmitters is of a great interest in the time–bandwidth product increases so that its spectral efficiency T synthetic aperture radar (SAR) community. It provides an and signal-to-noise ratio can be maximized [2], [7]. Finally, increase of degrees of freedom and dramatically improves SAR one can further exploit the linear frequency–time characteristics imaging performance when combined with multiple receivers, a of chirp in signal processing. It makes it easy to combine the so-called multiple-input multiple-output (MIMO) constellation proposed scheme with existing SAR processing algorithms, [1]. However, the waveform design for multiple transmitters has such as the dechirp-on-receive technique. been the most important and challenging issue in realizing the Focusing on a dual transmit antenna scenario, we develop MIMO SAR concept. Particularly for spaceborne SAR, aside the novel waveform scheme consisting of the modulation and from the orthogonality between waveforms for simultaneous demodulation algorithm, based on the conventional OFDM multiple pulse transmissions, a constant envelope of the wave- processing, and validate its potential. Special attention has to be form is desired, considering the high power amplifier (HPA) in paid to the demodulation since the classical OFDM demodula- transmitters. The HPAs in spaceborne SAR systems operate in tion assumes that the delay length of a received signal is shorter saturation in order to generate the maximum output power and than the length of the cyclic prefix (CP), but a SAR echo signal to ensure a stable output power level for amplitude variations is generally much longer than the transmitted pulse length. In in the HPA input signal [2]. A significant envelope variation this letter, we present a demodulation strategy for such a long of waveform therefore yields a clipping effect on the output SAR signal. waveform, and the orthogonality can be broken. This letter presents a novel waveform scheme to meet the aforementioned requirements, based on the principle of orthog- II. OFDM CHIRP MODULATION onal frequency division multiplexing (OFDM) proposed in [3]. In OFDM systems, an available signal bandwidth is divided into A. Principles multiple subbands, which is specified to be narrower than the The basic idea behind the proposed technique is to exploit the orthogonality of discrete frequency components, i.e., subcarriers. This means that the orthogonality of waveforms is Manuscript received April 20, 2012; revised June 29, 2012; accepted independent of the types of input sequences. July 16, 2012. Assume the input sequence (spectrum) S[¯p] with N discrete J.-H. Kim, M. Younis, and A. Moreira are with the Microwaves and Radar 2Δf Institute, German Aerospace Center (DLR), 82234 Oberpfaffenhofen, Germany spectral components, which are separated by as shown (e-mail: [email protected]). in Fig. 1. First, the input sequence S[¯p] is interleaved by N W. Wiesbeck is with the Institute of High Frequency Technique and Elec- zeros, which is S1[p] in Fig. 1, and then, the interleaved input tronics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany. sequence is shifted by Δf for the second data sequence S [p]. Color versions of one or more of the figures in this paper are available online 2 at http://ieeexplore.ieee.org. These data sequences are transformed into the time domain by Digital Object Identifier 10.1109/LGRS.2012.2213577 the 2N-point inverse discrete Fourier transform (IDFT), which 1545-598X/$31.00 © 2012 IEEE KIM et al.: NOVEL OFDM CHIRP WAVEFORM SCHEME FOR USE OF MULTIPLE TRANSMITTERS IN SAR 569 Fig. 1. Two orthogonal OFDM chirp waveforms are generated by zero interleaving and shift of a single chirp spectrum as an input sequence. is the OFDM modulation. As a result, we obtain two waveforms modulated by two orthogonal subcarrier sets that are mutually Fig. 2. Real parts of OFDM chirp waveforms in time domain with 50-MHz shifted by Δf. Thus, their demodulation must be performed by bandwidth and N = 4096. The phase change in s2(t) due to the subcarrier 2N-point DFT. It must be emphasized that both the sets contain offset must be remarked in comparison with s1(t).(a)s1(t).(b)s2(t). 2N subcarriers but use only N subcarriers to carry the input data, respectively. B. Signal Model As aforementioned, a chirp signal spectrum is used for the OFDM modulation in this work. The chirp signal spectrum, as input complex data, is obtained by 2 S[¯p]=F{s[n]} = F exp j · π · Kr · (nTs) (1) where s[n] denotes the discrete time samples of a complex chirp signal with the length of N, F{·}is the Fourier transform operator, T is the sampling interval, and K is the chirp rate, s r Fig. 3. Generic schematic of the proposed OFDM demodulator followed which is a ratio between the signal bandwidth B and the chirp by the polyphase decomposition and parallel matched filters for the range duration Tp (Kr = B/Tp). Using (1), we generate two input compression. data sequences by the zero interleaving and shift as follows: ··· − By introducing t = nTs and Δf =1/2NTs, it is noticed that S1[p]=[S[0], 0,S[1], 0, ,S[N 1], 0] (2) both waveforms are distinguishable by the subcarrier offset Δf. ··· − S2[p]=[0,S[0], 0,S[1], , 0,S[N 1]] (3) These modulated OFDM waveforms are converted to analog where p =0, 1, 2,...,2N − 1. Both data sequences contain to- forms by a digital-to-analog converter. The OFDM waveforms tal 2N components, respectively. Therefore, they are modulated in the time domain are plotted in Fig. 2. Due to the zero inter- by 2N-point IDFT. According to the Cooley–Tukey algorithm, leaving in the spectrum, the peak power level of the waveforms the DFT/IDFT can be performed by separate transforms with will be reduced. However, according to Parseval’s theorem [8], respect to the odd and even components of the input. Since the the total energy of the input sequence is conserved. even components in S1 are zeros, the inverse Fourier transform Using the aforementioned signal model, the OFDM wave- of S1[p] is equivalent to that of S[¯p]. Substituting p¯ for p/2,the forms can be also directly produced in the time domain. modulated waveform s1 is given by The time domain generation is valuable since a band-limited − input sequence can cause an overshoot in time domain N1 2π s [n]= S[¯p] · exp j pn¯ (4) waveforms [8]. 1 N p¯=0 where n =0, 1, 2,...,2N − 1. Since the inverse Fourier trans- III. OFDM SAR SIGNAL DEMODULATION form of S[¯p] is s[n] with the period of N, s1[n] can be expressed This section is dedicated to the development of an OFDM by a repetition of s[n] over the length of 2N demodulation algorithm applicable to a received SAR signal, n n − N s [n]=s[n] · rect + s[n − N] · rect . (5) which is typically much longer than the OFDM pulse length. 1 N N According to the classical OFDM demodulation scheme, the In the same way, using (p +1)/2=¯p +(1/2), the other orthogonality of subcarriers can be exploited only if the follow- modulated waveform s2 is derived as ing requirements are strictly fulfilled: synchronization between − the modulator and demodulator in length and no truncation of π N1 2π s [n]=exp j n S[¯p] · exp j pn¯ (6) the waveforms within IDFT/DFT windows. To meet the require- 2 N N p¯=0 ments, the demodulation algorithm developed in this section consists of the segmentation of the echo signal by spatial and using s[n], it can be also described as filtering (digital beamforming), the circular-shift addition, and − the conventional OFDM demodulation using DFT, as shown · n − · n N s2[n]= s[n] rect + s[n N] rect in Fig.

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