Comparison of OFDM Radar and Chirp Sequene Radar Johannes Fink, Friedrih K. Jondral Communiations Engineering Lab, Karlsruhe Institute of Tehnology Karlsruhe, GERMANY {Johannes.Fink, Friedrih.Jondral}@kit.edu Abstrat: The radar waveforms OFDM and hirp sequene are ompared in terms of auray, resolution apabilities, reeiver operating harateristis, required resoures and signal proessing. We show, that both waveforms an be parametrized in suh a way, that they yield the same baseband signal whih an be proessed using the same detetion and estimation algorithms. This key insight reveals, that in this ase, the waveforms perform idential. However, OFDM additionally allows simultaneous ommuniation using the radar signal at the ost of inreased signal proessing. 1. Introdution For today s radar appliations, espeially in the field of advaned driver assistane systems, powerful waveforms are needed. They should not only provide aurate and unambiguous measurements of range and veloity even of weak targets while at the same time eliminating ghost targets, but also they should not be demanding in terms of signal proessing in order to be implemented in small sensors with low power onsumption and at lowest ost. Two promising waveforms, whih are disussed in reent publiations are OFDM [1] and hirp sequene [3]. In this work, these two waveforms are reviewed, parametrization issues are disussed and a final omparison is drawn to show their advantages and disadvantages, whih an serve as a guideline to hoose the proper waveform for a given appliation. 2. OFDM Radar OFDM Radar uses an Orthogonal Frequeny Division Multiplexing (OFDM) signal known from ommuniations as radar waveform. Algorithmi details are extensively desribed in [1]. In the following, a short summary of the waveform and its parametrization for radar will be given with the goal of omparing the OFDM waveform with the hirp sequene (CS) waveform. 2.1. Waveform In OFDM, the frequeny band is divided into N subarriers. The subarriers are orthogonal to eah other, if the subarrier distane is f = U, where U N and T is the OFDM symbol T duration. To allow proessing in a multipath environment, a yli prefix of duration T G is
added at the beginning of eah OFDM symbol. Furthermore,M OFDM symbols are ombined to form an OFDM frame. The OFDM waveform in time-frequeny domain is shown in fig. 1a. The transmitted OFDM signal an be written into a matrix a 0,0 a 0,1 a 0,M 1 a 1,0 a 1,1 a 1,M 1 F tx =...... a N 1,0 a N 1,1 a N 1,M 1, (1) where a n,m denotes the modulation symbol on subarrier n of the m-th OFDM symbol. The time domain samples at a sampling rate of f S,OFDM = 1 an be alulated effiiently by N f applying an inverse fast fourier transformation (I) to eah olumn of F tx. At the reeiver a fast fourier transform () inverses this proess [1]. Assuming a Doppler shift of f D, a two-way time delay of τ and a enter frequeny f, then aording to [1], the elements of the matrix of the reeived OFDM eho signal after removal of yli prefix an be written as (F rx ) n,m = b(f tx ) n,m exp{j2πf D T O m}exp{ j2π(n f +f )τ}exp{j ϕ}, (2) where b is the attenuation, whih an be alulated using the radar range equation [2] and ϕ is an unknown phase shift. Sine the transmitted matrix is known, elementwise division of (2) by (1) eliminates the dependeny on the modulation symbols: (F) n,m = (F rx) n,m (F tx ) n,m = bexp{j2πf D T O m}exp{ j2π(n f)τ}exp{ j2πf τ}exp{j ϕ}. (3) Eq. (3) represents the baseband matrix, whih is used for radar proessing by means of a twodimensional as illustrated in fig. 1a. This allows estimating Doppler and range dependant frequeny, whih an be linearly transformed into the target parameters range and radial veloity. Further details an be found in [1]. 2.2. Parametrization The starting point for radar waveform design are requirements onerning resolution in range R and veloity v as well as maximum (unambiguous) range R max and veloity v max. All waveform parameters an be derived from these requirements [1]: 1. Bandwidth:B = N f 2 R, 2. Number of subarriers: N Rmax R 3. Subarrier spaing: f = B N, and to avoid deorthogonalization:n B 2v max, 4. Guard Intervall: T G 2Rmax,
subarrier number: N B f Δf Sample number: K B f samples analog waveform T S,CS 2 2 1 OFDM symbol number: T G T 1 2 M (a) OFDM waveform t 1 T Chirp number: 1 2 L (b) Chirp sequene waveform t Figure 1: Both waveforms in the time-frequeny plane and radar signal proessing sheme using two-dimensional. 5. OFDM symbol time: T = U, whereu N T f O = T +T G, with T O ( U max = 2f v max T G ), 2f v max 6. Number of OFDM symbols per frame: M 2f vt O with MT O R 2v max to avoid range ell migration, 7. Sampling rate:f S,OFDM = N f = B, if ommon OFDM proessing using I and is to be used. Alternative proessing (desribed below) allows a lowerf S,OFDM = N f U. These parameters fully desribe the OFDM waveform, whih meets the given requirements at lowest possible omplexity if bounds are hosen tight. If the sampling rate is hosen aording to f S,OFDM = N f with U > 1, then the time domain samples of the m-th OFDM symbol an U be expressed as ( ) N 1 i { s m = a n,m (exp j2π in U, (4) f S N}) i=0 whih differs from an I. If I/ proessing is to be used for OFDM modulation in the ase of U > 1, then the high sampling rate f S = N f = B is neessary along with up- and downsampling in freqeny domain at the transmitter and reeiver, respetively. Summarized, the resolution requirements determine neessary spetral resoures and illumination time, whereas maximum range and veloity requirements determine the size of the twodimensional of the radar detetor and thus the signal proessing ost.
Digital Signal Proessing: D D Control and Eho Analysis D VCO A Tx A Rx -90 A Figure 2: FMCW radar transeiver arhiteture using a diret onversion quadrature mixer. 3. Chirp Sequene Radar The CS waveform is a poweful FM radar waveform, whih is able to resolve targets unambiguously in range and Doppler [3]. The modulation signal of hirp sequene radar onsists of L onseutive linear frequeny ramps (hirps) with bandwith B and rise time f as shown in fig. 1b. It is proessed using a typial FMCW transeiver arhiteture as shown in fig. 2, where the transmitted signal is diretly mixed into omplex baseband. 3.1. Waveform Assuming a target at a distane R0 with a onstant radial veloity of v, the phase of the baseband signal of the l-th ramp an be approximated by [3] φx (k, l) 2π 2f v T l + {z } fd 2f v 2BR0 {z } (T{z Tol )} fd 2f R0 kts (5) fτ where f is the enter frequeny, the speed of light, fd the Doppler frequeny and fτ the Range dependant frequeny shift. The approximation holds for B f [3]. Compared to [3], a slight modifiation has been introdued to aount for the overlap time Tol, whih is the time interval at the beginning of a hirp, during whih the last part of the previous hirp is still reieved. The resulting beat frequeny during this time is of no use and thus should be disarded. This leads to slightly steeper ramps and a bandwidth inrease of Tol B/(T Tol ). φx (k, l) in (5) posesses a two-dimensional struture. The first term, whih depends solely on the Doppler frequeny fd is indexed by l and the term depending on the beat frequeny fb = fd +fτ is indexed by k. Thus, the omplex baseband signal with amplitude a and τ = 2R 0 may be written in matrix notation, yielding [3] (M)k,l = a exp {jφx (k, l)} = a exp {j2πfd T l} exp {j2πfb TS,CS k} exp { j2πf τ }.(6) The two frequenies fd and fb whih manifest along rows and olumns, respetively, an be estimated using a two-dimensional as hinted in fig. 1b and subsequently may be transformed into the target parameters R and v.
3.2. Parametrization As in OFDM Radar, the starting point for deriving design parameters of the CS waveform are requirements onerning R, v,r max and v max : 1. Bandwidth:B, as in OFDM, 2 R 2. Number of effetive samples per hirp: K Rmax, asn in OFDM, R 3. Maximum overlap time: T ol = 2Rmax = T G, 4. Chirp duration: T 2f v max, ast O in OFDM, 5. Number hirps per sequene: L = 2f vt, with LT R 2v max to avoid range ell migration, asm in OFDM, 6. Sampling rate: f S,CS = 1 T S,CS T K, where hoosing tight bounds leads to effetive use of resoures. 4. Comparison Both waveforms ahieve true two-dimensional resolution (in both range and Doppler). Furthermore, they an be parametrized in suh a way, that the information arrying signals of both waveforms are idential. A preondition for that is B T 1 (very steep ramps of the CS waveform), beause then,f B f τ in (6) and thus (M) k,l aexp{j2πf D T l}exp{ j2πk(b/(t T ol )T S,CS τ}exp{ j2πf τ}. (7) A omparison with (3) shows that both signals are idential exept for the phase term ϕ, whih is a nuissane parameter for the estimation problem [1] and thus an be negleted, if T = T O, T S,CS = T T ol f = T T ol B BT a = b = T T ol B(T O T G ) = 1 B = T S,OFDM, ift G = T ol Therefore, in this ase, both waveforms posses idential properties in terms of auray, resolution, reeiver operating harateristi, update rate and are equally demanding for the radar signal proessor. However, OFDM has the extra ost of the OFDM modulator and demodulater but posseses the ability to provide simultaneous ommuniation. The identified advantages and disadvantages of both waveforms are summarized in tab. 1.
Table 1: Comparison of OFDM and fast hirp radar waveforms Criteria OFDM Chirp Sequene Analog hardware standard transeiver arhiteture, quadrature mixer, mixer for downonversion VCO or DDS, quadrature mixer as diret onversion mixer Preproessing OFDM modulation and demodulation, storage of 2N M symbols, NM divisions storage ofnm symbols Radar signal proessing two-dimensional periodogram ommuniation possible not possible Advantages Reommended usage spetrum and hardware effiient method of ombined radar and ommuniation appliations where both radar and ommuniations are needed less hardware omplexity, no deorthogonalization issues and no onstraints for hirp duration appliations without a need for ommuniations 5. Conlusion and Outlook In this work, we have reviewed the two radar waveforms OFDM and hirp sequene and summarized the important steps to hoose their parameters for given appliation requirements. Furthermore, we have ompared both waveforms with respet to performane and required hardware and signal proessing omplexity. We have found, that the baseband signal of hirp sequene onverges to the signal used in OFDM radar for detetion (after preproessing and symbol removal), if the steepness of frequeny ramps approahes infinity. Thus, both waveforms will perform idential in that ase, whih is the key result of our work. Sine onvergene is only ahieved in the limit, simulations ould help to ompare the performane in different modes of operation, whih is a urrent researh task of the authors. Referenes [1] M. Braun, Ofdm radar algorithms in mobile ommuniation networks, Phd thesis, Institut für Nahrihtentehnik des Karlsruher Instituts für Tehnologie, Karlsruhe, 2014. [2] M. A. Rihards, Fundamentals of Radar Signal Proessing, 2nd ed. New York: MGraw-Hill, 2014. [3] M. Kronauge, Waveform Design for Continuous Wave Radars, 1st ed. Göttingen: Cuvillier Verlag, 2014.