Proceedings of the 11th European Radar Conference
Automotive MIMO OFDM Radar: Subcarrier Allocation Techniques for Multiple-User Access and DOA Estimation Yoke Leen Sit, Thomas Zwick Institut f¨ur Hochfrequenztechnik und Elektronik (IHE) Karlsruhe Institute of Technology (KIT) Karlsruhe, Germany
[email protected],
[email protected]
Abstract—This paper presents the analysis of the spectrally interleaved OFDM signal used for the system concept of the MIMO OFDM Radar for automotive applications at 24 GHz. The purpose of such a signal model besides the conventional sensing capability is twofold - 1) to enable multiple-user access and communication, 2) to accomplish angle estimation for object positioning by exploiting spatial diversity. There are however challenges associated with such a signal model in a multi-user and multi-path environment, which will incapacitate the radar’s sensing capabilities. The signal model implemented in a full radar system simulation is analyzed in this paper and the possible solutions are then presented.
I. I NTRODUCTION As vehicular technologies becomes more sophisticated, so have automotive radars. The capability of conventional radars that can only perform sensing in the form of range and relative velocity estimation is fast becoming stagnant as consumers now look forward to more functionality. Meanwhile car manufacturers are seeking to cram more capabilities and functions within a limited amount of space in the vehicle at a pragmatic cost. Instead of merely sensing the immediate surroundings, intelligent radars that can perform vehicle-tovehicle or vehicle-to-infrastructure communication will be able to add more information to their estimation capability, for instance being able to ’see’ further than the radar’s unambiguous range. It is for this reason that the concept of the RadCom (integrated radar and communication system) is introduced. The RadCom presented in [1] uses the same signals and hardware to perform sensing and communication simultaneously. This will ultimately lead to cost and space reduction as aspired by the vehicle manufacturers. Typical radars come in a single transmitter-receiver pair on a monostatic platform, which is only able to estimate the range and Doppler. In order to perform angular estimation, the radar’s beam must be able to ’sweep’ the cross-range to localize the targets. The ’sweeping’ in this sense is not practical for an automotive radar since it takes time to sweep the horizon yet being on the move and require a large antenna array, which again is impractical due to the limited amount of space for the aesthetic mounting of the antennas. As such, the direction-of-arrival (DOA)
978-2-87487-037-8 © 2014 EuMA
estimation method using multiple transmit-receive antennas to exploit the spatial diversity becomes an attractive option. To achieve simultaneous transmission as opposed to a time multiplexed signal solution, the signal emitted must be uncorrelated/orthogonal. Based on the above criteria the signal model must: • have minimal impact on the radar’s estimation quantities i.e. range and Doppler resolutions, maximum unambiguous range and Doppler, etc • have multiple uncorrelated/orthogonal signals within the radar bandwidth for simultaneous transmission over multiple antennas • be capable of taking advantage of the spatial diversity for DOA • be able to support multiple users within a scenario or network A signal model capable of fulfilling the criteria has been proposed in [2]. This spectrally interleaved OFDM signal works similarly as the conventional OFDM signal and is parameterized for automotive usage hence allowing data to be carried in the radar signal at the same time. As with communication systems using OFDM signals, there are risks of interference since OFDM is susceptible to interference due to subcarrier misalignment. This paper explores the signal model and its tolerance limit in terms of the resulting radar image dynamic range, the reliability of the DOA results in a multiple-user access and presents a subcarrier allocation technique as a possible solution to increase the radar’s estimation reliability in the automotive scenario. II. S IGNAL M ODEL Shown in Fig. 1 is the typical configuration of the OFDM signal. Within a normal single-input-single-output (SISO) radar, the whole bandwidth containing all subcarriers will be used. When a multiple-user access capability is desired along with a multiple-input-multiple-output (MIMO) configuration, selected OFDM subcarriers spanning the whole bandwidth can then be allocated to each antenna/channel. In this way, each antenna radiates the whole bandwidth with orthogonal signals.
153
8-10 Oct 2014, Rome, Italy
antenna of User A is then yq (t) = a ·
N Tx X
xp (t) · θch,p · xB (t) · θB + n(t),
p=1
Fig. 1.
N −1 X
2r exp (j2πfD t) (3) exp j2πn∆f t − c0 n∈nA N −1 X rB exp(j2πfB t) θB = exp j2πn∆f t − c0 n∈n
θch,p =
Interleaving OFDM signal structure for 4 channels.
B
c0 c0 = 2B 2N ∆f λc ∆v = MT
∆r =
(1)
In terms of the radar estimation capability, the effects of such an allocation scheme to the range and Doppler resolutions be seen from (1) where the range resolution ∆r only depends on the bandwidth B of the system, with c0 , N , ∆f being the speed of light, total number of subcarriers and OFDM subcarrier spacing respectively. The Doppler resolution ∆v on the other hand depends only on the total time of the signal, which is governed by λc = c0 /fc the operational wavelength, M the number of consecutive OFDM symbols sent and T the duration of one OFDM symbol. In other words, the spectrallyinterleaved OFDM scheme will only affect the maximum unambiguous range where it is reduced by the number of users, as explained in [2].
III. E FFECTS OF MULTIPLE - USER ACCESS Let there be 2 users in the scenario with User A being the primary radar and User B being the communication partner/interferer. In the following expressions, the effects of having a communication partner with imperfect synchronization as well as the channel effects will be shown. Assume that User A is allocated an arbitrary set of subcarriers nA (nA ∈ N ) while User B is assigned another arbirtrary set nB (nB ∈ N ), which might include some subcarriers from set nA . The time domain signal for the p-th transmit antenna of User A transmitting M consecutive OFDM symbols is written as
xp (t) =
M −1 N −1 X X m=0 n∈nA
t−mT dn,m exp(j2πn∆f t)rect T
(2)
where dn,m is the m-th symbol occupying the n-th subcarrier with n = 0, .., , N −1. Assuming that there is only one object at distance r moving with a Doppler fD and that User B is located at rB away and its transmit signal is xB (t) with a local oscillator offset of fB above fc used by User A with Doppler, the time domain received signal at the q-th receive
where signals from all NTx transmit antennas of User A will be received, with a accounting for the complex signal attenuation and channel coefficients of all xp (t) and xB (t) and n(t) is the additive noise term. Assuming the Nyquist criterion for sampling taken at Ts is satisfied, the receiver DFT output after the conventional OFDM serial-to-parallel operation are the modulation symbols, which at the n-th subcarrier and m-th OFDM symbol of the q-th receive antenna is given by 2r exp(j2πfD τ )+Nn,m [Zn,m ]q = b · [dn,m ]p exp −j2πn∆f c0 M −1 X where τ = Ts (n + m (N + LGI )) , and m=0
rB exp (j2πfB τ ) + WGN Nn,m = WB exp −j2πn∆f c0 (4) At this point, xB (t) is treated like white noise (WB ) with WGN being the white Gaussian noise. b contains all the channel coefficients from a and processing gains. τ is the time after serial-to-parallel conversion, and LGI is the guard interval length. The guard interval term is removed before radar processing. Perfect frequency synchronization When there is perfect frequency synchronization between User A and User B, considering only the subcarriers in nA with no overlapping subcarriers from nB , the demodulated symbol [Zn,m ]q contains only the contributions from the phase rotations caused by the object in the channel and WGN. Imperfect frequency synchronization The impact of imperfect frequency synchronization depends on two criteria - 1) the amount of phase shift and 2) the signal power of the interferer e.g. User B. Based on (4) it can be seen that the phase rotation terms can be expanded into three simpler terms - the one with LGI is constant and affects all symbols, the one with n grows according to the subcarrier index, and the one with m grows with the symbol (time) index. This shows that any phase rotations will affect the estimated modulation symbol linearly and progressively in both the frequency and time axes. The other influence is the power ratio between the radar’s reflected signal from an arbitrary number of objects to the communication signal received at User A. Assuming that
154
both Users transmit at the same power level, the signal-tointerference ratio (SIR) is given by X σobj,i Pobj r2 (5) SIR = = comm 4 Pcomm 4π robj,i i where Pobj is the power of the reflected radar signals from all the objects, computed with the radar equation, Pcomm is the power of User B’s signal attenuated by the channel, computed with the Friis equation, rcomm amd robj,i are the distances of User B and the i-th object from User A respectively, and σobj,i is the RCS of the i-th object. The relationship between fB in percentage relative to the subcarrier spacing used, SIR and the radar image dynamic range (signal-to-mean noise level) is shown in Fig. 2. Assuming a rule of thumb that a radar image dynamic range of between a minimum of 30 dB to 35 dB and above is required for reliable radar estimation (where targets will show up without being drowned by noise), the light area in the figure is thus the unreliable estimation region.
Fig. 2. Relation of the interferer frequency offset (fB ) in percentage relative to the subcarrier spacing and SIR to the radar image dynamic range.
IV. S UBCARRIER ALLOCATION FOR DOA The physical antenna array, which governs the angular field of vision is usually fixed in size. As an illustration, the Users are equipped with 4×4 uniform linear array (ULA) transmitreceive antennas per user, with λ/2 element spacing. When there is no other user in the scenario, the User A can use all subcarriers. When User B is within the scenario, subcarriers must be allocated to it (controlled via ad-hoc networking for instance) in order to mitigate the interference between both Users. Hardware-wise, this means that User 1 can disable some of its transmit antennas yet leave all its receive antennas ON. The DOA processing uses the concept of ’virtual antennas’ [3], which allows the 4×4 configuration to be turned into a virtual equivalent of 1×16 configuration. The DOA pseudospectrum is dependent on the physical antenna properties, namely the geometry, element spacing and antenna index, to track the minuscule phase differences of the signal that arrive at every antenna array element. These parameters control the width of the antenna radiation pattern’s main and side lobes
[4]. Hence it can be hypothesized that the transmit antennas and subcarriers sets for each User must be correctly assigned to result in a long as possible contiguous virtual antenna array (which then results in the linear phase rotation over these contiguous antenna elements) for a reliable and correct DOA estimation. V. S IMULATION AND RESULTS A system level model of the MIMO Radar is created in MATLAB. User A is the full radar system while User B only transmits. The assignment of the subcarriers to both systems can be set arbitrarily, as well as other parameters such as the number of antennas used, fB , the number of objects in the scenario (along with their respective range, relative velocity, radar cross section and position), and the basic OFDM signal parameters. The OFDM parameters have been customized for automotive applications with details found in [5]. A onedimensional ULA is implemented. Every antenna transmits only the subcarrier set assigned to it. At the channel, the transmitted waves encounters different delays, phase rotations and attenuations due to the multiple objects. These waves are then superimposed together to result in the received signal and then the radar processing is done according to [2]. After the received signals of User A has been processed, they are then fed to the MUSIC algorithm [6], which evaluates the subtle phase differences between all the transmitted-received signals at all the receive antennas. The MUSIC algorithm is selected over other DOA estimation algorithms due to its ability to separate the signal and noise subspace and to produce a pseudo-spectrum instead of just numbers. The MUSIC used here is the general algorithm with no adaptive threshold settings. In this simulation there are 3 objects of the same radar cross section located at different distances with different relative velocities to the radar. The subcarriers are divided into 4 subchannel blocks as depicted in Fig. 1. To make the simulation scenario realistic, User A is assigned the blocks of Tx 1, Tx 3 and Tx 4, while User B is assigned Tx 1 and Tx 2, with Tx 1 being used by both Users as a consequence of imperfect subcarrier allocation. A frequency offset of 4450 Hz is also added to the signals of User B, which is equivalent to User B traveling at around 200 km/h relative to User A. Lastly, User B is positioned at 7 m away from User A (equivalent to SIR of -30.9 dB at User A), which is at the boundary of the reliable estimation region in Fig. 2. Since the channel Tx 1 is shared between the two Users, User A has the option to disable Tx 1 to evaluate only Tx 3 and Tx 4. In doing so, all the channel effects belonging to User B in Tx 1 will be excluded from the radar process, thus mitigating the ghost targets from showing up in the radar estimation. However due to inter-carrier interference imposed by the frequency offset/Doppler of User B on User A through imperfect synchronization, the noise floor is significantly raised. The resulting radar image without post-processing is shown in Fig. 3. All 3 objects can still be clearly identified as per the rule-of-thumb in Fig. 2.
155
along with some traces of noise (Fig. 5 (right)). These traces can be calibrated out with a better noise subspace estimation and threshold parameter settings, which are not within the scope of this paper.
Fig. 3. Radar image of User A with imperfect synchronization, fB = 4450 Hz, SIR= −30.9 dB. Fig. 5. Pseudo-spectrum of User A with imperfect synchronization, fB = 4450 Hz, SIR= −30.9 dB, from (left) the erroneous DOA result of a noncontiguous virtual array, (right) a contiguous array showing the correct positions of the 3 objects some residues.
VI. C ONCLUSION
Fig. 4. Virtual receive antenna array: (top) The full 4×4 Tx-Rx configuration resulting in the full virtual array vs. (center) the selected 2 × 4 Tx-Rx configuration to result in the shorter but contiguous virtual antenna array, and (bottom) a non-contiguous virtual array.
The virtual receive antenna array is shown in Fig. 4. The top figure shows the full virtual array as a result from using all Tx-Rx pairs and the bottom figures show the selected TxRx pairs to form a contiguous/non-contiguous virtual array with λ/2 element spacing. While a non-contiguous virtual antenna array does not affect the range-Doppler estimation, the DOA estimation is dependent on the contiguity of the phase differences as evident in the MUSIC pseudo-spectrum shown in Fig. 5. The mutual interference due User B is regarded as noise, which can be separated from the signal in the subspace (MUSIC) method to a certain degree as can be seen in Fig. 5 (right). The selection of the physical transmitters, which leads to the non-contiguity of the virtual antennas’ phase however contribute to a change in the physical radiation characteristics of the antennas, namely the grating lobes, which causes the multiple ghost targets (Fig. 5 (left)). With the subcarrier allocation which results in a contiguous virtual antenna array all objects are clearly visible (at distance 15 m, 20 m and 35 m)
A signal model for use in an automotive MIMO Radar has been presented. The modified OFDM signal model is shown to retain the range and Doppler resolutions as compared to using the conventional OFDM signal. The modified signal, when assigned correctly to the multiple users in the radar network, is also capable of DOA estimation via the the exploitation of spatial diversity. It has been shown that such a DOA estimation technique is dependent on the characteristics of the physical antenna array, hence in allocating the subcarrier to the multiple users, the subcarrier set must be chosen so that the resulting virtual antennas have a contiguous linear phase rotation over the virtual antennas. This can be done by allocating at least 2 adjacent subcarriers to one user. The effect of imperfect frequency synchronization between the Users have also been shown and it is within the radar’s tolerable limits for automotive applications. R EFERENCES [1] C. Sturm, T. Zwick, W. Wiesbeck, and M. Braun, “Performance Verification of Symbol-based OFDM Radar Processing,” in Radar Conference, 2010 IEEE, May. 2010, pp. 60 –63. [2] C. Sturm, Y. Sit, M. Braun, and T. Zwick, “Spectrally interleaved multicarrier signals for radar network applications and multi-input multi-output radar,” Radar, Sonar Navigation, IET, vol. 7, no. 3, pp. 261–269, 2013. [3] D. Bliss and K. Forsythe, “Multiple-input multiple-output (MIMO) radar and imaging: degrees of freedom and resolution,” in Signals, Systems and Computers, 2004. Conference Record of the Thirty-Seventh Asilomar Conference on, vol. 1, 2003, pp. 54–59 Vol.1. [4] M. Harter, T. Mahler, T. Schipper, A. Ziroff, and T. Zwick, “2-D antenna array geometries for MIMO radar imaging by Digital Beamforming,” in Microwave Conference (EuMC), 2013 European, 2013, pp. 1695–1698. [5] M. Braun, C. Sturm, A. Niethammer, and F. Jondral, “Parametrization of Joint OFDM-based Radar and Communication Systems for Vehicular Applications,” in Personal, Indoor and Mobile Radio Communications, 2009 IEEE 20th International Symposium on, Sep. 2009, pp. 3020 –3024. [6] R. Schmidt, “Multiple emitter location and signal parameter estimation,” Antennas and Propagation, IEEE Transactions on, vol. 34, no. 3, pp. 276 – 280, Mar. 1986.
156
