Phase-Coded CW MIMO Radar Using ZCZ Sequence Sets

Millimeter-Wave Phase-Coded CW MIMO Radar Using Zero-Correlation-Zone Sequence Sets Heinz Haderer, Reinhard Feger, Clemens Pfeffer, and Andreas Stelzer Institute for Communications Engineering and RF-Systems, Johannes Kepler University Linz Altenberger Str. 69, 4040 Linz, Austria Email: h.haderer, r.feger, c.pfeffer, a.stelzerg@nthfs.jku.at

Abstract —We present a phase-coded continuous-wave (CW) multiple-input multiple-output (MIMO) radar approach based on code-division multiplexing. We use zero-correlation-zone (ZCZ) sequence sets to separate at the receivers signals from multiple transmitters. In particular, our approach uses equidistantly shifted almost-perfect autocorrelation sequences for efficient implementation. We carried out measurements using a software-defined radar platform with 16 MIMO channels to demonstrate the capability of the proposed approach.
IndexTerms—phase-coded CW radar, zero correlation sequence sets, APAS, MIMO, beamforming

Haderer, H.; Feger, R.; Stelzer, A., "A comparison of phase-coded CW radar modulation schemes for integrated radar sensors," Microwave Conference (EuMC), 2014 44th European , vol., no., pp.1896,1899, 6-9 Oct. 2014 doi: 10.1109/EuMC.2014.6986832

Abstract: For radar sensors, for example, automotive radar sensors based on integrated circuits, taking advantage of the growing capabilities of digital circuits is becoming of increasing interest. Currently used linear frequency-modulated continuous wave (FMCW) signals could be replaced with phase-coded ones. As a consequence, the codes used would become a significant design parameter. In our investigation, we applied three binary codes (binary m-sequence, almost perfect autocorrelation sequence, and Golay-complementary sequence), one two-valued code (Golomb's code), and one ternary sequence (Ipatov's ternary sequence) and used a linear FMCW signal for comparison. The codes were selected with a future realization of the radar system based on integrated circuits in mind. We provide brief instructions for generating each sequence. Finally, we demonstrate the performance of the phase-coded signals by means of measurements carried out with a SiGe-based RF IQ-transceiver.
keywords: {CW radar;Golay codes;sensors;FMCW signals;Golay complementary sequence;Golomb code;Ipatov ternary sequence;autocorrelation sequence;automotive radar sensors;binary m-sequence;digital circuits;integrated circuits;integrated radar sensors;linear FMCW signal;linear frequency modulated continuous wave;phase coded CW radar modulation scheme comparison;radar system;Correlation;Integrated circuits;Phase measurement;Polynomials;Radar cross-sections;Sensors},
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6986832&isnumber=6986339

Lei Xu; Qilian Liang, "Zero Correlation Zone Sequence Pair Sets for MIMO Radar," Aerospace and Electronic Systems, IEEE Transactions on, vol.48, no.3, pp.2100,2113, JULY 2012 doi: 10.1109/TAES.2012.6237581

Abstract: Inspired by recent advances in multiple-input multiple-output (MIMO) radar, we apply orthogonal phase coded waveforms to MIMO radar system in order to gain better range resolution and target direction finding performance. We provide and investigate a generalized MIMO radar system model using orthogonal phase coded waveforms. In addition, we slightly modify the system model to improve the system performance. Accordingly, we propose the concept and the design methodology for a set of ternary phase coded waveforms that is the optimized punctured zero correlation zone (ZCZ) sequence-pair set (ZCZPS). We also study the MIMO radar ambiguity function of the system using phase coded waveforms, based on which we analyze the properties of our proposed phase coded waveforms which show that better range resolution could be achieved. In the end, we apply our proposed codes to the two MIMO radar system models and simulate their target direction finding performances. The simulation results show that the first MIMO radar system model could obtain ideal target direction finding performance when the number of transmit antennas is equal to the number of receive antennas. The second MIMO radar system model is more complicated but could improve the direction finding performance of the system.
keywords: {MIMO radar;antenna arrays;orthogonal codes;phase coding;receiving antennas;ZCZ-ZCZPS;direction finding performance;generalized MIMO radar system model;multiple-input multiple-output radar;orthogonal phase coded waveforms;receive antennas;ternary phase coded waveforms;zero correlation zone sequence pair sets;zero correlation zone sequence-pair set;Correlation;MIMO;MIMO radar;Radar antennas;Receiving antennas;Transmitting antennas},
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6237581&isnumber=6237562

Source

Annotated bibliography - "Pulse compression in Radars"

Listing are chronological

• Woodward, P.M., Probability and Information Theory, With Applications to Radar, New York: McGraw-Hill Book Co. (1955).
  Fundamentals of resolution theory and ambiguity functions, including linear-FM pulse.
• Cook, C.E., "Modification of Pulse-Compression Waveforms," Proc. NEC 14, 1958, pp 1058-67.
  Basic paper on linear FM pulse compression technique.
• Cook, C.E., "Pulse Compression-Key to More Efficient Radar Transmission," Proc IRE 48, No 3, Mar. 60, pp 310-316.
  Basic paper on linear-FM pulse compression technique. Reprint Paper No. 1 in Source.
• Westerfield, E.C., Prager, R.H. and Stewart, J.L. "Processing Gains Against Reverberation (Clutter) Using Matched Filters," IRE Trans IT-6, No 3, Jun 1960, pp 342-349.
  Use of Woodward ambiguity function to calculate signal-to-clutter ratio in radar and sonar systems.
• Klauder, J.R. et. al., "The Theory and Design of Chirp Radars," BSTJ 39, No 4, Jul 1960, pp 745-808.
  Basic paper on linear-FM pulse compression theory, sidelobe reduction, and error effects. Reprint Paper No. 2 in Source.
• Klauder, J.R., "The Design of Radar Signals Having Both High Range Resolution and High Velocity Resolution," BSTJ 39, No 4, Jul 1960, pp 809-820.
  Derivation of waveform having circularly symmetric ambiguity function. Required amplitude modulation precludes efficient transmission.
• Key, F.L., Fowle, E.N. and Haggarty, R.D., "A Method of Designing Signals of Large Time-Bandwidth Product," IRE Conv Record, 1961, Pt. 4, pp 146-154.
  Design of signals for which envelope shape and autocorrelation function are separately specified.
• Ramp, H.O. and Wingrove, E.R., "Principles of Pulse Compression," IRE Trans M/L-5, No 2, Apr 1961, pp 109-116.
  Basic paper on linear-FM pulse compression principles and applications. Reprint Paper No. 3 in Source.
• Cook, C.E., "General Matched-Filter Analysis of Linear FM Pulse Compression," Proc IRE 49, No 4, Apr 1961, p 831.
  Considers effect of Doppler shift on output waveform of filter matched to linear-FM signal, including bandwidth restriction.
• DiFranco, J., "Closed-Form Solution for the Output of a Finite-Bandwidth Pulse-Compression Filter," Proc IRE 49, No 6, Jun 1961, pp 1086-87.
  Evaluation of integrals leading to output waveform in band limited cases.
• DiFranco, J.V. and Rubin, W.L., "An Interpretation of 'Paired Echo Theory' for Time-Domain Distortion in Pulsed Systems and an Extension to the Radar 'Uncertainty Function'," Proc IRE 49, No 9, Sep 1961, pp 1432-1433.
  Description of spurious outputs caused by frequency-domain and time-domain distortions.
• Reed, J., "Long-Line Effect in Pulse Compression Radar," Microwave Journal 4, No 9, Sep 1961, pp 99-100.
  Effect of transmission line mismatch on phase-vs-frequency response of radar system. Reprint Paper No. 4 in Source.
• Ramp, H.О. and Wingrove, E.R., "Performance Degradation of Linear FM Pulse Compression," Proc IRE 49, No 11, Nov 1961, p 1693.
  Analysis of output waveform of Doppler shifted signal, including second-order Doppler terms which can be important for large time-bandwidth product.
• Cook, C.E., "Effects of Phase-Modulation Errors on Radar Pulse Compression Signals," IRE Conv Record, 1962, Pt 4, pp 174-184.
  Analysis and experimental data on effect on sinusoidal phase errors on output waveform.
• Thor, R.C., "A Large Time-Bandwidth Product Pulse Compression Technique," IRE Trans MIL-6, No 2, Apr 1962, pp 169-173.
  Use of logarithmic, rather than linear, frequency modulation is shown to permit use of greater time-bandwidth products on targets with large radial velocity. Reprint Paper No. 5 in Source.
• DiFranco, J.V. and Rubin, W.L., "Analysis of Signal Processing Distortion in Radar Systems," IRE Trans MIL-6, No 2, Apr 1962, pp 219-227.
  Describes effects of phase and amplitude distortion on ambiguity function shape and sidelobe levels.
• Cook, C.E. and Heiss, W.H., "Linear FM Pulse Compression Doppler Distortion Effects," Proc IRE 50, No 6, Jun 1962, pp 1535-1536.
  Further discussion of dispersive Doppler effect and different viewpoints of Cook (1961) and Ramp and Wingrove (1961).
• Fryberger, D., "On the Use of Pulse Compression for the Enhancement of Radar Echoes from Diffuse Targets," Proc IRE 50, No 9, Sep 1962, pp 1993-1994.
  Compares effect of pulse compression on SNR and resolution for diffuse and discrete targets.
• Rubin, W.L. and DiFranco, J.V., "The Effects of Doppler Dispersion on Matched Filter Performance," Proc IRE 50, No 10, Oct 1962, pp 2127-2128.
  Expressions are derived for the difference between simple frequency shift and Doppler shift with dispersion, and it is shown that this difference is negligible for time-bandwidth products less than 1000.
• Fowle, E.N. el. al., "A Pulse Compression System Employing a Linear FM Gaussian Signal." Proc IEEE 51, No 2, Feb 1963, pp 304-312.
  Design and equipment considerations for low-sidelobe pulse compression systems using approximations to Gaussian weighting.
• Cook, C.E., "Pulse-Compression Paired-Echo Experiments," Proc IEEE 51, No 2, Feb 63, pp 383-384.
  Experimental verification of paired-echo response caused by sinusoidal phase errors in pulse compression signal.
• Temes, C.L. et. al. "Pulse Compression System for a Down-Range Tracker," IEEE Conv Rec 1963, Pt 8, pp 71-81.
  Description of 4 MHz 2 ms pulse compression waveform for 425 MHz instrumentation radar.
• Cook, C.E., "Transmitter Phase Modulation and Pulse Compression Waveform Distortion," Microwave Journal 6, No 5, May 1963, pp 63-69.
  Analysis of paired-echo effect of sinusoidal phase error, and sidelobe increase caused by localized phase error in chirp signal. Reprint Paper No. 6 in Source.
• Minis, W.B., "The Detection of Chirped Radar Signals by Means of Electron Spin Echoes," Proc IEEE 51, No 8, Aug 1963, pp 1127-1134.
  Theory and experimental results using compression filter based on paramagnetic resonance line at 6.7 GHz.
• Bernfeld, M., "Pulse Compression Techniques," Proc IEEE 51, No 9, Sep 63, p 1261.
  Comparison of systems using series and parallel dispersive elements to generate large time-bandwidth products.
• Lurin, E.S., "Digital Pulse Compression Using Polyphase Codes," Proc IEEE 51, No 9, Sep 63, pp 1262-1263.
  Implementation and ambiguity function of digital equivalent of linear and triangular-FM pulse compression.
• Fowle, F.N., "The Design of FM Pulse Compression Signals," IEEE Trans IT-10, No 1, Jan 1964, pp 61-67.
  Discusses design of waveform having arbitrary transmitted envelope, to produce given autocorrelation function.
• Cook, C.E. and Paolillo, J., "A Pulse Compression Predistortion Function for Efficient Sidelobe Reduction in a High-Power Radar," Proc IEEE 52, No 4, Apr 1964, pp 377-89.
  Describes use of increased sweep rate on leading and trailing edges of pulse to reduce paired-echo sidelobes.
• Cook, C.E., "A Class of Nonlinear FM Pulse Compression Signals," Proc IEEE 52, No 11, Nov 1964, pp 1369-1371.
  Analysis of nonlinear chirp to achieve sidelobe reduction, showing sensitivity to Doppler shift.
• Bernfeld, M. et. al., "Matched Filtering, Pulse Compression and Waveform Design," Microwave Journal, Oct, Nov, Dec 1964; Jan 1965, pp 57-64, 81-90, 70-76, 73-81.
  Thorough discussion and analysis of linear and nonlinear FM and discrete code waveforms and their ambiguity functions. Reprint Paper No. 7 in Source.
• Bogotch, S.E. and Cook, C.E., "The Effect of Limiting on the Detectability of Partially Time Coincident Pulse Compression Signals," IEEE Trans M/L-9, No 1, Jan 1965, pp 17-24.
  Theory and experimental results on suppression of small signals by overlap of expanded pulse from large, adjacent signal which would be resolvable except for receiver limiting. Reprint Paper No. 8 in Source.
• Peebles, P.Z. and Stevens, G.H., "A Technique for the Generation of Highly Linear FM Pulse Radar Signals," IEEE Trans M/L-9, No 1, Jan 1965, pp 32-38.
  A method is described for generating a staircase FM waveform, closely approximating linear sweep with very high accuracy.
• Rihaczek, A.W., "Radar Signal Design for Target Resolution," Proc IEEE 53, No 2, Feb 1965, pp 116-128.
  Relationships between resolution and measurement uncertainty are explored for different signals and clutter environments.
• Rihaczek, A.W., "Range Accuracy of Chirp Signals," Proc IEEE 53, No 4, Apr 1965, pp 412-13.
  It is shown that the diagonal ambiguity of chirp signals does not lead to range uncertainty on targets of unknown Doppler if the range reading is interpreted as applying at a time displaced from the actual echo time. Reprint Paper No. 9 in Source.
• Jacob, J.S., "Graphical Comparison of a Doppler-Shift Advantage for Three Pulse-Compression Techniques," Proc 9th Natl Conv on Military Electr, IELE, Wash, D.C., 1965, pp 382-387.
  Degradation in SNR with Doppler shift is compared for three waveforms, and linear FM is shown to be affected less than phase-coded or frequency-stepped waveforms.
• Ward, M.X., ''Matched Scan Rate Pulse-Compression Analysis," Proc IEEE 54, No 4, Apr 1966, pp 707-708.
  Derives output waveform for compression filter with arbitrary impulse response duration, showing approach to (sin x)/x shape for long durations.
• Rihaczek, A.W., "Doppler-Tolerant Signal Waveforms," Proc IEEE 54, No 6, Jun 1966, pp 849-857.
  Discussion of non-linear FM modulations and pulse trains for which Doppler distortions can be ignored.
• Hollis, E.E., "Comparison of Combined Barker Codes for Coded Radar Use," IEEE Trans AES-3, No 1, Jan 1967, pp 141-143.
  Sidelobe levels are determined for sequences of four 13-bit Barker Codes and thirteen 4-bit codes, showing maximum amplitude 13/52 times main lobe.
• Lipman, M.A. "A Useful Property of the Generalized Chirp Signal Ambiguity Function," Proc IEEE 55, No 7, Jul 1967, pp 1241-1242.
  Ambiguity function generalized to include mismatched sweep rate as well as delay and Doppler shift.
• Cook, C.E. and Bernfeld, M. Radar Signals, New York: Academic Press, 1967.
  Basic text on pulse compression principles and implementation.
• Kibbler, G.O.T.H., "The CLFM: a Method of Generating Linear Frequency-Coded Radar Pulses," IEEE Trans AES-4, No 3, May 68, pp 385-391.
  Describes coherent linear frequency modulator used in active generation of chirp signals and in conversion of received signals to constant frequency.
• Mitchell, R.L. and Rihaczek, A.W., "Matched-Filter Responses of the Linear FM Waveform," IEEE Trans AES-4, No 3, May 1968, pp 417-432.
  Equations and three-dimensional plots of ambiguity functions with and without weighting and mismatch.
• Rihaczek, A.W., and Mitchell, R.L., "Design of Zigzag FM Signals," IEEE Tram AES-4, No 5, Sep 1968, pp 680-692.
  Presents three-dimensional plots of ambiguity functions of simple and multiple-segment zigzag FM waveforms.
• Haggarty, R.D., Hart, L.A. and O'Leary, G.C, "A 10.000 to 1 Pulse Compression Filter Using a Tapped Delay Line Linear Filter Synthesis Technique," IEEE EASCON Rec, 1968, pp 306-314.
  Synthesis procedure and experimental results on delay-line filters for large time-bandwidth product pulse compression and other applications. Reprint Paper No. 10 in Source.
• Belknap, D.J., "An Experimental Measurement of the Detection Capability of a Linear FM Pulse Compression System," IEEE EASCON Rec, 1968, pp 315-318.
  Detection performance of 1000:1 pulse compression system is compared with ideal matched filter and with Doppler filter bank. Results are within a fraction of a dB of the matched filter.
• Ruttenberg, K. and Chanzit, L., "High Range Resolution by Means of Pulse-To-Pulse Frequency Shifting," IEEE EASCON Record, 1968, pp 47-51.
  Method of obtaining resolution in system using agile magnetron rather than intrapulse FM. Reprint Paper No. 11 in Source.
• Leith, E.N., "Optical Processing Techniques for Simultaneous Pulse Compression and Beamsharpening," IEEE Trans AES-4, No 6, Nov 1968, pp 879-885.
  Combined processing for synthetic aperture resolution and pulse compression, using two-dimensional optical filter.
• Bechtel, M.E., "Generalized Paired-Echo Analysis for Band-pass Systems," Proc IEEE 57, No 2, Feb 1969, pp 204-205.
  Description of phase and amplitude distortion terms in bandpass systems in terms of advanced and delayed replicas of ideal signal.
• Palmieri, C.A. and Cook, C.E., "The Ambiguity Properties of Multiple-Segment Linear FM Signals," Proc IEEE 57, No 7, Jul 1969, pp 1323-1325.
  Approximate analysis of mainlobe and near-sidelobe response of multiple-segment FM waveforms.
• Vannicola, V.C., "Range Dependent Waveform of an Active Weighted Pulse Compression Receiver," IEEE Trans AES-5, No 5, Sep 1969, pp 847-864.
  Output waveforms for pulse compression systems in which the signal is time weighted by a function not exactly centered on the received signal. Reprint Paper No. 12 in Source.
• Nathanson, F.E., Radar Design Principles, New York, McGraw-Hill, 1969.
  Text covering radar clutter and resolution requirements, with chapters devoted to phase coding and to linear-FM processing techniques.
• Rihaczek, A.W., Principles of High-Resolution Radar, New York: McGraw-Hill, 1969.
  Basic text on waveform design and results in resolution, detection and measurement in clutter.
• Campbell, B.D., "High-Resolution, Radar Coherent Linear FM Microwave Source," IEEE Trans AES-6, No 1, Jan 1970, pp 62-72.
  Design of BWO generator for 16 Hz FM Sweep at S-band.
• Millett, R.E., "A Matched-Filter Pulse-Compression System Using a Nonlinear FM Waveform," IEEE Trans AES-6, No 1, Jan 1970, pp 73-78.
  Design and test data on low-sidelobe pulse compression waveform having 0.1 dB mismatch loss. Reprint Paper No 13 in Source.
• Cohen, S.A., "Generalized Response of a Linear FM Pulse Compression Matched Filter," IEEE Trans AES-6, No 5, Sep 1970, pp 708-712.
  Curves are derived which show losses in peak output caused by mismatch of pulse width, sweep rate and center frequency.
• Caputi, W.J., Jr., "Stretch: A Time-Transformation Technique," IEEE Trans AES-7, No 2, Mar 1971, pp 269-278.
  Technique for very high resolution with relatively simple processor covering a limited range window. Reprint Paper No. 14 in Source.
• Hartt, J.K. and Sheats, L.F., "Application of Pipeline FFT Technology in Radar Signal and Data Processing," IEEE EASCON Record 1971, pp 216-221.
  Pipeline FFT processors for pulse compression and Doppler filtering are described. Reprint Paper No. 15 in Source.
• Halpern, H.M. and Perry, R.P. "Digital Matched Fitters Using Fast Fourier Transforms," IEEE EASCON Record 1971, pp 222-230.
  A 10-MHz bandwidth digital filter, suitable for high-resolution pulse compression, is described. Effects of different word lengths for signal and reference waveforms are explored by simulation. Reprint Paper No. 16 in Source.
• Woerrlein, N.H., "Spurious Target Generation Due to Hard Limiting in Pulse Compression Radars," IEEE Trans AES-7, No 6, Nov 1971, pp 1170-1178.
  Method and results for calculating spurious outputs caused by hard limiting of three overlapping signals, using phase-coded waveform.
• Rihaczek, A.W., "Radar Waveform Selection-A Simplified Approach," IEEE Trans AES-7, No 6, Nov 1971, pp 1078-1086.
  Waveforms are divided into four classes, each with distinct resolution properties, permitting a systematic approach to waveform selection. Reprint Paper No 17 in Source.
• Jones, W.S., Kempf, R.A. and Hartmann, C.S., "Practical Surface Wave Chirp Fillers for Modern Radar Systems," Microwave Journal, May 1972.
  Design, application and performance of surface acoustic wave filters for 8 MHz x 12.5 usec and 2 MHz x 25 usec pulse compression. Reprint Paper No 18 in Source.
• Ackroyd, M.H. and Ghani, F., "Optimum Mismatched Filters for Sidelobe Suppression," IEEE Trans AES-9, No 2, Mar 1973, pp 214-218.
  At some expense in complexity and small loss in SNR, time sidelobes can he reduced without amplitude weighting on transmit.
• Powell, Т.Н., Jr. and Sinsky, A.I., "A Time Sidelobe Reduction Technique for Small Time-Bandwidth Chirp," IEEE Trans AES-10, No 3, May 1974, pp 390-392.
  Digital filter design to compensate for effect of Fresnel ripples in spectrum of chirp signal.
• Hollan, M.G. and Claiborne, L.T., "Practical Surface Acoustic Wave Devices," Proc IEEE 62, No 5, May 1974, pp 582-611.
  Tutorial discussion of SAW devices and their application, with extensive bibliography.
• Fitzgerald, R.J., "Effects of Range-Doppler Coupling on Chirp Radar Tracking Accuracy," IEEE Trans AES-10, No 4, Jul 1974, pp 528-532.
  Describes interaction of chirp range-Doppler coupling with truncation error of GHK filler, such that positive chirp slope leads to reduced error of filtered data.
• Caputi, W.J., "Stabilized Linear FM Generator," IEEE Trans, AES-9, No 5, Sep 1973, pp 570-578.
  Closed-loop technique for controlling slope of linear frequency sweep generator, as applied to 240 MHz x 120 usec active pulse-compression waveform generator.

Source: Radars. Vol 3. Pulse Compression. By David K. Barton. Dedham: Artech House, Inc., 1975.