Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Signal processing for MIMO radars: Detection under Gaussian and non-Gaussian environments and application to STAP CHONG Chin Yuan Thesis Director: Marc LESTURGIE (ONERA/SONDRA) Supervisor: Fr´ ed´ eric PASCAL (SONDRA) 18th Nov 2011 PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Outline Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Outline Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions What is a MIMO Radar? M ultiple- I nput M ultiple- O utput ⇒ DIVERSITY!! Multiple-Input (MI) Multiple-Output (MO) ◮ Transmit waveform diversity ◮ Receive spatial diversity ◮ Transmit spatial diversity Statistical MIMO Radars Tx and Rx antennas are all widely separated Coherent MIMO Radars Tx and Rx antennas are closely spaced to form a single Tx and Rx subarray Hybrid MIMO Radars Widely separated Tx and Rx subarrays, each containing one or more antennas PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Statistical MIMO Radar ♦ Widely-separated antennas ⇒ spatial diversity ◮ Independent aspects of target → overcome fluctuations of target RCS, esp in case of distributed complex targets ⇒ diversity gain ◮ Moving targets have different LOS speeds for different antennas ⇒ geometry gain ◮ Possibility of target characterization and classification ♦ Without waveform diversity, transmit spatial diversity cannot be exploited at the receive end ♦ LPI advantage due to isotropic radiation ♦ Non-coherent processing → no coherent gain BUT no phase synchronization needed ♦ Applications: Detection, SAR PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Statistical MIMO Radar Vs Multistatic Radar Joint processing of all antennas Each rx antenna receives only signals from corresponding tx antenna → Centralized detection strategy → Decentralized detection strategy PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Coherent MIMO Radar ◦ No spatial diversity. Diversity comes only from waveforms ◦ Transmit and receive subarray can be sparse → improve resolution but can cause grating lobes ◦ Improved direction-finding capabilities at expense of diversity ◦ Improved parameter estimation (identifiability, resolution, etc) ◦ Applications: Direction-finding, STAP/GMTI PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Coherent MIMO Radar Vs Phased-Array Radar Different waveforms are transmitted from Only one transmit antenna or single waveform is transmitted from all each closely-spaced transmit antenna closely-spaced transmit antennas PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Configuration overview SISO SIMO MISO MIMO PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Configuration overview Phased-arrays SISO SIMO Coherent MIMO MISO MIMO Statistical MIMO PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Configuration overview Phased-arrays SISO SIMO Coherent MIMO Hybrid MIMO MISO MIMO Statistical MIMO PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Application: STAP Conclusions Hybrid Configuration General case with few assumptions! Effective number of subarrays K e : ◮ K e ≥ ˜ N + ˜ M if ˜ N , ˜ M > 1 (diversity gain) ◮ Big K e robust against target fluctuations → surveillance ◮ Small K e better gain → direction finding Effective number of elements N e : ˜ ˜ Config N N n M M m ◮ N e ≥ N rx + N tx if N rx , N tx > 1 (diversity gain) SISO 1 ≥ 1 1 ≥ 1 ◮ Maximum N e if N rx = N tx , SIMO 1 ≥ 1 > 1 ≥ 1 irregardless number of subarrays MISO > 1 ≥ 1 1 ≥ 1 ◮ Better to have more N rx for SIR gain ≥ 1 ≥ 1 MIMO > 1 > 1 PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Gaussian Detector Application: STAP Non-Gaussian Detector Conclusions Outline Overview of MIMO Radars MIMO Detectors Gaussian Detector Non-Gaussian Detector Application: STAP Conclusions PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Gaussian Detector Application: STAP Non-Gaussian Detector Conclusions Signal Model (1/2) Received signal after range matched-filtering: y = P α + z , where the vectors y , α and z are the concatenations of all the received signals, target RCS and clutter returns, respectively: 2 3 2 3 2 3 y 1 , 1 α 1 , 1 z 1 , 1 6 . 7 6 . 7 6 . 7 . . . y = 4 5 α = 4 5 z = 4 5 . . . y ˜ α ˜ z ˜ M , ˜ M , ˜ M , ˜ N N N 2 3 P is the ( P ˜ M , ˜ m , n = 1 M m N n ) x ˜ M ˜ p 1 , 1 0 N N matrix 6 7 ... P = 4 5 containing all the steering vectors: 0 p ˜ M , ˜ N PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Gaussian Detector Application: STAP Non-Gaussian Detector Conclusions Signal Model (2/2) Steering vector p m , n p m , n can be generalized to include different parameters, e.g. Doppler Interference z m , n ◮ z ∼ CN ( 0 , M ) : covariance matrix of each z i is given by M ii , inter-correlation matrix between z i and z j is given by M ij ◮ Takes into account correlation arising from insufficient spacing between subarrays and non-orthogonal waveforms PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Gaussian Detector Application: STAP Non-Gaussian Detector Conclusions MIMO Gaussian Detector Consider the following hypothesis test: H 0 : y = z interference only H 1 : y = P α + z target and interference Based on Maximum-Likelihood theory, the MIMO detector has been derived to be: H 1 Λ( y ) = y † M − 1 P ( P † M − 1 P ) − 1 P † M − 1 y λ. ≷ H 0 Equivalent to multi-dimensional version of OGD and can be considered as a generalized version of MIMO OGD as it becomes MIMO OGD when the subarrays are non-correlated. X | p † m , n M − 1 m , n y m , n | 2 MIMO OGD: p † m , n M − 1 m , n p m , n m , n PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Gaussian Detector Application: STAP Non-Gaussian Detector Conclusions Statistical Properties � H 0 : 1 2 χ 2 2 K e ( 0 ) d Λ( y ) = 1 2 χ 2 2 K e ( 2 α † P † M − 1 P α ) H 1 : ◮ Non-centrality parameter is equal to 2 α † P † M − 1 P α ◮ Detector is M -CFAR as distribution under H 0 does not depend on correlation between subarrays ◮ Requirement of independence between subarrays can be relaxed for some applications, e.g. regulation of false alarms PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Gaussian Detector Application: STAP Non-Gaussian Detector Conclusions Simulation Configurations Total number of antennas, N p = 13 SIMO Case One single transmit element and N p − 1 K e receive subarray with K e elements MISO Case K e transmit elements and one single receive subarray with N p − K e elements Variation of N e with K e for MISO and SIMO cases PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Gaussian Detector Application: STAP Non-Gaussian Detector Conclusions Detection Performance SIMO case MISO case P d against SIR pre (dash-dotted lines) and SIR post (solid lines). P fa = 10 − 3 Fluctuating target modeled similar to Swerling I target PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Gaussian Detector Application: STAP Non-Gaussian Detector Conclusions Detection Performance SIMO case ◮ N e remains the same → same SIR gain ◮ Threshold higher for higher DoF → causes performance to degrade ◮ But higher DoF more robust to target fluctuations ◮ High P d → better with large K e and small K e better at low P d PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
Overview of MIMO Radars MIMO Detectors Gaussian Detector Application: STAP Non-Gaussian Detector Conclusions Detection Performance MISO case ◮ Poor performance for K e = 12 due to high threshold and no SIR gain ◮ K e = 6 has high SIR gain to offset increase of threshold with DoF ◮ K e = 6 is more robust to target fluctuations → big advantage over K e = 3 at high P d PhD Thesis Defense 18th Nov 2011 Signal Processing for MIMO Radars
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