Correlated Waveform Design: A Step Towards a Software Radar

Transcription

1 Correlated Waveform Design: A Step Towards a Software Radar Dr Sajid Ahmed King Abdullah University of Science and Technology (KAUST) Thuwal, KSA sajid.ahmed@kaust.edu.sa December 9, 2014

2 Outlines Radar KAUST What is a Radar? Beampatterns of Fixed Antennas Beampatterns Using Antenna Array The Concept of MIMO Radar Waveform Covariance Matrix Design Correlated Waveform Design Group Publications 1

3 Radar KAUST Group Leader: Prof. Mohamed-Slim Alouini (FIEEE) Co-Investigator: Prof. Tareq Naffouri Co-Investigator: Dr Sajid Ahmed (Research Scientist) PhD Students Seifallah Jardak Hussain Ali (KFUPM + KAUST) MSc Students Taha Bachoucha John Lipor (PhD Student at University of Michigan Ann Arbor) Intern Students Abdulrahman Alsaggaf (KFUPM) Ayman Magrabi (KFUPM) 2

4 Radar KAUST Major Research Directions: Covariance Matrix Design for Linear and Planar Beampatterns Finite Alphabet Correlated Waveform Design Target Parameter Estimation Detection Using Compressive Sensing Algorithms Development of Prototype Radar Strengths: Radar System Modelling Novel Closed-Form Solutions for Covariance Matrices Design Novel Closed-Form Solutions for Waveform Design Low Complexity Target Parameter Estimation Techniques 3

5 Radar KAUST Accomplishments (since Feb. 2012): Four Journal and six conference papers Three Journal and four conference papers are under review One patent (invention disclosour) filed One grant from OCRF of KAUST One proposal under review in KACST, Riyadh, Saudi Arabia One proposal under review in QNRF, Doha, Qatar 4

6 What is a Radar? (1/2) Radar stand for RAdio Detection And Ranging. Radar is an object detection system that uses electromagnetic waves to detect the range, location and radial speed of both moving and stationary targets such as Aircraft Ship Motor vehicle Cloud Generally radar has two basic parts, a transmitter and a receiver, which are usually colocated. 5

7 What is a Radar? (2/2) Figure 1: Basic radar system. 6

8 Beampattern of Isotropic Antenna An Isotropic antenna transmits power in all directions equally. To increase the range and reflected power, the power is transmitted only in the region-of-interest z y x

9 Beampattern of Parabolic Antenna Parabolic antenna focus the transmitted power in one direction. To scan the target at different locations the antenna platform is mechanically rotated. Figure 2: Parabolic antenna. Figure 3: Beampattern of parabolic antenna. 8

10 Beampatterns Using Antenna Array (1/2) In an antenna array M antennas are used to transmit the signals The received signal at an angle ψ can be written as M r(n,ψ) = x m (n)e jπ(m 1)sin(ψ) = a T T(ψ)x(n), m=1 where a T (ψ)= [ 1 e jπsin(ψ) e jπ(m 1)sin(ψ)] T,x(n)=[x1 (n)x 2 (n) x M (n)] T. 9

11 Beampatterns Using Antenna Array (2/2) The power received at an angleψ can be found as P(ψ) = E{ a T T(ψ)x(n) 2 }, = E{a H T (ψ)x(n)x(n) H a T (ψ)}, = a H T (ψ)e { x(n)x(n) H} a T (ψ), = a H T (ψ)ra T (ψ), where R is the correlation or covariance matrix of the waveform. 10

12 Phased Array Radar (1/3) Phased array radar focus the transmitted power in the given direction. Figure 4: Phased-array radar. M r(n,ψ) = x(n)e jπ(m 1)sin(ψ) e jπ(m 1)sin(ψ). m=1 P(ψ) = a H T (ψ)ra T (ψ). 11

13 Phased Array Radar (2/3) The transmitted waveform from different antennas in vector form can be written as [ ] T x(n) = x(n) x(n)e jπsin(ψ) x(n)e jπ(m 1)sin(ψ). In phased-array radar the covariance matrix of the transmitted waveforms is R = E{x(n)x H (n)}, 1 e jπsin(ψ) e jπ(m 1)sin(ψ) e = jπsin(ψ) e jπsin(ψ) e jπ(m 1)sin(ψ) e jπsin(ψ) 1. 12

14 Phased Array Radar (3/3) Phased array radar focus the transmitted power in the given direction 10 Normalised Beampattern (db) Angle Figure 5: Beampattern of Phased Array radar for ψ = 20 degrees. 13

15 Concept of MIMO-radar (1/2) In MIMO-radars the waveforms can be independent or partially correlated Figure 6: MIMO-radar. 14

16 Concept of MIMO-radar (2/2) In MIMO-radar the waveforms can be independent R = Waveforms can be partially correlated 1 ρ 12 ρ 1M ρ R = ρ M 1,M ρ M1. ρ M,M 1 1 MIMO-radar yields M2 M 2 degree-of-freedom 15

17 Waveforms Covariance Matrix Design For the desired beampattern The transmitted power from MIMO-radar at the location θ k is given by P(θ k ) = a H (θ k )Ra(θ k ). To synthesize R for the desired beampattern, φ(θ k ), the cost functions can be defined as J 1 (R) = 1 K a H (θ k )Ra(θ k ) αφ(θ k ) 2, K subject to the constraints k=1 C 1. R 0 C 2. R(m,m) = c, form = 1,...,M 16

18 Beampattern Design Example (1/3) 25 Designed Beampattern Desired Beampattern 20 Transmit Power Angle (degree) Figure 7: Symmetric beampattern of 60 degrees. The number of transmit antenna is

19 Beampattern Design Example (2/3) Designed Beampattern Desired Beampattern 50 P(θk) θ k Figure 8: Beampattern of two main lobes. The number of transmit antennas is

20 Beampattern Design Example (3/3) Designed Beampattern Desired Beampattern 30 Transmit Power Angle (degree) Figure 9: Non symmetric beampattern of 40-degrees width. The number of transmit antenna is

21 Correlated Waveforms Matrix Design To reduce the side-lobe-levels J 1 (R) = 1 K K k=1 a H (θ k )Ra(θ k ) αφ(θ k ) 2, To control main and side-lobe-levels following constraints can be added in the problem C 1. R 0 C 2. R(m,m) = c, form = 1,...,M C 3. max{a H (θ m )Ra H (θ m )} min{a H (θ m )Ra H (θ m )} δ C 4. max{a H (θ s )Ra H (θ s )} ǫ. Convex optimisation toolbox of Matlab can be used to optimise the covariance matrix R. 20

22 Beampattern Design Example (1/2) δ = δ = 1.5 δ = 0.1 Transmit Power Angle (degree) Figure 10: Demonstration of direct ripple control using constraint C 3 for various values of δ, where the region of interest isθ p [ 30,30 ] and the number of transmit antennas is

23 Beampattern Design Example (2/2) 10 2 ǫ = ǫ = 10 ǫ = 5 Transmit Power Angle (degree) Figure 11: Demonstration of direct ripple control using constraint C 4 for various values of ǫ, where the region of interest isθ s [ 90, 60 ]&[60,90 ] and the number of transmit antennas is

24 Finite Alphabet Correlated Waveform Design (1/2) Once the covariance matrixris found,m waveforms each of L symbols, X = [x 1 x 2 x M ] C L M to realise it can be found as X = X g R 1/2. (1) 4 2 x 1 (n) 0 2 Waveform Using (1) Sample time n 2 1 Desired Waveform x 1 (n) Sample time n Figure 12: Waveforms using (1) and desired amplitude waveform. 23

25 Finite Alphabet Correlated Waveform Design (2/2) Gaussian random variable,x, can be mapped onto BPSK random variable,y, using the relation y = sign(x). The relationship between the covariance matrix of Gaussian and BPSK RV s can be established as ( π ) R g = sin 2 R. The matrix of Gaussian RV s can be found with de-whitening transform X = X g R 1/2 g. The matrix of desired BPSK waveform can be obtained as Y = sign(x). 24

26 Group Publications 1. T. Bouchoucha, S. Ahmed, T. AlNaffouri, and M.S. Alouini, Closed-form solution to directly design FACE waveforms for beampatterns using planar array, Under Review in IEEE Trans. on Signal Processing, Jul S. Jardak, S. Ahmed and M. S. Alouini, Generation of correlated finite alphabet waveforms using Gaussian random variables, IEEE Transaction on Signal Processing, vol. 62, no. 17, pp , Sep S. Ahmed and M. S. Alouini, MIMO-radar transmit beampattern design without synthesising the covariance matrix, IEEE Transaction on Signal Processing, vol. 62, no. 9, pp , May John Lipor, S. Ahmed, and M. S. Alouini, Fourier-based transmit beampattern design using MIMO radar, IEEE Transaction on Signal Processing, vol. 62, no. 9, pp , May S. Ahmed and M. S. Alouini, MIMO-radar waveform covariance matrix for high SINR and low side lobe levels, IEEE Transaction on Signal Processing, vol. 62, no. 8, pp , Apr S. Ahmed, J. S. Thompson and B. Mulgrew, Finite alphabet constant-envelope waveform design for MIMO radar beampattern, IEEE Transaction on Signal Processing,, vol. 59, no. 11, pp , Nov S. Ahmed, J. S. Thompson and B. Mulgrew, Unconstrained synthesis of covariance matrix for MIMO radar transmit beampattern, IEEE Transaction on Signal Processing, vol. 59, no. 8, pp , Aug

27 8. H. Ali, S. Ahmed, Tareq Y. AlNaffouri, and M. S. Alouini, Reduction of snapshots for MIMO radar detection by block/group orthogonal matching pursuit, in proc. IEEE International Radar Conference, Lille, France, Oct S. Jardak, S. Ahmed and M. S. Alouini, Low complexity joint estimation of reflection coefficient, spatial location, and Doppler shift for MIMO radar by exploiting 2D-FFT, in proc. IEEE International Radar Conference, Lille, France, Oct J. Lipor, S. Ahmed and M. S. Alouini, Closed form Fourier based transmit beamforming for MIMO radar, in proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, (ICASSP2014), Florence, Italy, May S. Ahmed and M. S. Alouini, Transmit waveform covariance matrix for improved SINR and low side lobe levels, in proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP2013), Vancouver, Canada, May S. Ahmed and M. S. Alouini, Low complexity receiver design for MIMOradar, in proc. IEEE Globecom Workshop on Radar and Sonar Networks (GlobeCom. 2012), Disneyland, USA, Dec S. Jardak and S. Ahmed, and M. S. Alouini, Generating correlated QPSK waveforms by exploiting Gaussian random variables, in proc. IEEE Conference on Signals, Systems and Computers (ASILOMAR2012), California, USA, Oct., S. Ahmed and J. S. Thompson and B. Mulgrew, Fast computations of constant envelope waveforms for MIMO radar transmit beampattern, in proc. IEEE International Radar Conference, Washington DC, USA, pp , May