MATLAB Examples

Example 11.4.1. - Time-Delay Steering to Counteract a Widweband Interferer.

Consider the radar interference scenario that is occuring with a single jammer at an angle $\phi_i = 30^{\circ}$ with a jammer-to-noise ratio $JNR$ = 50dB. Again, we have $M$ = 10 element array with $\lambda/2$ spacing. The center frequency of the received signal is $F_c$ = 1GHz and the bandwidth is $B$ = 10MHz for a fractional bandwith $B_{fr}$ = 1%.

Copyright 2017-2027, Ilias S. Konsoulas.

Contents

Workspace Initialization.

clc; clear; close all;

Signal Definitions.

M      = 10;        % Number of Array Elements.
c      = 299792458; % Speed of Light in m/sec.
Fc     = 10^9;      % Interference Centre frequency in Hz.
lambda = c/Fc;      % Incoming Signal Wavelength in (m).
d      = lambda/2;  % Interelement Distance in (m).
phi_i  = 30;        % Interference angle in degrees
INR    = 50;        % Interference Power in dBs
sigmaw = 1;         % Thermal Noise Power.
B      = 10^7;      % Interference Signal BW in Hz.

u_i = (d/lambda)*sin(phi_i*pi/180);        % Interferer Normalized Spatial Frequency.
v_i = exp(-1i*2*pi*u_i*(0:M-1).')/sqrt(M); % Interferer Steering vector.

Calculation of the Interference + Noise autocorrelation matrix.

R_i_nb   = 10^(INR/10)*(v_i*v_i');
R_ipn_nb = R_i_nb + sigmaw^2*eye(M);
InvRipn = inv(R_ipn_nb);

Construct the Wideband Interference Correlation Matrix:

Rd = zeros(M,M);
for m=1:M
    for n=1:M
        Rd(m,n) = sinc((m-n)*d*B*sin(phi_i*pi/180)/c);
    end
end

Ri_wb   = Rd.*R_i_nb;
Ripn_wb = Ri_wb + sigmaw^2*eye(M);
InvRipn_wb = inv(Ripn_wb);

Calculate the Time-Delay Steering Vector and Matrix:

m = 1:M;
tm = (d/lambda)*(m-1)*sin(phi_i*pi/180);
v_td = exp(-1i*2*pi*tm)/sqrt(M);

V = diag(v_td);

Ripn_td    = V'*Ri_wb*V + sigmaw^2*eye(M);
InvRipn_td = inv(Ripn_td);

Calculate the SINR loss factor for the Optimum, Wideband and Time-Delay Steered beamformers:

Nsamples = 4e3;
Lsinr_opt = zeros(Nsamples,1);
Lsinr_wb  = zeros(Nsamples,1);
Lsinr_td  = zeros(Nsamples,1);
angle = -50:100/Nsamples:50-100/Nsamples;

for k=1:Nsamples
    u = (d/lambda)*sin(angle(k)*pi/180);
    v = exp(-1i*2*pi*u*(0:M-1)')/sqrt(M); % Azimuth Scanning Steering Vector.
    Lsinr_opt(k) = v'*InvRipn*v;    %#ok<MINV>
    Lsinr_wb(k)  = v'*InvRipn_wb*v; %#ok<MINV>
    Lsinr_td(k)  = v'*InvRipn_td*v; %#ok<MINV>
end

Plot SINR Loss Factor.

figure('NumberTitle', 'off','Name','Figure 11.21');
plot(angle,10*log10(abs(Lsinr_opt)),'LineWidth',1.5);
hold on;
plot(angle,10*log10(abs(Lsinr_wb)),'r--', 'LineWidth',1.5);
plot(angle+phi_i,10*log10(abs(Lsinr_td)),'g', 'LineWidth',1.5);
ylim([-60 10]);
xlim([0 50]);
xlabel('Angle (deg)');
ylabel('SINR Loss (dB)');
title('SINR Loss for the WB Jammer and TD-Steering');
legend('Optimum','WB Jammer','Time-Delay','Location','SouthWest');
grid on;