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 with a jammer-to-noise ratio = 50dB. Again, we have = 10 element array with spacing. The center frequency of the received signal is = 1GHz and the bandwidth is = 10MHz for a fractional bandwith = 1%.

Copyright 2017-2027, Ilias S. Konsoulas.

## 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;