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Coexistence of Radar and Communication Systems Channel Modeling using MATLAB by Ahmed Abdelhadi Review Article with MATLAB Instructions 2019 University of Houston
Coexistence of Radar and Communication Systems
Channel Modeling using MATLAB
by
Ahmed Abdelhadi
Review Article with MATLAB Instructions
2019
University of Houston
Table of Contents
List of Tables iii
List of Figures iv
Chapter 1. Introduction 1
1.1 Motivation, Background, and Related Work . . . . . . . . . . . 1
1.2 Radar Communications Model . . . . . . . . . . . . . . . . . . 2
Chapter 2. Interference Mitigation 5
2.1 Interference Channel Azimuth Angles . . . . . . . . . . . . . . 5
2.1.1 Used Algorithm for Projection . . . . . . . . . . . . . . 6
Bibliography 10
ii
List of Tables
iii
List of Figures
2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Output simulation using MATLAB Code . . . . . . . . . . . . 9
iv
Chapter 1
Introduction
This article provides a MATLAB simulation tutorial for the paper in [1]. The
article starts with a brief background on the problem of radar and commu-
nications coexistence with the relevant literature review of this topic. Later,
this article presents the MATLAB code for plotting the figures in [1].
1.1 Motivation, Background, and Related Work
On the radar side, the President Council of Advisers on Science and Tech-
nology (PCAST) [2] stated that the sharing of underutilized shipborne radar
spectrum for commercial use [3–5] will have significant benefits to the United
States both on technological and economical levels. The Federal Communi-
cations Commission (FCC) mentioned that shipborne radar spectrum [6, 7]
can be shared with commercial mobile network spectrum [8, 9]. The National
Telecommunications and Information Administration (NTIA) [10–12] studied
effects of radar and communications coexistence with respect to interference.
Radar and communications coexistence problem is further studied in [13–16]
and simulation results are presented in [17–19].
Multiple input multiple output (MIMO) radar has many advantages with re-
spect to phased-array radar [20–25] due to waveform diversity. It is anticipated
to replace phased-array radar for civil and military applications [26–31]. Addi-
tionally, it is a suitable model for coexistence as it represent higher degrees of
freedom over phased-array radar [15,32–43]. Furthermore, an extended MIMO
model, a.k.a. overlapped MIMO radar, is introduced in [44, 45].
On the communications side, the need for throughput increase can be strongly
witnessed for wireless communications [46–49]. Multiple access schemes have
played an important role in increasing the spectrum usage [50–54] specially
1
with exploiting the spatial dimension of the MIMO communication systems
[55–59]. These advancements and needs are also accompanied with the users
demands and expectations for enhancement of quality of service (QoS) [60–62]
and quality of experience (QoE) [63,64]. Some examples are in [65–68] for QoS
of Open Systems Interconnection (OSI) Model for network layer and others
are addressed in [69,70] for physical layer, while in [71,72] authors focused on
application layer.
Game theory utilization and energy efficiency considerations were presented
in [73–76] and [77–79], respectively, for LTE third generation partnership
project (3GPP) [80–82], Worldwide Interoperability for Microwave Access
(WiMAX) [83–85], Mobile Broadband [86, 87], and Universal Mobile Terres-
trial System (UMTS) [88–90]. Authors included cross-layer design benefits for
enhancing QoS in [91, 92], scheduling and shaping in [93–99] with battery life
and embedded-based systems in [100–104].
For wireless communications, the coexistence scenario benefits wireless re-
source allocation algorithms for applications such as delay-tolerant applica-
tions [74, 105]. These applications use resource allocation algorithms such
as proportional fairness in [106–108], max-min fairness in [109–112], and op-
timal allocation in [113–116]. Other applications are the real-time applica-
tions [117–126] with resource allocation algorithms such as approximate so-
lutions in [127–129] and optimal solutions in [130–137] using convex opti-
mization techniques [138–143]. Developed carrier aggregation methods for
resource allocation are essential to coexistence and utilizing the radar band.
For instance, some non-convex carrier aggregation optimization techniques are
shown in [144–148] while convex optimal techniques are presented in [149–154].
Extension of this work to other fields with utilization of the simulation tools
presented here is relevant to topics such as multi-cast networks [155], ad-hoc
networks [156–159], machine to machine (M2M) communications [160–162],
and other wireless networks [163–167].
1.2 Radar Communications Model
In the simulation of results in [1], uses the following system model
2
We start the MATLAB code by clearing and closing other programs using.
In MATLAB:
1 %%%%%%%%%%%%%%%%%%%%%%%%%
2
3 close all;
4 clear all;
5
6 %%%%%%%%%%%%%%%%%%%%%%%%%
The simulation parameters for our model are:
In MATLAB:
1 %%%%%%%%%%%%%%%%%%%%%%%%%
2
3 %% Define Parameters
4 c = 3*10ˆ8; % Speed of
light
5 Nr=20; % Comm Antennas
6 Mt=100; % Mr Radar
Transmitters
7 Mr=Mt; % Mr Radar
Receivers
8 SNR = 10ˆ(20/10); % SNR
9 v_r = 2000; % Radial
velocity of 2000 m/s
10 r_0 = 5000; % (m) Radar
reference point distance (target range)
11 f_c = 3.5*10ˆ9; % Carrier
frequency 3.5GHz
12 omega_c=2*pi*f_c; % Angular
carrier frequency
13 lambda = (2*pi*c)/omega_c;
14 omega_d= (2*omega_c*v_r)/c; % Doppler
angular frequency
15 Tau_r = 2*r_0/c; % Two way
propagation delay
3
16 alpha = 0.5*exp(-1i*omega_c*Tau_r); % Path loss to
target
17 distance = 10000; % Communication
/Radar distance
18 a = exp(-1i*omega_c*distance/c); % Path loss to
target
19 delta_comm = 1/2; % Communication
antennas interspacing coeff.
20 delta_radar = 1/2; % Radar
antennas interspacing coeff.
21 G_null=zeros(5000,1);
22 theta = pi/180*(-45:.1:45);
23 G = zeros(1,length(theta));
24 thetaD = pi/180*([0]); % Target angle
25
26 %%%%%%%%%%%%%%%%%%%%%%%%%
The antenna spacing calculation are as:
In MATLAB:
1 %%%%%%%%%%%%%%%%%%%%%%%%%
2
3 % Antenna spacing calculation
4 AntSpacing = 1*lambda/2;
5 Rs = eye(Mt);
6 Tx_array=[AntSpacing*(0:1:Mt-1)];
7 Rx_array=[AntSpacing*(0:1:Mr-1)];
8
9 %%%%%%%%%%%%%%%%%%%%%%%%%
4
Chapter 2
Interference Mitigation
2.1 Interference Channel Azimuth Angles
Figure 2.1: System Model
In [1] simulation, we consider two systems one is MIMO radar and the other
is MIMO communications system as shown in Figure 2.1. The parameters
of both models are shown in Chapter 1. The below parameters show the
interference channel and azimuth angles between radar and communications
systems.
In MATLAB:
1 %%%%%%%%%%%%%%%%%%%%%%%%%
2
3 % Interference Channel Angles
4 azimuth_blocked = [-7:0.5:-6];
5
6 % Interference Channel Azimuth Angles
5
7 thetaComm = pi/180*(90 - azimuth_blocked); %
Communication/Radar angle
8 Dir_cosine = cos(thetaComm); %
Directional cosine
9 for b=1:length(Dir_cosine)
10 % Channel model
11 Hr = 1/sqrt(Nr)*[exp(-1i * 2 * pi * (0:Nr-1) *delta_comm * Dir_cosine(b))];
12 Ht = 1/sqrt(Mt)*[exp(-1i * 2 * pi * (0:Mt-1) *delta_radar * Dir_cosine(b))];
13 H = a * Hr’ * Ht;
14 end
15
16 %%%%%%%%%%%%%%%%%%%%%%%%%
2.1.1 Used Algorithm for Projection
The MATLAB code below shows the steps to implement singular value decom-
position (SVD) on the channel between radar and communications systems
followed by null space projection to mitigate harmful interference.
In MATLAB:
1 %%%%%%%%%%%%%%%%%%
2
3 for kk=1:length(thetaD)
4 omega_tau_t = (2*pi)/lambda*thetaD(kk)*Tx_array;
5 omega_tau_r = (2*pi)/lambda*thetaD(kk)*Rx_array;
6 a_T_thetaD = transpose(exp(-1i*omega_tau_t));
% Transmit
steering matrix
7 a_R_thetaD = transpose(exp(-1i*omega_tau_r));
% Receive steering
matrix
8
9 for ii=1:length(theta)
10 omega_tau_t = (2*pi)/lambda*(theta(ii))*Tx_array;
6
11 omega_tau_r = (2*pi)/lambda*(theta(ii))*Rx_array;
12 a_T_theta = transpose(exp(-1i*omega_tau_t));
% Transmit
steering matrix
13 a_R_theta = transpose(exp(-1i*omega_tau_r));
% Receive
steering matrix
14 G(ii) =abs(ctranspose(a_T_theta)*transpose(
Rs)*a_T_thetaD);
15
16 for ll=1:1
17 [U,S,V] = svd(H);
% SVD of H
18 P_v = null(H) * ctranspose(null(H));
19 Rs_null = P_v * eye(Mt) * ctranspose(
P_v);
20 G_null(ll,:) = abs(ctranspose(a_T_theta
)*transpose(Rs_null)*a_T_thetaD);
21 end
22
23 G_null_mean(ii) = mean(G_null);
24 G_norm_null = G_null_mean/max(G_null_mean);
% normalized
25 G_norm_no_proj = G/max(G);
% normalized
26
27 end
28 G_total_null(kk,:) = G_norm_null;
29
30 end
31
32 %%%%%%%%%%%%%%%%%%
• The beamform without projection.
In MATLAB
7
1 %%%%%%%%%%%%%%%%%%
2
3 G_dB_no_proj = mag2db(G_norm_no_proj);
4
5 %%%%%%%%%%%%%%%%%%
• The beamform with projection.
In MATLAB
1 %%%%%%%%%%%%%%%%%%
2
3 G_dB_null(b,:) = mag2db(G_total_null);
4
5 %%%%%%%%%%%%%%%%%%
• Plotting both beamforms with and without projection. The plot is shown
in Figure 2.2.
In MATLAB:
1 %%%%%%%%%%%%%%%%%%
2
3 % Figure
4 grid on
5
6 hold on
7 plot(180/pi*(theta),G_dB_no_proj,’-r’,’LineWidth’
,2)
8 plot(180/pi*(theta),G_dB_null(length(thetaComm),:),
’-’,’LineWidth’,2)
9 hold off
10
11 xlim([-20 15])
12 xlabel(’\theta (degree)’,’fontsize’,14)
13 ylabel(’Power (dB)’,’fontsize’,14)
14 legend(’Not Projected’,’Projected’)
15 title(’Null Projected Radar Waveform’,’fontsize’
,14)
8
-20 -15 -10 -5 0 5 10 15
(degree)
-80
-70
-60
-50
-40
-30
-20
-10
0
Po
we
r (d
B)
Null Projected Radar Waveform
Not Projected
Projected
Figure 2.2: Output simulation using MATLAB Code
16
17 %%%%%%%%%%%%%%%%%%
9
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