Aerospace and Electronic Systems Magazine May 2018 - 38

FDA-OFDM for Integrated Navigation, Sensing, and Communication Systems

Figure 5.

Block scheme of integrated radar and communication system.

FDA-OFDM MODULATION AND DEMODULATION
Figure 5 shows the FDA-OFDM chirp modulation and demodulation schemes for the integrated system. Note that either singleelement antenna or multiple-element antenna is allowed for the
FDA-OFDM scheme. Without loss of generality, only "receiver"
is mentioned in the figure. First, the binary communication data
is divided into parallel streams, and mapped onto complex-valued
phase-shift keyed symbols. Next, the standard OFDM waveform
xo(t) can be obtained by an inverse fast Fourier transform. The
OFDM waveform is further processed to produce multiple signals
with distinct carrier frequencies according to the OFDM coding
sequence, which are then transformed into analog signals with
digital-to-analog convertors. Finally, after being mixed with a local oscillator signal exp( j2πf0t + jπkrt2) with a carrier frequency f0,
the generated Nc-carrier OFDM chirp signals are radiated by an
M-element FDA antenna towards the desired region.
The returned signals from a reflecting object at the distance R
can be expressed as
2
N s −1 N c −1

 2R 
 2R  
π
y ( t ) =   ck,n exp  j 2π f n  t −
j
k
t
+
−

 
r

c0 
c0  
k =0 n =0





2R

 t − kTw − c
j 2π f d t
0
rect 
e
Tw











(7)

where fd is the Doppler shift. Note that, here, we consider only the
baseband signal and ignore the carrier frequency associated terms,
which will be canceled out by the RF mixer and corresponding receiver multichannel processing. The subsequent receiver processing steps are then carried out in an inverse order of the transmitter's
processing steps.
The radar functionality can be achieved by exploiting the baseband signals x(t) and y(t) with matched filtering, which calculates
the radar range profile by correlating the received time-domain signal y(t) with the transmitted time-domain signal x(t), namely, z(τ) =
∫y(t)x(t − τ)dt, where τ is just the time delay of the range profile to
be measured. But this approach may result in high sidelobe levels in
the radar range profile due to imperfect waveform auto-correlation.
38

The novel OFDM radar processing approach proposed in [1] can be
employed to circumvent this disadvantage. The basic idea is to use
the transmitted information and the received information at the output of the OFDM demultiplexer before the channel equalization and
decoding. In doing so, the distortion from the channel is fully contained in the complex modulation symbols. Since all information
symbols in one OFDM symbol are transmitted through the channel
at different carrier frequencies separated by Δf, the received information symbols can be used to perform channel sensing at discrete
frequencies like that in a stepped frequency radar.
In the same time, the receiver recovers the individual modulation symbols for the communication functionality by observing
the received signal for only the elementary OFDM chirp symbol
duration T. This implies that, when the guard interval duration Tg
is properly designed, we can cut the observed samples and accordingly the time shift of the rect(·)in (7) can be neglected. In this
case, (7) can be represented by
y0 ( t ) =

N s −1 N c −1

 c
k =0 n = 0

k, n



 2R 
 t − kTw 
exp  j 2π f n  t −
 + j 2π f d t  rect 


c
0 

 Tw 



(8)

where we assume the chirp rate kr associated terms have been canceled out or compensated in the dechirp-on-receive operation. At
this step, y0(t) is equal to the received signal in a standard OFDM
communication system and thus, the transmitted information can
be simply recovered by classic OFDM communication algorithms.

INTEGRATED COMMUNICATION AND RADAR
PERFORMANCE
For communication functionality, the frequency components e j 2π f 0t
should be removed by multiplying a RF carrier e − j 2π f0t. The separation of the Nc summation terms and the removal of ej2πnΔft can be
achieved by the following orthogonality property
1
2iπ

2π (ξ + i )

 πξ
2

0, p ≠ q
e − jpx e jqx dx = 
1, p = q.

(9)

In order to successfully recover the communication information, the time t has to be confined within the range between ξ/Δf
and (ξ + i)/Δf [28], where ξ denotes a positive real number. That is,
it is essential for the symbol duration Tw to be i/Δf. In communication aspects, the performance is often evaluated by the bit error
rate (BER):
 2 Eb
P = Q
 N0







(10)

where Q(·) is the complementary Gaussian error function and
Eb/N0 is the signal-to-noise ratio (SNR) per bit with Eb and N0 denoting the signal and noise, respectively. It is obvious that the BER
of the OFDM chirp waveform is the same as that of a standard
OFDM waveform.

IEEE A&E SYSTEMS MAGAZINE

MAY - JUNE 2018

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine May 2018