Detection of OFDM-CPM Signals over Multipath Channels
Imran A. Tasadduq and Raveendra K. Rao
Department of Electrical & Computer Engineering
Elborn College, 1201 Western Road
The University of Western Ontario
London, ON N6G 1H1, Canada.
Abstract—A class of Orthogonal Frequency Division Multiplex-
ing - Continuous Phase Modulation (OFDM-CPM) signals is in-
troduced in which binary data sequence is mapped to complex
symbols using the concept of correlated phase states of a CPM
signal. Canonical optimum and suboptimum multiple-symbol-
observation OFDM-CPM receivers are derived. Multipath chan-
nel with AWGN is assumed. The receivers are analyzed for bit-
error-rate (BER) performance in terms of high- and low-SNR
bounds. These bounds are illustrated as a function of parameter
h
, time delay and attenuation level. It is shown through numeri-
cal computation that OFDM-CPM system outperforms a similar
OFDM-PSK system in a two-ray multipath model. Moreover, an
OFDM-CPM system gives the best error performance when the
parameter
h
is 0.5 with observation interval of 2.
I. INTRODUCTION
O
FDM is a good candidate for wireless multimedia com-
munication by virtue of its excellent properties in
frequency-selective fading environment [1], [2]. In OFDM, we
transmit data over several parallel low data rate channels. This
provides data integrity due to fading, relative to modulation
methods that employ single channel for high data rate transmis-
sion. Among other benefits of OFDM is that it fully exploits
the advantages of digital signal processing concepts [3].
A typical OFDM transmitter works as follows: Serial en-
coded data is sent to a mapper that outputs a complex number.
A serial-to-parallel converter serially takes in the complexnum-
bers and forms a parallel stream by increasing their time period.
This stream has as many complex numbers as the number of
subchannels. Inverse Fast Fourier Transform (IFFT) is then ap-
plied to the parallel stream that results in orthogonal signals
on the subchannels. The orthogonal signals are then converted
back into a serial stream and after up converting the signal to
desired carrier frequency the signal is transmitted.
While in the literature OFDM-PSK, QAM, DPSK and
DAPSK have been considered [4]-[7],OFDM-CPM signals that
use the concept of correlated phase states of a CPM signal have
not been considered to-date. One of the advantages of OFDM-
CPM signals is that we can systematically introduce correlation
amongst adjacent OFDM symbols by an appropriate choice of
parameter
h
(in typical CPM signals
h
is modulation index).
Furthermore, this correlation can be exploitedin order to reduce
the BER in such a system. Thus in the paper we address the
detection problem of observing
n
OFDM-CPM symbols and
arriving at an optimum decision on one of the symbols. The
channel is modeled as multipath and AWGN.
The paper is organized as follows: In section II we describe
OFDM-CPM signaling scheme. We address the detection prob-
lem in section III and arrive at the receiver structure. In section
IV high and low SNR bounds on the performance of the op-
timum OFDM-CPM receiver are derived. These bounds are
illustrated through numerical computation in section V. The pa-
per is concluded in section VI.
II. OFDM-CPM SIGNALING SCHEME
As shown in Fig. 1, serial bit stream
b
i
,
i
=0
1
2
:::
with
bit duration of
T
b
seconds is converted into blocks of
N
bits
representedby
a
kp
k
=0
1
2
:::
and
p
=0
1
2
:::N
;
1
where
N
denotes the number of carriers and
a
kp
=
1
.For
example,
a
0
p
would denote the first blockof
N
bits and
a
1
p
the
second block of
N
bits and so on. The CPM mappers transform
the incoming
a
kp
into appropriate complex numbers
c
kp
given
by
c
kp
=
cos
(
kp
)+
j
sin
(
kp
)
(1)
with
kp
=
a
kp
h
+
h
k
;
1
X
q
=0
a
qp
+
(2)
where
h
,
0
<h<
1
, is a parameter and
represents the initial
mapping point that is assumed zero without loss of generality.
It is evident from (2) that the angles
kp
depend not only on
the current data but also on the past data. Fig. 2 shows all the
possible values of
kp
as a function of time when
h
= 0
:
5
.
Current value of
is determined by adding
+
h
(if data bit is
a
+1
)or
;
h
(if data bit is a
;
1
) to the previous value of
.
Fig. 1. OFDM-CPM Transmitter and Channel
1651
0-7803-7400-2/02/$17.00 © 2002 IEEE
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