Pulse or digital communications – Receivers – Particular pulse demodulator or detector
Reexamination Certificate
2000-02-02
2004-01-13
Ghayour, Mohammad H. (Department: 2631)
Pulse or digital communications
Receivers
Particular pulse demodulator or detector
C375S262000, C375S265000, C370S208000, C714S708000
Reexamination Certificate
active
06678339
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for data communication of signals in units of a frame using an orthogonal frequency division modulation (OFDM) algorithm, and in particular, to a method to find and synchronize the initial frame using a globally optimal maximum likelihood (ML) estimate of joint carrier frequency offset and symbol timing error at the receiver.
2. Description of the Prior Art
OFDM system is a viable modulation scheme for data transmission over time varying dynamic channels. However, it is known that performance of such system is highly susceptible to non-ideal synchronization parameters. Specifically, symbol timing and carrier frequency offset become an increasingly important issue in implementation of OFDM systems for practical applications. It is known that carrier frequency offset deteriorates performance of OFDM systems by introducing interference among the sub-channels. To overcome this imperfection, various compensation methods for estimation and correction of synchronization parameters are known in the prior art.
These prior art methods for synchronization of OFDM systems can be classified into two main subclasses, namely minimum mean square error (MMSE) and ML estimators. In MMSE approach, the estimator uses the information provided by the reference signal (pilot tones) in order to minimize a cost function associated with the synchronization parameters. A salient feature of this approach is that no probabilistic assumptions are made with regard to the data. Although MMSE estimators usually result in a tractable (globally stable) and easy to implement realization, no optimal criteria (probabilistic) is associated with these estimators. Also, since part of the transmitted information is allocated to the reference pilots, the bandwidth efficiency of these methods is lower in comparison to the non-pilot schemes.
On the other hand, ML estimators provide the estimate of the unknown parameter subject to minimum probability of error criteria. Although not perfectly efficient, ML estimators are asymptotically minimum variance unbiased (MVU), i.e., their variance attains that of MVU estimator as the length of data record goes to infinity. However, due to the physical constraints, systems with infinitely long data records are not feasible for implementation purposes.
P. H. Moose, in “A Technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction,” IEEE Trans. on Communications, Vol. 42, No. 10, pp. 2098-2913, October 1994, describes the use of a retransmission technique in order to reveal the frequency offset parameter in the likelihood function of the received signal. Due to the redundancy introduced by repeating the data block, the data rate efficiency is decreased by a factor of two. To avoid this imperfection, a ML estimator based on cyclic prefix (CP) is described by J. van de Beek, M. Standel and P. O. Borjesson, in “ML Estimation of Timing and Frequency Offset in OFDM Systems,” IEEE Trans. on Signal Processing, Vol. 45, No. 3, pp. 1800-1805, July 1997. In this approach, the side information provided by the CP is used to obtain the likelihood function for joint estimation of symbol timing error and frequency offset in an OFDM system.
The likelihood function described in the Van de Beek reference does not globally characterize the observation vector over the entire range of the timing offset. The ML estimator of the prior art results in a considerable performance loss over finite range of timing offset parameter. More specifically, for a given symbol length, the probability of false ML estimation approaches one as the length of cyclic prefix increases.
Currently, there is increasing interest in multi-carrier modulation (MCM) for dividing a communication channel into several subchannels and transmitting many subcarriers through a single band using frequency division multiplexing (FDM) techniques. In the MCM method, however, because several subcarriers occupying a narrow frequency domain are transmitted at one time, a relatively longer symbol period results compared with a single carrier modulation method. The MCM method has, owing to such characteristics, the advantages that equalization is easily performed and that it has immunity to impulse noise. OFDM is a type of the MCM designed to maximize the working frequency efficiency by securing orthogonality among the multiplexed subcarriers. OFDM is applied to mobile radio channels to attenuate multipath fading.
In an OFDM transmitting/receiving system, modulation and demodulation of parallel data are carried out using the Fast Fourier Transform (FFT). It is required that the sampled data be sent in predetermined frames, having passed through a FFT routine, been time-division multiplexed, and transmitted, then restored at the receiving end. However, if the synchronization is in error in the course of restoring the frame, the signals demodulated after the FFT will be influenced by interchannel and intersymbol interference. Accordingly, the problem of synchronization in reforming the frame, especially any joint carrier frequency offset or symbol timing error, must be addressed as a matter of importance.
Conventional synchronization methods as above-described encounter problems in that the process of synchronization is not only very complex, but the synchronization is not realized rapidly.
SUMMARY OF THE INVENTION
Accordingly, the present invention is directed at a synchronization method that substantially obviates on or more of the problems due to limitations and disadvantages of the prior art.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be apparent from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the methods particularly pointed out in the written description and claims hereof, as well as the appended drawings.
To achieve these and other advantages, and in accordance with the purpose of the invention as embodied and broadly described, there is provided a method of estimating joint carrier frequency and symbol timing errors in a received sample bit stream including an observation vector (OV), having an observed carrier frequency timing offset &egr;, and a plurality of data-symbol frames, having an observed symbol timing error &thgr;. The method comprises the steps of generating a probability density function (PDF) based on the OV, and generating from the PDF a joint maximum likelihood (ML) estimate of a joint carrier frequency offset and a symbol timing error, the maximization performed globally over the entire span of the estimation vector [&egr;, &thgr;]. In another aspect of the invention, wherein the OV comprises an L-bit cyclic extension portion and a first and a second N-bit synchronization frame, the method calls for the PDF to comprise a first term, p1, based on the observed timing error &thgr; being within the span 1 to N and a second term, p2, based on the observed timing error &thgr; being within the span N+1 to N+L.
In yet another aspect of the method wherein the received bit stream has uncorrelated independent identically distributed random signal and noise sequence variables with power of &sgr;
s
2
and &sgr;
n
2
, respectively, and wherein the OV is denoted x, the PDF is given by
p
(
x
,&egr;,&thgr;)=
p
1
(
x
,&egr;,&thgr;)(
U[&thgr;−
1]−
U[&thgr;−N−
1])+
p
2
(
x
,&egr;,&thgr;)(
U[&thgr;−N−
1]−
U[&thgr;−N−L+
1])
wherein U[n] is the discrete time unit step function, and wherein
if (1≦&thgr;≦N)
R
=
[
r
xx
[
0
]
I
(
ϑ
)
0
0
0
T
(
N
+
L
)
0
0
0
r
xx
[
0
]
I
(
N
-
ϑ
)
]
R
-
1
=
[
I
(
ϑ
)
r
xx
[
0
]
0
0
0
T
(
N
+
L
)
-
1
0
0
0
I
(
N
-
ϑ
)
r
xx
[
0
]
]
T
M
=
&Dgr;
Toeplitz (
r
xx
[0]
r
xx
&ls
Agere Systems Inc.
Ghayour Mohammad H.
Ghulamali Qutub
Hughes Ian M.
Mendelsohn Steve
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