FIELD OF THE INVENTION
The present invention relates to multicarrier communication systems. More particularly, the
invention relates to a method and system for minimizing means square estimation error (MSEE)
and bit error rate during channel estimation and equalization in orthogonal frequency division
multiplexing (OFDM) systems.
BACKGROUND AND THE PRIOR ART
Orthogonal frequency division multiplexing (OFDM) is a multi-carrier communication scheme in
which, data at a high rate is divided into sub-streams and transmitted over orthogonal carriers,
thus enabling data transmission over a frequency selective fading channel, in a bandwidth
efficient manner.
Channel estimation is an important constituent of coherent OFDM receivers. Guard intervals are
inserted between adjacent OFDM block symbols, to take care of Inter Block Interference (IBI).
Transmitting a Cyclic Prefix (CP) of the data during this interval makes the channel circularly
convolutive, simplifying the channel equalization problem. Specifically, channel equalization in
the frequency domain can be done using one tap filters. This is because the CP makes the
channel matrix circulant, which is diagonalized by the inverse discrete Fourier transform (IDFT)
and DFT operations. The challenge in frequency domain channel equalization lies in estimating
the channel frequency coefficients at all the subcarriers.
In conventional OFDM systems, channel estimation is done using pilot tones along with data. In
slow fading environments, channel estimation can be done by inserting pilot tones into all of the
subcarriers of the OFDM symbol with a specific period during which the channel is assumed to
be quasi-static. In fast fading environments pilot tones are inserted at specific subcarriers in
each OFDM symbol. The channel frequency coefficients at the data tones are then determined
by interpolation based approximations resulting in channel estimation errors, which could be
significant in a frequency selective fading channel. Also, pilot tone insertion reduces the
bandwidth efficiency of the system. The need for higher data rates and mobility only aggravates
the problem. This motivates the need for blind estimators which exploits the statistics of the
transmitted data, or some redundancy in the transmitted data to estimate the channel without
2

employing pilots. Traditionally blind estimators have been found to have a slow convergence
time and also there is a possibility of convergence of the performance surface to a local
minimum. Semi-blind equalization allows for a trade-off between performance and bandwidth
efficiency by making use of blind as well as pilot assisted techniques.
"Channel estimation using implicit training," IEEE Transactions on Signal Processing, vol. 52,
no. 1, January 2004 by A.G. Orozco-Lugo, M. Lara, D. McLernon discloses a new method to
perform channel estimation. It is shown that accurate estimation can be obtained when a
training sequence is actually arithmetically added to the information data as opposed to being
placed in a separate empty time slot.
Article "Superimposed Training for OFDM: a peak-to-average power ratio analysis," IEEE
Transactions on Signal Processing, vol. 54, no. 6, pp. 2277- 2287, June 2006 by N. Chen and
G.T. Zhou describes an orthogonal frequency division multiplexing (OFDM) transmission with
superimposed training. The PAR of the OFDM signal is examined with superimposed training,
and its complementary cumulative distribution function (CCDF) is derived. Achievable lower and
upper bounds on the CCDF are also determined. In addition, the PAR change is linked to the
effective signal-to-noise ratio (SNR) and thus the bit-error-rate (BER) performance under the
fixed dc power constraint.
Article Proceedings of the IEEE-GLOBECOM, vol.2, no. 2, pp. 878-882, Dec. 2003 by N.
Ohkubo and T. Ohtsuki teaches added pilot semi-blind channel estimation for OFDM packet
transmission.
ETRI Journal, vol.28, no. 5, pp. 688-691, Oct. 2006 by Q. Yang and K. S. Kwak teaches "Time-
varying multipath channel estimation with superimposed training in CP-OFDM systems". A
time-domain channel estimation scheme for time-varying multipath channels is developed by
using superimposed sequences. The idea behind this scheme is to split the one-OFDM-symbol-
period time-domain channel into equi-spaced time-slotted subchannels, so that the time
variation for each subchannel can be assumed to be negligible;then, each subchannel is
estimated by a linear least square (LS) estimator.
Article Proceedings of the IEEE-GLOBECOM, Missouri, USA, December 2005, pp. 2229-2233T
by Cui and C. Tellambura discloses "Superimposed pilot symbols for channel estimation in
OFDM systems". Article Proceedings of the IEEE-GLOBECOM, Texas, USA, November 2001,
3075-3079 by C. K. Ho, B. Farhang-Boroujeny and F. Chin discloses "Added pilot semi-blind
3

channel estimation scheme for OFDM in fading channels". Article IEEE Communications
Letters, vol. 7, no. 1, pp. 30-32,January 2003 by H. Zhu, B. Farhang-Boroujeny and C. Schlegel
teahces "Pilot embedding for joint channel estimation and data detection in MIMO
communication systems". Further the article Proceedings of the IEEE-GLOBECOM, Dallas,
USA, November 2004, pp. 1244-1248 by S. Balasubramanian, B. Farhang-Boroujeny and V.
John Mathews describes "Pilot embedding for channel estimation and tracking in OFDM
systems".
United States Patent US 6990153 B1 describes a channel estimation scheme that provides
good performance in a communication channel having varying frequency and time
characteristics, while preserving the usable bandwidth of the communication channel.
There is a need for bandwidth efficient channel estimation techniques for OFDM with good
performance. Recently, superimposed training (ST) based channel estimation techniques have
been proposed. In this scheme, training symbols known to the receiver are algebraically added
on to the data at a low power, thus avoiding the need for additional time slots for training. At the
receiver these known symbols, in the presence of unknown data and noise, are exploited for
channel estimation. These methods for channel estimation are attractive compared to pilot
assisted techniques as they are bandwidth efficient. ST based methods for channel estimation
in OFDM have been considered in the literature, the focus being on iterative source channel
estimation techniques, the optimality criteria for the training sequences and peak to average
power (PAPR) analysis.
The state of the art however, leaves many critical issues unanswered. Iterative channel
estimation techniques to get improved accuracy and also to cancel the interference of the data
on the estimate are used. However the initial LS channel estimate used in the first iteration does
not exploit the nature of the block frequency selective fading channel that occurs in practice.
The ST sequence used for channel estimation plays a pivotal role in system performance. The
cost function that is used to characterize the optimal training sequences is the minimization of
the mean square estimation error (MSEE) or the Cramer-Rao lower bound (CRLB). These are
also the optimization criteria generally used for pilot assisted techniques which is reasonable
because in this case the training is separated from the data. However, in the superimposed
training scheme both of these criteria result in characterizations that does not take into account
the interference of the training sequences on the data detection. Moreover the training
sequences used in the existing art will not be applicable in currently standardized wireless
4

OFDM systems because of the existence of frequency components at the band edges which
are generally used in the brick wall shaping of the transmit spectrum. It was not known in the
prior art that the number of OFDM symbols experiencing the same channel may be used to
improve the channel estimation accuracy by averaging over several symbols depending on the
coherence time of the channel and/or the desired estimation accuracy. Hence the number of
OFDM symbols averaged to estimate the channel impulse response making it suitable to the
characteristics of the channel encountered in different standards by the superimposed training
based OFDM system was not in the prior art.
Thus there is a need to provide for a system and method for minimizing the means square
estimation error (MSEE) and bit error rate during channel estimation and equalization in
orthogonal frequency division multiplexing (OFDM) systems.
Thus in a quest for obtaining an optimal equalizer, the present inventors have got a new idea
and found that channel MSEE and the BER can be jointly minimized thereby arrived at a
digitized linear frequency modulation (LFM) based optimal training sequence that fairly
distributes the interference due to the training on the data on all the used sub-carriers for
superimposed training based OFDM systems and further introduced averaging of the channel
estimates beyond one OFDM symbol so as to obtain an improved channel estimation from
OFDM symbols experiencing the same fading coefficients. This improves channel estimation in
OFDM systems without using additional bandwidth for the purpose of channel estimation and
equalization.
OBJECTS OF THE INVENTION
Accordingly one object of the present invention is to address the shortcomings/disadvantages of
the prior art.
Another one object of the present invention there is provided a system for minimizing means
square estimation error (MSEE) and bit error rate during channel estimation and equalization in
superimposed training based orthogonal frequency division multiplexing (OFDM) systems
without using additional bandwidth for the purpose of channel estimation and equalization.
5

Another object of the present invention is to provide a method for minimizing means square
estimation error (MSEE) and bit error rate during channel estimation and equalization in
superimposed training based orthogonal frequency division multiplexing (OFDM) systems.
SUMMARY OF THE INVENTION
Thus according to one aspect of the present invention there is provided a method for minimizing
means square estimation error (MSEE) and bit error rate during channel estimation and
equalization in orthogonal frequency division multiplexing (OFDM) systems, said method
comprising:
receiving superimposed training based OFDM signals without guard interval as an input,
cross-correlating said received OFDM signal to a specific lag determined by the rms delay
spread of the channel, with a specific known training sequence stored in a register, and which is
also the sequence that is added to the data at the transmitter in the time domain having a
prescribed pilot to data power ratio,
wherein the said cross-correlated data being averaged over a length of samples depending on
the coherence time of the channel and processed along with the stored values of the inverse of
autocorrelation values of superimposed training (ST) sequence so as to obtain a reliable least
squares based channel estimate.
According to another aspect of the present invention there is provided a system for minimizing
means square estimation error (MSEE) and bit error rate during channel estimation and
equalization in orthogonal frequency division multiplexing (OFDM) systems, said system
comprising:
receiver means for receiving superimposed training based OFDM signals without guard interval
as input;
wherein said receiver means comprises means for cross-correlating said received OFDM signal
to a specific lag determined by the rms delay spread of the channel, with a specific known
training sequence stored in the receiver means, and which is also the sequence that is added to
the data at the transmitter in the time domain having a prescribed pilot to data power ratio,
wherein the correlated data being averaged over a length of samples depending on the
coherence time of the channel and processed along with the stored values of the inverse of
6

autocorrelation values of superimposed training (ST) sequence so as to obtain a reliable least
squares based channel estimate.
Further, the embodiment comprises of an interference canceller to reduce the effect of the
superimposed training sequences on the data, which multiplies the DFT of the specific training
sequence with the frequency coefficients of the channel estimate and subtracts these signals
from the DFT of the received signals.
Another very important characteristic of the invention is the use of a training sequence for the
above channel estimation method that is stored in a register in the channel estimator module in
the receiver, and which is also the sequence that is added to the data at the transmitter, that are
samples of a digitized linear frequency modulated (LFM) signal having uniform energy
components in all the subcarriers of the OFDM symbol, which are shaped by the virtual
subcarriers according to specifications of the standard to which the OFDM based system
complies. This sequence is optimal in terms of minimizing the bit error rate (BER) of the OFDM
system in addition to minimizing the MSEE. Approximations of the LFM may be used with an
associated loss in performance.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of the equivalent baseband transmitter of the superimposed training
based OFDM system.
FIG. 2 is a block diagram of the equivalent baseband channel encountered in a typical
superimposed training based OFDM system.
FIG. 3 is a block diagram of the equivalent baseband receiver of the superimposed training
based OFDM system.
FIG. 4 is a representation of the channel equalizer and canceling of interference due to the
training sequence used in the receiver of the superimposed training based OFDM system.
7

FIG. 5 is an alternative representation of the transmitter as in Fig.1, wherein the DFT of the
training sequence is added to the data in the frequency domain at a particular pilot to data
power ratio.
Fig. 6 is an alternative representation of the receiver as in Fig. 3, wherein the frequency domain
equivalent of the time domain channel estimation method is carried out.
Fig.7. is BER vs. SNR graph for the Modified SUM, SUI2 and ITU Vehicular Channel Model A
with the simulation parameters of Table.1, using the training sequencec,(«).
Fig.8. is MSEE vs. SNR graph showing comparison between the training sequencesc,(«)
andc». Here N = 512, Q = 8, TP = 2, and the exponential power delay profile used was

Fig.9. is BER vs. SNR graph showing comparison between the training sequencesc,(«) andc2(«).
Here N = 512, Q = 8, Tp =2, and the exponential power delay profile used was e',/ = {0,i,..g-i}
Fig.10. is a comparison of the magnitude spectrum of c» and/?,(«). /?,(«) loses its spectral
flatness because of appending an additional -1 to the m-length PN sequence having a period
of Aw.
DETAILED DESCRIPTION OF THE INVENTION
Fig. 1 is the block diagram of the transmitter of a superimposed training based OFDM system.
Although not necessary, perfect synchronization is assumed here for illustration. Binary data is
grouped into symbols depending on the level of QAM modulation used. Vectors sk of such
symbols are formed which are then passed to the IDFT block. Here k stands for the OFDM
symbol index. Some of the entries are zeros to serve the spectral mask requirements of the
OFDM system. The output of the IDFT block is whereFis the normalized NxN DFT
matrix with and F" is the complex conjugate transpose. Here (m,n) is used
to denote the mth row and nth column of the matrix. A parallel to serial converter serially outputs
the simultaneous IDFT outputs. A training sequence ck is then algebraically added to this IDFT
output with a specific low pilot to data power ratio to get,

8

A characteristic of the invention is the training sequence that is added to the data. These are
samples of a digitized linear frequency modulated (LFM) signal. The LFM sequence occupies all
the sub-bands of the OFDM system with equipowered components for optimum performance in
terms of fairness and residual interference in data detection.

Here m denotes the mth row of the vector. The sequence is generalized to incorporate the
guard bands that are specified in many of the currently standardized OFDM based systems. In
this case the training sequence is given by,

Here w(k) is the frequency domain window function used to satisfy the spectral mask
requirements of the OFDM based system, if any. Here W(k) can be any spectral mask including
a rectangular function defined for 0 <_kL and L is replaced by R in the dimensions ofhandct. Here
the summation is considered for the LS estimate over TP number of OFDM symbols to consider
generalization of the LS estimate to extend the same to coherently integrate overrp symbols.
Prior art does not exploit the quasi-stationary channel to obtain improved estimates of the
channel. Also prior art makes use of computationally intensive 2D Wiener filtering to obtain the
frequency coefficients of the channel at all the subcarriers. These methods require prior
knowledge of the channel correlation functions at the receiver. In our case the N point DFT of
the sequence performs a time domain interpolation to obtain the frequency coefficients of the
channel at all the subcarriers. This method is of reduced complexity and also has negligible
performance degradation compared to the Wiener interpolator.
The received vectors are input to the DFT biock for demodulation and the frequency domain
received vector yk = Fy^ is obtained. Another characteristic of the invention is the method of
canceling the interference of the superimposed training sequences on the data. FIG. 4 in
conjunction with FIG.3 illustrates the method. The N point DFT of the channel estimate ht is
computed and multiplied with the N point DFT of the training sequence^ =Fct which is stored
at the receiver. These are then subtracted fromy^ to reduce the effect of the training on the
data.
A one tap equalizer is then employed to reverse the effects of the channel on the received data.
The interference cancelled and equalized output is given by,

Here u and H are diagonal matrices with diagonal entries being the frequency coefficients of
the channel and its estimate respectively. These are then presented to the other blocks of a
typical communication receiver like the detector, channel decoder etc for further processing.
11

Fig. 5 and Fig. 6 shows equivalent baseband transmitter and receiver respectively, with the
equivalent frequency domain representations of the time domain superimposed training
sequence at the transmitter as shown in Fig. 1 and the time domain channel estimation method
at the receiver as shown in Fig. 3. As these methods are straightforward, they are not
elaborated here for brevity.
OPTIMALITY OF THE PROPOSED TRAINING SEQUENCES
The proposed LFM sequence occupies all the used sub-bands of the OFDM system with
equipowered components for optimum performance in terms of fairness and residual
interference of the training sequence in data detection.
This condition, that is the optimality of the training sequences, is obtained by first finding a
closed form expression for the mean squared estimation error (MSEE) in the channel estimate.
This MSEE is minimized under a fixed power constraint on the training sequence and the
condition on the training sequence to minimize the MSEE is found. Then, of all sequences that
satisfy this condition sequences that minimize the BER of the OFDM system are found.
This is done by finding the expression of the BER of the OFDM system on each subcarrier. The
BER of the OFDM system then, is the mean of the BER of all the used subcarriers if the
modulation format on each subcarrier is the same. The BER is found to be affected by the
residual interference of the training symbols on the data. It is also seen that the BER of the
OFDM system is dominated by the worst case BER of the subcarriers. As a result, under a
power constraint on the training sequences, it is reasoned that the BER of the OFDM system is
minimized by fairly distributing the residual interference on all the used subcarriers.
Hence the proposed training sequence is optimal in terms of jointly minimizing the MSEE and
the BER of the OFDM system.
Advantages:
1) The proposed digitized LFM sequence jointly minimizes the channel MSEE and the BER of
the OFDM system unlike prior art which minimizes the MSEE of the channel only leading to the
proposition of training sequences that result in better BER performance than the prior art.
12

2) The channel estimation accuracy is further improved due to the averaging of the channel
estimate over the duration of the quasi-stationary channel encountered by the system compliant
to a standard with out extending the unfairness in the interference to that duration.
3) Also the estimator is of reduced complexity due to the time domain interpolation of the
channel estimate to obtain the frequency coefficients of the channel on all the used subcarriers.
Testing:
1) Performance over Mobile WiMaX channels: The performance of the proposed channel
estimation scheme with the proposed optimal superimposed training sequence ck(n) as in (2) is
shown in Fig.7 over channels typically encountered in the Mobile WiMaX environments. The ITU
Vehicular Channel A is used and also the Stanford University Interim (SUI) channels. The SUI
channels are typically specified for fixed broadband wireless access, but these channels are
modified to incorporate mobility by replacing the Doppler filter in the specifications. A mobility of
120 km/hr leads to a coherence time of approximately 0.003s resulting in around 29 OFDM
symbols experiencing the same fading coefficients. The data takes the format of the IEEE
802.16-2004, Wireless MAN OFDM PHY layer standard. The only difference is that instead of
using the 8 pilots allocated at certain subcarriers, the data is allowed to be transmitted at all the
useful subcarriers. Symbol spaced channel coefficients were generated from the multipath
spaced channel coefficients using an FIR interpolation with a Gaussian function whose variance
was normalized by the rms delay spread of the channel. The sample spaced power delay
profile is
Here, Pt and r, are the power and the delay respectively, associated with the ith path,
is the rms delay spread of the channel.
Table 1 gives simulation parameters used for the channels Modified SUI-1, Modified SUI-2 and
ITU Vehicular Channel A with rms delay spreads 0.0903/«, 0.1032//.? and 0.364us
respectively. It is seen Fig. 7 that as the rms delay spread of the channel increases, the BER
keeps increasing.
13

Table 1
Sym Simulation \/o|i loc
bol Parameters V dlUco
f. Center 3 GHz
frequency
BW Channel 5MHz
Bandwidth
f. Signal 5.76
sampling rate MHz
Maximum 333 Hz
Doppler
frequency
CP Cyclic Prefix 8
samples
Q Order of the 8
estimator samples
T, Number of 29
OFDM symbols
symbols used
for channel
estimation
2) Performance comparison: In this simulation, a block frequency selective fading channel
model with Q = 8 and Tp = 4 (definitions as in Table 1), is used to compare the performance of
the training sequences proposed in the prior art.
Each channel realization is drawn from a zero mean complex Gaussian process with the
variance in each path normalized to follow an exponentially decaying power delay profile. The
MSEE and BER were averaged over 500 Monte Carlo iterations. As discussed earlier, the
MSEE of these two sequences as seen in Fig. 8 are the same but the BER performance with
c,O)is better in the high SNR regime as observed in Fig. 9. Hencec,(«) is the optimal training
sequence in terms of jointly minimizing the BER and the MSEE for OFDM systems employing
superimposed training because it ensures a fair distribution of the interference due to the
training on the data on all the subcarriers.
3) Comparison of the digitized LFM sequence with a PN sequence.
The performance of the proposed training sequence c,(«) with a PN sequence which is
commonly used as a training sequence for channel estimation in single carrier systems is
14

compared. The PN sequence is periodic with period N, denoted by P1(n). This is generated by
an N-1 length maximum length PN sequence and appended by -1. Each value may be
multiplied by a complex scale factor. It is seen that c1,(n) has a more even distribution of energy
in all the subcarriers as compared to P1(n) as shown in Fig. 10, thus being more suitable for
15
superimposed training based OFDM systems. Therefore this method provides a better fairness
than the prior art in terms of residual interference in the different subcarriers.

FIELD OF THE INVENTION
The present invention relates to multicarrier communication systems. More particularly, the
invention relates to a method and system for minimizing means square estimation error (MSEE)
and bit error rate during channel estimation and equalization in orthogonal frequency division
multiplexing (OFDM) systems.
BACKGROUND AND THE PRIOR ART
Orthogonal frequency division multiplexing (OFDM) is a multi-carrier communication scheme in
which, data at a high rate is divided into sub-streams and transmitted over orthogonal carriers,
thus enabling data transmission over a frequency selective fading channel, in a bandwidth
efficient manner.
Channel estimation is an important constituent of coherent OFDM receivers. Guard intervals are
inserted between adjacent OFDM block symbols, to take care of Inter Block Interference (IBI).
Transmitting a Cyclic Prefix (CP) of the data during this interval makes the channel circularly
convolutive, simplifying the channel equalization problem. Specifically, channel equalization in
the frequency domain can be done using one tap filters. This is because the CP makes the
channel matrix circulant, which is diagonalized by the inverse discrete Fourier transform (IDFT)
and DFT operations. The challenge in frequency domain channel equalization lies in estimating
the channel frequency coefficients at all the subcarriers.
In conventional OFDM systems, channel estimation is done using pilot tones along with data. In
slow fading environments, channel estimation can be done by inserting pilot tones into all of the
subcarriers of the OFDM symbol with a specific period during which the channel is assumed to
be quasi-static. In fast fading environments pilot tones are inserted at specific subcarriers in
each OFDM symbol. The channel frequency coefficients at the data tones are then determined
by interpolation based approximations resulting in channel estimation errors, which could be
significant in a frequency selective fading channel. Also, pilot tone insertion reduces the
bandwidth efficiency of the system. The need for higher data rates and mobility only aggravates
the problem. This motivates the need for blind estimators which exploits the statistics of the
transmitted data, or some redundancy in the transmitted data to estimate the channel without
2

employing pilots. Traditionally blind estimators have been found to have a slow convergence
time and also there is a possibility of convergence of the performance surface to a local
minimum. Semi-blind equalization allows for a trade-off between performance and bandwidth
efficiency by making use of blind as well as pilot assisted techniques.
"Channel estimation using implicit training," IEEE Transactions on Signal Processing, vol. 52,
no. 1, January 2004 by A.G. Orozco-Lugo, M. Lara, D. McLernon discloses a new method to
perform channel estimation. It is shown that accurate estimation can be obtained when a
training sequence is actually arithmetically added to the information data as opposed to being
placed in a separate empty time slot.
Article "Superimposed Training for OFDM: a peak-to-average power ratio analysis," IEEE
Transactions on Signal Processing, vol. 54, no. 6, pp. 2277- 2287, June 2006 by N. Chen and
G.T. Zhou describes an orthogonal frequency division multiplexing (OFDM) transmission with
superimposed training. The PAR of the OFDM signal is examined with superimposed training,
and its complementary cumulative distribution function (CCDF) is derived. Achievable lower and
upper bounds on the CCDF are also determined. In addition, the PAR change is linked to the
effective signal-to-noise ratio (SNR) and thus the bit-error-rate (BER) performance under the
fixed dc power constraint.
Article Proceedings of the IEEE-GLOBECOM, vol.2, no. 2, pp. 878-882, Dec. 2003 by N.
Ohkubo and T. Ohtsuki teaches added pilot semi-blind channel estimation for OFDM packet
transmission.
ETRI Journal, vol.28, no. 5, pp. 688-691, Oct. 2006 by Q. Yang and K. S. Kwak teaches "Time-
varying multipath channel estimation with superimposed training in CP-OFDM systems". A
time-domain channel estimation scheme for time-varying multipath channels is developed by
using superimposed sequences. The idea behind this scheme is to split the one-OFDM-symbol-
period time-domain channel into equi-spaced time-slotted subchannels, so that the time
variation for each subchannel can be assumed to be negligible;then, each subchannel is
estimated by a linear least square (LS) estimator.
Article Proceedings of the IEEE-GLOBECOM, Missouri, USA, December 2005, pp. 2229-2233T
by Cui and C. Tellambura discloses "Superimposed pilot symbols for channel estimation in
OFDM systems". Article Proceedings of the IEEE-GLOBECOM, Texas, USA, November 2001,
3075-3079 by C. K. Ho, B. Farhang-Boroujeny and F. Chin discloses "Added pilot semi-blind
3

channel estimation scheme for OFDM in fading channels". Article IEEE Communications
Letters, vol. 7, no. 1, pp. 30-32,January 2003 by H. Zhu, B. Farhang-Boroujeny and C. Schlegel
teahces "Pilot embedding for joint channel estimation and data detection in MIMO
communication systems". Further the article Proceedings of the IEEE-GLOBECOM, Dallas,
USA, November 2004, pp. 1244-1248 by S. Balasubramanian, B. Farhang-Boroujeny and V.
John Mathews describes "Pilot embedding for channel estimation and tracking in OFDM
systems".
United States Patent US 6990153 B1 describes a channel estimation scheme that provides
good performance in a communication channel having varying frequency and time
characteristics, while preserving the usable bandwidth of the communication channel.
There is a need for bandwidth efficient channel estimation techniques for OFDM with good
performance. Recently, superimposed training (ST) based channel estimation techniques have
been proposed. In this scheme, training symbols known to the receiver are algebraically added
on to the data at a low power, thus avoiding the need for additional time slots for training. At the
receiver these known symbols, in the presence of unknown data and noise, are exploited for
channel estimation. These methods for channel estimation are attractive compared to pilot
assisted techniques as they are bandwidth efficient. ST based methods for channel estimation
in OFDM have been considered in the literature, the focus being on iterative source channel
estimation techniques, the optimality criteria for the training sequences and peak to average
power (PAPR) analysis.
The state of the art however, leaves many critical issues unanswered. Iterative channel
estimation techniques to get improved accuracy and also to cancel the interference of the data
on the estimate are used. However the initial LS channel estimate used in the first iteration does
not exploit the nature of the block frequency selective fading channel that occurs in practice.
The ST sequence used for channel estimation plays a pivotal role in system performance. The
cost function that is used to characterize the optimal training sequences is the minimization of
the mean square estimation error (MSEE) or the Cramer-Rao lower bound (CRLB). These are
also the optimization criteria generally used for pilot assisted techniques which is reasonable
because in this case the training is separated from the data. However, in the superimposed
training scheme both of these criteria result in characterizations that does not take into account
the interference of the training sequences on the data detection. Moreover the training
sequences used in the existing art will not be applicable in currently standardized wireless
4

OFDM systems because of the existence of frequency components at the band edges which
are generally used in the brick wall shaping of the transmit spectrum. It was not known in the
prior art that the number of OFDM symbols experiencing the same channel may be used to
improve the channel estimation accuracy by averaging over several symbols depending on the
coherence time of the channel and/or the desired estimation accuracy. Hence the number of
OFDM symbols averaged to estimate the channel impulse response making it suitable to the
characteristics of the channel encountered in different standards by the superimposed training
based OFDM system was not in the prior art.
Thus there is a need to provide for a system and method for minimizing the means square
estimation error (MSEE) and bit error rate during channel estimation and equalization in
orthogonal frequency division multiplexing (OFDM) systems.
Thus in a quest for obtaining an optimal equalizer, the present inventors have got a new idea
and found that channel MSEE and the BER can be jointly minimized thereby arrived at a
digitized linear frequency modulation (LFM) based optimal training sequence that fairly
distributes the interference due to the training on the data on all the used sub-carriers for
superimposed training based OFDM systems and further introduced averaging of the channel
estimates beyond one OFDM symbol so as to obtain an improved channel estimation from
OFDM symbols experiencing the same fading coefficients. This improves channel estimation in
OFDM systems without using additional bandwidth for the purpose of channel estimation and
equalization.
OBJECTS OF THE INVENTION
Accordingly one object of the present invention is to address the shortcomings/disadvantages of
the prior art.
Another one object of the present invention there is provided a system for minimizing means
square estimation error (MSEE) and bit error rate during channel estimation and equalization in
superimposed training based orthogonal frequency division multiplexing (OFDM) systems
without using additional bandwidth for the purpose of channel estimation and equalization.
5

Another object of the present invention is to provide a method for minimizing means square
estimation error (MSEE) and bit error rate during channel estimation and equalization in
superimposed training based orthogonal frequency division multiplexing (OFDM) systems.
SUMMARY OF THE INVENTION
Thus according to one aspect of the present invention there is provided a method for minimizing
means square estimation error (MSEE) and bit error rate during channel estimation and
equalization in orthogonal frequency division multiplexing (OFDM) systems, said method
comprising:
receiving superimposed training based OFDM signals without guard interval as an input,
cross-correlating said received OFDM signal to a specific lag determined by the rms delay
spread of the channel, with a specific known training sequence stored in a register, and which is
also the sequence that is added to the data at the transmitter in the time domain having a
prescribed pilot to data power ratio,
wherein the said cross-correlated data being averaged over a length of samples depending on
the coherence time of the channel and processed along with the stored values of the inverse of
autocorrelation values of superimposed training (ST) sequence so as to obtain a reliable least
squares based channel estimate.
According to another aspect of the present invention there is provided a system for minimizing
means square estimation error (MSEE) and bit error rate during channel estimation and
equalization in orthogonal frequency division multiplexing (OFDM) systems, said system
comprising:
receiver means for receiving superimposed training based OFDM signals without guard interval
as input;
wherein said receiver means comprises means for cross-correlating said received OFDM signal
to a specific lag determined by the rms delay spread of the channel, with a specific known
training sequence stored in the receiver means, and which is also the sequence that is added to
the data at the transmitter in the time domain having a prescribed pilot to data power ratio,
wherein the correlated data being averaged over a length of samples depending on the
coherence time of the channel and processed along with the stored values of the inverse of
6

autocorrelation values of superimposed training (ST) sequence so as to obtain a reliable least
squares based channel estimate.
Further, the embodiment comprises of an interference canceller to reduce the effect of the
superimposed training sequences on the data, which multiplies the DFT of the specific training
sequence with the frequency coefficients of the channel estimate and subtracts these signals
from the DFT of the received signals.
Another very important characteristic of the invention is the use of a training sequence for the
above channel estimation method that is stored in a register in the channel estimator module in
the receiver, and which is also the sequence that is added to the data at the transmitter, that are
samples of a digitized linear frequency modulated (LFM) signal having uniform energy
components in all the subcarriers of the OFDM symbol, which are shaped by the virtual
subcarriers according to specifications of the standard to which the OFDM based system
complies. This sequence is optimal in terms of minimizing the bit error rate (BER) of the OFDM
system in addition to minimizing the MSEE. Approximations of the LFM may be used with an
associated loss in performance.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of the equivalent baseband transmitter of the superimposed training
based OFDM system.
FIG. 2 is a block diagram of the equivalent baseband channel encountered in a typical
superimposed training based OFDM system.
FIG. 3 is a block diagram of the equivalent baseband receiver of the superimposed training
based OFDM system.
FIG. 4 is a representation of the channel equalizer and canceling of interference due to the
training sequence used in the receiver of the superimposed training based OFDM system.
7

FIG. 5 is an alternative representation of the transmitter as in Fig.1, wherein the DFT of the
training sequence is added to the data in the frequency domain at a particular pilot to data
power ratio.
Fig. 6 is an alternative representation of the receiver as in Fig. 3, wherein the frequency domain
equivalent of the time domain channel estimation method is carried out.
Fig.7. is BER vs. SNR graph for the Modified SUM, SUI2 and ITU Vehicular Channel Model A
with the simulation parameters of Table.1, using the training sequencec,(«).
Fig.8. is MSEE vs. SNR graph showing comparison between the training sequencesc,(«)
andc». Here N = 512, Q = 8, TP = 2, and the exponential power delay profile used was

Fig.9. is BER vs. SNR graph showing comparison between the training sequencesc,(«) andc2(«).
Here N = 512, Q = 8, Tp =2, and the exponential power delay profile used was e',/ = {0,i,..g-i}
Fig.10. is a comparison of the magnitude spectrum of c» and/?,(«). /?,(«) loses its spectral
flatness because of appending an additional -1 to the m-length PN sequence having a period
of Aw.
DETAILED DESCRIPTION OF THE INVENTION
Fig. 1 is the block diagram of the transmitter of a superimposed training based OFDM system.
Although not necessary, perfect synchronization is assumed here for illustration. Binary data is
grouped into symbols depending on the level of QAM modulation used. Vectors sk of such
symbols are formed which are then passed to the IDFT block. Here k stands for the OFDM
symbol index. Some of the entries are zeros to serve the spectral mask requirements of the
OFDM system. The output of the IDFT block is whereFis the normalized NxN DFT
matrix with and F" is the complex conjugate transpose. Here (m,n) is used
to denote the mth row and nth column of the matrix. A parallel to serial converter serially outputs
the simultaneous IDFT outputs. A training sequence ck is then algebraically added to this IDFT
output with a specific low pilot to data power ratio to get,

8

A characteristic of the invention is the training sequence that is added to the data. These are
samples of a digitized linear frequency modulated (LFM) signal. The LFM sequence occupies all
the sub-bands of the OFDM system with equipowered components for optimum performance in
terms of fairness and residual interference in data detection.

Here m denotes the mth row of the vector. The sequence is generalized to incorporate the
guard bands that are specified in many of the currently standardized OFDM based systems. In
this case the training sequence is given by,

Here w(k) is the frequency domain window function used to satisfy the spectral mask
requirements of the OFDM based system, if any. Here W(k) can be any spectral mask including
a rectangular function defined for 0 <_kL and L is replaced by R in the dimensions ofhandct. Here
the summation is considered for the LS estimate over TP number of OFDM symbols to consider
generalization of the LS estimate to extend the same to coherently integrate overrp symbols.
Prior art does not exploit the quasi-stationary channel to obtain improved estimates of the
channel. Also prior art makes use of computationally intensive 2D Wiener filtering to obtain the
frequency coefficients of the channel at all the subcarriers. These methods require prior
knowledge of the channel correlation functions at the receiver. In our case the N point DFT of
the sequence performs a time domain interpolation to obtain the frequency coefficients of the
channel at all the subcarriers. This method is of reduced complexity and also has negligible
performance degradation compared to the Wiener interpolator.
The received vectors are input to the DFT biock for demodulation and the frequency domain
received vector yk = Fy^ is obtained. Another characteristic of the invention is the method of
canceling the interference of the superimposed training sequences on the data. FIG. 4 in
conjunction with FIG.3 illustrates the method. The N point DFT of the channel estimate ht is
computed and multiplied with the N point DFT of the training sequence^ =Fct which is stored
at the receiver. These are then subtracted fromy^ to reduce the effect of the training on the
data.
A one tap equalizer is then employed to reverse the effects of the channel on the received data.
The interference cancelled and equalized output is given by,

Here u and H are diagonal matrices with diagonal entries being the frequency coefficients of
the channel and its estimate respectively. These are then presented to the other blocks of a
typical communication receiver like the detector, channel decoder etc for further processing.
11

Fig. 5 and Fig. 6 shows equivalent baseband transmitter and receiver respectively, with the
equivalent frequency domain representations of the time domain superimposed training
sequence at the transmitter as shown in Fig. 1 and the time domain channel estimation method
at the receiver as shown in Fig. 3. As these methods are straightforward, they are not
elaborated here for brevity.
OPTIMALITY OF THE PROPOSED TRAINING SEQUENCES
The proposed LFM sequence occupies all the used sub-bands of the OFDM system with
equipowered components for optimum performance in terms of fairness and residual
interference of the training sequence in data detection.
This condition, that is the optimality of the training sequences, is obtained by first finding a
closed form expression for the mean squared estimation error (MSEE) in the channel estimate.
This MSEE is minimized under a fixed power constraint on the training sequence and the
condition on the training sequence to minimize the MSEE is found. Then, of all sequences that
satisfy this condition sequences that minimize the BER of the OFDM system are found.
This is done by finding the expression of the BER of the OFDM system on each subcarrier. The
BER of the OFDM system then, is the mean of the BER of all the used subcarriers if the
modulation format on each subcarrier is the same. The BER is found to be affected by the
residual interference of the training symbols on the data. It is also seen that the BER of the
OFDM system is dominated by the worst case BER of the subcarriers. As a result, under a
power constraint on the training sequences, it is reasoned that the BER of the OFDM system is
minimized by fairly distributing the residual interference on all the used subcarriers.
Hence the proposed training sequence is optimal in terms of jointly minimizing the MSEE and
the BER of the OFDM system.
Advantages:
1) The proposed digitized LFM sequence jointly minimizes the channel MSEE and the BER of
the OFDM system unlike prior art which minimizes the MSEE of the channel only leading to the
proposition of training sequences that result in better BER performance than the prior art.
12

2) The channel estimation accuracy is further improved due to the averaging of the channel
estimate over the duration of the quasi-stationary channel encountered by the system compliant
to a standard with out extending the unfairness in the interference to that duration.
3) Also the estimator is of reduced complexity due to the time domain interpolation of the
channel estimate to obtain the frequency coefficients of the channel on all the used subcarriers.
Testing:
1) Performance over Mobile WiMaX channels: The performance of the proposed channel
estimation scheme with the proposed optimal superimposed training sequence ck(n) as in (2) is
shown in Fig.7 over channels typically encountered in the Mobile WiMaX environments. The ITU
Vehicular Channel A is used and also the Stanford University Interim (SUI) channels. The SUI
channels are typically specified for fixed broadband wireless access, but these channels are
modified to incorporate mobility by replacing the Doppler filter in the specifications. A mobility of
120 km/hr leads to a coherence time of approximately 0.003s resulting in around 29 OFDM
symbols experiencing the same fading coefficients. The data takes the format of the IEEE
802.16-2004, Wireless MAN OFDM PHY layer standard. The only difference is that instead of
using the 8 pilots allocated at certain subcarriers, the data is allowed to be transmitted at all the
useful subcarriers. Symbol spaced channel coefficients were generated from the multipath
spaced channel coefficients using an FIR interpolation with a Gaussian function whose variance
was normalized by the rms delay spread of the channel. The sample spaced power delay
profile is
Here, Pt and r, are the power and the delay respectively, associated with the ith path,
is the rms delay spread of the channel.
Table 1 gives simulation parameters used for the channels Modified SUI-1, Modified SUI-2 and
ITU Vehicular Channel A with rms delay spreads 0.0903/«, 0.1032//.? and 0.364us
respectively. It is seen Fig. 7 that as the rms delay spread of the channel increases, the BER
keeps increasing.
13

Table 1
Sym Simulation \/o|i loc
bol Parameters V dlUco
f. Center 3 GHz
frequency
BW Channel 5MHz
Bandwidth
f. Signal 5.76
sampling rate MHz
Maximum 333 Hz
Doppler
frequency
CP Cyclic Prefix 8
samples
Q Order of the 8
estimator samples
T, Number of 29
OFDM symbols
symbols used
for channel
estimation
2) Performance comparison: In this simulation, a block frequency selective fading channel
model with Q = 8 and Tp = 4 (definitions as in Table 1), is used to compare the performance of
the training sequences proposed in the prior art.
Each channel realization is drawn from a zero mean complex Gaussian process with the
variance in each path normalized to follow an exponentially decaying power delay profile. The
MSEE and BER were averaged over 500 Monte Carlo iterations. As discussed earlier, the
MSEE of these two sequences as seen in Fig. 8 are the same but the BER performance with
c,O)is better in the high SNR regime as observed in Fig. 9. Hencec,(«) is the optimal training
sequence in terms of jointly minimizing the BER and the MSEE for OFDM systems employing
superimposed training because it ensures a fair distribution of the interference due to the
training on the data on all the subcarriers.
3) Comparison of the digitized LFM sequence with a PN sequence.
The performance of the proposed training sequence c,(«) with a PN sequence which is
commonly used as a training sequence for channel estimation in single carrier systems is
14
compared. The PN sequence is periodic with period N, denoted by P1(n). This is generated by
an N-1 length maximum length PN sequence and appended by -1. Each value may be
multiplied by a complex scale factor. It is seen that c1,(n) has a more even distribution of energy
in all the subcarriers as compared to P1(n) as shown in Fig. 10, thus being more suitable for
15
superimposed training based OFDM systems. Therefore this method provides a better fairness
than the prior art in terms of residual interference in the different subcarriers.

The present invention relates to a method for minimizing means square estimation error (MSEE) and bit error rate during channel estimation and equalization between a transmitter and a receiver of an orthogonal frequency division multiplexing (OFDM) systems. The method comprises transmitting from said transmitter to said receiver a training sequence for channel
estimation being superimposed onto data at specific pilot to data power ratio (PDPR), receiving the OFDM signals along with the training sequence as an input, cross-correlating said received signal to a specific lag determined by the rms delay spread of the channel, with a specific known training sequence stored in a register, and which is also the sequence that is added to the data
at the transmitter in the time domain having a prescribed pilot to data power ratio,. The cross-correlated data being processed over a length of samples which can be extended to exploit the coherence time of the channel and processed along with the stored values of the inverse of autocorrelation values of superimposed training (ST) sequence so as to obtain a reliable least
squares based channel estimate in a way the PDPR is limited or otherwise. The invention also relates to a system comprising means for computing a time domain least squares (LS) based channel estimate at the receiver.