FIELD OF INVENTION
The invention relates to a method and system for carrier frequency offset
estimation and correction in wireless communication systems based on Multi-
input Multi - output orthogonal Frequency Division multiplexing (MIMO-OFDM)
technique.
BACKGROUND OF INVENTION
Orthogonal Frequency Division Multiplexing (OFDM), is one of the underlying
technology in MIMO-OFDM. A multicarrier communication system based on
OFDM, converts a high data rate stream into a group of parallel low data rate
streams which change the frequency selective fading situation encountered in a
wireless channel to tractable flat fading scenario. Digital communications using
multiple input multiple output (MIMO) wireless links has recently emerged as one
of the most promising technology in wireless communications . The core idea of
MIMO systems is space-time signal processing in which time is complemented
with a spatial dimension which is inherent in the use of multiple spatially
distributed antennas. Such a signal processing, results in diversity gain or
multiplexing gain or both. A combination explored, to further enhance the
bandwidth efficiency and throughput performance, is MIMO-OFDM. Here OFDM
is used to convert the frequency selective channel in the conventional MIMO
systems into a set of parallel frequency flat channels. Space-time coding is then
applied to a group of tones in an OFDM symbol or on a per tone basis across the
OFDM symbols.

While MIMO-OFDM is robust to frequency selective fading, it is very sensitive to
frequency offset caused by Doppler shifts and/or oscillator instabilities like the
conventional OFDM systems. The presence of carrier frequency offset (CFO) will
introduce severe inter-carrier interference (ICI), which, if not properly
compensated, would result in loss of orthogonality and significantly degrade the
system performance. The current demand for low-cost receivers make the design
of frequency synchronization block more challenging as the order of frequency
offsets need to estimate and correct would be in the range of a few multiples of
subcarrier spacing. On the other hand, the receiver complexity and the training
overhead have to be kept at a minimum level.
Many techniques are found in state of the arts which deal with carrier frequency
offset estimation in conventional single input single output (SISO) OFDM
systems. For example, Schmidl-Cox algorithm employs two training OFDM
symbols to achieve an overall frequency estimation range of two subcarrier
spacings. A modified forms of Schmidl-Cox algorithm is proposed in where one
training symbol with P identical subparts in time domain are used to yield an
estimation range of +/- P/2 subcarrier spacings. There is a class of carrier
frequency offset estimators which use either the intrinsic virtual carriers present
in some of the OFDM based wireless communication standards or deliberately
introduced null subcarriers in between the data carriers. They estimate the
frequency offset by employing a cost function which minimize the total null
subcarrier energy with the help of a global search technique. Liu and Tureli
proposed a subspace based frequency offset estimation approach using
consecutively placed virtual carriers at the band edges of the OFDM symbol. Ma
et al. suggested the use of distributed null subcarriers, to minimize the

estimation errors associated with the use of consecutively virtual subcarriers
proposed in. Recently a null subcarrier based method is proposed which uses
one complete OFDM symbol with all odd subcarriers and most of the even
subcarriers as null subcarriers which are allocated based on an extended PN
sequence.
But only a few methods are available which exclusively address the CFO
estimation in MIMO-OFDM systems. There are various shortcomings in the state
of the art methods. Training preamble based frequency offset estimation
methods are proposed, which are extensions of similar techniques reported for
SISO-OFDM like. These techniques need large bandwidth overheads in order to
send specific training sequences or pilot signals. A few other methods exist
which aim at reducing the training overhead but the number of computations
required for estimating the CFO are very high. Higher computations amounts to
higher cost and/ or higher latency and both are undesirable properties. Another
performance measure of CFO estimation algorithms is the range of frequency
offset that they can provide. While the maximum frequency offset estimation
range is equal to the OFDM bandwidth, all of the training preamble based
estimation techniques provide at the most l/8th or 1/4th of it only. On the
contrary, methods which offer very high estimation range are computationally
inefficient. In view of the growing popularity, efficient techniques for the CFO
estimation with excellent performances are needed for practical MIMO -OFDM
system implementations.

OBJECTS OF THE INVENTION
It is therefore an object of the invention to propose a system for estimation and
correction of carrier frequency offset in wireless communications systems based
on MIMO-OFDM technique.
Another object of the invention is to propose a system for estimation and
correction of carrier frequency offset in wireless communications systems based
on MIMO-OFDM technique, which can be adapted in all the space -time coding
logic used with MIMO-OFDM systems for CFO estimation.
A still another object of the invention is to propose a method for estimation and
correction of carrier frequency offset (CFO) in MIMO-OFDM based wireless
communication systems.
Yet another object of the invention is to propose a method for estimation and
correction of carrier frequency offset (CFO) in MIMO-OFDM based wireless
communication systems, in which the computational complexities and training
overhead requirement is substantially low.
A further object of the invention is to propose a method for estimation and
correction of carrier frequency offset (CFO) in MIMO-OFDM based wireless
communication systems, which eliminates the requirement of MIMO-channel
estimation to arrive at the CFO - estimation.

A still further object of the invention is to propose a method for estimation and
correction of carrier frequency offset (CFO) in MIMO-OFDM based wireless
communication systems, which is adaptable to the conventional OFDM systems
too.
Yet further object of the invention is to propose a method for estimation and
correction of carrier frequency offset (CFO) in MIMO-OFDM based wireless
communication systems, which implements a Fibonaci series based null
subcarrier allocation logic thereby ensuring a CFO - estimation range equal to
OFDM bandwith.
SUMMARY OF INVENTION
In order to address the limitations of the prior art, a null subcarrier based CFO
estimation technique for MIMO-OFDM is provided which is efficient in terms of
bandwidth overhead and computational complexity. The invention further
provides a Fibonacci series based logic for allocating null subcarriers in the
training OFDM symbols on each of the transmitting antennas, which ensures full
frequency offset acquisition range equal to the OFDM bandwidth, without any
ambiguity.
A preferred embodiment of the inventive system comprises a MIMO-OFDM
transmitter with Nt transmit antennas where the number of transmit antennas
are decided by the order of space-time encoding scheme used, with each
transmit branch processes a block of space-time data coming from a space-time
encoder and each of these frequency domain blocks of size N samples are

transformed in to time domain signals by separate N point IDFTs and copy the
last L samples on each branch to the beginning of the time domain OFDM
symbols and such signals from all the transmit branches are further processed
to meet the RF requirements and transmitted. Such K number of OFDM symbols
is commonly denoted as an OFDM frame with the first OFDM symbol in the
frame on each transmit antennas denoted as beacon symbols are specially
generated by imposing specific subcarriers as null subcarriers before the IDFT
operation, whose locations are specified by a modified Fibonacci sequence so as
to help estimation of carrier frequency offset at the receiver and the remaining
subcarriers in the beacon symbol are used for useful data transmission along
with other OFDM symbols in the frame thus resulting in enhanced bandwidth
efficiency.
The system comprises a receiver with Nr receive antennas where each receive
antenna receive the superposition of signals transmitted by all the transmitting
antennas with multipath distortions and with a possible timing and carrier
frequency offset where the frequency offset can be fractions or multiples of
subcarrier spacings of used in the OFDM symbols. By assuming a perfect timing
correction, the cyclic prefix associated with OFDM symbols received on all
transmit antennas are removed and the covariance matrix of this signal is
computed on each receiving antenna and the individual covariance matrices on
all receive branches are combined using maximal ratio combining (MRC) or
equal gain combining (EGC). The carrier frequency offset, which is assumed to
be the same for the signals received on all receive branches which is a fare
assumption as transmit and receive branches usually use same oscillators for all
the branches, is estimated by a two stage cost function minimization in which

the first stage minimization yield the integer frequency estimate by calculating
the total energy spilled on the null subcarrier locations due to the frequency
offset by a search procedure, which is essentially a post DFT operation where
the energy at the DFT output corresponding to the null subcarriers is computed
for each integer shifts from -N/2 to +N/2 and by finding the integer shift which
yield the minimum energy and once this is found , a correction for the same is
applied by multiplying the received signal samples with the complex conjugate
of the estimated integer frequency offset and by assuming that the integer
frequency offset is perfectly compensated for, a second step can be initiated to
estimate the fractional frequency offset by minimizing the same cost function
but now with a co-variance matrix which is obtained after integer frequency
offset correction, by minimizing it over a fixed number of fractional values from
-1 to +1, where the number of such minimization points are decided by the
resolution required for the fractional estimation, where the minimization
procedure is same as the one used for integer frequency offset estimation and
thereby the fractional frequency offset can be estimated and upon estimation it
can be compensated for, before proceeding for rest of the receiver processing.
A special characteristic of the invention is the use of a modified Fibonacci series
based null subcarrier allocation logic which ensures a CFO estimation range
equal to the OFDM bandwidth, which is the maximum CFO that any MIMO-
OFDM communication system can experience.

BRIEF DESCRIPTION OF THE ACOMPANYING DRAWINGS
FIG. 1 is a block diagram of the baseband transmitter of the proposed Null
subcarrier based MIMO-OFDM system corresponding to the training block.
FIG. 2 is a block diagram of the generalized receiver of the null subcarrier based
MIMO-OFDM system for the training block, showing the usual receiver
processing.
FIG. 3 is a flowchart of the method of estimating the integer frequency offset
from the received beacon symbol after combining all the received signals on all
receiving antennas.
FIG. 4 is a flowchart of the method of correcting the integer frequency offset
experienced by the received signals.
FIG. 5 is flowchart of the method of estimating the fractional frequency offset
from the received beacon symbol after correcting the integer frequency offset.
Fig. 6 is a flowchart of the method of correcting the fractional frequency offset
experienced by the received integer frequency offset corrected signals.

DETAILED DESCRIPTION OF THE INVENTION
Figure 1 represents the block diagram of a generalized MIMO-OFDM transmitter
corresponding to the transmission of the beacon symbol which consists of a
specific sequence of null subcarriers. Each transmitter branch receives complex
block of data from a space-time encoder with a block size of N samples as the
underlying OFDM modulation uses N subcarriers spaced at a separation
F = B/N, where B is the total system bandwidth. Out of the total N subcarriers
in the beacon symbol, R subcarriers are data carriers and the remaining N-R
subcarriers are null subcarriers (Z). These selected subcarriers are imposed as
nulls by employing a special permutation matrix. Each OFDM block is preceded
by a cyclic prefix whose duration is longer than the delay spread of the
propagation channel, so that inter-block interference can be eliminated at the
receiver, without affecting the orthogonality of the sub-carriers. Signals in all Nt
transmit branches are processed in the same way and then transmitted after the
required RF Processing.
The transmitted signals from each transmit antenna is given by

wheren = -L,..,0,..N-1 , dk is the data symbol at the k-th subcarrier, Γd is the
set of indices of the data subcarriers and L is the length of the cyclic prefix.
A general block schematic of the OFDM receiver corresponding to the beacon
symbol is shown in Fig. 2. The signals received on all receive antennas will be a
superposition of all the transmitted signals, which in general are impaired by a

common carrier frequency offset of the order of a few subcarrier spacing due to
oscillator mismatches and/or Doppler frequency shifts and a time shift. The
received signal will also have the usual impairments due to complex additive
white Gaussian noise and multipath channels. The timing offset, sampling
frequency offset, carrier frequency offset and multipath channel impairments are
corrected before space-time decoding. The present embodiment assumes that
the timing and sampling frequency offset are perfectly compensated. Hence the
received signals on the ith receive antennas is given by

where, Hi,J(k)is the channel frequency response at the k-th subcarrier between
ith transmit antenna and jth receive antenna, is the normalized (to the
subcarrier spacing) frequency offset, which is the sum of integer frequency offset
(between -N/2 to + N/2) and fractional frequency offset between -1 to +1, and
zt(n)is complex AWGN for the ith receiver.
Figure 3 is a flow chart of the method of estimating the integer frequency offset
wherein the signals received on all receiving antennas are combined using any of
the diversity combining techniques and applied to the integer frequency offset
estimation unit. The cyclic prefix associated with the received OFDM signal is
removed and applied to the DFT unit which converts the signal to the frequency
domain by an N-point DFT operation and the energy of the all the subcarriers at
the DFT output are computed. Next the total energy of subcarriers corresponding
to the designated null subcarrier indices are computed by introducing cyclic shifts

from 0 to N-1, and stored against the corresponding integer shift introduced.
Thus an N element array containing the energies is obtained and a search is
carried to find out the minimum energy and the corresponding integer shift,
which is designated as the integer frequency offset estimate. Alternatively this
process can be expressed by means of a cost function as
After removing the CP, combined received signal can be written in vector
notation as

where

is a diagonal matrix containing the integer

frequency offsets experienced by each samples. W is an NxNd FFT matrix,

Hd with H representing the channel matrix


and, a cost function that is to be
Using the log-likelihood function for


minimized can be expressed as
where vr is the r-th column of the FFT matrix and Γz represents set containing
the null subcarrier indices. The integer frequency offset is estimated by a search
technique by initializing P each time with the trail integer offset value. If P is the
actual frequency offset estimate, the cost function will reach a minimum.
Figure 4 is a flowchart showing a method of correcting the integer frequency
offset where the the offset vector which is the diagonal element of matrix P is
generated with the complex conjugate of the estimated frequency offset and

point to point amultiplied with the received cyclic prefix removed signal block of
size N so as to counter rotate the samples of the received signal by the same
amount of angular rotation experienced due to the integer frequency offset.
Figure 5 is a flowchart of the method of estimating the fractional frequency
offset wherein the integer frequency offset corrected signal is point to point
multiplied with frequency offset vector corresponding to the trail value where the
trail values are selected between -1 and +1, according to the resolution
requirements of the fractional frequency offset estimation and after the said
multiplication, the DFT is performed and the total energy corresponding to the
designated null subcarriers are found and stored in a register along with the trail
value used for generating the frequency offset vector and this process is
repeated till the trial values are completed and then a search is conducted to find
out the trail value which yield the minimum null subcarrier energy and the said
trail value is designated as the estimated fractional frequency offset. The
fractional frequency offset estimation can also depicted using Eq. (4) by
initializing the matrix P with the trail values used for fractional frequency offset
estimation.
Figure 6 is a flowchart of the method of correcting the fractional frequency offset
where the integer frequency corrected signal samples are point to point
multiplied with the frequency offset vector which is the diagonal element of the
matrix P by initializing it with the estimated fractional frequency offset and
thereby obtain the CFO compensated received signal.

A preferred embodiment of the invention described through Figs. 1 to 6 with
one transmit antenna instead of Nt transmit antennas and with one or more
receive antennas can be applied to the carrier frequency offset estimation of
related downsized systems described as a single input single output orthogonal
frequency division multiplexing (SISO-OFDM) or single input multi output
orthogonal frequency division multiplexing (SIMO-OFDM) and the same null
subcarrier allocation technique based on Fibonacci series can be applied to the
above said systems as well.
Fibonacci series based Null Subcarrier Allocation
The null subcarrier allocation in the beacon symbol is extremely important for
ensuring the estimation of CFO without any ambiguity. Methods reported in prior
art include PN sequence based allocation and geometric series based allocation.
While the PN sequence based allocation suffers with the disadvantage of high
bandwidth overhead, the geometric series based allocation is suitable for small
values of N only. The present embodiment of the work suggests the use of a
modified Fibonacci series based allocation of null subcarriers which ensures the
identifiability of frequency offset over the entire range of OFDM bandwidth,
where the Fibonacci series is generated by the following recurrence relation

where F(n) represents the nth element of the Fibonacci series. The first few
numbers of the series are 0,1,1, 2, 3, 5, 8,13, 21, 34, 55, 89,144, and so on.
The present embodiment of the work uses a truncated Fibonacci series by

removing the first two elements from the series. The subcarrier indices as
specified by the remaining numbers in the beacon symbol are imposed as null
subcarriers. For example, when N=64, we select the null subcarrier indices as {1,
2, 3, 5, 8, 13, 21, 34, 55}. For large N, sometimes more null subcarriers may be
required than that is provided by the proposed allocation, to meet a specific
mean square estimation error requirement. In this case, more null subcarriers
can be allocated by introducing a few more null subcarriers between two widely
spaced null subcarriers. For example, when N=512, the last two null subcarriers
indices are at 233 and 377 respectively. If desired, more null subcarriers can be
introduced between these two, again based on Fibonacci series, by assuming
233 and 377 as the first and last null subcarrier indices, still retaining the
identifiability of carrier frequency offset.
Performance of the present MIMO-OFDM CFO estimator is studied by considering
an OFDM system with 256 subcarriers, with a subcarrier separation of 62.5 kHz,
which meets the basic requirement of IEEE 802.16a standard. Each OFDM
symbol is preceded by a CP of 16 samples. All simulations studies are conducted
for simultaneous presence of AWGN and multipath fading channels. SUI-5
channel model proposed by IEEE 802.16 broadband wireless access working
group, which provides a strong fading environment, is considered for the
realization of the multipath fading channel. The performance metrics which are
chosen are the widely accepted ones; the Normalized Mean Square Error (NMSE)
of CFO estimator and the Bit Error Rate (BER) of the MIMO-OFDM receiver
employing the proposed CFO estimator.

Figure 7 shows the MSE performances of the proposed method for various
transmits-receive antenna pairs. The representative frequency offset considered
is 50.4 subcarrier spacings which is a real testing value. We consider two cases,
viz Nt=Nr=2 and Nt=Nr=3. It can be observed that the proposed technique
achieves an MSE of 10"4 at an SNR of 12 dB and it is less than 10"5 from 15 dB
onwards for the first case. For the 3X3 scenario, the MSE is less than 10-6 from
13 dB onwards. This will meet the requirements of a typical practical
implementation. The proposed method is found to yield a performance which is
superior to that of [9] which uses a null subcarrier hoping technique for the CFO
estimation. For example, for the 2X2 system, the proposed technique yields an
SNR improvement of 6 dB at an MSE of 10'4. This mainly comes from the use of
two stage frequency offset estimation instead of the null subcarrier line search
used in [2], and the use of Fibonacci series based null subcarrier allocation.
The uncoded BER performances of the MIMO-OFDM system employing the
proposed estimator are shown in Fig. 8. This is a more suitable metric than
coded BER as the impact of fading channel on the frequency offset estimation
technique will be clearly revealed. The modulation scheme used is 4-QAM with
perfect channel estimation and zero forcing equalization. Error free channel
estimation makes the study focussed on the impact of synchronization errors
introduced by various estimators. The curves shown are again for 2X2 and 3X3
systems. The proposed method achieves BERs of 10-3 at SNRs of 13 dB and 16
dBs, respectively for 2X2 and 3X3 systems. The 3X3 system achieves a BER less
than 10"5 from 19 dB onwards which is very suitable for any kind of wireless
communication systems. Also the proposed method for the 3X3system performs
4 dB and 6 dB superior to [9] at BERs of 10-3 and 10-4 respectively.

ADVANTAGES OF THE INVENTION
1) The proposed CFO estimation scheme can be used any type of space-time
coding scheme usually used with MIMO-OFDM systems, with minor
modifications.
2) The computational complexity and training overhead requirements of the
proposed scheme are very low as compared to many state-of-art methods.
3) The method does not require MIMO channel estimates for the CFO estimation,
which is a pre-requisite for many state-of-art methods, and which is complex to
obtain.
4) The method can also be applied for the CFO estimation in conventional OFDM
systems called SISO-OFDM and SIMO-OFDM.

5) The Fibonacci series based null subcarrier allocation has never been reported
in the prior-art.
6) The two stage null subcarrier based integer and fractional frequency offset
estimation approach used for reducing the number of computations is a
potentially powerful technique but never been reported in the state of the art.
7) Bandwidth efficiency of the proposed technique is very high as compared to
the state of the art methods which use training preambles.
8) None of the prior art reported in (a) for MIMO-OFDM provide a frequency
offset estimation range equal to the OFDM bandwidth
9) The bandwidth overhead and computational complexities of the present
embodiment are very low as compared to many prior art methods.

REFERENCES CONSIDERED :
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In order to address the limitations of the prior art, a null subcarrier based CFO estimation technique for MIMO-OFDM is provided which is efficient in terms of bandwidth overhead and computational complexity. The invention further
provides a Fibonacci series based logic for allocating null subcarriers in the training OFDM symbols on each of the transmitting antennas, which ensures full frequency offset acquisition range equal to the OFDM bandwidth, without any
ambiguity. A preferred embodiment of the inventive system comprises a MIMO-OFDM
transmitter with Nt transmit antennas where the number of transmit antennas are decided by the order of space-time encoding scheme used, with each transmit branch processes a block of space-time data coming from a space-time encoder and each of these frequency domain blocks of size N samples are transformed in to time domain signals by separate N point IDFTs and copy the
last L samples on each branch to the beginning of the time domain OFDM symbols and such signals from all the transmit branches are further processed to meet the RF requirements and transmitted. Such K number of OFDM symbols
is commonly denoted as an OFDM frame with the first OFDM symbol in the frame on each transmit antennas denoted as beacon symbols are specially
generated by imposing specific subcarriers as null subcarriers before the IDFT operation, whose locations are specified by a modified Fibonacci sequence so as to help estimation of carrier frequency offset at the receiver and the remaining subcarriers in the beacon symbol are used for useful data transmission along with other OFDM symbols in the frame thus resulting in enhanced bandwidth efficiency.