Abstract:
This invention relates to a Multi-Input Multi-Output Orthogonal Frequency Divisional Multiplexing (MIMO-OFDM) is a transmission technology for many current and next generation wireless communication systems. Carrier Frequency Offset (CFO) Estimation and Correction is one of the most important requirement of the proper reception of MIMO-OFDM Signals. The invention provides a null subcarrier based scheme to accomplish this task. The CFO is estimated by employing the covariance matrix of the signals on all receiving antennas with a cost function which minimizes the energy falling on the null subcarrier locations due to frequency offset. The proposed approach results in very low computational complexity as it uses a two step procedure, making it very attractive for real time applications. Also a new null subcarrier allocation scheme based on Fibonacci series is proposed which ensures a frequency offset estimation range equal to the maximum possible range equal to the OFDM bandwidth.

Description:
FIELD OF INVENTION 
     The present invention generally relates to carrier frequency offset estimation and correction in Multi-Input Multi-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) based wireless communication systems in particular but can be applied to the conventional OFDM and other multicarrier communication systems as well. More particularly, the invention relates to a method and apparatus for determining carrier frequency offset including correction of the frequency offset in MIMO-OFDM based wireless communication systems. 
     BACKGROUND OF INVENTION 
     Orthogonal Frequency Division Multiplexing (OFDM), one of the underlying technology in MIMO-OFDM is a multicarrier communication system which converts a high data rate stream into a set of parallel low data rate streams thereby modifying the prior art problem in a wireless channel, namely frequency selective fading to a tractable flat fading. Digital communications using multiple input multiple output (MIMO) wireless links has recently emerged as one of the most promising research areas in wireless communications. The core idea of the MIMO systems is space-time signal processing in which time is complemented with the spatial dimension inherent in the use of multiple spatially distributed antennas, resulting in diversity gain or multiplexing gain or both. An exciting 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 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 results 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 amount of frequency offsets need to be 10 estimated and corrected would be in the range of a few multiples of the 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 art which deal with carrier frequency offset estimation in conventional single input single output (SISO) OFDM systems [1-5]. For example, Schmidl-Cox algorithm [1] 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 [2] 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 estimate approach using consecutively placed virtual carriers at the band edges of the OFDM symbol [3]. Ma et al. suggested the use of distributed null subcarriers [4], to minimize the estimation errors associated with the use of consecutively placed virtual subcarriers proposed in [3]. 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 [5]. 
     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 known [6-8], which are extensions of similar techniques reported for SISO-OFDM like [1-2]. 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 [9-11]. 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 ⅛ th  or ¼ th  of it only. On the contrary, methods which offer very high estimation range are computationally inefficient. An attempt for reducing the computational complexity associated with the CFO estimation is done in [12]. A few granted patents [P.1-P.2] and patent applications [P.3-P.4] also exist in the state of the art. In view of the growing popularity, efficient techniques for the CFO estimation with excellent performances are still needed for practical MIMO_OFDM system implementations. 
     OBJECTS OF THE INVENTION 
     It is therefore an object of the invention to propose a method of determining and correcting carrier frequency offset (CFO) in Multi-input Multi-output Orthogonal Frequency Division Multiplexing (MIMO-OFDM)-based wireless communication systems, which eliminates disadvantages of prior art. 
     Another object of the invention is to propose a method of CFO-estimation in null subscriber based MIMO-OFDM systems, which is efficient in terms of bandwith overhead and computational complexity. 
     A further object of the invention is to propose a method for allocating null subcarriers in the training of OFDM symbols, which is based on a modified Fibonacci series. 
     A still further object of the invention is to propose a method for allocating null subcarriers in the training of OFDM symbols, which enables a full frequency offset acquisition range equal to the OFDM-bandwith. 
     Yet another object of the invention is to propose a method of CFO-estimation in MIMO-OFDM systems, which is capable of determining and correcting integer and fractional frequency offsets separately. 
     SUMMARY OF INVENTION 
     A preferred embodiment of the invention comprises a MIMO-OFDM transmitter with N t  transmit antennas (N t ≧1) where the number of transmit antennas are selected by the order of space-time encoding scheme used, with each transmit branch processing frequency domain block of space-time data transmitting from the space-time encoder, each of the frequency domain blocks of size N samples being transformed in to time domain signals by separate N point IDFTs. The last L samples are copied on each branch to the beginning of the time domain OFDM symbols. Such signals from all the transmit branches are further processed to meet the RF requirements and transmitted. Such K number of OFDM symbols as processed are commonly denoted as an OFDM frame with the first OFDM symbol in the frame on each transmit antenna (denoted as beacon symbols) is generated by imposing specific subcarriers as null subcarriers before the IDFT operation. The locations of the beacon symbols are specified by a modified Fibonacci sequence so as to help estimation of carrier frequency offset at the receiver. The remaining subcarriers in the beacon symbol are used for useful data transmission along with other OFDM symbols in the frame, thus resulting in an enhanced bandwidth efficiency. 
     A preferred embodiment of the invention comprises a receiver with N r  receive antennas where each antenna receives the superposition of signals transmitted by all the transmitting antennas with multipath distortions with a possible timing, including the carrier frequency offset. The carrier frequency offset can be fractions or multiples of subcarrier spacings which are used in the OFDM symbols. Thus the normalized carrier frequency offset is the sum of integer frequency offset (IFO) and fractional frequency offset (FFO). By assuming a perfect timing correction, the cyclic prefix associated with the OFDM symbols are removed and the covariance matrix of this signal is computed on each receiving antenna. The individual covariance matrices on all receive branches are combined using a maximal ratio combining (MRC) or equal gain combining (EGC). The carrier frequency offset is assumed to be identical for the signals received on all receive branches. Such an assumption is considered to be a fare assumption as the transmit and receive branches usually use the same oscillators for all the branches. The CFO is estimated by a two stage cost function minimization in which a first stage minimization yields the integer frequency estimate by calculating the total energy spilled on the null subcarrier locations due to the frequency offset by a search procedure. Thus, the first stage yield 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 the integer shift is evaluated which yields 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. Now assuming that the integer frequency offset is perfectly compensated for, a second step is initiated to estimate the fractional frequency offset by minimizing the same cost function but now with a co-variance matrix of the received signal which is obtained after integer frequency offset correction. Minimizing of the cost function over a fixed number of fractional values from −0.5 to +0.5, the fractional frequency offset can be estimated. The number of such minimization points is decided by the resolution required for the fractional estimation, the minimization procedure being the same as the one used for integer frequency offset estimation. And upon estimation, the fractional frequency offset can be compensated for, before proceeding for rest of the receiver processing. 
     A special technical feature of the invention is the determination and adaptation of a modified Fibonacci series—based null subcarrier allocation method 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 ACCOMPANYING 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 a 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. 
       FIG.  7 —a graphical representation of the normalized mean square frequency error as a function of SNR for 2 and 3 Transmit-Receive antenna pairs. 
       FIG.  8 —a graphical representation of the bit error rate as a function of SNR for 2 and 3 Transmit-Receive antenna pairs. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  shows a block diagram of a generalized MIMO-OFDM transmitter (T) corresponding to the transmission of the beacon symbol, which comprises a specific sequence of null subcarriers. Each transmitter branch (T 1 , T 2 ) receives complex block of data from a space-time encoder ( 1 ) with a block size of N samples as the underlying OFDM modulation uses N subcarriers spaced at a separation of ΔF=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 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 N t  transmit branches (T 1 , T 2 ) are processed in the same way and then transmitted after the required RF Processing. 
     The transmitted signal from the j th  transmit antenna (j=1, 2, . . . , Nt) is represented by 
                         u   j   ′     ⁡     (   d   )       =       1     N       ⁢       ∑     k   =   0       N   -   1       ⁢         s   j     ⁡     (   k   )       ⁢     exp   ⁡     (       j2π   ⁢           ⁢   d   ⁢           ⁢   k     N     )               ⁢     
     ⁢         with   ⁢           ⁢   d     =     -   L       ,     -     (     L   -   1     )       ,   …   ⁢           ,   0   ,   1   ,   2   ,   …   ⁢           ,     N   -   1               (   1   )               
where s j (k) is the data symbol at the k-th subcarrier and L is the length of the cyclic prefix.
     1. A general block schematic of the OFDM receiver (R) corresponding to the beacon symbol is shown in  FIG. 2 . The signals received on all receive antennas ( 4 , 5 ) 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 mismatchings 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 by a space-time decoder ( 6 ). The present embodiment assumes that the timing and sampling frequency offset are perfectly compensated. Hence received signals for example on the i th  antenna (i=1, 2, . . . , Nr) of the receiver is given by:   

                         r   i     ⁡     (   d   )       =         1     N       ⁢       ∑     j   =   1       N   t       ⁢       ∑     k   =   0       N   -   1       ⁢         H     i   ,   j       ⁡     (   k   )       ⁢       s   j     ⁡     (   k   )       ⁢     exp   ⁡     (         j2π   ⁢           ⁢   d     N     ⁡     [     k   +     ϕ   m       ]       )               +       z   i     ⁡     (   d   )           ⁢     
     ⁢         with   ⁢           ⁢   d     =     -   L       ,     -     (     L   -   1     )       ,   …   ⁢           ,   0   ,   1   ,   2   ,   …   ⁢           ,     N   -   1               (   2   )               
where, H i,j (k) is the channel frequency response at the k-th subcarrier between i th  transmit antenna and j th  receive antenna, φ 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 −0.5 to +0.5, and z i (n) is complex additive white Gaussian noise (AWGN) for the i th  receiver.
 
       FIG. 3  is a flow chart of the method of estimating the integer frequency offset wherein the OFDM beacon signals received ( 7 ) on all receiving antennas ( 4 , 5 ) are combined using any of the diversity combining techniques and applied to an integer frequency offset estimation unit. The cyclic prefix associated with the received OFDM signal is removed ( 8 ) and applied ( 9 ) to a 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 ( 10 ) by introducing ( 11 ) cyclic shifts from 0 to N−1, and stored ( 12 ) against the corresponding integer shift introduced. Thus an N element array containing the energies is obtained and a search is carried-out ( 13 ) to find the minimum energy and the corresponding integer shift, which is designated as the integer frequency offset estimate ( 14 ). Alternatively this process can be expressed by means of a cost function as the combined received signal after removing the CP can be written in vector notation as 
                     y   i     =       β   ⁢           ⁢     P   ⁡     (   ϕ   )       ⁢       ∑     j   =   1     Nt     ⁢       FD   ⁡     (     H     i   ,   j       )       ⁢     s   j           +     z   i               (   3   )               
where
 
                 P   ⁡     (   ϕ   )       =     Diag   (     1   ,     ⅇ     j   ⁢       2   ⁢   π     N     ⁢   ϕ       ,   …   ⁢           ,     ⅇ     j   ⁢       2   ⁢     π   ⁡     (     N   -   1     )         N     ⁢   ϕ         )       ,         
is a diagonal matrix containing the carrier frequency offsets experienced by each samples, β=√{square root over (N/(N-R))} is a scaling factor, F is the IFFT matrix, D(H i,j )=Diag(H i,j (0),H i,j (1), . . . , H i,j (N−1)) containing the frequency domain channel coefficients with H i,j (k) denoting the frequency response of the channel at frequency 2πk/N between j-th transmit antenna and i-th receive antenna and s j  is the data vector.
 
     Using the log-likelihood function for the original data vector and integer frequency offset φ i , a cost function that is to be minimized can be expressed as 
                     Ji   ⁡     (     ϕ   ′     )       =       ∑     i   =   1     Nr     ⁢       ∑     r   ∈     Γ   z         ⁢       v   r   H     ⁢       P   H     ⁡     (     ϕ   ′     )       ⁢     y   i     ⁢     y   i   H     ⁢     P   ⁡     (     ϕ   ′     )       ⁢     v   r                   (   4   )               
where Γ z  denote the set of null subcarrier indices, v r  is the r-th column of the FFT matrix and P(φ′) is similar to P(φ) but initialized every time with a trial integer frequency offset φ′ i .
 
     The integer frequency offset is estimated by a search technique by initializing P(φ′) each time with the trail integer offset value. If P(φ′) is the actual integer frequency offset estimate, the cost function will reach a minimum. 
       FIG. 4  is a flowchart showing a method of correcting the integer frequency offset where an offset vector which is the diagonal element of matrix P is generated ( 15 ) by applying ( 14 ) a complex conjugate of the estimated frequency offset multiply ( 16 ) the offset vector point to point with the received cyclic prefix removed signal block of size N. Counter rotating the samples of the received signal by the same amount of angular rotation experienced due to the integer frequency offset to receive ( 17 ) signal after integer offset correction. 
       FIG. 5  is a flowchart of the method of estimating the fractional frequency offset wherein the integer frequency offset corrected signal is received ( 18 ) and point to point multiplied ( 19 ) with frequency offset vector corresponding to the trail value where the trail values are selected between −0.5 and +0.5, according to the resolution requirements of the fractional frequency offset estimation and after the said multiplication, the DFT is performed ( 20 ) and the total energy corresponding to the designated null subcarriers are extracted ( 21 ) and stored ( 22 ) in a register along with the trail value used for generating the frequency offset vector and this process is repeated ( 23 ) till the trial values are completed and then a search is conducted ( 24 ) to find out ( 25 ) 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 {circumflex over (P)} with the trail values used for fractional frequency offset estimation. 
       FIG. 6  is a flowchart of the method of correcting the fractional frequency offset where the integer frequency corrected signal samples are received ( 26 ) to generate ( 27 ) the complex conjugate of offset vector, and are point to point multiplied ( 28 ) 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 ( 29 ) the CFO compensated received signal. 
     A preferred embodiment of the invention described through  FIGS. 1 to 6  with one transmit antenna instead of N t  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 invention 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 with a very small bandwidth overhead, where the Fibonacci series is generated by the following recurrence relation 
                           F   ⁡     (   n   )       =       0   ⁢           ⁢   if   ⁢           ⁢   n     =   0                 =       1   ⁢           ⁢   if   ⁢           ⁢   n     =   1                 =         F   ⁡     (     n   -   1     )       +       F   ⁡     (     n   -   2     )       ⁢           ⁢   if   ⁢           ⁢   n       &gt;   2                   (   5   )               
where F(n) represents the n th  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 invention 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, the null subcarrier indices can be selected 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.
 
     ADVANTAGES OF THE INVENTION 
     
         
         1) The proposed CFO estimation method can be used with any type of space-time coding scheme usually employed in MIMO-OFDM systems, with minor modifications. 
         2) The computational complexity and training overhead requirements of the proposed method are very low as compared to many state-of-art methods. 
         3) The method does not require MIMO channel estimate 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 is not known 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 is not disclosed 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 training preamble based 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. 
       
    
     TESTING OF THE SYSTEM AND METHOD OF INVENTION 
     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 802.16d 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. 
       FIG. 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 N t =N r =2 and N t =N r =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 3×3 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 2×2 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 focused on the impact of synchronization errors introduced by various estimators. The curves shown are again for 2×2 and 3×3 systems. The proposed method achieves BERs of 10 −3  at SNRs of 13 dB and 16 dBs, respectively for 2×2 and 3×3 systems. The 3×3 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 3×3 system performs 4 dB and 6 dB superior to [9] at BERs of 10 −3  and 10 −4  respectively. 
     REFERENCES CONSIDERED 
     
         
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