Patent Application: US-98951709-A

Abstract:
this invention relates to a multi - input multi - output orthogonal frequency divisional multiplexing is a transmission technology for many current and next generation wireless communication systems . carrier frequency offset 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:
fig1 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 fig2 . 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 . fig3 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 ) 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 . fig4 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 . fig5 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 . fig6 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 fig1 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 . 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 . 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 . 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 . fig7 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 - 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