Patent Publication Number: US-8116394-B2

Title: Long term evolution (LTE) radio link timing synchronization

Description:
TECHNICAL FIELD 
     The present disclosure relates to mobile wireless networks and in particular to radio link timing synchronization of long term evolution based wireless networks. 
     BACKGROUND 
     Timing and frequency synchronization is a crucial part of wireless communication such as Orthogonal Frequency Division Multiplexing (OFDM) technology based 3GPP Long Term Evolution (LTE) system. In fact, it is widely recognized that an OFDM based communication system is very sensitive to frequency and timing error and existing techniques do not meet the performance requirement for LTE uplink (UL) synchronization. The challenge for LTE UL timing synchronization is that, to keep the synchronization overhead as low as possible to preserve LTE system overall capacity, the radio resources are limited for timing estimation. That means only very narrow radio bandwidth, limited time duration and limited signal to noise ratio (SNR) for the reference signal are available, especially at cell edge. Accordingly, improved methods of radio link timing synchronization in LTE systems remain highly desirable. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Further features and advantages will become apparent from the following detailed description, taken in combination with the appended drawings, in which: 
         FIG. 1  is a block diagram of wireless mobile device; 
         FIG. 2  is a block diagram of a wireless base station; 
         FIG. 3  is a schematic representation of a simplified OFDM transmitter; 
         FIG. 4  is a schematic representation of a simplified OFDM receiver; 
         FIG. 5  is graph of a typical urban channel delay profile; 
         FIG. 6  is a method of performing timing synchronization; 
         FIGS. 7A-D  are estimated time delay profiles for simulation Case  1 ; 
         FIGS. 8A-D  are estimated time delay profiles for simulation Case  2 ; 
         FIGS. 9A-D  are estimated time delay profiles for simulation Case  3 ; 
         FIGS. 10A-D  are time estimation errors for simulation Case  1 ; 
         FIGS. 11A-D  are time estimation errors for simulation Case  2 ; and 
         FIGS. 12  A-D are time estimation errors for simulation Case  3 . 
     
    
    
     It will be noted that throughout the appended drawings, like features are identified by like reference numerals. 
     DETAILED DESCRIPTION 
     In accordance with an embodiment of the present disclosure there is provided a method for performing a radio link timing estimation for synchronization to a wireless communications channel. The method comprises obtaining a channel frequency response estimate from a received reference signal comprising multiple non-coherent sounding reference signal (SRS) Orthogonal Frequency Division Multiplexing (OFDM) symbols, generating a frequency response covariance matrix from the channel frequency response estimate and estimating timing offsets of the received reference signal using covariance matrix and timing offset estimation algorithms. 
     In accordance with another embodiment the present disclosure there is provided a mobile wireless device operating on wireless network. The mobile wireless device comprises a receiver and a processor coupled to the receiver. The processor performs a radio link timing estimation for synchronization to a wireless communications channel. The timing estimation comprises obtaining a channel frequency response estimate from a received reference signal comprising multiple non-coherent sounding reference signal (SRS) Orthogonal Frequency Division Multiplexing (OFDM) symbols, generating a frequency response covariance matrix from the channel frequency response estimate and estimating timing offsets of the received reference signal using covariance matrix and timing offset estimation algorithms. 
     In accordance with another embodiment of the present disclosure there is provided a base station transceiver in a wireless network. The base station transceiver comprises a receiver and a processor coupled to the receiver. The processor performing a radio link timing estimation for synchronization to a wireless communications channel. The timing estimation comprises obtaining a channel frequency response estimate from a received reference signal comprising multiple non-coherent sounding reference signal (SRS) Orthogonal Frequency Division Multiplexing (OFDM) symbols, generating a frequency response covariance matrix from the channel frequency response estimate and estimating timing offsets of the received reference signal using covariance matrix and timing offset estimation algorithms. 
     In Orthogonal Frequency Division Multiplexing (OFDM) technology based 3GPP Long Term Evolution (LTE) system, two types of timing estimation techniques: time-domain based techniques and frequency-domain based techniques can be used in the receivers during synchronization. When there is little or no frequency error, a very straightforward and very efficient timing estimation technique is the correlation technique. With this technique, the receiver in the time domain correlates a known sequence with the received sounding reference signal (SRS) or demodulation reference signal (DRS) that has been modulated by a known sequence. The result of the correlation produces a peak that indicates signal arriving time offset. This timing estimation technique relies on the good circular correlation properties of the reference sequence. Ideally, the sequence should have zero circular autocorrelation when the time shift is not zero. When there is no time shift, the circular autocorrelation should produce a very high peak. Sequences generated with Zadoff-Chu codes have this property. 
     The correlation technique can directly be applied in a wireless multi-path environment. When the signal bandwidth is sufficiently wide, resolution of the different peaks (correspond to different paths) improves and this correlation technique can detect the time of arrival of the different paths by searching for the multiple correlation peaks. When a frequency offset (due to local oscillator drifting or Doppler shift) exists as well as the timing offset, the performance of this time domain correlation technique degrades to some degree. 
     This time-domain correlation timing estimation technique is based on a known sequence with good circular correlation property. Another type of time-domain timing estimation is based on exploring the periodic pattern of the reference signal. In general, when there is no significant frequency offset, the timing estimation techniques based on simple correlation with known reference sequence has better performance than these techniques based on exploring the periodic pattern of the reference signal. 
     For single-path radio propagation channels with ideal reflector, the channel impulse response would be a delta function with unknown time shift. This time shift is what the timing synchronization task needs to estimate and to correct later. In multi-path channel environment, the ideal channel impulse response would be multiple delta functions with different time shifts that correspond to the different paths&#39; travel distances. The timing synchronization task should adjust the transmitter time to align the time of arrival of the first path with the receiver time. 
       FIG. 1  is a block diagram of a wireless mobile device  100  incorporating a communication subsystem having both a receiver  112  and a transmitter  114 , as well as associated components such as one or more embedded or internal antenna elements  116  and  118 , local oscillators (LOs)  113 , and a processing module such as a digital signal processor (DSP)  120 . The particular design of the communication subsystem will be dependent upon the communication network in which the device is intended to operate such as in a 3GPP LTE network. 
     The wireless mobile device  100  performs synchronization, registration or activation procedures by sending and receiving communication signals over the network  102 . UL signals received by antenna  116  through communication network  100  are input to receiver  112 , which may perform such common receiver functions as signal amplification, frequency down conversion, filtering, channel selection and the like, and in the example system shown in  FIG. 1 , analog to digital (A/D) conversion. A/D conversion of a received signal allows more complex communication functions such as demodulation, decoding and synchronization to be performed in the DSP  120 . 
     In a similar manner, signals to be transmitted are processed, including modulation and encoding for example, by DSP  120  and input to transmitter  114  for digital to analog conversion, frequency up conversion, filtering, amplification and transmission over the communication network  102  via antenna  118 . DSP  120  not only processes communication signals, but also provides for receiver and transmitter control. For example, the gains applied to communication signals in receiver  112  and transmitter  114  may be adaptively controlled through automatic gain control algorithms implemented in DSP  120 . 
     Wireless device  100  preferably includes a radio processor  111  and a control processor  138  which together control the overall operation of the device. DSP  120  is located on radio processor  111 . Communication functions are performed through radio processor  111 . 
     Radio processor  111  interacts with receiver  112  and transmitter  114 , and further with flash memory  162 , random access memory (RAM)  160 , the subscriber identity module  164 , a headset  168 , a speaker  170 , and a microphone  172 . 
     Microprocessor  138  interacts with further device subsystems such as the display  122 , flash memory  140 , random access memory (RAM)  136 , auxiliary input/output (I/O) subsystems  128 , serial port  130 , keyboard  132 , other communications  142  and other device subsystems generally designated as  144 . 
     Some of the subsystems shown in  FIG. 1  perform communication-related functions, whereas other subsystems may provide “resident” or on-device functions. Notably, some subsystems, such as keyboard  132  and display  122 , for example, may be used for both communication-related functions, such as entering a text message for transmission over a communication network, and device-resident functions such as a calculator or task list. 
     Software used by radio processor  111  and microprocessor  138  is preferably stored in a persistent store such as flash memory  140  and  162 , which may instead be a read-only memory (ROM) or similar storage element (not shown). Those skilled in the art will appreciate that the operating system, specific device applications, or parts thereof, may be temporarily loaded into a volatile memory such as RAM  136  and RAM  260 . Received communication signals may also be stored in RAM  136 . 
     As shown, flash memory  140  can be segregated into different areas for computer programs  146 , device state  148 , address book  150 , other personal information management (PIM)  152  and other functionality generally designated as  154 . These different storage types indicate that each program can allocate a portion of flash memory  140  for their own data storage requirements. Control processor  138 , in addition to its operating system functions, preferably enables execution of software applications on the mobile station. 
     For voice communications, overall operation of wireless mobile device  100  is similar, except that received signals would preferably be output to the speaker  170  or headset  168  and signals for transmission would be generated by the microphone  172 . Alternative voice or audio I/O subsystems, such as a voice message recording subsystem, may also be implemented on mobile station  102 . 
     Serial port  130  in  FIG. 1  would normally be implemented in a wireless mobile device that have PDA functionality for which synchronization with a user&#39;s desktop computer (not shown) may be desirable, but is an optional device component. Such a port  130  would enable a user to set preferences through an external device or software application and would extend the capabilities of wireless mobile device  100  by providing for information or software downloads to wireless mobile device  100  other than through a wireless communication network. The alternate download path may for example be used to load an encryption key onto the device through a direct and thus reliable and trusted connection to thereby enable secure device communication. 
     Other device subsystems  144 , such as a short-range communications subsystem, is a further optional component which may provide for communication between wireless mobile device  100  and different systems or devices, which need not necessarily be similar devices. For example, the subsystem  144  may include an infrared device and associated circuits and components or a Bluetooth™ communication module to provide for communication with similarly enabled systems and devices. 
       FIG. 2  is a block diagram of wireless base station  103  connected to wireless network  102 . The wireless base station  103  communicates with a plurality of wireless mobile devices located in the service region. A receiver  212  is coupled to one or more receive antennas  202  for processing signals from the wireless mobile devices. Downlink (DL) signals from wireless mobile devices are received by antenna  202  are input to receiver  212 , which may perform common receiver functions as signal amplification, frequency down conversion, filtering, channel selection and analog to digital (A/D) conversion. A/D conversion of a received signal allows more complex communication functions such as demodulation, decoding and synchronization to be performed in the receive processor  214 . In the transmission path, one or more transmit antennas  204  are coupled to a transmitter  216 . The transmitter  216  provides frequency up-conversion including modulation, amplification and transmission over the communication to wireless mobile device  100 . Digital to analog conversion and encoding can be performed by transmit processor  218 . The processor  220  provides additional processing of the received and transmitted signals and interfaces with backhaul interfaces  230  and OA&amp;M  232  interfaces with the rest of the wireless network  102  for operation of the BTS  103 . The receive processor  214  may additional perform timing synchronization on signals received from wireless mobile devices  100  on the wireless network  102 . 
     In OFDM systems, it is much easer to estimate the channel frequency response than to estimate channel impulse response directly. Under the assumption that the transmitter and receiver are roughly synchronized, the receiver can correctly sample the wireless mobile device&#39;s UL SRS OFDM symbol without inter symbol interference (ISI).  FIG. 3  shows a simplified OFDM transmitter  300  as would be implemented in transmitter  114  and DSP  120  in the wireless mobile device  100  and transmitter  216  and transmit processor  218  in the BTS  103 . The input is a sequence of reference symbols which is provided to serial to parallel converter  302 . The parallel symbol stream is processed by an inverse-Fourier transform (IFFT)  304  and converted by a parallel to serial converter  306 . A cyclic prefix can then be inserted at  308  prior to digital to analog converter  310 . The signal can the be amplified and modulated before transmission via channel  312 . 
       FIG. 4  shows a simplified receiver  400 . Upon receiving the signal through channel  312 , the signal is down-converted and demodulated. The analog to digital converter  402  then provides a digital stream for cyclic prefix removal  404 . The data stream is then converted from a serial to parallel stream at  406 . Taking an FFT  408  of this time-domain sampled sequence to transform it into the frequency domain, the channel frequency response can be derived by dividing the received frequency-domain sequence by the reference sequence that is modulated on the sub-carriers. The simplest way to get the channel impulse response is to do an IDFT on the frequency response, either use a windowed IDFT or a non-windowed IDFT. 
       FIG. 5  illustrates a typical urban radio channel (TU  30 ) delay profile which has been used for GSM system performance evaluation providing similar characteristics to an LTE system as would be defined by channel  312 . Table 1 shows the similarity of the channel impulse response estimation, signal spectrum estimation and the direction of arrival (DOA) estimation in array signal processing. Note that equally-spaced sampling on the observing domains is assumed for comparison purposes in the following table. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Similarity of timing, spectrum and DOA estimation 
               
            
           
           
               
               
               
               
            
               
                   
                 Timing 
                 Spectrum 
                 DOA 
               
               
                   
                 estimation 
                 estimation 
                 estimation 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                 Observation 
                 Frequency 
                 Time 
                 Space 
               
               
                 domain 
                 domain 
                 domain 
                 domain 
               
               
                 Samples of 
                 Samples on 
                 Samples on 
                 Samples on 
               
               
                 one 
                 different 
                 different time 
                 different sensor 
               
               
                 observation 
                 frequency 
                 [x 1   t , x 2   t , . . . , x N-1   t ] T   
                 of the array 
               
               
                   x  = 
                 (sub-carrier) 
                   
                 [x 1   s , x 2   s , . . . , x N-1   s ] T   
               
               
                   
                 [x 1   f , x 2   f , . . . , x N-1   f ] T   
               
               
                 Target 
                 Time domain 
                 Frequency domain 
                 DOA angle domain 
               
               
                 domain 
                   
                   
                 (cos(θ) domain) 
               
               
                   
               
               
                 Domain transformation vector ā 
                 
                   
                     
                       
                         
                           
                             a 
                             _ 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                         
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                                 1 
                               
                             
                             
                               
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     πΔft 
                                   
                                 
                               
                             
                             
                               
                                 ⋮ 
                               
                             
                             
                               
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       πΔf 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           N 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                     ⁢ 
                                     l 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             a 
                             _ 
                           
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         = 
                         
                           [ 
                           
                             
                               
                                 1 
                               
                             
                             
                               
                                 
                                   e 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
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                                     ⁢ 
                                     πΔTf 
                                   
                                 
                               
                             
                             
                               
                                 ⋮ 
                               
                             
                             
                               
                                 
                                   e 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       πΔT 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           N 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                     ⁢ 
                                     f 
                                   
                                 
                               
                             
                           
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                             a 
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                           ⁡ 
                           
                             ( 
                             θ 
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                         = 
                         
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                                   e 
                                   
                                     
                                       - 
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                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       πl 
                                       · 
                                       
                                         
                                           cos 
                                           ⁡ 
                                           
                                             ( 
                                             θ 
                                             ) 
                                           
                                         
                                         / 
                                         λ 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 ⋮ 
                               
                             
                             
                               
                                 
                                   e 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
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                                       πl 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           N 
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                                     ⁢ 
                                     
                                       
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                                         ⁡ 
                                         
                                           ( 
                                           θ 
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                                       / 
                                       λ 
                                     
                                   
                                 
                               
                             
                           
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                 Domain 
                 IDFT 
                 DFT 
                 DFT-like 
               
               
                 transformation 
                 ā(t) T  ·  x   
                 ā(f) T  ·  x   
                 transformation 
               
               
                   
                   
                   
                 ā(θ) T  ·  x   
               
               
                   
               
            
           
         
       
     
     In the table above, Δf denotes the frequency spacing between each sample in frequency domain; ΔT denotes the time spacing between each sample in time domain; and l, λ and θ denote the distance between each sensor of the array, carrier wavelength and signal arrival angle respectively. 
     From the comparison in table 1, it can be seen that the timing estimation, spectrum estimation and DOA estimation are all same from a mathematical point of view. They differ only in that they have a different constant factor in the transformation vector. That means all the algorithms for spectrum estimation and DOA estimation can be used for timing estimation, if the frequency domain observations can be easily obtained. 
     In an OFDM system like LTE, the channel frequency response can be easily obtained when the timing is roughly synchronized between the transmitter and the receiver. The UL frequency can also be assumed to be synchronized. The radio propagation channel is generally modeled as multi-path channel. This channel model is similar with multiple, different frequency sinusoid wave signal model in spectrum estimation. It is also similar with the signal model in array signal processing that has multiple signals arrive from different directions. This similarity opens an opportunity to apply the DOA estimation algorithms and spectrum estimation algorithms to timing estimation, for example, linear Fourier Analyzing (FA) algorithm, sub-space decomposition based Multiple Signal Classification (MUSIC) algorithm, or sub-space fitting based Maximum Likelihood (ML) algorithm. 
     Current LTE UL timing estimation algorithms use just one OFDM symbol to estimate the signal timing offset; therefore, relatively high signal to noise ratio (SNR) is required for these algorithms to be effective. At the cell edge, the SNR is normally very low and these algorithms may not meet the LTE system performance requirement. 
     It is assumed that the wireless mobile device uplink is already roughly synchronized. That means the wireless mobile device UL timing offset is within a certain range. In this range, with the cyclic prefix (CP) in place, the enhanced Node B (eNB) can correctly sample the SRS OFDM symbol&#39;s baseband signal in time domain without any ISI, but the timing offset information is contained in the samples. It is also assumed that the wireless mobile device&#39;s frequency error is small and can be ignored. (Frequency offset estimation and correction will not be discussed in this disclosure). After the FFT operation on these time domain samples, a frequency domain sample of the SRS OFDM symbol can be obtained. Note
 
   r     k   =[r   1   (k)   , r   2   (k)   , . . . , r   N   (k) ] T   (1)
 
as the sampled vector of the k-th SRS OFDM symbol in frequency domain at the sub-carriers that the wireless mobile device is assigned to transmit the SRS. Where, N is number of total sub-carriers the SRS is transmitted on, and K is the total number of SRS OFDM symbols sampled. Let
 
   c =[c   1   , c   2   , . . . , c   N ] T   (2)
 
denote the indexes of the sub-carriers assigned to the wireless mobile device. The SRS reference sequence (the input in  FIG. 3 ) is noted as:
 
   s =[s   1   , s   2   , . . . , s   N ] T   (3)
 
     Generally, a constant amplitude complex sequence s 1 , s 2 , . . . , s N  is used in LTE. 
     Assume that there are M multi-paths in the radio propagation channel with different time delays t m  and complex attenuation factor h m   (k) , and m=1, 2, . . . , M at the instance of the k-th SRS symbol. It is assumed that the multi-paths complex attenuation factors are stochastic processes and are not coherent with each other. Within one timing estimation period, it is assumed the time offset t 1 , t 2 , . . . , t M  for the M multi-paths are constants. Denote the following vectors:
 
   h     k   =[h   1   (k)   , h   2   (k)   , . . . , h   M   (k) ] T   (4)
 
 ā   i     m     =[e   j2πΔfc     1     t     m     , e   j2πΔfc     2     t     m     , . . . , e   j2πΔfc     N     t     m   ] T   (5)
 
 Ā=[ā   t     1     , ā   y     2     , . . . , ā   t     M   ]  (6)
 
     Where Δf is the sub-carrier spacing in the OFDM system. It is further assumed that the signal is a narrow bandwidth signal. With the above assumptions and notations, the frequency domain sample of the received baseband signal for the k-th SRS OFDM symbol can be expressed as:
 
   r     k   =  s ∘Ā·  h     k   +  n     k   (7)
 
     In the equation above, the “∘” denotes the Hadamard product (matrix element product) operator, and  n   k  denotes the additive noise in the frequency domain. We assume that the sampled noise in time domain is additive white Gaussian noise. It is obvious that the frequency domain noise  n   k  is still additive white Gaussian noise with independent identical distribution (i.i.d.). 
     The estimate of the channel frequency response based on the k-th SRS OFDM symbol is denoted as:
 
   x     k   =[x   1   (k)   , x   2   (k)   , . . . , x   N   (k) ] T   (8)
 
     From the discussion above, the channel frequency response can be estimated as:
 
   x     k   =  r ·/  s =Ā·  h     k   +  n     k   ·/  s     (9)
 
     Where “·/” denotes the matrix element dividing operator. With the assumption that the SRS reference sequence in frequency domain has constant amplitude across the sub-carriers, it is easy to see that  n   k ·/  s  is still white Gaussian noise with independent identical distribution. We still make the following note for simplicity:
 
   x     k   =Ā·  h     k   +  n     k   (10)
 
     The above equation is the system signal model. In the equation, the vector  x   k  can be simply obtained from the frequency domain observed vector  r   k . Unknown time offset parameters t 1 , t 2 , . . . , t M  within the matrix Ā are the parameters that need to be estimated. The unknown channel complex parameters  h   k  are not of interest for the LTE UL timing synchronization. 
     A large number of algorithms for spectrum estimation and array signal DOA estimation can be applied in LTE UL timing estimation. Three well-known DOA estimation algorithms, linear Fourier Analyzing algorithm, sub-space decomposition based MUSIC algorithm and sub-space fitting based Maximum Likelihood (ML) algorithm, are presented for the LTE UL timing estimation without mathematic derivation. 
     It should be pointed out that the current timing offset estimation algorithms are based on single OFDM symbol samples. In the present disclosure samples of multiple non-coherent OFDM symbols are used to combat low SNR at the cell edge of LTE system. 
     First, the covariance matrix of the channel frequency response is estimated as: 
     
       
         
           
             
               
                 
                   
                     X 
                     _ 
                   
                   = 
                   
                     
                       1 
                       K 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         K 
                       
                       ⁢ 
                       
                         
                           
                             x 
                             _ 
                           
                           k 
                         
                         · 
                         
                           
                             x 
                             _ 
                           
                           k 
                           H 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The (·) H  in above equation denotes Hermitian operation. The covariance matrix collects the information from all samples. Be aware that the covariance operation does not increase the SNR. It is not a coherent accumulation. The benefit of the covariance matrix is that it decreases the variance of the estimated noise power and signal power with increasing numbers of samples, but does not decrease the average noise power or increase the signal power. 
     If the frequency response is sampled with equal spacing in frequency domain, the exact covariance matrix (mathematically expectation) should not only be a Hermitian matrix (conjugate symmetric matrix), but also should a Teoplitz matrix, in which the value of the elements along each descending diagonal is a constant. With a limited number of symbols (small value of K), the estimated covariance matrix X will lose the properties of Hermitian and Teoplitz matrix in some degree. To improve the covariance matrix estimate accuracy, the value of the matrix elements along each descending diagonal can be replaced with their average value. Mathematically, the averaged covariance matrix can be expressed as: 
                         X   _     ^     =     [             x   ^     0             x   ^     1             x   ^     2         …           x   ^       N   -   1                   x   ^     1   *             x   ^     0             x   ^     1         …           x   ^       N   -   2                   x   ^     2   *             x   ^     1   *             x   ^     0         …           x   ^       N   -   3               ⋮       ⋮       ⋮       ⋱       ⋮               x   ^       N   -   1     *             x   ^       N   -   2     *             x   ^       N   -   3     *         …           x   ^     0           ]       ,           (   12   )               
where the elements {circumflex over (x)} i  of the averaged matrix  {circumflex over (X)}  is calculated from the elements x l,m  of the matrix  X  as:
 
 {circumflex over (x)}   i =average{ x   l,m   , x*   m,l , for all ( l−m )= i}   (13)
 
     Notation (5) is rewritten as:
 
 ā ( t )=[ e   j2πΔfc     1     t   , e   j2πΔfc     2     t   , . . . , e   j2πΔfc     N     t ] T   (14)
 
     The linear Fourier Analyzing (FA) algorithm is given as searching for the position in time axis where the following metric reaches its peaks:
 
 m   BF ( t )= ā ( t ) H   ·  X ·ā ( t )  (15)
 
     The sub-space decomposition based MUSIC algorithm&#39;s searching metric is given by: 
     
       
         
           
             
               
                 
                   
                     
                       m 
                       MUSIC 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     1 
                     
                       
                          
                         
                           
                             
                               
                                 a 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             H 
                           
                           · 
                           
                             
                               E 
                               _ 
                             
                             N 
                           
                         
                          
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Where, in above equation, Ē N  denotes the noise sub-space matrix of the covariance matrix  X . Ē N  is composed of (N−M) eigenvectors corresponding to the (N−M) smallest eigenvalues of the matrix  X  and can be expressed as: Ē N =[ē 1 , ē 2 , . . . , ē N−M ], where ∥·∥ denotes vector norm operation. 
     The subspace-fitting based Maximum Likelihood (ML) algorithm has more computational complexity, it involves a joint multiple dimension optimization. The ML algorithm can be formulated as: 
     
       
         
           
             
               
                 
                   
                     
                       m 
                       ML 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           t 
                           1 
                         
                         , 
                         
                           t 
                           2 
                         
                         , 
                         … 
                         ⁢ 
                         
                             
                         
                         , 
                         
                           t 
                           M 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         1 
                       
                       K 
                     
                     ⁢ 
                     
                       
                         
                           x 
                           _ 
                         
                         k 
                         H 
                       
                       · 
                       
                         
                           
                             P 
                             _ 
                           
                           A 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               t 
                               1 
                             
                             , 
                             
                               t 
                               2 
                             
                             , 
                             … 
                             ⁢ 
                             
                                 
                             
                             , 
                             
                               t 
                               M 
                             
                           
                           ) 
                         
                       
                       · 
                       
                         
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                       ML 
                     
                     ⁡ 
                     
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                           t 
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     Where,  P   A (t 1 , t 2 , . . . , t M )=Ā·(Ā H ·Ā) −1 ·Ā H  is a projection matrix of Ā and it is a function of the multiple time offset of the propagation paths. 
     It is well known that the ML performs better than the FA and MUSIC timing offset estimation algorithms, especially with a limited number of samples and limited SNR. However, the additional computational complexity is very costly to implement with present hardware technology. 
       FIG. 6  presents a method of performing Long Term Evolution (LTE) Radio Link Timing Synchronization utilizing the techniques discussed above. At  602  a channel frequency response estimate  x   k  is obtained from a received UL signal. The channel frequency response covariance matrix  X  is then generated at  604 . For MUSIC and ML algorithms a known number of multi-paths is required. There are some techniques that can be used to estimation the number of multi-paths, however it is assumed as a known parameter. When the averaged covariance matrix  {circumflex over (X)}  is to be utilized, YES at  606 , they are generated at  608 , and Fourier Analyzing and MUSIC timing offset estimation algorithms are identified as modified Fourier Analyzing (FAmod) algorithm and modified MUSIC (MUSICmod) algorithm respectively. Otherwise, NO at  606 , original covariance matrix will be used. 
     For one-dimensional metrics timing offset estimation algorithms, for example, FA algorithm and MUSIC algorithm, YES at  612 , the position of the first peak offers a more meaningful time delay estimate. The first-peak searching can then be performed through  618  to  630 . The metric m(t) is calculated according to FA or MUSIC algorithm in the defined searching window. The maximum and minimum value of the metric: m max  and m min  in the searching window is found at  620 . The threshold as m th =m min +α·(m max −m min ) is calculated at  622  where α takes value from 0 to 1. The metric is limited by m(t)=max(m(t),m th ) to reduce the chance of finding false peak at  624 . A search is performed for first ascending point where the metric goes up at  626 . From the point found at  626 , a search is performed for the first descending point where the metric goes down at  628 . This is the position of the first peak. From the first peak a timing estimate can be determined at  630 . The estimate of the first peak is then used to synchronize the device to the UL and processing of overhead information can then proceed. For multi-dimensional algorithms like ML algorithm, NO at  612 , a multi-dimensional metric peak search is performed at  614  and a timing estimate is determined to enable synchronization to the UL. 
     Simulations are presented for the Fourier Analyzing (FA) algorithm and MUSIC algorithm in three cases for LTE UL timing synchronization in  FIGS. 7 to 12 . 
     Simulation Case  1  represents the cell edge situation in which low SNR, low SRS signal bandwidth and limited number of SRS OFDM symbols are available for timing estimation. The simulation parameters are set as: TU30 channel, ( FIG. 5  illustrates the TU channel profile), 20 SRS symbols in rate of 40 Hz for one estimation; 6 resource blocks (RBs—each RB has 12 sub-carriers with 15 kHz spacing; all the sub-carriers are allocated continuously with each other); and −13.8 dB SNR. 
     Simulation Case  2  increases the SNR to 0 dB and the number of SRS OFDM symbols to 50 in rate of 100 Hz to simulation better radio link situation. Simulation Case  3  further increases SRS signal bandwidth to 12 RBs to examine the performance potential of the algorithms. These three cases are summarized in Table 2. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Parameters used in the simulation cases. 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Channel 
                 SRS symbols/Rate 
                 Number of 
                   
               
               
                   
                 Model 
                 (Hz) 
                 RBs 
                 SNR (dB) 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 Case 1 
                 TU30 
                 20/40  
                 6 
                 −13.8 
               
               
                 Case 2 
                 TU30 
                 50/100 
                 6 
                 0 
               
               
                 Case 3 
                 TU30 
                 50/100 
                 12 
                 0 
               
               
                   
               
            
           
         
       
     
       FIGS. 7A-D  show an example timing estimation metrics of the proposed algorithms in simulation Case  1 . With  FIGS. 7A-D  and the following figures, figures A to D correspond to FA, FAmod, MUSIC and MUSICmod timing offset estimation algorithms respectively. It can be seen from this figure that the all proposed algorithms cannot resolve the first three peaks (see  FIG. 5  for the channel profile). While, the MUSIC and the modified MUSIC algorithms can show only one peak clearly. 
       FIGS. 8A-D  shows, as an example, the algorithms&#39; metrics in simulation Case  2 . It can be seen from this figure that the modified MUSIC algorithm&#39;s resolution shows some improvement. It shows a total 5 peaks. The closely located first three peaks still can not be resolved. The FA and FAmod algorithms resolution don&#39;t have significant difference compared with that in case  1 . 
       FIGS. 9A-D  shows the algorithm metric examples in simulation Case  3 . With increased signal bandwidth, all four algorithms&#39; resolution gets improved. From this figure, it can be seen that the FA and FAmod algorithms can resolve the two peaks located around the 2 μsec positions, the MUSIC algorithm shows two peaks in the first 0.5 μsec period, which should be three peaks. The modified MUSIC (MUSICmod) algorithm clearly resolves all peaks. 
       FIGS. 10A-D  to  12 A-D show the algorithms&#39; performance (histogram) in the three simulation cases. In simulation Case  1 , value of parameter α in the First-Peak Searching algorithm is set to 0.4 for all FA, FAmod, MUSIC, MUSICmod metrics. In Case  2  and Case  3 , value of α is set as 0.4 for FA and FAmod metrics, but 0.01 for MUSIC and MUSICmod metrics. The simulation results were taken from 2000 Monte-Carlo tests. The timing drift and Doppler frequency drift that cause by the wireless mobile device movement in one timing estimation have been taken into account in the simulation. The results of the algorithms&#39; performance simulation are summarized in the following table. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Simulation results summary 
               
            
           
           
               
               
               
               
               
            
               
                   
                 FA 
                 FAmod 
                 MUSIC 
                 MUSICmod 
               
               
                   
                 (μsec) 
                 (μsec) 
                 (μsec) 
                 (μsec) 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Case 1 
                 Mean 
                 0.23 
                 0.23 
                 0.23 
                 0.23 
               
               
                   
                 Std 
                 0.15 
                 0.13 
                 0.16 
                 0.14 
               
               
                   
                 95 th   
                 0.23 
                 0.22 us 
                 0.25 
                 0.23 
               
               
                   
                 Percentile 
               
               
                 Case 2 
                 Mean 
                 0.24 
                 0.24 
                 0.23 
                 0.08 
               
               
                   
                 Std 
                 0.03 
                 0.03 
                 0.04 
                 0.04 
               
               
                   
                 95 th   
                 0.06 
                 0.06 
                 0.09 
                 0.08 
               
               
                   
                 Percentile 
               
               
                 Case 3 
                 Mean 
                 0.18 
                 0.18 
                 0.13 
                 0.02 
               
               
                   
                 Std 
                 0.04 
                 0.05 
                 0.02 
                 0.06 
               
               
                   
                 95 th   
                 0.08 
                 0.09 
                 0.04 
                 0.13 
               
               
                   
                 Percentile 
               
               
                   
               
            
           
         
       
     
     From the simulation results, it can be seen that all these algorithms meet the 0.5 μsec 95 th  percentile performance requirement for LTE UL timing synchronization even in worst case of the three simulation scenarios. In simulation Case  1  with low SNR, narrow bandwidth, and low number of SRS OFDM symbols, the FA, FAmod, MUSIC and MUSICmod algorithms have similar performance. In simulation Case  2 , which has high SNR, more SRS OFDM symbols, but same bandwidth comparing with Case  1 , the MUSICmod algorithm has significantly improved the performance of the mean error of the time estimate. However, the performance of the standard deviation (STD) and 95 th  percentile of the timing estimation of MUSIC and MUSICmod algorithms have decreased slightly comparing to the FA and FAmod algorithms. In simulation Case  3 , where the signal bandwidth is doubled comparing with in case  2 , the MUSIC algorithm has slightly better mean error, STD and 95 th  percentile performance than FA and FAmod algorithms. While, the MUSICmod algorithm has the greatest mean error performance, although has slightly worse STD and 95 th  percentile performance, comparing with other algorithms. This very low mean error performance of the MUSICmod algorithm has benefited from the high resolution of the algorithm. 
     Though the proposed timing estimate algorithms are for LTE UL timing synchronization, they can be applied to DL link timing synchronization as well due to similar reference signal structure in both LTE uplink and downlink. 
     While a particular embodiment of the present method for Long Term Evolution (LTE) Radio Link timing synchronization has been described herein, it will be appreciated by those skilled in the art that changes and modifications may be made thereto without departing from the disclosure in its broadest aspects and as set forth in the following claims.