Patent Publication Number: US-7720177-B2

Title: System and method for detecting known sequence in transmitted sequence

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This application relates generally to the fields of frame synchronization, carrier acquisition and tracking, and locating known symbol sequences within transmitted sequences, and, more specifically, to methods of detecting known symbol sequences in transmitted sequences through differential signal processing. 
     2. Related Art 
     In applications where data is transmitted to receivers in the form of discrete groupings of symbols, such as frames, packets or the like, there is a need to identify the frame or packet boundaries so that the data can be recovered and understood. The process of identifying the frame or packet boundaries may be referred to as frame synchronization. 
     Frame synchronization is typically achieved through cooperative action between the transmitter and receiver. At the transmitter, a known sequence of symbols is embedded within each frame of data symbols at a known offset from the frame boundary. Upon receipt of the transmitted signal, the conventional receiver locates the known sequence through coherent detection. Since the known sequence is located at a known offset from the frame boundary, this procedure also locates the frame boundary. 
     A problem arises because, with coherent detection, frame synchronization is delayed by the often substantial time it takes for the receiver to determine the correct orientation of the constellation of possible symbols as mapped onto the complex two-dimensional I-Q plane. 
     Moreover, as an accumulator must be maintained for each of the possible symbol values and their spectral inversion for the purpose of correlating the known sequence with the received sequence for each of the possible orientations of the symbol constellation, coherent detection can be costly. Thus, for a QPSK symbol constellation, eight accumulators must be maintained, one for each of the four possible QPSK symbols, and another for the spectral inversion of each of the four possible QPSK symbols. 
     Even in applications involving continuous streams of data, knowledge of the positions of known symbols in a data flow can assist if not enable carrier acquisition and tracking, particularly at low SNRs. However, the use of error control codes (ECC) and the like cannot generally assist in carrier acquisition and tracking at low SNRs. 
     SUMMARY 
     The invention provides a method, performed within or by a receiver, of locating a known sequence within a transmitted sequence of symbols, which may be continuous or in discrete groupings. 
     In this method, one or more first values are formed from symbols within a portion or more of the transmitted sequence, each representing an estimated difference in phase between first and second symbols that are offset from one another. 
     One or more second values, formed from symbols from the known sequence, each representing an estimated difference in phase between first and second symbols within the known sequence that are likewise offset from one another, are also provided. 
     The estimated differences in phase represented by the first values are then compared with corresponding ones of the estimated differences in phase represented by the second values. If the one or more estimated differences in phase represented by the one or more first values are substantially equal to corresponding ones of the one or more estimated differences in phase represented by the one or more second values, the symbols within the portion or more of the transmitted sequence are determined to be or include the known sequence. 
     Other systems, methods, features and advantages of the invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The invention can be better understood with reference to the following figures. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Moreover, in the figures, like reference numerals designate corresponding parts throughout the different views. 
         FIG. 1A-1C  illustrate the process of successively estimating phase differences between offsetting symbols within the sliding window, and  FIG. 1D  illustrates the subsequent repositioning of the sliding window within the transmitted sequence. 
         FIG. 2A  illustrates a buffer holding the known sequence, and  FIGS. 2B-2D  illustrate the process of successively estimating phase differences between offsetting symbols within the known sequence. 
         FIG. 3A  illustrates a statistic that achieves a resonance condition at a local maxima and  FIG. 3B  illustrates a statistic that achieves a resonance condition at a local minima. 
         FIG. 4  is a flowchart showing a method of synchronizing frames performed by or within a receiver. 
         FIGS. 5A and 5B  illustrate possible frame formats, as well as the undifferentiated data stream of concatenated frames typically received at the receiver. 
         FIG. 6  is a block diagram of a system for locating a known sequence within a transmitted sequence. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1A , in one embodiment of the invention, a transmitted sequence of symbols  100   a ,  100   b ,  100   c  is received by a receiver and then either processed by a filter (not shown) in real time or stored in buffer  102  and then processed by a filter. Each of the symbols in the transmitted sequence is complex, having an in-phase (I) and quadrature (Q) component. A sliding window  104  having a length of N symbols, N being an integer of two or more, is relatively positioned within the sequence at a position i, such that the sliding window  104  encompasses at least a portion of the transmitted sequence. 
     Then, a total of N−k first values are successively formed from the N symbols within the sliding window, where k is an integer of one or more that is less than N. Each of these first values X n , 0≦n≦N−k−1, is computed as x n ·x n+k *, where x n  is the nth symbol within the sliding window, and x n+k * is the complex conjugate of the (n+k)th symbol within the sliding window. As both X n  and x n+k  can be expressed in the form of |A|e jθ , where |A|=√{square root over (I 2 +Q 2 )} and 
               θ   =       tan     -   1       ⁡     (     Q   I     )         ,         
I being the in-phase component of the symbol, and Q being the quadrature component, it can be seen that x n ·x n+k  represents the phase difference Δθ n =θ n −θ n+k  between the two symbols x n  and x n+k  inasmuch as x n =|A n |e jθn , x n+k *=|A n+k |e −jθn+k , and x n ·x n+k *=|A n |·|A n+k |e j(θn−θn+k)  or |A n |·|A n+k |e jΔθn .
 
     In this embodiment, these first values are successively formed in the following order: X 0 , X 1 , . . . , X N−k−1 .  FIG. 1A  illustrates the computation of X 0  from the symbols x 0  and X k  within the sliding window, identified respectively with numerals  106  and  108 , that is representative of the phase difference Δθ 0  between these symbols.  FIG. 1B  illustrates the computation of X 1  from the symbols x 1  and x k+1  within the sliding window, identified respectively with numerals  110  and  112 , that is representative of the phase difference Δθ 1  between these symbols. Finally,  FIG. 1C  illustrates the computation of X N−k−1  from the symbols x N−1  and x N−1+k  within the sliding window, identified respectively with numerals  114  and  116 , that is representative of the phase difference Δθ N−1  between these symbols. 
     Referring to  FIG. 2A , the known sequence of symbols  200   a ,  200   b ,  200   c  may be stored in  202 . Each of the symbols in the known sequence is complex, having in-phase (I) and quadrature (Q) components. Then, a total of N−k second values are successively formed from the N symbols within the known sequence. Each of these second values Y n , 0≦n≦N−k−1, is computed as s n ·s n+k *, where s n  is the nth symbol within the known sequence, and s n+k * is the complex conjugate of the (n+k)th symbol within the known sequence. As both s n  and s n+k  can be expressed in the form of |B|e jφ  where |B|=√{square root over (I 2 +Q 2 )} and 
               φ   =       tan     -   1       ⁡     (     Q   I     )         ,         
I being the in-phase component of the symbol, and Q being the quadrature component, it can be seen that S n ·s n+k  represents the phase difference Δφ n =φ n −φ n+k  between the two symbols s n  and s n+k  inasmuch as s n =|B n |e jφn , s n+k *=|B n+k |e −jφn+k , and s n ·s n+k *=|B n |·|B n+k |e j(φn−φn+k)  or |B n |·|B n+k|e   jΔφn .
 
     In this embodiment, these second values are successively formed in the following order: Y 0 , Y 1 , . . . , Y N−k−1 .  FIG. 2B  illustrates the computation of Y 0  from the symbols s 0  and s k  within the known sequence, identified respectively with numerals  204  and  206 , that is representative of the phase difference Δφ 0  between these symbols.  FIG. 2C  illustrates the computation of Y 1  from the symbols s 1  and s k+1  within the known sequence, identified respectively with numerals  208  and  210 , that is representative of the phase difference Δφ 1  between these symbols. Finally,  FIG. 2D  illustrates the computation of Y N−k−1  from the symbols s N−k−1  and s N−1  within the known sequence, identified respectively with numerals  212  and  214 , that is representative of the phase difference Δφ N−1  between these symbols. These second values Y 0 , Y 1 , . . . , Y N−k−1  have a correspondence with the first values X 0 , X 1 , . . . , X N−k−1 , with the correspondence indicated by the index. Thus, Y 0  corresponds with X 0 , Y 1  corresponds with X 1 , and so on. 
     A statistic Z i , where the index is the relative position i of the sliding window within the transmitted sequence, is then formed from the first and second values. In one example, the statistic, Z i , representing the aggregate difference between the phase differentials represented by the first and second values at a particular stage of the computation, is computed and set equal to: 
                       ∑     n   =   0       N   -   k   -   1       ⁢       Re   ⁡     (     X   n     )       ⨯     Re   ⁡     (     Y   n     )           ±       Im   ⁡     (     X   n     )       ⨯     Im   ⁡     (     Y   n     )                 (   1   )               
where Re is an operator that returns the real part of a complex symbol, and Im is an operator that returns the imaginary part of a complex symbol.
 
     The sliding window  104  is then successively repositioned, and, at each stage, the first values X n  and the statistic Z i  recomputed in the manner previously described, resulting in a set of values of the statistic Z i  over a range of possible positions of the sliding window.  FIG. 1D  depicts the process of recomputing the first values and the statistic from the symbols  118   a ,  118   b ,  118   c  that occurs after the sliding window has been repositioned to position j. The second values Y n  need not be recomputed at each stage as they are invariant to the relative position of the sliding window  104 . 
     The statistic Z i  is then plotted as a function of i, and the location r where the statistic resonates is identified. As shown in  FIG. 3A , the location r may be a local maxima or, as shown in  FIG. 3B , a local minima, depending on the specific form of the equation used to compute the statistic. This location, indicating the location of the sliding window where the aggregate of the phase differences represented by the first values are substantially equal to the aggregate of the phase differences represented by the second values, is determined to be the location of the known sequence within the transmitted sequence. 
     The foregoing represents one embodiment of the invention, and it should be appreciated that many alternative embodiments are possible. For example, in lieu of repositioning a sliding window within the transmitted sequence at each stage of the computation, the location of the sliding window may be fixed, and a different portion of the transmitted sequence shifted into the portion of the buffer encompassed by the sliding window at each stage of the computation. 
     As another example, many expressions for computing the statistic Z i  are possible. In lieu of equation (1), for example, the following expression may be used: 
                       ∑     n   =   0       N   -   k   -   1       ⁢       Re   ⁡     (     X   n     )       ⨯     Im   ⁡     (     Y   n     )           ±       Im   ⁡     (     X   n     )       ⨯     Re   ⁡     (     Y   n     )                 (   2   )               
Alternatively, the statistic may be computed as any of one of:
 A n   2 +B n   2   (3) |A n |+|B n |  (4) max(|A n |,|B n |)  (5) 
where
 
     
       
         
           
             
               
                 
                   
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     In one application, the foregoing method may be utilized by or within a receiver to synchronize frames. Referring to  FIG. 4 , a flowchart of one embodiment  400  of the foregoing method as applied to frame synchronization is illustrated. 
     In step  402 , a portion or more of a frame is received, the frame conforming to a format (assumed known to the receiver) calling for a sequence of N known symbols to be located within the frame at a known offset (which could be zero) from one of the frame ends. Thus, as shown in  FIG. 5A , the known sequence  502  may be located at the beginning of frame  500  or, as shown in  FIG. 5B , at a known offset of p symbols from the beginning of the frame. Although the frame format is assumed known to the receiver, as the frame is often part of an undifferentiated data stream, with other frames (shown in phantom in  FIGS. 5A and 5B ) having like format concatenated to the received frame, the frame ends are often not known to the receiver. The goal of the method is to first locate the known sequence  502  within a frame, and then, using the known format, locate the frame end  504 , as well as subsequent frame ends  506  (using the total frame size that is also known to the receiver). 
     Returning to  FIG. 4 , in step  404 , a sliding window of size N is relatively positioned such that the sliding window encompasses N symbols at position i within the frame. 
     In step  406 , N−k first values X 0 , X 1 , . . . , X N−k−1  are successively formed from symbols within the sliding window as previously described, each representing an estimated difference in phase between first and second symbols within the sliding window that are offset from one another by k symbols, where k is an integer of one or more that is less than N, which offset may be known or unknown to the receiver. 
     In step  408 , N−k−1 second values Y 0 , Y 1 , . . . , Y N−k−1  successively formed from symbols within the known sequence as previously described are provided, each representing an estimated difference in phase between first and second symbols within the known sequence that are offset from one another by k symbols, and each having a correspondence with one of the first values X 0 , X 1 , . . . , X N−k− 1. A statistic Z i  is formed from the first and second values in the manner previously described. 
     In step  410 , a query is made whether the substantial entirety of the frame has been covered by the sliding window. For example, assuming M symbols within the frame, the method determines whether values of the statistic Z i  have been obtained for values of the index i that substantially span the range of 0 to M. If not, the method jumps back to step  404  and performs another iteration after the sliding window has been relatively positioned to a new location. If so, the method proceeds to step  412 . 
     In step  412 , the value of index i where the statistic Z i  achieves a resonance condition is identified. This location is determined to be the location of the known sequence within the frame. Using the known frame format, the method then identifies a frame end, and, using the known frame size, the ends of subsequent frames. 
       FIG. 6  illustrates an embodiment  600  of a system, within or forming part of a receiver, for locating a known sequence of symbols within a transmitted sequence of symbols, the known sequence having a size of N symbols, wherein N is an integer of two or more. 
     The transmitted sequence is serially clocked into shift register  602  on a first-in-first-out basis through a serial input  606 . The clocking of the shift register  602  is controlled by processor  608  through one or more control signals (not shown). An end portion  604  of shift register  602  having a length of N symbols forms a sliding window that is relatively positioned as the transmitted data serially progresses through the shift register  602 . The relative position of the sliding window in relation to the transmitted sequence at a particular moment forms an index i. 
     A parallel output  605  of width N provides the N symbols within the end portion  604  to a processor  608  that is configured to compute the N−k−1 first values X 0 , X 1 , . . . , X N−k− 1, from the N symbols within the end portion  604  in the manner previously described. 
     A memory  610  accessible by processor  608  holds the N−k second values Y 0 , Y 1  . . . , Y N−k−1  previously computed by processor  608  from the known sequence in the manner previously described. During a previous initialization process, an array  612  of M locations  614   a ,  614   b ,  614   c  was reserved in the memory  610  for population by the computed values of the statistic Z i . 
     A flag  618   a ,  618   b ,  618   c  maintained within memory  610  for each of these M locations indicates whether the corresponding location is populated or not. If set, the flag indicates the corresponding location has been populated. If reset, the flag indicates the corresponding location has not been populated. During the previously mentioned initialization process, each of these flags is reset. 
     During a particular stage of operation, the processor  608  calculates the statistic Z i  as previously described and stores it at the specific location in the array corresponding to the value of the index i. To indicate that the memory location has been populated, the processor  608  also sets the associated flag. 
     The processor  608  then examines the flags  618   a ,  618   b ,  618   c . If the flags indicate that any of the locations  614   a ,  614   b ,  614   c  remain unpopulated, the processor  608  directs the shift register  602  to shift the transmitted sequence until the sliding window represented by the end portion  604  is relatively positioned at a position corresponding to one of the unpopulated entries. With the sliding window relatively repositioned, the first values and the statistic are recomputed. The foregoing process is then repeated until all of the locations in the array have been populated. 
     The processor  608  then identifies the index r at which the statistic Z i  achieves a resonance condition, and uses that to locate the known sequence within the transmitted sequence. 
     While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible that are within the scope of this invention. For example, in lieu of the embodiment illustrated in  FIG. 6 , embodiments are possible where any of the described functionality may be performed by one or more logic devices, components, or modules, keeping in mind that, for purposes of this disclosure, the logic may be implemented as hardware, software, or a combination of hardware and software. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.