Abstract:
A method for differential phase evaluation of M-ary communication data is employed in which the data consists of N sequential symbols r 1  . . . r N , each having one of M transmitted phases. Selected sequences of N−1 elements that represent possible sequences of phase differentials are evaluated using multiple-symbol differential detection. Using r 1  as the reference for each phase differential estimate, s N−1  phase differential sequences are selected in the form (P 2i , P 3i , . . . , P Ni ) for i=1 to s for evaluating said symbol set, where s is predetermined and 1&lt;s&lt;M. Each set of s phase differential estimate values are chosen based on being the closest in value to the actual transmitted phase differential value. These s phase differential estimates can be determined mathematically as those which produce the maximum results using conventional differential detection.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This application is a continuation of U.S. patent application Ser. No. 11/015,220, filed on Dec. 17, 2004, which in turn is a continuation of U.S. patent application Ser. No. 10/279,238, filed on Oct. 24, 2002. 

   FIELD OF THE INVENTION 
   This invention relates to wireless telecommunications. 
   BACKGROUND OF THE INVENTION 
   Conventionally, communication receivers use two types of MPSK modulated signal detection: coherent detection and differential detection. In coherent detection, a carrier phase reference is detected at the receiver, against which subsequent symbol phases are compared to estimate the actual information phase. Differential detection processes the difference between the received phases of two consecutive symbols to determine the actual phase. The reference phase is the phase of the first of the two consecutive symbols, against which the difference is taken. Although differential detection eliminates the need for carrier phase reference processing in the receiver, it requires a higher signal-to-noise ratio at a given symbol error rate. 
   Differential detection in an Additive White Gaussian Noise (AWGN) channel is preferred over coherent detection when simplicity of implementation and robustness take precedence over receiver sensitivity performance. Differential detection is also preferred when it is difficult to generate a coherent demodulation reference signal. For differential detection of multiple-phase shift keying (MPSK) modulation, the input phase information is differentially encoded at the transmitter, then demodulation is implemented by comparing the received phase between consecutive symbol intervals. Therefore, for proper operation, the received carrier reference phase should be constant over at least two symbol intervals. 
   Multiple-symbol differential detection (MSDD) uses more than two consecutive symbols and can provide better error rate performance than conventional differential detection (DD) using only two consecutive symbols. As in the case of DD, MSDD requires that the received carrier reference phase be constant over the consecutive symbol intervals used in the process. 
   Detailed discussions of MSDD and Multiple Symbol Detection (MSD) are found in, “Multiple-Symbol Differential Detection of MPSK” (Divsalar et al., IEEE TRANSACTIONS ON COMMUNICATIONS, Vol. 38, No. 3, Mar. 1990) and “Multiple-Symbol Detection for Orthogonal Modulation in CDMA System” (Li et al., IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, Vol. 50, No. 1, January 2001). 
   Conventional MPSK MSDD is explained in conjunction with  FIGS. 1 and 2  below.  FIG. 1  shows an AWGN communication channel  101  with an MPSK signal sequence r that comprises N consecutive symbols r 1  . . . r N  received by receiver  110 . Symbol r k  represents the k th  component of the N length sequence r, where 1≦k≦N. The value for r k  is a vector represented by Equation (1): 
                   r   k     =             2   ⁢     E   S         T   S         ⁢     ⅇ       jϕ   k     +     jθ   k           +     n   k               Eq   .           ⁢     (   1   )                 
having symbol energy Es, symbol interval Ts and transmitted phase φ k  where j=√{square root over (−1)}. Value n k  is a sample taken from a stationary complex white Gaussian noise process with zero mean. Value θ k  is an arbitrary random channel phase shift introduced by the channel and is assumed to be uniformly distributed in the interval (−π, π). Although channel phase shift θ k  is unknown, differential detection conventionally operates assuming θ k  is constant across the interval of observed symbols r 1  to r N . For differential MPSK (DMPSK), phase information is differentially encoded at the transmitter, and transmitted phase φ k  is represented by:
 φ k =φ k-1 +Δφ k   Eq. (2) 
where Δφ k  is the transmitted information phase differential corresponding to the k th  transmission interval that takes on one of M uniformly distributed values within the set Ω={2 πm/M, m=0, 1, . . . , M−1}around the unit circle, as in a Gray mapping scheme. For example, for QPSK, M=4 and Δφ k =0, π/2, π, or 3π/2 for each k from 1 to N.
 
   It is assumed for simplicity that arbitrary phase value θ k  is constant (θ k =θ) over the N-length of the observed sequence. 
   At the receiver, optimum detection using multiple-symbol differential detection (MSDD) is achieved by selecting an estimated sequence of phase differentials {d{circumflex over (φ)} 1 , d{circumflex over (φ)} 2 , . . . , d{circumflex over (φ)} N−1 } which maximizes the following decision statistic: 
   
     
       
         
           
             
               
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   By Equation (3), the received signal is observed over N symbol time intervals while simultaneously selecting the optimum estimated phase sequence {d{circumflex over (φ)} 1 , d{circumflex over (φ)} 2 , . . . , d{circumflex over (φ)} N−1 }. The maximized vector sum of the N-length signal sequence r k , provides the maximum-likelihood detection, where estimated phase differential d{circumflex over (φ)} m  is the difference between estimated phase {circumflex over (φ)} m+1  and the estimate of the first phase {circumflex over (φ)} 1 .
 
 d{circumflex over (φ)}   m ={circumflex over (φ)} m+1 −{circumflex over (φ)} 1 .  Eq. (4)
 
The estimate of transmitted information phase sequence {Δ{circumflex over (φ)} 1 , Δ{circumflex over (φ)} 2 , . . . , Δ{circumflex over (φ)} N−1 } is obtained from the estimated phase sequence {d{circumflex over (φ)} 1 , d{circumflex over (φ)} 2 , . . . , d{circumflex over (φ)} N−1 } using Equation (5).
 
                   d   ⁢           ⁢       ϕ   ^     m       =       ∑     k   =   1     m     ⁢     Δ   ⁢           ⁢       ϕ   ^     k                 Eq   .           ⁢     (   5   )                 
Value Δ{circumflex over (φ)} k  is an estimate of transmitted phase differential Δφ k . Since d{circumflex over (φ)} k  (1≦k≦N−1) takes on one of M uniformly distributed Ω values {2 πm/M, m=0, 1, . . . , M−1}, the conventional MSDD detection searches all possible phase differential sequences and there are M N−1  such phases. The error rate performance improves by increasing the observed sequence length N, which preferably is selected to be N=4 or N=5. As an example, for 16PSK modulation with N=5, the number of phase differential sequences to search is 16 4 =65536. As evident by this considerably large number of sequences, simplicity in the search sequence is sacrificed in order to achieve a desirable error rate performance.
 
     FIG. 2  shows the process flow diagram for algorithm  200 , which performs conventional MSDD. It begins with step  201  where N consecutive symbols r k  for k=1 to N is observed. Next, the possible sets of phase differential sequences {d{circumflex over (φ)} 1 , d{circumflex over (φ)} 2 , . . . , d{circumflex over (φ)} N−1 } where each d{circumflex over (φ)} k , for k=1 to N−1, is one from the set of M uniformly distributed phase values in the set Ω={2 πm/M, m=0, 1, . . . , M−1}. There are M N−1  possible sets.  FIG. 5  shows an example of an array of such sets, where N=4 and M=4, which illustrates the 4 4-1 =64 possible sets of phase differential sequences. In step  203 , each possible phase sequence is attempted in the expression 
                      r   1     +       ∑     m   =   2     N     ⁢       r   m     ⁢     ⅇ       -   j     ⁢           ⁢   d   ⁢           ⁢       ϕ   ^       m   -   1                      2     ,         
giving a total of M N−1  values. Next, in step  204 , the maximum value is found for step  203 , which indicates the best estimate phase differential sequence. Finally, in step  205 , the final information phase sequence {Δ{circumflex over (φ)} 1 , Δ{circumflex over (φ)} 2 , . . . , Δ{circumflex over (φ)} N−1 } is estimated from {d{circumflex over (φ)} 1 , d{circumflex over (φ)} 2 , . . . , d{circumflex over (φ)} N−1 } using Equation (5) and the information bits are obtained from Gray de-mapping between phase and bits.
 
   Although MSDD provides much better error performance than conventional DD (symbol-by-symbol), MSDD complexity is significantly greater. Therefore, it is desirable to provide an improved method and system for MSDD with less complexity. 
   SUMMARY 
   A method for multiple-symbol differential detection phase evaluation of M-ary communication data is employed in which the data consists of N sequential symbols r 1  . . . r N , each having one of M transmitted phases. Selected sequences of N−1 elements that represent possible sequences of phase differentials are evaluated using multiple-symbol differential detection. Next, using r 1  as the reference for each phase differential estimate, s N−1  phase differential sequences are selected in the form (P 2i , P 3i , . . . , P Ni ) for i=1 to s for evaluating said symbol set, where s is predetermined and 1&lt;s&lt;M. Rather than attempting every one of the M possible phase differential values during the estimation, the reduced subset of s phase differential estimate values are chosen based on being the closest in value to the actual transmitted phase differential value. These s phase differential estimates can be determined mathematically as those which produce the maximum results in the differential detection expression |r 1 +r k+1 e −jβ     k   | 2 . 
   Each of the s N−1  phase differential sequences are then evaluated using MSDD to determine the final maximum likelihood phase sequence. The resulting final phase sequence can be used to determine the information phase estimates and the phase information bits by Gray de-mapping. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a representation of a channel symbol stream for a receiver; 
       FIG. 2  shows a process flow diagram of an algorithm  200  for conventional MSDD; 
       FIG. 3A  shows a process flow diagram of an algorithm  300  for reduced complexity MSDD; 
       FIG. 3B  shows a detailed process flow diagram for step  302  of  FIG. 3A ; 
       FIGS. 4A ,  4 B,  4 C show a block diagram of an implementation of the reduced complexity MSDD algorithm; 
       FIG. 5  shows a table of possible phase sequences processed by a conventional MSDD algorithm; and 
       FIG. 6  graphically shows a comparison of the symbol error rate performances for the conventional and simplified MSDD algorithms. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 3A  shows a MSDD algorithm  300  that reduces the search complexity of the MSDD of algorithm  200 , using a subset search concept. First, in step  301 , N consecutive symbols r k  are observed for 1≦k≦N−1. In step  302 , s N−1  sets of phase differential estimate sequences {β 1 , β 2 , . . . , β N−1 } are selected as optimum estimates from among the full set of M N−1  phase estimates attempted in algorithm  200 . Turning to  FIG. 3B , step  302  is broken down in further detail. In step  302 A, the initial received signal r 1  is selected as a preferred reference for determining phase differentials between r 1  and each subsequent r k . In step  302 B, a small candidate subset of s phase differential estimates {β k1 , β k2 , . . . , β ks }(1≦k≦N−1), among all M possible phases {2 πm/M, m=0, 1, . . . , M−1} where 1&lt;s&lt;M and s is predetermined. The s phase estimates that are selected are the closest in value to the actual phase differential Δφ k . In order to obtain the closest values for the phase differential estimates, each β k  is applied to the conventional DD expression |r 1 +r k+1 e −jβ     k   | 2  from which the s phase differential estimates {β k1 , β k2 , . . . , β ks } that produce the maximum resulting value are selected. With the inclusion of this symbol-by-symbol DD process step ( 302 B), it can be seen that algorithm  300  is a combination of MSDD and DD processing. In step  302 C, there are now s N−1  sets of optimum phase differential sequences, where P k ={β k1 , β k2 , . . . , β ks }. Returning to  FIG. 3A , the result of step  302  is s N−1  sequences of phases (P 1 , P 2 , . . . P N−1 ). These are the maximum-likelihood phase differential candidates. That is, the s values for P 1  are the closest in value to the actual phase differential Δφ 1 , the s values for P 2  are the closest to actual phase differential Δφ 2 , and so on. 
   In step  303 , all s N−1  possible phase sequences (P 1 , P 2 , . . . P N−1 ) are attempted within the expression 
                      r   1     +       ∑     m   =   2     N     ⁢       r   m     ⁢     ⅇ       -   j     ⁢           ⁢     β     m   -   1                      2     .         
These sets of phase candidates are significantly reduced in number compared with algorithm  200  since s&lt;M and s N−1 &lt;M N−1 . When s is very small, the number of phase differential sequences to search becomes much smaller, which leads to significant complexity savings. As an example, for s=2, N=4 and M=4, there will be eight (8) sets of phase differential sequences that will result. This is a much smaller subset of the sixty-four (64) phase differential sequences shown in  FIG. 5 , which would be processed in a conventional MSDD algorithm, such as algorithm  200 .
 
   In step  304 , the maximum resulting vectors from step  303  determine the optimum phase differential sequence {β 1 , . . . , β 2 , . . . , β N−1 }. Steps  303  and  304  in combination can be expressed by the following decision statistic: 
                   η   new     =       max         β   1     ∈     P   1       ,   …   ⁢           ,       β     N   -   1       ∈     P     N   -   1             ⁢              r   1     +       ∑     m   =   2     N     ⁢       r   m     ⁢     ⅇ       -   j     ⁢           ⁢     β     m   -   1                      2               Eq   .           ⁢     (   6   )                 
When s=M, the statistic is simply η new =η.
 
   In step  305 , the final information phase sequence {Δ{circumflex over (φ)} 1 , Δ{circumflex over (φ)} 2 , . . . , Δ{circumflex over (φ)} N−1 } is estimated from the optimum phase differential sequence {β 1 , β 2 , . . . , β N−1 } using Equation (7) and the phase information bits are obtained by Gray de-mapping. 
   
     
       
         
           
             
               
                 
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     FIG. 4  shows a block diagram of MSDD parallel implementation  400 , where N=4, s=2. Since N=4, there are N−1=3 parallel selection circuits  401 ,  402 ,  403 , for determining s N−1  (i.e., 8) subsets (P 1 , P 2 , P 3 ) of candidate phases. Selection circuit  401  comprises delay blocks  410 ,  411 ; conjugator  412 , multiplier  413 , multiplier  415   k  (k=0 to N−1), amplitude blocks  416   k  (k=0 to N−1), decision block  417  multipliers  418 ,  419  and switch  450 . Input symbol r k+3  passes through delays  410 ,  411  for establishing r k  as the reference symbol and r k+1  as the consecutive symbol against which the phase differential is to be estimated. The output of conjugator  412  produces conjugate r k *, which when multiplied with consecutive symbol r k+1  by multiplier  413 , produces a phase difference value. Next, the phase difference is multiplied by multipliers  415   k  to each phase in the set β k , where β k =(2 πk/M, k=0, 1, . . . , M−1). Next, the products are passed through amplitude blocks  415   k  and input to decision block  417 , which selects the maximum s=2 inputs for the subset P 1 =[β k1 , β k2 ]. The outputs of block  401  are the products r k+1 e −jβk1  and r k+1 e −jβk2  output by multipliers  418 ,  419 . 
   Decision circuits  402  and  403  comprise parallel sets of similar elements as described for block  401 . Decision circuit  402  includes delay blocks  420 ,  421 , which allow processing of reference symbol r k  with r k+2 , whereby decision block  427  chooses candidate phases P 2 =[β k3 , β k4 ]. Likewise, block  403  includes delay block  431  to allow decision block  437  to select phase differential candidates P 3 =[β k5 , β k6 ] for reference symbol r k  and symbol r k+3 . Summer  404  adds alternating combinations of outputs from blocks  401 ,  402  and  403  alternated by switches  450 ,  451 ,  452 , respectively, plus reference symbol r k . Since s=2, there are 2 3 =8 combinations of phase differential sequence (P 1 , P 2 , P 3 ) produced by switches  450 ,  451 ,  452 . Decision block  405  selects the optimum phase differential sequence {β 1 , β 2 , β 3 }, which is the phase differential sequence (P 1 , P 2 , P 3 ) that produces the maximum sum. 
     FIG. 6  shows the symbol error rate (SER) performance of the MSDD algorithm for 16PSK, where s=2 for different symbol observation lengths N=3, 4 and 5. As shown in  FIG. 6 , reduced-complexity MSDD algorithm  300  with s=2 provides almost the same performance as the original MSDD algorithm  200  where s=M. This is because the MSDD algorithm  300  selects one of the two closest phases between the vector r k+1 e −jβ     k    (1≦k≦N−1) and r 1  in order to maximize the statistic of Equation (6). Therefore, for 2&lt;s&lt;M, the performance is essentially the same as for s=2, which means there is no benefit to increasing the complexity of algorithm  300  to s&gt;2. Therefore, the optimum results are gained using the simplest possible choice for s, that is s=2. 
   Table 1 shows the complexity comparison of algorithm  300  with s=2 for symbol observation length N=5 against algorithm  200 . The number of phase differential sequences to search is reduced significantly, resulting in faster processing speeds. 
   
     
       
             
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
                 
                 
               No. of phase 
               No. of phase 
                 
                 
             
             
                 
                 
               differential 
               differential 
             
             
                 
                 
               sequences to 
               sequences to 
                 
               Speed 
             
             
                 
                 
               search 
               search 
                 
               factor 
             
             
                 
                 
               for MSDD 200 
               for MSDD 300 
               Reduction 
               (x times 
             
             
               M 
               Modulation 
               (M N−1 ) 
               (s N−1 ) 
               factor 
               faster) 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               4 
               4 PSK 
               256 
               16 
               16 
               12 
             
             
               8 
               8 PSK 
               4096 
               16 
               256 
               229 
             
             
               16 
               16 PSK  
               65536 
               16 
               4096 
               3667 
             
             
                 
             
           
        
       
     
   
   Although features and elements are described above in particular combinations, each feature or element can be used alone without the other features and elements or in various combinations with or without other features and elements. The methods or flow charts provided herein may be implemented in a computer program, software, or firmware incorporated in a computer-readable storage medium for execution by a general purpose computer or a processor. Examples of computer-readable storage mediums include a read only memory (ROM), a random access memory (RAM), a register, cache memory, semiconductor memory devices, magnetic media such as internal hard disks and removable disks, magneto-optical media, and optical media such as CD-ROM disks, and digital versatile disks (DVDs). 
   Suitable processors include, by way of example, a general purpose processor, a special purpose processor, a conventional processor, a digital signal processor (DSP), a plurality of microprocessors, one or more microprocessors in association with a DSP core, a controller, a microcontroller, Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) circuits, any other type of integrated circuit (IC), and/or a state machine. 
   A processor in association with software may be used to implement a radio frequency transceiver for use in a wireless transmit receive unit (WTRU), user equipment (UE), terminal, base station, radio network controller (RNC), or any host computer. The WTRU may be used in conjunction with modules, implemented in hardware and/or software, such as a camera, a video camera module, a videophone, a speakerphone, a vibration device, a speaker, a microphone, a television transceiver, a hands free headset, a keyboard, a Bluetooth® module, a frequency modulated (FM) radio unit, a liquid crystal display (LCD) display unit, an organic light-emitting diode (OLED) display unit, a digital music player, a media player, a video game player module, an Internet browser, and/or any wireless local area network (WLAN) or Ultra Wide Band (UWB) module.