Abstract:
Methods and arrangements are provided where signaling of the modulation type by means of rotation of the training sequence is provided. For each modulation type, a set of rotation angles is chosen. These sets have no element in common. New training sequences are generated by rotating one original training sequence. The rotation angle that minimizes the PAPR of the transmit signal can be chosen. At the receiver side, knowing the original training sequence, the receiver estimates blindly the rotation angle among the known possible rotation angles. The estimated rotation angle in the receiver maps to a unique modulation type.

Description:
RELATED APPLICATIONS 
       [0001]    This application claims priority to PCT/SE2011/050184 filed Feb. 18, 2011, and U.S. Provisional Patent Application No. 61/308,340, filed Feb. 26, 2010, both of which are incorporated herein by reference in their entireties. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates to a method and arrangement in a telecommunication system, in particular to a method and an arrangement to jointly reduce Peak to Average Power Ratio (PAPR) and signal modulation for pre-coded Enhanced General Packet Radio Service (EGPRS). 
       BACKGROUND 
       [0003]    Despite the fact that Global System for Mobile Communication (GSM) networks have been commercially deployed for almost two decades, interest on the continued improvement of the GSM/Enhanced Data rates for GSM Evolution (EDGE) technology has not dwindled. Network equipment manufacturers, mobile equipment manufacturers and telecom operators continue to develop the GSM system further. Improvements to the hardware/spectral efficiencies for both voice and packet data services are being actively sought. To this end, precoded EGPRS/EGPRS phase 2 (EGPRS2) has been proposed. Precoding involves transformation of the symbol sequence using some suitable transform. Typically a Fourier Transformation is used.  FIG. 1  gives a high level view of precoded EGPRS/EGPRS2. 
         [0004]    The blocks within the dashed box in  FIG. 1  will now be described. After burst formatting, the bit sequence (b n ) has the following structure. 
         [0000]    
       
         
           
             ( 
             
               
                 
                   
                     b 
                     1 
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     b 
                     α 
                   
                 
                 
                    
                   guard 
                 
               
               , 
               
                 
                   
                     b 
                     
                       α 
                       + 
                       1 
                     
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     b 
                     β 
                   
                 
                 
                    
                   tail 
                 
               
               , 
               
                 
                   
                     b 
                     
                       β 
                       + 
                       1 
                     
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     b 
                     γ 
                   
                 
                 
                    
                   data 
                 
               
               , 
               
                 
                   
                     b 
                     
                       γ 
                       + 
                       1 
                     
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     b 
                     δ 
                   
                 
                 
                    
                   training 
                 
               
               , 
               
                 
                   
                     b 
                     
                       δ 
                       + 
                       1 
                     
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     b 
                     ɛ 
                   
                 
                 
                    
                   data 
                 
               
               , 
               
                 
                   
                     b 
                     
                       ɛ 
                       + 
                       1 
                     
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     b 
                     ϕ 
                   
                 
                 
                    
                   tail 
                 
               
               , 
               
                 
                   
                     b 
                     
                       ϕ 
                       + 
                       1 
                     
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     b 
                     φ 
                   
                 
                 
                    
                   guard 
                 
               
             
             ) 
           
         
       
     
         [0005]    These bits are mapped to symbols drawn from a Phase Shift Keying (PSK)/Quadrature Amplitude Modulation (QAM) symbol constellation. The letters s, x, t, g will be used to denote PSK/QAM symbols that carry training, payload, tail or guard bits respectively. Thus, 
         [0000]      ( b   1   , . . . , b   α   , b   φ+1   , . . . , b   φ )→{right arrow over ( g )}=( g   1   , . . . , g   η )(guard)
 
         [0000]      ( b   α+1   , . . . , b   β   , b   ε+1   , . . . , b   φ )→{right arrow over ( t )}=( t   1   , . . . , t   v )(tail)
 
         [0000]      ( b   β+1   , . . . , b   γ   , b   δ+1   , . . . , b   ε )→{right arrow over ( x )}=( x   1   , . . . , x   D )(payload)
 
         [0000]      ( b   γ+1   , . . . , b   δ )→{right arrow over ( s )}=( s   1   , . . . , s   N     tr   )(training symbols),
 
         [0000]    where η is the total number of guard symbols, v is the total number of tail symbols, D is the total number of payload symbols and N tr  is the number of training symbols. The total number of payload plus training symbols is N=D+N tr  and the total number of symbols in the burst is K=N+η+v. 
         [0006]    The output of the symbol mapping block is the sequence of symbols 
         [0000]    
       
         
           
             
               [ 
               
                 
                   c 
                   1 
                 
                 , 
                 … 
                  
                 
                     
                 
                 , 
                 
                   c 
                   K 
                 
               
               ] 
             
              
             
               = 
               def 
             
              
             
               
                 [ 
                 
                   
                     g 
                     -&gt; 
                   
                   , 
                   
                     t 
                     -&gt; 
                   
                   , 
                   
                     x 
                     -&gt; 
                   
                   , 
                   
                     d 
                     -&gt; 
                   
                 
                 ] 
               
               . 
             
           
         
       
     
         [0007]    It is convenient to intercalate the training symbols and the payload symbols for synchronization and channel estimation purposes. A vector {right arrow over (z)} of length N is constructed from the payload {right arrow over (x)} and training symbols {right arrow over (s)} accordingly. 
         [0000]    
       
         
           
             
               z 
               -&gt; 
             
             = 
             
               
                 
                   [ 
                   
                     
                       z 
                       1 
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       z 
                       N 
                     
                   
                   ] 
                 
                 T 
               
                
               
                 = 
                 def 
               
                
               
                 
                   
                     [ 
                     
                       
                         x 
                         1 
                       
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         s 
                         1 
                       
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         x 
                         p 
                       
                       , 
                       
                         s 
                         m 
                       
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         s 
                         
                           N 
                           tr 
                         
                       
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         x 
                         D 
                       
                     
                     ] 
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                   ↕ 
                   
                       
                   
                   ↕ 
                   
                       
                   
                   ↕ 
                   
                       
                   
                   ↕ 
                   
                       
                   
                   ↕ 
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     k 
                      
                     
                       ( 
                       1 
                       ) 
                     
                   
                 
                  
                 
                     
                 
                  
                 … 
                  
                 
                     
                 
                  
                 
                   n 
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
                  
                 
                     
                 
                  
                 … 
                  
                 
                     
                 
                  
                 
                   k 
                    
                   
                     ( 
                     p 
                     ) 
                   
                 
                  
                 
                     
                 
                  
                 
                   n 
                    
                   
                     ( 
                     m 
                     ) 
                   
                 
                  
                 
                     
                 
                  
                 
                   n 
                    
                   
                     ( 
                     
                       N 
                       tr 
                     
                     ) 
                   
                 
                  
                 
                     
                 
                  
                 
                   k 
                    
                   
                     ( 
                     D 
                     ) 
                   
                 
               
             
           
         
       
     
         [0008]    The location of the training symbols is given by the indices (n(m)) m=1   N     tr   . Likewise, the location of the payload symbols is given by (k(m)) m=1   D . That is, z n(p) =s p  and z k(p)=x   p . The location of the training symbols should be chosen carefully as it has a large impact on the receiver performance. Discrete Fourier Transform (DFT)-precoding is applied to {right arrow over (z)} to form a new sequence of complex numbers {right arrow over (Z)} as follows. Let W be the Fourier transform matrix of size N×N whose entry in the m-th row and i-th column is 
         [0000]    
       
         
           
             
               
                 W 
                 
                   m 
                   , 
                   i 
                 
               
                
               
                 = 
                 def 
               
                
               
                 
                   1 
                   
                     N 
                   
                 
                  
                 
                   exp 
                    
                   
                     ( 
                     
                       
                         - 
                         j 
                       
                        
                       
                           
                       
                        
                       2 
                        
                       
                         π 
                          
                         
                           ( 
                           
                             m 
                             - 
                             1 
                           
                           ) 
                         
                       
                        
                       
                         
                           ( 
                           
                             i 
                             - 
                             1 
                           
                           ) 
                         
                         / 
                         N 
                       
                     
                     ) 
                   
                 
               
             
             , 
             
               
                 for 
                  
                 
                     
                 
                  
                 1 
               
               ≤ 
               m 
             
             , 
             
               i 
               ≤ 
               
                 N 
                 . 
               
             
           
         
       
     
         [0000]    The pre-coding operation is {right arrow over (Z)}=W H ·{right arrow over (z)}. 
         [0009]    Multiplication by the matrix W H  can be implemented efficiently using the fast Fourier transform. Next, an integer L≧0 is chosen and the last L terms in {right arrow over (Z)} are appended at the beginning of {right arrow over (Z)} to form a new vector {right arrow over (Z)} P . In other words, a cyclic prefix of length L is added. For example the values L=0 (no prefix) or L=5 (typical GSM channel length) may be used. Using vector notation, the precoded symbols with the cyclic prefix added are 
         [0000]    
       
         
           
             
               
                 Z 
                 -&gt; 
               
               P 
             
             = 
             
               
                 [ 
                 
                   
                     Z 
                     1 
                     P 
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     Z 
                     
                       N 
                       + 
                       L 
                     
                     P 
                   
                 
                 ] 
               
                
               
                 = 
                 def 
               
                
               
                 
                   [ 
                   
                     
                       Z 
                       
                         N 
                         - 
                         L 
                       
                     
                     , 
                     
                       Z 
                       
                         N 
                         - 
                         L 
                         + 
                         1 
                       
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       Z 
                       N 
                     
                     , 
                     
                       Z 
                       1 
                     
                     , 
                     
                       Z 
                       2 
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       Z 
                       N 
                     
                   
                   ] 
                 
                 . 
               
             
           
         
       
     
         [0010]    The output of the vector precoding (IDFT) block is the sequence of complex numbers 
         [0000]    
       
         
           
             
               [ 
               
                 
                   d 
                   1 
                 
                 , 
                 
                   d 
                   2 
                 
                 , 
                 … 
                  
                 
                     
                 
                 , 
                 
                   d 
                   K 
                 
               
               ] 
             
              
             
               = 
               def 
             
              
             
               
                 [ 
                 
                   
                     
                       
                         g 
                         1 
                       
                       , 
                       … 
                     
                     
                        
                       guard 
                     
                   
                    
                   
                       
                   
                   , 
                   
                     
                       
                         t 
                         1 
                       
                       , 
                       … 
                     
                     
                        
                       tail 
                     
                   
                    
                   
                       
                   
                   , 
                   
                     
                       
                         Z 
                         1 
                         P 
                       
                       , 
                       
                         Z 
                         2 
                         P 
                       
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         Z 
                         
                           N 
                           + 
                           L 
                         
                         P 
                       
                     
                     
                        
                       
                         payload 
                         + 
                         pilots 
                       
                     
                   
                   , 
                   
                     
                       … 
                        
                       
                           
                       
                       , 
                       
                         t 
                         v 
                       
                     
                     
                        
                       tail 
                     
                   
                   , 
                   
                     
                       … 
                        
                       
                           
                       
                       , 
                       
                         g 
                         η 
                       
                     
                     
                        
                       guard 
                     
                   
                 
                 ] 
               
               . 
             
           
         
       
     
         [0011]    This sequence is upsampled, filtered, upmixed, amplified and sent to the air using a linear modulator such as the EDGE modulator used in a GSM/EDGE Base Transceiver Station (BTS). 
         [0012]    In EGRPS and EGPRS2 the modulation used is not known at the receiver and must be detected. This procedure is called blind detection of modulation. In particular, in EGPRS/EGPRS2, the modulation used is signalled through rotation of the transmitted symbols. Different rotation angles correspond to different modulation types (e.g. 3π/8 for 8PSK, π/4 for 16QAM, −π/4 for 32 QAM are used in EGPRS2-A). 
         [0013]    One of the main drawbacks of precoded EGPRS is that the Peak to Average Power Ratio (PAPR) of the transmitted signal is very large. 
         [0014]    It is known that it is possible to use different training sequences in order to reduce PAPR. The method can be summarized as follows. A finite set of M training sequences is designed and fixed. For any given burst, M different transmit signals are generated, all sharing the same payload, but differing in the training sequence. Of the M generated transmit signals, the one with the lowest PAPR is chosen, and it is transmitted over the air. The other M−1 signals are discarded and are not transmitted. At the receiver side, the receiver uses blind detection in order to estimate the training sequence that was actually used among the possible M training sequences. This is also described in Orthogonal Pilot Sequences for Peak-to-Average Power Reduction in OFDM, M. J. Fernandez-Galatino, J. M. Paez-Borrallo, O. Edfors, Vehicular Technology Conference, 2001. VTC 2001 Fall. IEEE VTS 54th. 
         [0015]    A problem with this method is that M different transmit signals must be generated at the transmitter. The computation of each signal requires either memory resources (e.g. by pre-computing and saving in memory the Inverse Discrete Fourier Transform (IDFT) of the M training sequences) or computational resources (e.g. by computing the Inverse Discrete Fourier Transform of each of the M different transmitted signals). 
         [0016]    These computations required for PAPR reduction might seem like a minor issue. However, it is a fact that a significant number of installed GSM/EDGE base stations worldwide are old. Therefore, any increase in memory usage and/or computational complexity must be kept to a minimum in order to make precoded EGPRS/EGPRS2 backwards compatible with legacy base station hardware. 
       SUMMARY 
       [0017]    Embodiments herein provide blind detection of the modulation technique in EGPRS/EGPRS2. Thus, embodiments herein avoid introducing additional signaling in precoded EGPRS/EGPRS2. Also, the receiver detects whether EGPRS/EGPRS2 or precoded EGPRS/EGPRS2 is being used for each radio block, as well as the modulation type used. 
         [0018]    Accordingly, it is an object of the present invention to provide an improved method and arrangement for transmitting precoded EGPRS. 
         [0019]    It is another object of the present invention to achieve a method and arrangement for reducing and minimizing the memory usage and/or the computational complexity when introducing precoded EGPRS/EGPRS2. 
         [0020]    At least one of the above objects is achieved by a method and arrangement where signalling of the modulation type by means of rotation of the training sequence and PAPR reduction are combined into one single step. For each modulation type, a set of rotation angles is chosen. These sets have no element in common. New training sequences are generated by rotating one original training sequence. The rotation angle that minimizes the PAPR of the transmit signal is chosen. At the receiver side, knowing the original training sequence, the receiver estimates blindly the rotation angle among the known possible rotation angles. The estimated rotation angle in the receiver maps to a unique modulation type. 
         [0021]    In accordance with embodiments described herein a set of rotation angles are calculated that allow PAPR reduction in a computationally efficient way. The proposed technique require only one Inverse Discrete Fourier Transformation (IDFT) computation, independently of the number of rotation angles, or equivalently, independently of the number of training sequences used for PAPR reduction. This results in significant savings in either memory or Central Processor Unit (CPU) cycles (or both) in the transmitter. Moreover, the set of possible rotation angles is large. Hence, the rotation angles can be properly chosen in order to minimize PAPR and maximize the probability of correct blind detection. 
         [0022]    In accordance with one embodiment a method of transmitting a pre-coded EGPRS/EGPRS2 symbol sequence is provided, where the symbol sequence comprises data sequence symbols and training sequence symbols. In accordance with the method a modulation method is selected and a set of rotation angles are set in response to the selected modulation. The sets of rotation angles for each selectable modulation method have no element (rotation angle) in common. Further, a set of training sequences is generated from one original training sequence by rotating the original training sequence by the angles of the set of rotation angles associated with the selected modulation method, and a rotation angle from the set of rotation angles of the selected modulation method is selected. Finally the EGPRS/EGPRS2 symbol sequence is pre-coded and transmitted using the selected modulation method with the training symbol sequence rotated using the selected rotation angle. On the receiver side the receiver can receive such a transmitted symbol sequence using blind detection and knowledge of the original symbol sequence because each rotational angle is unique to a used modulation method. 
         [0023]    In accordance with one embodiment the rotation angle is selected such that the peak to average power ratio of the transmitted precoded signal is minimized among the peak to average power ratio of all precoded signals generated from the user data and the and the set of training sequences. 
         [0024]    In accordance with one embodiment all the angles in the sets of possible rotation angles are integer multiples of 2π divided by the total number of precoded data and training symbols. 
         [0025]    In accordance with one embodiment the precoded signals are generated by adding a vector of precoded symbols to circular shifts of the vector of precoded training symbols. 
         [0026]    A first advantage of the proposed blind detection method is that blind detection and PAPR reduction are combined into one single step, in a computationally efficient way. 
         [0027]    A second advantage is the efficient algorithm to perform DFT-precoding and PAPR reduction that allows saving in either Central Processor Unit (CPU) cycles, or memory, or both. Some legacy GSM/EDGE base stations have been in operation for more than 10 years, and have undergone numerous software upgrades. Therefore, the amount of computational resources available for any new functionality in legacy base stations may be very limited. Hence, any savings in computational complexity/memory are of the utmost importance. Since it is desired to upgrade legacy base stations so that they can support precoded EGPRS/EGPRS2, every extra byte of memory and every extra CPU cycle are critical. 
         [0028]    Embodiments herein also extend to methods of receiving a symbol sequence transmitted in accordance with the above using blind detection. Thus in accordance with one embodiment a method of receiving a pre-coded EGPRS/EGPRS2 symbol sequence, where the symbol sequence comprising data sequence symbols and training sequence symbols is provided. In accordance with the method first a symbol sequence having a rotated training symbol sequence is received wherein the rotation of the training symbol sequence uniquely identifies the used modulation method. Knowing the original, unrotated training symbol sequence, the receiver then blindly detects the received symbol sequence and determining the modulation method of the received symbol sequence by determining the rotation angle of the training sequence. 
         [0029]    Embodiments herein further extend to a transmitter and a receiver arranged to perform the methods as described herein. The transmitter and receiver can be provided with a controller/controller circuitry for performing the above methods. The controller(s) can be implemented using suitable hardware and or software. The hardware can comprise one or many processors that can be arranged to execute software stored in a readable storage media. The processor(s) can be implemented by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared or distributed. Moreover, a processor or may include, without limitation, digital signal processor (DSP) hardware, ASIC hardware, read only memory (ROM), random access memory (RAM), and/or other storage media. 
     
    
     
       FIGURES 
         [0030]    The invention will now be described in more detail by way of non-limiting examples and with reference to the accompanying drawings, in which: 
           [0031]      FIG. 1  shows a high level view of an EGPRS/EGPRS2 linear modulator with vector pre-coding (Tx chain), 
           [0032]      FIG. 2  is a flow chart illustrating some procedural steps performed when transmitting a pre-coded EGPRS/EGPRS2 symbol sequence, 
           [0033]      FIG. 3  illustrates a transmitter, 
           [0034]      FIG. 4  illustrates a receiver, and 
           [0035]      FIG. 5  is a flow chart illustrating steps performed when transmitting pre-coded EGPRS/EGPRS2 symbol sequence. 
       
    
    
     DETAILED DESCRIPTION 
       [0036]    The column vector of transmitted complex-valued symbols {right arrow over (x)} of length N consists of both payload and training symbols. It can be written in the form 
         [0000]        {right arrow over (x)}={right arrow over (d)}+{right arrow over (t)}.   (1)
 
         [0000]    Here {right arrow over (d)} is a vector of length N consisting only of user data symbols or zeros. Each entry is either 0 or a complex-valued data symbol. Similarly, the vector {right arrow over (t)} of length N consists of training symbols or zeros only. 
         [0037]    Let W be the DFT matrix of size N×N. The column vector of transmitted complex-valued symbols {right arrow over (x)} of length N is precoded by multiplying it with the IDFT matrix. 
         [0000]        {right arrow over (X)}=W   H   ·{right arrow over (x)}.   (2)
 
         [0038]    Assume that there are P possible modulation types. (E.g. P=3 if 8PSK, 16QAM, 32QAM modulations are used.) Suppose also that M different rotations are used for each modulation type. A total of P×M different angles are chosen and grouped into P sets: 
         [0000]      Ψ 1 ={θ 1   1 , . . . , θ 1   M }, . . . , Ψ P ={θ P   1 , . . . , θ P   M }.  (3)
 
         [0039]    Each angle is of the form 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       θ 
                       p 
                       m 
                     
                     = 
                     
                       
                         2 
                          
                         
                           π 
                           · 
                           
                             k 
                             
                               m 
                               , 
                               p 
                             
                           
                         
                       
                       N 
                     
                   
                   , 
                   
                     1 
                     ≤ 
                     p 
                     ≤ 
                     P 
                   
                   , 
                   
                     1 
                     ≤ 
                     m 
                     ≤ 
                     M 
                   
                   , 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where k m,p  is an integer, and 0≦k m,p &lt;N. 
         [0040]    For any angle θ define the rotation matrix 
         [0000]        R (θ)=diag(1 , e   jθ   , e   j2θ   , . . . , e   j(N−2)θ   , e   j(N−2)θ ).  (5)
 
         [0000]    This is a diagonal matrix of size N×N. 
         [0041]    If the signal to be transmitted has the p-th modulation type, 1≦p≦P, then M precoded transmit vectors are computed as follows. First the rotated training sequence is added to the vector of data symbols. 
         [0000]        {right arrow over (x)} (θ p   m )= {right arrow over (d)}+R (θ p   m )· {right arrow over (t)},  1 ≦m≦M.   (6)
 
         [0042]    The candidates for the precoded transmit vectors are simply 
         [0000]        {right arrow over (X)} (θ m   p )= W   H   ·{right arrow over (x)} (θ m   p ), 1 ≦m≦M.   (7)
 
         [0043]    Let PAPR({right arrow over (X)}) denote the PAPR of a modulated signal built from the precoded transmit symbols {right arrow over (X)}. The optimum rotation angle is computed as 
         [0000]    
       
         
           
             
               
                 
                   
                     θ 
                     opt 
                   
                   = 
                   
                     
                       argmin 
                       
                         
                           θ 
                           p 
                           m 
                         
                         : 
                         
                           1 
                           ≤ 
                           m 
                           ≤ 
                           M 
                         
                       
                     
                      
                     P 
                      
                     
                         
                     
                      
                     A 
                      
                     
                         
                     
                      
                     P 
                      
                     
                         
                     
                      
                     
                       
                         R 
                         ( 
                         
                           
                             X 
                             -&gt; 
                           
                            
                           
                             ( 
                             
                               θ 
                               P 
                               m 
                             
                             ) 
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The transmitted signal is then {right arrow over (X)}(θ opt ). The other signals are discarded and are not transmitted. 
         [0044]    In  FIG. 2  a flowchart illustrating some steps performed when transmitting an EGPRS/EGPRS2 symbol sequence comprising data symbols and training symbols. First, in a step  201  a modulation method is selected and also a set of rotation angles set in response to the selected modulation. The sets of rotation angles for each selectable modulation method do no element in common, which will ensure that the modulation method can be determined by a receiver using blind detection. Next in a step  203 , a set of training sequences is generated from one original training sequence by rotating the original training sequence by the angles of the set of rotation angles associated with the selected modulation method. Then in a step  205 , a rotation angle from the set of rotation angles of the selected modulation method is selected. Finally, in a step  207 , the transmitter pre-codes and transmits the EGPRS/EGPRS2 symbol sequence using the selected modulation method and rotating the training symbol sequence using the selected rotation angle. Thus, the training symbol sequence is transmitted using a rotation angle that uniquely identifies the modulation type since the angles in the different sets of angles for each selectable modulation method have no element in common, i.e. the same angle cannot be found in two different sets. Hereby the receiver can, using blind detection and knowledge of the original training symbol sequence, determine the selected modulation method by blind detection of the rotation angle associated with a received EGPRS/EGPRS2 training symbol sequence and demodulate the received symbol sequence. This is thus made possible by assigning mutually different rotation angles to all possible modulation methods and rotated original training symbols sequences. 
         [0045]    In  FIG. 3  a transmitter  300  configured to transmit an EGPRS/EGPRS2 burst in accordance with the methods described herein is depicted. The transmitter  300  comprises controller circuitry  301  for performing the above methods. The controller(s) can be implemented using suitable hardware and or software. The hardware can comprise one or many processors that can be arranged to execute software stored in a readable storage media. The processor(s) can be implemented by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared or distributed. Moreover, a processor or may include, without limitation, digital signal processor (DSP) hardware, ASIC hardware, read only memory (ROM), random access memory (RAM), and/or other storage media. 
         [0046]    At the receiver side the receiver estimates the most likely rotation angle {circumflex over (θ)} among all the P×M possible angles (3). Since there exists only one  p  such that {circumflex over (θ)}εΨ   p   , then this  p  indicates the modulation type. 
         [0047]    In  FIG. 4  a receiver  400  configured to receive an EGPRS/EGPRS2 burst transmitted in accordance with the methods described herein is depicted. The transmitter  400  comprises controller circuitry  401  for performing the above methods. The controller(s) can be implemented using suitable hardware and or software. The hardware can comprise one or many processors that can be arranged to execute software stored in a readable storage media. The processor(s) can be implemented by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared or distributed. Moreover, a processor or may include, without limitation, digital signal processor (DSP) hardware, ASIC hardware, read only memory (ROM), random access memory (RAM), and/or other storage media. 
         [0048]    Next, it is explained how the computation of the optimum rotation angle in (8) can be performed with only one Fourier transform. Define 
         [0000]        {right arrow over (D)}=W   H   ·{right arrow over (d)},   (9)
 
         [0000]        {right arrow over (T)}=W   H   ·{right arrow over (t)}.   (10)
 
         [0049]    Also define the circular shift function by m steps that applied to a vector {right arrow over (t)} of length N removes the last m entries and places them at the beginning. That is, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           circshift 
                           ( 
                           
                             
                               t 
                               -&gt; 
                             
                             , 
                             m 
                           
                           ) 
                         
                         = 
                           
                          
                         
                           circshift 
                            
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     t 
                                     0 
                                   
                                   , 
                                   
                                     t 
                                     1 
                                   
                                   , 
                                   … 
                                    
                                   
                                       
                                   
                                   , 
                                   
                                     t 
                                     
                                       N 
                                       - 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                               , 
                               m 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 t 
                                 
                                   N 
                                   - 
                                   m 
                                 
                               
                               , 
                               … 
                                
                               
                                   
                               
                               , 
                               
                                 t 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               , 
                               
                                 t 
                                 0 
                               
                               , 
                               
                                 t 
                                 1 
                               
                               , 
                               … 
                                
                               
                                   
                               
                               , 
                               
                                 t 
                                 
                                   N 
                                   - 
                                   m 
                                   - 
                                   1 
                                 
                               
                             
                             ) 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    For each angle θ p   m , 1≦m≦M the candidate signal must be computed 
         [0000]        {right arrow over (X)} (θ p   m )= W   H   ·{right arrow over (x)} (θ p   m )= W   H ·( {right arrow over (d)}+R (θ p   m )·{right arrow over ( t )})= W   H   ·{right arrow over (d)}+W   H   ·R (θ p   m )· {right arrow over (t)}   (12)
 
         [0050]    However, by the shift property of the Inverse Discrete Fourier Transform and due to the definition (4) of the rotation angles, it can be shown that 
         [0000]        W   H   ·R (θ p   m )· {right arrow over (t)} =circshift( W   H   ·{right arrow over (t)},N−k   m,p ).  (13)
 
         [0000]    Using (9), (10) and (13) we may re-write (12) in the form 
         [0000]        {right arrow over (X)} (θ p   m )= {right arrow over (D)} +circshift( {right arrow over (T)},N−k   m,p ).  (14)
 
         [0051]    Thus, the precoded signals can be generated by adding the vector of precoded symbols to circular shifts of the vector of precoded training symbols. Note that a circular shift requires no operations and can be trivially implemented using circular pointer arithmetic. Moreover, the vector {right arrow over (T)} may be pre-computed and stored in memory. Thus, only one IDFT needs to be performed. A straightforward calculation of (8) requires roughly M times more arithmetic operations than an efficient computation based on (14). Alternatively, a straightforward implementation of (8) requires roughly M times more memory than an efficient implementation based on (14). 
         [0052]    Finally, note that the remarkable reduction in computational complexity in (14) is due to the fact that the different training sequences are generated by rotation of one original training sequence, and that the rotation angles are of the special form (4). The reduction in complexity is not possible in general if arbitrary training sequences are used. 
         [0053]    The precoding, modulation signaling and PAPR reduction process is illustrated in  FIG. 5 . First in a step  501 , a desired modulation type, precoded user symbols, precoded training symbols and a predefined collection of M rotation angles constitute the input to the modulation signaling and PAPR reduction algorithm. In a second step  503 , M candidate precoded signals are generated by addition of the precoded data symbols and circularly shifted versions of one precoded training sequence, each circular shift corresponding to one rotation angle. In a third step  505 , the rotation angle that yields the precoded signal with the smallest PAPR is chosen among the M candidate rotation angles. In the last step  507 , the precoded signal that yields the smallest PAR is pulse shaped and sent to the RF modulator to be transmitted through the air. 
         [0054]    The present invention may, of course, be carried out in other ways than those specifically set forth herein without departing from essential characteristics of the invention. The present embodiments are to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.