Abstract:
There is provided an apparatus and method for performing unique word detection and frequency offset estimation for a receiver for DPSK signals comprising in-phase I and quadrature Q components for a plurality of symbols k. The apparatus comprises: a differential detector for performing differential detection of a received signal over a given symbol span; a frequency corrector for performing an initial correction of I and Q using a previously estimated value of the frequency offset; accumulators for averaging I and Q for each symbol k over a given number K of symbols, where K is the number of symbols in the unique word to be detected; a frequency offset estimation block for calculating an estimate of the frequency offset from averaged I and averaged Q; and a unique word detection block for determining, from differentially detected I, differentially detected Q, averaged I and averaged Q, whether or not the unique word is present in a received signal.

Description:
FIELD OF THE INVENTION  
       [0001]     The invention relates to performing unique word detection and frequency offset estimation in a receiver for DPSK signals. In particular, the invention relates to an apparatus and method for performing both unique word detection and frequency offset estimation.  
       BACKGROUND OF THE INVENTION  
       [0002]     Phase Shift Keying (PSK) and Differential Phase Shift Keying (DPSK) modulation schemes are widely used in wireless communication. In DPSK, the phase of the carrier is discretely varied in relation to the phase of the immediately preceding signal element and in accordance with the data being transmitted. Differential Quadrature Phase Shift Keying (DQPSK) and Differential Bi-Phase Shift Keying (DBPSK) are other variations.  
         [0003]     Two important processes in demodulation at the receiver side are residual frequency offset estimation and UW (unique word) detection.  
         [0004]     Regarding frequency offset estimation, when receiving and de-modulating a digitally modulated signal, an estimated replica of the received carrier frequency is used to recover the signal. Ideally, the transmitter generates a carrier signal that exists at some known frequency and the received signals are then demodulated at the receiver using the same known frequency. However, inaccuracies in the transmitter and receiver oscillators, along with the effect of Doppler Shifting, result in carrier frequency offsets. If the frequency offset is excessive and not suitably compensated for, the performance of the demodulator will be degraded and the original signal may not be recoverable. In frequency offset estimation, an estimate of the frequency offset error is made and used in frequency offset error correction and/or compensation, so as to compensate for the frequency difference between transmitted and received carriers.  
         [0005]     Regarding UW detection, the UW in a slot is a portion of the slot used for synchronization and/or identification. UW detection is popular in TDMA burst communication systems. The UW is typically around 5% to 10% of the slot length. Detecting the UW symbols enables the receiver to ascertain the type of slot and to synchronize the symbol timing.  
         [0006]     The system described in “Personal Handy Phone System”, ARIB Standard, Version 4.0, February 2003, uses  
       π   4       
 
 DQPSK modulation to achieve 32 kbps in each slot. In a more advanced version (Advanced Personal Handy Phone System) 16 QAM (16-state Quadrature Amplitude Modulation) and 64 QAM (64-state Quadrature Amplitude Modulation) are introduced to increase the transmission rate from 32 kbps to 64 kbps and 96 kbps respectively. 
 
         [0007]     The slot structure for the Advanced Personal Handy Phone System is shown in  FIG. 1 . The slot comprises a first portion which is  
       π   4       
 
 DQPSK modulated, comprising a preamble and UW, and a second portion which is  
       π   4       
 
 DQPSK and/or QAM modulated, comprising the information stream itself and a number of GT (Guard Time) symbols. The GT symbols represent a portion of the slot where nothing is being transmitted; this helps combat the problem of inter symbol interference. The receiver usually performs quick algorithms to demodulate the burst slots and the use of QAM symbols in the information stream means that a more accurate demodulation is required since QAM (particularly 64 QAM) is rather sensitive to errors in frequency offset estimation. 
 
         [0008]      FIG. 2  shows a known way to estimate and correct the frequency offset, as described in Proakis, Digital Communications, “Chapter 6: Carrier and symbol synchronization,” McGraw-Hill International Editions, Singapore, 3 rd  edition, 1995.  
         [0009]     The received signal is represented by I r  and Q r , I r  being the in-phase component and Q r  being the quadrature component. Block  201  performs differential detection of one symbol span, with each symbol having an order k, i.e. 
 
 I   d ( k )= I   r ( k ) I   r ( k− 1)+ Q   r ( k ) Q   r ( k− 1)  [1]
 
 Q   d ( k )= Q   r ( k ) I   r ( k− 1)− I   r ( k ) Q   r ( k− 1)  [2]
 
         [0010]     Block  203  performs a frequency correction using a previously estimated value of the frequency offset Δ f ′ (using a frequency offset estimation algorithm) to compensate for the differential detection output. That is, this correction is performed on the differential detection outputs which contain frequency offset error. The correction at block  203  is a first stage of frequency offset error correction. 
 
 I   c ( k )= I   d ( k )cos φ+ Q   d ( k )sin φ  [3]
 
 Q   c ( k )= Q   d ( k )cos φ− I   d ( k )sin φ  [4]
 
 where φ=2πΔ f ′k. 
 
         [0011]     Block  205  uses hard decisions for the I and Q signals to rotate I c  and Q c  towards the x-axis of the first quadrant. This decision-based rotation block may or may not be included.  
         [0012]     Block  207  is an accumulation block and performs the summing up of the I and Q signals:  
               I   a     =       ∑   0     K   -   1       ⁢     I   h               [   5   ]                 Q   a     =       ∑   0     K   -   1       ⁢     Q   h               [   6   ]             
 
 where K is the number of symbols used for the frequency estimation. Because the symbols are spread around the x-axis, summing up the I and Q actually gives an average I and an average Q. (If there is no rotation block  205 , the accumulation block will sum I c  and Q c .) 
 
         [0013]     Block  209  is an arctan computation block and computes the angle formed by the average I and the average Q from equations [5] and [6]. Since tan of each angle is  
         Q   I     ,       
 
 we have for the summed I and the summed Q, an average angle with respect to the x-axis of:  
             arctan   ⁡     [       Q   a       I   a       ]             [   7   ]             
 
         [0014]     This angle corresponds to the secondary frequency offset error Δ f ″ which was not used for correction at block  203 .  
         [0015]     Block  211  is a frequency offset calculation block and updates the frequency error offset, to produce an improved estimate Δ f ′ imp , by adding the secondary frequency offset error from the computed average angle i.e. 
 
Δ f ′ imp =Δ f ′+Δ f ″  [8]
 
         [0016]     Δ f ″ is smaller than Δ f ′ so this update represents a fine tuning of the correction already made at block  203 .  
         [0017]      FIG. 3  shows the known basic structure for UW detection. The general idea is to compare known UW bits with the received sample and hence decide whether or not UW is present. Referring to  FIG. 3 , the received signal is again represented by I r  and Q r . Block  301  uses a comparison algorithm to compare the received I r  and Q r  with known UW bits. The comparison algorithm is usually a bit to bit comparison or symbol to symbol comparison. Block  303  makes the decision as to whether UW is present or not. The decision making is usually a threshold comparison function.  
         [0018]      FIGS. 2 and 3  show the prior art arrangements for frequency error estimation and UW detection respectively. It can be seen that frequency estimation and UW detection take up a considerable amount of demodulation resources and any implementation which would reduce complexity and allow more demodulation resources to be spent on the demodulation itself would be useful.  
       SUMMARY OF THE INVENTION  
       [0019]     It is an object of the invention to provide an apparatus and method, which mitigate or substantially overcome the problems of prior art arrangements described above. It is a further object of the invention to provide an apparatus and method for performing both frequency offset estimation and unique word detection.  
         [0020]     According to a first aspect of the invention, there is provided apparatus for performing unique word detection and frequency offset estimation for a receiver for DPSK signals comprising in-phase I and quadrature Q components for a plurality of symbols k, the apparatus comprising:  
         [0021]     a differential detector for performing differential detection of a received signal over a given symbol span;  
         [0022]     a frequency corrector for performing an initial correction of I and Q using a previously estimated value of the frequency offset;  
         [0023]     an accumulator for averaging I for each symbol k over a given number K of symbols, where K is the number of symbols in the unique word to be detected;  
         [0024]     an accumulator for averaging Q for each symbol k over the given number K of symbols;  
         [0025]     a frequency offset estimation block for calculating an estimate of the frequency offset from averaged I and averaged Q; and  
         [0026]     a unique word detection block for determining, from differentially detected I, differentially detected Q, averaged I and averaged Q, whether or not the unique word is present in a received signal.  
         [0027]     The differential detector, the frequency corrector and the accumulators are shared between the functions of the frequency offset estimation and the unique word detection. The final stages of the frequency offset estimation and the unique word detection are performed in the frequency offset estimation block and the unique word detection block respectively. This greatly simplifies the construction.  
         [0028]     Typically, the differential detector will perform differential detection over a symbol span of one symbol.  
         [0029]     Typically, the previously estimated value of the frequency offset will have been estimated using a frequency offset estimation algorithm.  
         [0030]     The frequency offset estimation block may comprise: a computation block for calculating the angle formed by averaged I and averaged Q; and a frequency offset calculation block for calculating the estimate of the frequency offset from the angle formed by averaged I and averaged Q.  
         [0031]     Preferably, the computation block performs the arctan function for calculating the angle formed by averaged I and averaged Q. The computation block may perform the arctan function using, for example, a CORDIC (Coordinate Rotation Digital Computer) algorithm or a Look Up Table (LUT) algorithm.  
         [0032]     The unique word detection block preferably comprises:  
         [0033]     a first portion for generating a first factor dependent on differentially detected I and differentially detected Q;  
         [0034]     a second portion for generating a second factor dependent on averaged I and averaged Q; and  
         [0035]     a comparator for comparing the first factor and the second factor to determine whether the unique word is present in the received signal.  
         [0036]     Because K is the number of unique word symbols, the unique word detection block effectively looks at each received sequence of K symbols and determines whether or not this sequence is equal to the unique word and therefore determines whether or not the unique word is present.  
         [0037]     In one embodiment, the first factor is dependent on the square of differentially detected I and the square of differentially detected Q and the second factor is dependent on the square of averaged I and the square of averaged Q.  
         [0038]     The first factor may equal the summation over K symbols of the sum of the square of differentially detected I and the square of differentially detected Q. In that case, the first portion of the unique word detection block may comprise a first block for squaring differentially detected I, a second block for squaring differentially detected Q, an addition block for adding the square of differentially detected I and the square of differentially detected Q and an accumulation block for performing the summation over K symbols of the sum of the square of differentially detected I and the square of differentially detected Q.  
         [0039]     The second factor may equal the sum of the square of averaged I and the square of averaged Q. In that case, the second portion of the unique word detection block may comprise a first block for squaring averaged I, a second block for squaring averaged Q and an addition block for adding the square of averaged I and the square of averaged Q.  
         [0040]     In an alternative embodiment, the first factor is dependent on the absolute value of differentially detected I and the absolute value of differentially detected Q and the second factor is dependent on the absolute value of averaged I and the absolute value of averaged Q.  
         [0041]     The first factor may equal the summation over K symbols of the sum of the absolute value of differentially detected I and the absolute value of differentially detected Q. In that case, the first portion of the unique word detection block may comprise a first block for obtaining the absolute value of differentially detected I, a second block for obtaining the absolute value of differentially detected Q, an addition block for adding the absolute value of differentially detected I and the absolute value of differentially detected Q and an accumulation block for performing the summation over K symbols of the sum of the absolute value of differentially detected I and the absolute value of differentially detected Q.  
         [0042]     The second factor may equal the sum of the absolute value of averaged I and the absolute value of averaged Q. In that case, the second portion of the unique word detection block may comprise a first block for obtaining the absolute value of averaged I, a second block for obtaining the absolute value of averaged Q and an addition block for adding the absolute value of averaged I and the absolute value of averaged Q.  
         [0043]     The comparator may be arranged to calculate the ratio of the first factor to the second factor and compare that ratio with a predetermined value. In that arrangement, the predetermined value may be set by a user. If the ratio is either above or below the predetermined value, the unique word is judged to be present whereas if the ratio is the other of above and below the predetermined value, the unique word is judged not to be present.  
         [0044]     The unique word detection block may be arranged, if the unique word has been detected, to determine from the detected unique word, a frequency offset estimation. This frequency offset estimation may be used as the previously estimated value of the frequency offset at the frequency corrector.  
         [0045]     According to a second aspect of the invention, there is provided apparatus for performing unique word detection for a receiver for DPSK signals comprising in-phase I and quadrature Q components for a plurality of symbols k, the apparatus being arranged to receive, for each received I and Q, a differentially detected I, a differentially detected Q, a processed form of the received I and a processed form of the received Q, the apparatus comprising:  
         [0046]     a first portion for generating a first factor dependent on differentially detected I and differentially detected Q;  
         [0047]     a second portion for generating a second factor dependent on processed I and processed Q; and  
         [0048]     a comparator for comparing the first factor and the second factor to determine whether a unique word is present in the received signal.  
         [0049]     Preferably, the processed I has been generated by the steps of: differential detection of the received signal over a given symbol span; frequency correction of I and Q using a previously estimated value of the frequency offset; and accumulation of I over a given number of symbols K, where K is the number of symbols in the unique word to be detected.  
         [0050]     Similarly, preferably, the processed Q has been generated by the steps of: differential detection of the received signal over a given symbol span; frequency correction of I and Q using a previously estimated value of the frequency offset; and accumulation of Q over a given number of symbols K, where K is the number of symbols in the unique word to be detected.  
         [0051]     In one embodiment, the first factor is dependent on the square of differentially detected I and the square of differentially detected Q and the second factor is dependent on the square of processed I and the square of processed Q.  
         [0052]     The first factor may equal the summation over K symbols of the sum of the square of differentially detected I and the square of differentially detected Q, where K is the number of symbols in the unique word being detected. In that case, the first portion may comprise a first block for squaring differentially detected I, a second block for squaring differentially detected Q, an addition block for adding the square of differentially detected I and the square of differentially detected Q and an accumulation block for performing the summation over K symbols of the sum of the square of differentially detected I and the square of differentially detected Q.  
         [0053]     The second factor may equal the sum of the square of processed I and the square of processed Q. In that case, the second portion may comprise a first block for squaring processed I, a second block for squaring processed Q and an addition block for adding the square of processed I and the square of processed Q.  
         [0054]     In an alternative embodiment, the first factor is dependent on the absolute value of differentially detected I and the absolute value of differentially detected Q and the second factor is dependent on the absolute value of processed I and the absolute value of processed Q.  
         [0055]     The first factor may equal the summation over K symbols of the sum of the absolute value of differentially detected I and the absolute value of differentially detected Q, where K is the number of symbols in the unique word being detected. In that case, the first portion of the unique word detection block may comprise a first block for obtaining the absolute value of differentially detected I, a second block for obtaining the absolute value of differentially detected Q, an addition block for adding the absolute value of differentially detected I and the absolute value of differentially detected Q and an accumulation block for performing the summation over K symbols of the sum of the absolute value of differentially detected I and the absolute value of differentially detected Q.  
         [0056]     The second factor may equal the sum of the absolute value of processed I and the absolute value of processed Q. In that case, the second portion of the unique word detection block may comprise a first block for obtaining the absolute value of processed I, a second block for obtaining the absolute value of processed Q and an addition block for adding the absolute value of processed I and the absolute value of processed Q.  
         [0057]     Preferably, the comparator is arranged to calculate the ratio of the first factor to the second factor and to compare that ratio with a predetermined value. In that arrangement, the predetermined value may be set by a user. If the ratio is one side of the predetermined value, the unique word is judged to be present whereas if the ratio is the other side of the predetermined value, the unique word is judged not to be present.  
         [0058]     According to a third aspect of the invention, there is provided a method for performing unique word detection and frequency offset estimation for received DPSK signals comprising in-phase I and quadrature Q components at a plurality of symbols k, the method comprising the steps of:  
         [0059]     a) performing differential detection of a received signal over a given symbol span;  
         [0060]     b) performing an initial correction of I and Q using a previously estimated value of the frequency offset; c) averaging I for each symbol k over a given number of symbols K, where K is the number of symbols in the unique word to be detected;  
         [0061]     d) averaging Q for each symbol k over the given number of symbols K;  
         [0062]     e) calculating an estimate of the frequency offset from averaged I and averaged Q; and  
         [0063]     f) determining, from differentially detected I, differentially detected Q, averaged I and averaged Q, whether or not a unique word is present in a received signal.  
         [0064]     In this method, steps a), b), c) and d) of differential detection, frequency correction and accumulation are shared between the frequency offset estimation and the unique word detection. The final stages of the frequency offset estimation and the unique word detection are performed at steps e) and f) respectively. Sharing the majority of steps in this way, rather than having a completely separate set of steps for the two processes, greatly simplifies the method.  
         [0065]     Typically, the step of performing differential detection over a given symbol span comprises performing differential detection over a symbol span of one symbol.  
         [0066]     Preferably, steps c) and d) are carried out in parallel. Preferably, steps e) and f) are carried out in parallel.  
         [0067]     Step e) of calculating an estimate of the frequency offset from averaged I and averaged Q may comprise: calculating the angle formed by averaged I and averaged Q; and calculating the estimate of the frequency offset from the angle formed by averaged I and averaged Q. In that case, the step of calculating the angle formed by averaged I and averaged Q may comprise using the arctan function for calculating the angle formed by averaged I and averaged Q. In that case, the step of calculating the angle may be performed using, for example, a CORDIC algorithm or a LUT algorithm.  
         [0068]     Because K is the number of unique word symbols, step f) effectively involves looking at each received sequence of K symbols and determining whether or not this sequence matches the unique word.  
         [0069]     Preferably, step f) of determining, from differentially detected I, differentially detected Q, averaged I and averaged Q, whether or not a unique word is present in a received signal comprises:  
         [0070]     generating a first factor dependent on differentially detected I and differentially detected Q;  
         [0071]     generating a second factor dependent on averaged I and averaged Q; and  
         [0072]     comparing the first factor and the second factor to determine whether the unique word is present in the received signal.  
         [0073]     Preferably, the step of generating the first factor and the step of generating the second factor are carried out in parallel.  
         [0074]     In one embodiment, the first factor is dependent on the square of differentially detected I and the square of differentially detected Q and the second factor is dependent on the square of averaged I and the square of averaged Q.  
         [0075]     The first factor may equal the summation over K symbols of the sum of the square of differentially detected I and the square of differentially detected Q. In that case, the step of generating the first factor may comprise the steps of squaring differentially detected I, squaring differentially detected Q, adding the square of differentially detected I and the square of differentially detected Q and performing summation over K symbols of the sum of the square of differentially detected I and the square of differentially detected Q. The steps of squaring differentially detected I and squaring differentially detected Q are preferably carried out in parallel.  
         [0076]     The second factor may equal the sum of the square of averaged I and the square of averaged Q. In that case, the step of generating the second factor may comprise the steps of squaring averaged I, squaring averaged Q and adding the square of averaged I and the square of averaged Q. The steps of squaring averaged I and squaring averaged Q are preferably carried out in parallel.  
         [0077]     In an alternative embodiment, the first factor is dependent on the absolute value of differentially detected I and the absolute value of differentially detected Q and the second factor is dependent on the absolute value of averaged I and the absolute value of averaged Q.  
         [0078]     The first factor may equal the summation over K symbols of the sum of the absolute value of differentially detected I and the absolute value of differentially detected Q. In that case, the step of generating the first factor may comprise the steps of obtaining the absolute value of differentially detected I, obtaining the absolute value of differentially detected Q, adding the absolute value of differentially detected I and the absolute value of differentially detected Q and performing summation over K symbols of the sum of the absolute value of differentially detected I and the absolute value of differentially detected Q. The steps of obtaining the absolute value of differentially detected I and obtaining the absolute value of differentially detected Q are preferably carried out in parallel.  
         [0079]     The second factor may equal the absolute value of averaged I added to the absolute value of averaged Q. In that case, the step of generating the second factor may comprise the steps of obtaining the absolute value of averaged I, obtaining the absolute value of averaged Q and adding the absolute value of averaged I and the absolute value of averaged Q. The steps of obtaining the absolute value of averaged I and obtaining the absolute value of averaged I are preferably carried out in parallel.  
         [0080]     The step of comparing the first factor and the second factor preferably comprises calculating the ratio of the first factor to the second factor and comparing that ratio with a predetermined value. In that arrangement, the predetermined value may be set by a user. If the ratio is either above or below the predetermined value, the unique word is judged to be present whereas, if the ratio is either below or above the predetermined value, the unique word is judged not to be present.  
         [0081]     If the unique word has been detected, the method may further comprise the step of, determining from the detected unique word, a frequency offset estimation. This frequency offset estimation may be used as the previously estimated value of the frequency offset at step b) of performing an initial correction of I and Q.  
         [0082]     Features described in relation to one aspect of the invention may be applicable to another aspect of the invention. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0083]     Some known arrangements have already been described with reference to FIGS.  1  to  3  of the accompanying drawings, of which:  
         [0084]      FIG. 1  shows the slot structure for a prior art arrangement;  
         [0085]      FIG. 2  is a block diagram of a prior art receiver side performing frequency offset error estimation; and  
         [0086]      FIG. 3  is a block diagram of a prior art receiver side performing UW detection.  
         [0087]     Some exemplary embodiments of the invention will now be described with reference to FIGS.  4  to  6  of the accompanying drawings, of which:  
         [0088]      FIG. 4  is a block diagram of the combined UW detection and frequency offset estimation according to an embodiment of the invention;  
         [0089]      FIG. 5  shows a first embodiment of block  409  of  FIG. 4 ; and  
         [0090]      FIG. 6  shows a second embodiment of block  409  of  FIG. 4 . 
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0091]     According to the invention, the process of frequency offset estimation and UW detection are combined as far as possible. This reduces implementation complexity and implementation delay time.  
         [0092]      FIG. 4  shows the structure of the combined UW detection and frequency offset estimation according to an embodiment of the invention. Differential detection, frequency correction and accumulation are shared by the frequency offset estimate and UW detection procedures.  
         [0093]     The received signal is represented by I r (k) and Q r (k). I(k) is the in-phase component at symbol k and Q(k) is the quadrature component at symbol k. Block  401  performs differential detection of one symbol span i.e. 
 
 I   d ( k )= I   r ( k ) I   r ( k− 1)+ Q   r ( k ) Q   r ( k− 1)  [1]
 
 Q   d ( k )= Q   r ( k ) I   r ( k− 1)− I   r ( k ) Q   r ( k− 1)  [2]
 
         [0094]     The outputs from the differential detection block  401  are I d (k) and Q d (k).  
         [0095]     Block  403  performs phase rotation (equivalent to frequency correction) using a known phase φ UW (k), to produce I c (k) and Q c (k), as follows: 
 
 I   c ( k )= I   d ( k )cos φ UW   +Q   d ( k )sin φ UW   [9]
 
 Q   c ( k )= Q   d ( k )cos φ UW   −I   d ( k )sin φ UW   [10]
 
 φ UW (k) is the differentially encoded signal phase obtained from a pair of UW bits. 
 
 φ UW (0) is obtained from UW bit  0  and UW bit  1  
 
 φ UW (1) is obtained from UW bit  1  and UW bit  2 , 
 
 φ UW (2) is obtained from UW bit  2  and UW bit  3 , 
 
 and so on. 
 
         [0096]     φ UW (k) takes one of four possible values,  
         π   4     ,     
     ⁢       3   ⁢   π     4     ,     
     ⁢         -   3     ⁢   π     4         
     and     
           -   π     4     ,       
 
 and they are mapped according to the particular encoding convention used. For example, with Gray code:  
           if   ⁢           ⁢   bit   ⁢           ⁢   0     =       bit   ⁢           ⁢   1     =   0       ,       ϕ   UW     =     π   4       ,     
     ⁢       if   ⁢           ⁢   bit   ⁢           ⁢   0     =       1   ⁢           ⁢   and   ⁢           ⁢   bit   ⁢           ⁢   1     =   0       ,       ϕ   UW     =       3   ⁢   π     4       ,     
     ⁢       if   ⁢           ⁢   bit   ⁢           ⁢   0     =       bit   ⁢           ⁢   1     =   1       ,       ϕ   UW     =         -   3     ⁢   π     4       ,     
     ⁢   and       
           if   ⁢           ⁢   bit   ⁢           ⁢   0     =       0   ⁢           ⁢   and   ⁢           ⁢   bit   ⁢           ⁢   1     =   1       ,       ϕ   UW     =         -   π     4     .           
 
         [0097]     Blocks  405   a  and  405   b  perform accumulation. Block  405   a  receives input I c (k) and outputs I a (k) as follows:  
               I   a     =       ∑   0     K   -   1       ⁢     I   c               [   11   ]             
 
         [0098]     Block  405   b  receives input Q c (k) and outputs Q a (k) as follows:  
               Q   a     =       ∑   0     K   -   1       ⁢     Q   c               [   12   ]             
 
         [0099]     Since we are using the blocks  405   a  and  405   b  for both frequency offset estimation and UW detection, we set K to be equal to the number of symbols in the unique word. Thus, in the unique word detection block  409 , we are effectively looking at each sequence of K symbols in the received message to see whether it matches the UW.  
         [0100]     Block  407  performs the final stage for frequency estimation detection and block  409  performs the final stage for UW detection.  
         [0101]     Block  407  receives input I a (k) from block  405   a  and input Q a (k) from block  405   b  and computes the average angle with respect to the x-axis by the arc tan function:  
             arctan   ⁡     [       Q   a       I   a       ]             [   7   ]             
 
         [0102]     This average angle corresponds to the secondary frequency offset error for fine tuning of the frequency offset. This is a well known procedure and may be performed by a CORDIC (Coordinate Rotation Digital Computer) algorithm, by a Look Up Table (LUT) algorithm or by any other suitable algorithm.  
         [0103]     Block  409  receives input I a (k) from block  405   a , input Q a (k) from block  405   b  and I d (k) and Q d (k) i.e. the originally received signal in-phase and quadrature components after differential detection. The UW detection may be performed in a number of ways.  
         [0104]     A first embodiment of UW detection is shown in  FIG. 5 . In this embodiment P 1 ( k ) and P 2 ( k ) are computed and compared to decide whether the particular sequence of K symbols (=number of UW symbols) matches the UW. P 1 ( k ) is the average power of the set of symbols and it functions as a normalizer. P 2 ( k ) is a measure of the deviation of the K input symbols from the UW symbols. Or, putting it another way, P 2 ( k ) can be thought of as a measure of the correlation between the set of input symbols and the unique word.  
         [0105]     In this arrangement  
               P   ⁢           ⁢   1   ⁢     (   k   )       =         ∑   k     K   -   1   +   k       ⁢            I   d          2       +            Q   d          2               [   13   ]                 P   ⁢           ⁢   2   ⁢     (   k   )       =                ∑   k     K   -   1   +   k       ⁢     I   c            2     +              ∑   k     K   -   1   +   k       ⁢     Q   c            2               [   14   ]             
 
         [0106]     From equations [11] and [12], we see that P 2 ( k ) is dependent on I a  and Q a .  
         [0107]     If the set of input symbols matches the UW and the quality of the input symbols is perfect (i.e. no noise, no frequency offset) I c (k)=1 and Q c (k)=0 and P 2 ( k )=K 2 . If the symbols do not match, P 2 ( k ) is less than K 2 .  
         [0108]     We see from equations [3] and [4] that I c (k) is actually the instantaneous estimation of cos(Δf) and Q c (k) is actually the instantaneous estimation of sin(Δf).  
         P   ⁢           ⁢   1   ⁢     (   0   )       =           ∑   0     K   -   1       ⁢            I   d          2       +              Q   d          2     ⁢           ⁢   and   ⁢             ⁢             ⁢   P   ⁢           ⁢   2   ⁢     (   0   )         =                ∑   0     K   -   1       ⁢     I   c            2     +              ∑   0     K   -   1       ⁢     Q   c            2             
         and   ⁢           ⁢   P   ⁢           ⁢   1   ⁢     (   1   )       =           ∑   1   K     ⁢            I   d          2       +              Q   d          2     ⁢           ⁢   and   ⁢             ⁢             ⁢   P   ⁢           ⁢   2   ⁢     (   1   )         =                ∑   1   K     ⁢     I   c            2     +              ∑   1   K     ⁢     Q   c            2             
 
 and so on. 
 
         [0109]     Thus, P 1 ( k ) depends solely on the received signal components after differential detection I d  and Q d , whereas P 2 ( k ) depends on the components I a  and Q a  i.e. the components outputted from the accumulation blocks  405   a  and  405   b.    
         [0110]     If the set of symbols matches the UW perfectly and there is no noise and no frequency offset (i.e. the ideal limit),  
           P   ⁢           ⁢   2   ⁢     (   k   )         P   ⁢           ⁢   1   ⁢     (   k   )         =     K   power         
 
 where power is the transmitted power per symbol. i.e.  
       K   power       
 
 is the theoretical maximum of  
         [       P   ⁢           ⁢   2   ⁢     (   k   )         P   ⁢           ⁢   1   ⁢     (   k   )         ]     .       
 
 Obviously, in practice,  
       [       P   ⁢           ⁢   2   ⁢     (   k   )         P   ⁢           ⁢   1   ⁢     (   k   )         ]       
 
 is less than this, but we set threshold A  
       (       with   ⁢           ⁢   0     &lt;   A   &lt;     K   power       )       
 
 such that, if  
       [       P   ⁢           ⁢   2   ⁢     (   k   )         P   ⁢           ⁢   1   ⁢     (   k   )         ]       
 
 exceeds A, the UW is judged as power P 1 ( k ) detected. Thus, the higher A is set, the stricter the detection requirement, since  
       [       P   ⁢           ⁢   2   ⁢     (   k   )         P   ⁢           ⁢   1   ⁢     (   k   )         ]       
 
 then has to be closer to its theoretical maximum before the UW is detected i.e. the input symbols need to match the UW symbols very closely and be almost free of noise and frequency offset. 
 
         [0111]     Once the UW sequence is successfully detected, the frequency offset estimation can be obtained from those input symbols which have satisfied the detection requirement and used at block  403  (in known phase φ=2πΔ f ′k) to improve the frequency offset estimation.  
         [0112]     Referring to  FIG. 5 , P 1 ( k ) is calculated in the upper portion of UW detection block  409  and P 2 ( k ) is calculated in the lower portion of UW detection block  409 . I d , Q d , I a  and Q a  are received in the UW detection block.  
         [0113]     Referring to the upper portion, |I d | 2  is calculated at block  501  and |Q d | 2  is calculated at block  503 . At addition block  505 , |I d | 2  and |Q d | 2  are added together and, at accumulation block  507 , P 1 ( k ) is calculated, according to equation [13].  
         [0114]     Referring to the lower portion, |I a | 2  is calculated at block  509  and |Q d | 2  is calculated at block  511 . P 2 ( k ) is calculated, according to equation [14] at addition block  513 .  
         [0115]     Comparison block  515  compares P 1 ( k ) and P 2 ( k ) to decide whether the UW is detected or not.  
         [0116]     A second embodiment of UW detection is shown in  FIG. 6 . Again, in this embodiment P 1 ( k ) and P 2 ( k ) are computed and compared to decide whether the particular sequence of K symbols matches the UW. In this arrangement  
               P   ⁢           ⁢   1   ⁢     (   k   )       =       ∑   k     K   -   1   +   k       ⁢     {            I   d          +          Q   d            }               [   15   ]                 P   ⁢           ⁢   2   ⁢     (   k   )       =              ∑   k     K   -   1   +   k       ⁢     I   c            +            ∑   k     K   -   1   +   k       ⁢     Q   c                      [   16   ]             
 
         [0117]     From equations [11] and [12], we see that P 2 ( k ) is dependent on I a  and Q a .  
       Thus   ,       P   ⁢           ⁢   1   ⁢     (   0   )       =         ∑   0     K   -   1       ⁢       {            I   d          +          Q   d            }     ⁢           ⁢   and   ⁢           ⁢   P   ⁢           ⁢   2   ⁢     (   0   )         =              ∑   0     K   -   1       ⁢     I   c            +            ∑   0     K   -   1       ⁢     Q   c                      
         and   ⁢           ⁢   P   ⁢           ⁢   1   ⁢     (   1   )       =         ∑   1   K     ⁢       {            I   d          +          Q   d            }     ⁢           ⁢   and   ⁢           ⁢   P   ⁢           ⁢   2   ⁢     (   1   )         =              ∑   1   K     ⁢     I   c            +            ∑   1   K     ⁢     Q   c                    
 
 so on. 
 
         [0118]     Thus, as with the first embodiment, P 1 ( k ) depends solely on the differentially detected received signal components I d  and Q d , whereas P 2 ( k ) depends on the components I a  and Q a  i.e. the components outputted from the accumulation blocks  405   a  and  405   b.    
         [0119]     Referring to  FIG. 6 , P 1 ( k ) is calculated in the upper portion of UW detection block  409  and P 2 ( k ) is calculated in the lower portion of UW detection block  409 . I d , Q d , I a  and Q a  are received in the UW detection block.  
         [0120]     Referring to the upper portion, the absolute value of I d , |I d | is obtained at block  601  and the absolute value of Q d , |Q d | is obtained at block  603 . At addition block  605 , |I d | and |Q d | are added together and, at accumulation block  607  P 1 ( k ) is calculated, according to equation [15].  
         [0121]     Referring to the lower portion, |I a | is obtained at block  609  and |Q a | is obtained at block  611 . P 2 ( k ) is calculated, according to equation [16], at addition block  613 .  
         [0122]     Comparison block  615  compares P 1 ( k ) and P 2 ( k ) to decide whether the UW is detected or not.  
         [0123]     As with the first embodiment, as long as  
       [       P   ⁢           ⁢   2   ⁢     (   k   )         P   ⁢           ⁢   1   ⁢     (   k   )         ]       
 
 exceeds a certain threshold A′. the UW is judged as detected. In this embodiment, the theoretical maximum of  
         [       P   ⁢           ⁢   2   ⁢     (   k   )         P   ⁢           ⁢   1   ⁢     (   k   )         ]     ⁢           ⁢   is   ⁢           ⁢     1       2   ⁢   xpower             
 
 so A′ satisfies  
       0   &lt;     A   ′     &lt;       1       2   ⁢   xpower         .         
 
 Within these limits, A′ an be set appropriately, depending on how strict a detection is required. 
 
         [0124]     Once again, the frequency offset estimation obtained from the successfully detected UW can be used at block  403  to improve the frequency offset estimation.  
         [0125]     Two particular ways of detecting UW have been described with reference to  FIGS. 5 and 6 , but the invention is not limited to one or other of those embodiments.