Patent Publication Number: US-6657949-B1

Title: Efficient request access for OFDM systems

Description:
STATEMENT OF RELATED APPLICATIONS 
     The present application is related to the subject matter of the following previously filed U.S. Patent Applications. 
     U.S. patent application Ser. No. 09/019,938, entitled MEDIUM ACCESS CONTROL PROTOCOL FOR OFDM WIRELESS NETWORKS, filed on Feb. 6, 1998. U.S. patent application Ser. No. 09/282,589, entitled DIFFERENTIAL OFDM USING MULTIPLE RECEIVER ANTENNAS, filed on Mar. 31, 1999. 
     U.S. patent application Ser. No. 09/234,629, entitled SYSTEM FOR INTERFERENCE CANCELLATION, filed on Jan. 21, 1999. 
     The co-filed, co-assigned U.S. Patent Application entitled OPTIMAL USE OF REQUEST ACCESS TDMA SLOTS FOR AUTOMATIC LEVEL CONTROL is also related to the subject matter of the present application. 
     All of the related patent applications are herein incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to digital communication systems and more particularly to digital communication systems employing orthogonal frequency division multiplexing (OFDM). 
     A point to multipoint wireless communication system represents a potentially effective solution to the problem of providing broadband network connectivity to a large number of geographically distributed points. Unlike optical fiber, DSL, and cable modems, there is no need to either construct a new wired infrastructure or substantially modify a wired infrastructure that has been constructed for a different purpose. 
     In order to conserve scarce spectrum, the data communication devices of a point to multipoint wireless communication system may all share access to a common frequency. In a typical scenario one or more frequency channels are allocated to downstream broadcast communication from a central access point to a plurality of subscriber units and one or more separate frequency channels are allocated to upstream communication from the subscriber units to the central access point. For upstream communication there is a medium access control (MAC) protocol that determines which subscriber unit is permitted to transmit at which time so as not to interfere with transmission from other subscriber units. For a given upstream frequency, the time domain is divided into frames which are typically of equal duration where each frame represents an individually allocable unit in the time domain. For frames transmitting upstream data, one subscriber unit transmits in each frame. Certain other frames are, however, reserved for access requests by subscriber units. The access request frames are not reserved for any particular subscriber unit in advance. Any subscriber unit wishing to transmit data upstream may transmit its access request in the access request frame. If multiple subscriber units transmit simultaneously in an access request frame there is a collision. The colliding subscriber units will detect the collision and attempt to retransmit their access request after a wait period that is defined pseudo-randomly at each subscriber unit so as to reduce the probability of further collisions. 
     Orthogonal frequency division multiplexing (OFDM) systems offer significant advantages in many real world communication systems, particularly in environments where multipath effects impair performance. OFDM divides the available spectrum within a channel into narrow subchannels. In a given so-called “burst,” each subchannel transmits one data symbol. Each subchannel, therefore, operates at a very low data rate compared to the channel as a whole. To achieve transmission in orthogonal subchannels, a burst of frequency domain symbols are converted from the time domain by an inverse Fast Fourier Transform (IFFT) procedure. To assure that orthogonality is maintained in dispersive channels, a cyclic prefix is added to the resulting time domain sequence. The cyclic prefix is a duplicate of the last portion of the time domain sequence that is appended to its beginning. To assure orthogonality, the cyclic prefix should be as long as the duration of the impulse response of the channel. It is desirable to use OFDM in point to multipoint networks where multipath effects are a concern. 
     Upstream access requests typically contain very little data. Using an entire frame for an access request from a single subscriber unit is therefore very inefficient. One solution is to multiplex multiple access requests from multiple subscriber units within the same frame in a way that avoids collisions. In an OFDM system one way to accomplish this is to allocate different frequency domain subchannels to different subscriber units so that multiple subscriber units effectively share an OFDM burst and may each transmit their own access request within their own grouping of subchannels. Such a technique is disclosed in U.S. patent application Ser. No. 09/019,938. 
     To assure maximum performance, an OFDM burst carrying data from a subscriber unit should contain v frequency domain training symbols having predetermined values to assist the receiver in estimating the channel response where vis greater than or equal to the number of symbol periods in a duration of the impulse response from the subscriber unit to the central access point. Symbols used for training are then unavailable for transmission of data. Loss of efficiency due to the inclusion of training symbols is compounded where multiple subscriber units share a single OFDM burst. In the system described in U.S. patent application Ser. No. 09/019,938, each subscriber unit must transmit v training symbols as part of its own grouping within the access request OFDM burst. Thus within a single OFDM burst, there are R*v symbols devoted to training where R is the number of subscriber units sharing the burst. What is needed are systems and methods for more efficiently multiplexing transmissions of multiple subscriber units within the same OFDM burst. 
     SUMMARY OF THE INVENTION 
     Systems and methods for efficient multiplexing of multiple access requests from disparate sources within a single OFDM burst are provided by virtue of the present invention. Each of multiple subscriber units employ non-overlapping groups of OFDM frequency domain symbols within a single burst for upstream transmission of their access requests. In one embodiment, the OFDM frequency domain symbols are differentially encoded to eliminate the need for upstream transmission of training information. In an alternative embodiment, the group of frequency domain symbols within the burst employed by any particular subscriber unit are contiguous to one another. Channel training for a given subscriber unit need only be performed over the subband occupied by its group of frequency domain symbols. This greatly reduces the number of training symbols required for reception. The reduction or elimination of training symbols increases the number of access requests that may be accommodated within a single burst and/or allows for greater redundancy in transmission of access request data. 
     One aspect of the present invention provides apparatus for operating a selected data communication device to request access to a shared medium employed by a digital communication system. The apparatus includes a burst forming system that forms frequency domain symbols of an OFDM burst. A first group of frequency domain symbols within the burst includes differentially encoded data and a second group of frequency domain symbols in the burst includes zero values to allow for data transmitted by other data communication devices. The apparatus further includes a converter that transforms frequency domain symbols of the OFDM burst into time domain symbols, and a transmitter system that transmits the time domain symbols as a request for access to the shared medium. 
    
    
     Further understanding of the nature and advantages of the invention herein may be realized by reference to the remaining portions of the specification and the attached drawings. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 depicts a point to multipoint communication network suitable for implementing one embodiment of the present invention. 
     FIGS. 2A-2C depict the internal structure of an OFDM request access burst incorporating reduced training information according to one embodiment of the present invention. 
     FIG. 3 depicts internal structure of an OFDM request access burst incorporating differential coding according to one embodiment of the present invention. 
     FIG. 4 depicts apparatus for transmitting the request access burst of FIG. 2 according to one embodiment of the present invention. 
     FIG. 5 depicts apparatus for receiving the request access burst of FIG. 2 according to one embodiment of the present invention. 
     FIG. 6 depicts apparatus for performing channel training on a subband of the request access burst of FIG. 2 according to one embodiment of the present invention. 
     FIG. 7 depicts apparatus for transmitting the request access burst of FIG. 3 according to one embodiment of the present invention. 
     FIG. 8 depicts apparatus for receiving the request access burst of FIG. 3 according to one embodiment of the present invention. 
    
    
     DESCRIPTION OF SPECIFIC EMBODIMENTS 
     FIG. 1 depicts a point to multipoint wireless communication network  100  suitable for implementing one embodiment of the present invention. Network  100  includes a central access point or headend  102  and multiple subscriber units  104 . All communication is typically either to or from central access point  102 . Communication from central access point  102  to one or more subscriber units  104  is herein referred to as downstream communication. Communication from any one of subscriber units  104  to central access point  102  is herein referred to as upstream communication. In one embodiment, different frequencies are allocated to upstream and downstream communication. In some alternative embodiments, subscriber units  104  may communicate with one another directly. 
     Each of one or more upstream frequencies is common to multiple subscriber units. To prevent collisions between subscriber units when accessing the shared medium to transmit data upstream, a medium access control (MAC) protocol is provided. For each upstream frequency, the time domain is divided into frames or slots. An individual frame may be allocated for upstream data transmission by a particular subscriber unit. The schedule of which subscriber units are permitted to transmit in which frames is distributed in a scheduling message sent downstream by central access point  102 . In a typical system, when a particular subscriber unit wishes to transmit data upstream, it sends a special transmission known as an access request upstream to central access point  102  to request access to the shared medium. Particular frames or slots are reserved for transmission of the access request. According to the present invention, multiple subscriber units may transmit access requests upstream within the same access frame without causing a collision. 
     Network  100  may employ OFDM. The abbreviation “OFDM” refers to Orthogonal Frequency Division Multiplexing. In OFDM, the available bandwidth is effectively divided into a plurality of subchannels that are orthogonal in the frequency domain. During a given symbol period, the transmitter transmits a symbol in each subchannel. To create the transmitted time domain signal corresponding to all of the subschannels, an FFT is applied to a series of frequency domain symbols. The resulting time domain burst is augmented with a cyclic prefix prior to transmission. The cyclic prefix addition process can be characterized by the expression: 
     
       
         [ z ( 1 ). . .  z ( N )] T   |→[z ( N−v +1) . . .  z ( N ) z ( 1 ) . . .  z ( N )] T   
       
     
     On the receive end, the cyclic prefix is removed from the received time domain symbols. An IFFT is then applied to recover the simultaneously transmitted frequency domains symbols. The cyclic prefix has length v where v is greater than or equal to a duration of the impulse response of the channel. The cyclic prefix assures orthogonality of the frequency domain subchannels. 
     There are other ways of creating transmitted bursts of symbols in orthogonal subchannels or substantially orthogonal subchannels including, e.g., use of the Hilbert transform, use of the wavelet transform, using a batch of frequency upconverters in combination with a filter bank, etc. Wherever the term OFDM is used, it will be understood that this term includes all alternative methods of simultaneously communicating a burst of symbols in orthogonal or substantially orthogonal subchannels defined by procedures performed on a time domain sequence. The term frequency domain should be understood to refer to any domain that is divided into such orthogonal or substantially orthogonal subchannels. 
     FIGS. 2A-2C depict the contents of a request access OFDM burst according to one embodiment of the present invention wherein each of multiple subscriber units are allocated contiguous subgroups of OFDM frequency domain symbols. In the discussion that follows, the frequency domain symbols are also referred to as “tones.” An OFDM request access (RA) burst includes data tones, channel training tones and zero tones. FIGS. 2A-2C show the tone positions as they would appear at the receiver end. At either end of the burst, there are N edge  zero tones where N edge  equals between (N−v)/10 and (N−v)/20 where N is the IFFT size and v is the number of training symbols to be included within the burst. 
     Besides the edge tones, the remaining tones are evenly divided into N user  RA tone sets of size N ra . Each subscriber unit transmits using only one of the RA tone sets and sets the remaining tone sets to have zero value. When requesting access, each subscriber unit pseudo-randomly determines the tone set that it will use. Each RA tone set contains N tt  training tones that in the depicted example occupy every fourth tone starting with the first tone in the tone set. The training tones will have one of four values: 
     
       
           Z   T ( n )={ A,−A,iA,−iA},   
       
     
     where the amplitude A will depend on which constellation type (e.g., 4-QAM, 16-QAM) is being used for data. This choice of training tone values removes the need for any division or multiplication of these values in the channel estimation processing. The number of training tones in each RA tone set may be less than the impulse response duration in symbol periods. 
     Each tone set includes N ra  tones. The remaining N ra −N tt  tones are used to transmit the subscriber unit&#39;s access request data and some zero tones. To increase the probability of accurate reception of the access request data even under difficult channel conditions, the access request data is duplicated N red  times to implement repetition coding. For each repetition of the data there are N zm  zero tones. Furthermore, at the beginning of the RA tone set there are N zs  zeros and at the end of the RA tone set there are N ze  zero tones. Each repetition of the data includes N data  data tones so that each RA tone set includes N d =N data N red  data tones. Zero tones are positioned to ensure that the data tones are centered within the training tones, that the training tones are spaced evenly across RA tone sets as seen by the receiver, and that there is equal spacing between all redundant data tones within a tone set. 
     FIG. 4 depicts a system for generating and transmitting a single RA tone set within request access burst  200  as will be generated by a single subscriber unit. Binary request access data is input into a symbol mapper  402 . The request access data is has preferably been coded employing error correction coding techniques such as convolutional coding, block coding, Reed-Solomon coding, etc. A random number generator  406  selects for each access request the particular RA tone set that will be used by the subscriber unit. A redundant symbol formation block  404  positions the RA data symbols within the burst and creates the redundant data sets as shown in FIGS. 2A-2C. A zero-filling block  408  positions the zero tones within the burst including the zero values corresponding to the non-selected RA tone sets. 
     The phases of the frequency domain symbols within the RA burst are scrambled prior to transmission. The phases are scrambled according to a scrambling pattern or scrambling code that assigns a scrambling phase value to each tone position within the burst. Each RA tone set therefore has its own unique section of the phase scrambling pattern. The reason for the phase scrambling is that certain combinations of request access data symbols will result in an excessive peak to mean power ratio (PMPR) for the burst as received. If the phase scrambled symbol values generated for a particular request access burst result in excessive PMPR, the receiver FFT will saturate resulting in a failed access request. In response to the lack of acknowledgement, the access request will be retransmitted. Now, however, random number generator  406  will likely select a different RA tone set for use in requesting access. The request access tones will be shifted to a different portion of the burst and subject to phase scrambling by a different section of the phase scrambling pattern giving rise to a different PMPR value. Repeated transmissions using different RA tone sets will quickly result in a successful transmission that does not saturate the receiver FFT. It is highly probable that the second transmission will be successful if the first transmission results in saturation. 
     The phase scrambling pattern consists of a series of values ranging from 0 to 3. A phase scrambling storage block  410  generates the values of the pattern in succession. A complex exponential block  412  represents the translation of the values ranging from 0 through 3 into four possible phase rotation values: 0, π/2, π, 3π/2. A phase rotator  414  applies the phase scrambling phase shifts to the zero-filled and repetition coded RA symbols. A training tone selection block  416  generates training tones at the appropriate positions depending on the RA tone sets selected by random number generator  406 . A multiplexer  418  selects between the zero filled redundant sets of RA data symbols and the training tones depending on the position within the burst. The output of multiplexer  418  is the complete set of frequency domain symbols for the burst as transmitted by a particular subscriber unit  104 . 
     IFFT block  420  converts the frequency domain symbol burst into a time domain symbol burst and affixes the cyclic prefix to the beginning of the time domain symbol burst. A transmitter system  422  performs all additional digital and analog signal processing necessary to generate an RF signal for transmission over the airwaves where the RF signal has been modulated using the baseband time domain symbols output by IFFT block  420 . Transmitter system  422  transmits the RF signal upstream via an antenna  424 . 
     FIG. 5 depicts a system  500  for receiving and processing the OFDM RA burst of FIGS. 2A-2C. System  500  would typically be implemented at central access point  102 . System  500  takes advantage of signals received via M R  antennas  502 . However, the present invention may also be applied in the context of receivers only employing a single antenna. 
     For each antenna  502 , there is a receiver system  504 . Receiver system  504  performs all of the analog and digital signal processing operations necessary to recover baseband time domain symbols from the modulated RF signal received via the antennas  502 . A series of FFT blocks  506  remove the cyclic prefix from successive time domain OFDM bursts and convert the time domain OFDM bursts to the frequency domain using the FFT. A group of selection blocks  508  then separate the tones from each RA tone set depicted in FIGS. 2A-2C. The selection blocks  508  are aware of a number of users  510  for which RA OFDM burst  200  has been configured. Each selection block  508  outputs data tone values and zero tone values for all subscriber units as received via a particular antenna. Each selection block  508  also outputs training values for each user as received by a particular one of antennas  502 . 
     Channel estimations are performed separately for each subscriber unit based on the training tones within the subscriber unit&#39;s RA tone set. According to the present invention, each RA tone set in burst  200  includes a number of training tones sufficient to establish channel response within the tone set but not over the burst as a whole. An interpolation technique is used to establish the channel response over all the tones of the tone set based on the training tone values as received. Each of a series of interpolation filters  512  obtains the channel response for a single combination of antenna and RA tone set. The predetermined training tone values as transmitted are obtained from an inverse phase sequence/training tone block  514 . 
     Each of interpolation filters  512  operates as follows. Let the vector Z t  be the ideal N tt  training tones in an RA tone set, and the vector X t,i  be the received values from antenna i for the training tones. An estimate of the channel at the training tone positions is formed by a quotient block  602  taking the quotient of these two values: 
     
       
           Ĥ   t,i =( X   t,i   ÷Z   t ), 
       
     
     where the symbol ÷ represents element-by-element division. Since Z t  is defined as given earlier, this operation does not require any multiplies or divides. 
     An estimate of the channel at the data tones is formed by interpolating Ĥ t,i . This is done by first extending Ĥ t,i , zero-stuffing the resultant extended vector with r int −1 zeros, and convolving the zero-stuffed vector with an interpolation filter, G, of length 2L+1. Therefore: 
     1. Let Ĥ t,i  be a vector of values Ĥ t,i  an extrapolation block  604  forms 
     
       
           Ĥext   t,i   =[Ĥlow   t,i   Ĥ   t,i   Ĥhigh   t,i ], 
       
     
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           Ĥlow   t,i ( n )= Ĥ   t,i ( 1 )− n ( Ĥ   t,i ( 2 )− Ĥ   t,i ( 1 )), n =1  . . . L   
       
     
     
       
           Ĥhigh   t,i ( n )= Ĥ   t,i ( N   TT )− n ( Ĥ   t,i ( N   TT −1)− Ĥ   t,i ( N   TT )), n =1  . . . L   
       
     
     2. An upsampler  606  zero-stuffs according to: 
     
       
           Ĥext   t,i   =[Ĥext   t,i ( 1 )00 . . . 0 Ĥext   t,i ( 2 )0 . . . ] 
       
     
     3. A filter block  608  then filters according to: 
     
       
         
           
             
               
                 
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     The number of complex operations required to form Ĥ i (n) for each data tone in an RA slot, neglecting multiplications involving zero, is (2L+1)N red N data . This channel estimation technique provides an adequate estimate over a particular subband even when the number of training tones is less than the number of symbol periods in the channel impulse response from the subscriber unit to the central access point. 
     Inverse phase sequence/training tone block  514  outputs an inverse phase scrambling pattern that is an inverse of the phase scrambling pattern applied at the subscriber units  104 . A set of phase rotators  516  for each antenna  502  applies the phase rotation to undo the effects of phase scrambling. A channel correction and antenna combining block  518  corrects the access request data as received based on the measured channel response, optimally combines the request access data as received via the multiple antennas  502 , and furthermore optimally combines the multiple repetitions of data within each RA tone set. The output of block  518  is a series of cost metric or soft decision values for each bit which can then be used by a Viterbi decoder or trellis decoder to remove the effects of convolution encoding. A later stage or stages can then remove the effects of other error correcting codes applied at the transmit end. The operation of block  518  will first be explained with reference to an embodiment wherein there is no repetition of data within an RA tone set. 
     After conversion to the frequency domain, the receive value for each symbol is: 
     
       
           X   i ( n )= H   i,j ( n ) Z   j ( n )+ W   i ( n ) 
       
     
     where X i  and W i  are the frequency domain received symbol and noise/interference values at tone position n. 
     The term H ij (n) is the channel response at tone n from user j to antenna i. The term Z j (n) is the transmitted symbol by user j in tone n. The use of both j and n is redundant since for any tone value n, there is just one user j. However, this notation will be used in order to emphasize certain aspects of the processing. 
     The maximum likelihood solution for decoding the received symbols when there is no redundancy in an RA tone set is 
     
       
         
           
             
               
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     1. Antenna Combining and Channel Correction: 
     
       
         
           
             
               
                 
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     Constellation bit mapping (CBM) is used to determine the cost metrics of each bit in the symbol at tone n. Details of CBM are described in U.S. patent application Ser. No. 09/234,629. The interference energy, σ 2   ij (n) is calculated as 
     
       
           σ   i,j   2 ( n )= E{|X ( n )−Ĥ i,j ( n ) Z   i,j ( n )|} 2   
       
     
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     The expectation σ 2   ij (n) is performed across all the data tones in an RA. Thus, there will be one power estimate for each RA slot and each antenna. 
     The above technique can be modified with bursts that employ redundancy as in FIGS. 2A-2C. The data should be coherently combined across redundant subsets within each tone set. In the antenna combining and channel correction step each redundant set of data is treated as originating with a separate antenna. 
     Interference energy estimates are, however, averaged over redundant subsets, so that there is only one value of σ 2   ij  for each user and each antenna. The weighted-Euclidean cost function is then obtained by: 
     
       
         
           
             
               
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     where J red  is the set of tones n that have redundant data. Then, 
     
       
         
           
             
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     Constellation bit mapping is performed for each combined symbol Z(n) as described earlier. 
     FIG. 3 depicts an alternative request access OFDM burst structure  300 . In burst  300 , as in the burst structure depicted in FIGS. 2A-2C, there are multiple request access tone sets. In burst  300 , however, there are no tones allocated to training. This increases the number of tones that are allocated to data. It is therefore possible to have each subscriber unit transmit more data within its access request, include more access requests within the same OFDM burst, and/or include more redundant sets of access request data. The structure of burst  300  is similar to that of burst  200  except that training tones have been replaced by data tones. Although data tones for each subscriber unit are depicted as contiguous, this is not necessary. In order to function without the use of training symbols, the access request data of burst  200  is differentially encoded as phase differences between successive frequency domain symbols. Because the receiver system does not take received magnitude into account in estimating the transmitted data, variation in channel response magnitude does not affect system performance. Variations in phase response within bounds also do not corrupt data transmission because any phase difference applied by the channel is effectively subtracted out as a part of the differential decoding process. 
     FIG. 7 depicts a system  700  for developing and transmitting the OFDM burst of FIG. 3 according to one embodiment of the present invention. System  700  will be employed in one of subscriber units  104 . A mapper  702  generates successive frequency domain symbols based on request access data that has already been subject to error correction coding. Symbols selected by mapper  702  preferably belong to a phase shift key (PSK) consellation where all symbols have the same magnitude but different phase. Mapper  702  operates so that phase differences between each two consecutive symbols represents one or more bits of coded request access data, the number of bits depending on the particular PSK scheme used. Details of differential coding techniques are disclosed in U.S. patent application Ser. No. 09/282,589. A random number generator  704  selects a value that identifies which RA tone set within the burst is to be employed. A redundant symbol formation block  706  then places the symbols output by mapper  702  within the burst according to the RA tone set assigned by random number generator  704  and includes redundant tones as was discussed with reference to FIG. 4. A zero-filling block  708  supplies zero values at the appropriate tone positions. 
     A scrambler  710  generates the phase scrambling pattern of values 0 through 3 as was discussed with reference to FIG. 4. A complex exponential block  712  then determines a phase difference corresponding to each value generated by scrambler  710 . A phase rotator  714  applies the appropriate phase difference for each frequency domain symbol position within the burst. 
     An IFFT block  716  then converts the phase scrambled frequency domain symbols to the time domain and adds a cyclic prefix. The time domain symbols output by IFFT block  716  are baseband digital values. A transmitter system  718  converts the baseband values to analog and performs all analog and digital signal processing operations necessary for generating an RF signal modulated with the OFDM time domain signal. 
     FIG. 8 depicts a system  800  for receiving and processing the request access OFDM burst of FIG.  3 . System  800  is depicted to take advantage of multiple antennas but the present invention may also be employed in conjunction with a single receiver antenna. System  800  would typically be implemented within central access point  102 . 
     RF signals from subscriber units  104  are received via M R  receiver antennas  802 . For each of antennas  802 , there is a receiver system  804  that performs all the analog to digital signal processing operations necessary to recover baseband time domain symbols from the received RF signals. For each antenna, one of FFT blocks  806  removes the cyclic prefix from successive OFDM time domain bursts and converts the time domain symbols to the frequency domain. Phase descrambling blocks  808  removes the effects of the phase scrambling code as was described in reference to FIG.  5 . 
     For each antenna  802 , a differential decoding stage  810  recovers the differentially encoded access request data based on the frequency domain symbols output by the corresponding FFT block  806  as phase descrambled by phase descrambling blocks  808 . For each two successive phase descrambled frequency domain symbols, each differential decoder finds detection symbols: 
     
       
           a   i ( n,k )= x   i *( n,k ), x   i ( n +1 ,k ) 
       
     
     where x refers to a received frequency domain symbol, i identifies a particular antenna, n identifies a frequency domain symbol position within a burst, and k identifies a particular burst. 
     A combination element  812  combines the detection symbols obtained via the multiple antennas from differential decoding stages  810  to form a combined detection symbol estimate. In one embodiment, combination element  112  finds the combined detection symbol to be: 
     
       
         
           
             
               a 
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                 ( 
                 
                   n 
                   , 
                   k 
                 
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                   R 
                 
               
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     The recovered phase difference value is then: 
     
       
           {circumflex over (z)} ( n,k )=∠ a ( n,k ). 
       
     
     The output of combination block  812  is preferably the series of cost metric or soft decision values to be used by a Viterbi decoder to remove the effects of error correction coding. The cost metric values are estimated to be: 
       c ( n,k )=| a ( n,k )| 2   |{circumflex over (z)} ( n,k )− {overscore (z)} ( n,k )| 2    
     where {overscore (z)}(n,k) is the nearest ideal phase difference value to {circumflex over (z)}(n,k). For example, the ideal phase difference values for QPSK would be {0, π/2, −π/2, π}. 
     The term |a(n,k)| 2  serves as a confidence value which weights phase differences received by the various antennas according to their associated symbol magnitudes. 
     These cost metric values as described above are generated on a symbol by symbol basis. U.S. patent application Ser. No. 09/282,589 describes a technique for developing cost metric values for individual bits rather than symbols. In the above equations symbols that are repeated due to the use of repetition coding are treated as if they are received via multiple antennas. 
     It is understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to persons skilled in the art and are to be included within the spirit and purview of this application and scope of the appended claims and their full scope of equivalents. For example, the present invention may be applied to wireline systems. All publications, patents, and patent applications cited herein are hereby incorporated by reference.