in a time division multiple access ( tdma ) system , data from a digital information source is encoded as symbols in a transmitter and transmitted in a radio - frequency ( rf ) signal to a receiver which samples the received rf signal to provide a series of frames and time slots comprised of data samples . each user is allotted one time slot to transmit data and receive data . typically , a transmitter transmits a header or preamble of known reference symbols followed by data symbols in each time slot . the preamble or known reference symbols are used for functions such as synchronization , slot identification , addressing and estimating the channel . the frame and slot structure used in u . s . digital cellular tdma system for transmission between base station and mobile station is illustrated in fig1 and described on p . 85 - 86 of january &# 39 ; 91 eia / tia &# 34 ; interim standard -- cellular system , dual mode mobile station -- base station compatibility standard &# 34 ; publication is - 54 - a by the electronics industries assoc ., engineering dept . fig1 shows a continuous rf transmission signal which is sectioned into frames of data . each frame , such as frame 140 is divided into three time slots or data slots , one of which is slot 2 , 144 of fig1 . even though the slot illustrated in fig1 is u . s . digital cellular telephone communication format , the present invention applies equally to other formats for digital transmission , but the tdma u . s . cellular telephone format was chosen for purposes of describing the invention . a u . s . digital cellular telephone communication slot is comprised of a preamble 166 , a slow associated control channel ( sacch ) block 168 , the encoded data 174 and 178 ( which may be encoded speech data ), a coded digital verification color code ( cdvcc ) block of data 176 and a reserved block of data 179 described on p . 85 - 86 of january &# 39 ; 91 eia / tia &# 34 ; interim . standard -- cellular system , dual mode mobile station -- base station compatibility standard &# 34 ; publication is - 54 - a by the electronics industries assoc ., engineering dept . after transmission of the rf signal to a receiver , an equalizer in the receiver minimizes errors incurred in transmission such as reflected echoes known as mulipath propagation and transients of a symbol signal which continue into another symbol period , known as intersymbol interference . the equalizer compares known symbols to received samples to determine a channel impulse response ( cir ). initially this is very straight - forward with stored reference symbols being the known symbols , being compared to the received reference samples . after the reference symbols are exhausted , however , other known symbols must be used . previously demodulated samples are now used as the known symbols with the newly received samples being compared to them to determine the cir . the equalizer requires an estimate of the cir to begin demodulation of the signal , therefore the cir estimate is always based upon the previously demodulated samples after the reference symbols have been demodulated as described in &# 34 ; an adaptive mlse receiver for tdma digital mobile radio &# 34 ;, by r . d &# 39 ; avella , et al , ieee journal on selected areas in communications , vol . 7 , no . 1 , january 1989 , pp . 122 - 129 . the equalizer can make use of the known reference symbols such as preambles 166 , 181 , or cdvcc 176 to estimate the cir . errors occur in decoding when the channel conditions are poor , such as when the signal drops in strength for a short period of time known as a &# 34 ; fade &# 34 ;. when decoding errors occur , they are fed into the cir estimator which incorrectly estimates cir values which in turn causes incorrect demodulation of subsequent samples producing more errors . this effect is known as error propagation . fig2 illustrates a fade in the received rf signal during a single data slot . the fade occurs at point x in the slot which is closer to the beginning of the slot . if the slot is being demodulated in a forward sense errors would begin to occur at point x . due to error propagation , not only is there an error in demodulating the faded portion of the signal , but the demodulated information leads to incorrect cir estimates and corrupts the process employed in demodulating subsequent samples . this results in numerous errors beginning at point x and continuing throughout the remainder of the slot . this will result in incorrect data from point x until the end of the slot . however , if the slot were demodulated in a reverse sense starting from the end of the slot and working back to the beginning of the slot , the fade point x would not be encountered until most of the slot has been demodulated . therefore , most of the slot would be demodulated correctly with errors beginning at point x and continuing in a reverse direction to the beginning of the slot resulting in a smaller portion of the demodulated data being incorrect . it therefore would be most beneficial to demodulate a slot in the forward and reverse directions and meet at the fade point x , thereby obtaining the best results . the frame / slot structure of the u . s . digital cellular system for continuous base to mobile transmission provides the known data sequences , reference symbols , spanning each data slot as shown in fig3 namely , preamble 166 at the beginning of the slot , cdvcc 176 at the middle of the slot , and preamble 181 at the end of the slot which is actually the preamble of the next slot ( slot 3 of fig1 ). the slots of fig1 may each be divided into a first and second halfslot 148 , 149 respectively , preferably divided at the cdvcc as shown in fig3 . the remaining portion of the halfslots are subdivided into subslots numbered from 1 to n . the size of the subslots is chosen from channel conditions , signal level , antenna type , vehicle speed , carrier frequency , modulation scheme and data rate . the optimal subslot size is chosen to correspond to the average fade duration . this technique of sectioning the slot into subslots for decoding helps isolate a fade within a particular subslot . for instance , in the u . s . digital cellular system , assuming that there is uncorrectable error for a fade corresponding to a signal level of - 20 db relative to a reference signal level at 0 db in a rayleigh fading channel , when a vertical monopole antenna is used at a carrier frequency of 900 mhz and vehicle speed of 100 kmph , it can be shown that the average fade duration is approximately 482 microseconds as described in &# 34 ; a power - spectral theory of propagation in the mobile - radio environment &# 34 ; by m . j . gans , ieee transactions on vehicular technology , vol . vt - 21 , no . 1 , pp . 27 - 38 , february 1972 . for a data rate of 48 . 6 kbps and π / 4 - shifted differentially encoded quadrature phase shift keying ( dqpsk ) modulation , the above fade duration spans 12 symbols . hence , the subslot size for the preferred embodiment having the above - mentioned parameters is chosen to be 12 symbols long . ( different subslot lengths may be determined by adjusting the parameters above .) the order and direction which the subslots are demodulated are determined for each subslot based upon a measure of the snr of previously demodulated subslots . the process begins with subslot 1 being demodulated in a forward direction , forward sense , with the samples of this subslot least recently received being demodulated before the most recently received samples as indicated by arrows 151 . subslot n is demodulated in a reverse direction , reverse sense , as indicated by arrows 153 . next , a forward metric f 11 is computed for subslot 1 in the forward direction , and a reverse metric r 1n is computed from subslot n , wherein the first subscript index indicates the halfslot and the second represents the subslot being demodulated . many conventional metrics which indicate the inverse of the snr may be employed . for example , if an equalizer such as described in the aforementioned publication by d &# 39 ; avella is used , the path metrics associated with two best survivor states will provide a measure of the inverse snr . alternatively , the metric may be chosen as the average noise power over the subslot . this will be provided by the path metric associated with the best survivor state . the reverse metric r xx is completed the same as the forward metric f xx with the exception that the data on which it is calculated is in the reverse order . in the preferred embodiment , the order in which the samples are demodulated is the order in which the metric is calculated , a subslot demodulated in reverse sense has the metric calculated in reverse sense . the demodulation is then extended to the subslot adjacent the last demodulated subslot having a greater snr as indicated by the metrics . since the metrics are inversely proportional to the snr , and proportional to the noise power , the direction of decoding is chosen based upon the lower of the two metrics . if f 11 & lt ; r 1n , then subslot 2 is demodulated in the forward sense and f 12 is obtained . f 12 is then compared to r 1n and once again the decoding is extended in the direction of the better metric . if f 11 & gt ; r 1n then subslot n - 1 is demodulated in the reverse direction . this recursive process continues until the two directions of decoding overlap over one subslot . after all subslots have been demodulated into digital information , the information is arranged in the original order of the samples from which they were demodulated to produce one continuous stream of digital information for the entire slot . this information is then provided to an output device capable of utilizing the digital information . fig4 illustrates a block diagram of the present invention showing a digital information source 5 , a transmitter 20 , a receiver 120 and an output means 100 . digital information from digital information source 5 desired to be transmitted is provided to a block assembly unit 8 . the digital information may be digitized speech data from an operator speaking into a handset 2 to create an analog voltage signal that is sampled by analog to digital ( a / d ) converter 4 and analyzed by a vocoder to provide coded speech data to a block assembly unit 8 . block assembly unit 8 combines digital information , reference symbols and other required data stored in a reference symbol storage means , shown here as a read only memory ( rom ) 7 , in a slot of data having a standardized format interleaved with other data slots ( such as shown in fig1 ) to be communicated through a tdma system . encoder 10 encodes the slot of data in a desired manner and passes the encoded data to a mapper 12 which maps several bits to a symbol of a predetermined symbol constellation . mapped symbols are provided to a digital to analog ( d / a ) converter 14 which converts the mapped samples to an analog signal at a rate governed by a transmit clock 16 and transmit oscillator 17 . the analog signal is then filtered by a lowpass filter 18 , modulated by modulator 19 and passed to a radio frequency ( rf ) amplifier 22 which creates an rf signal transmitted through antenna 24 . the transmitted signal is sensed by a receiving antenna 124 , passed to rf preamplifier 122 and heterodyned by a down converter 118 to provide an intermediate frequency ( if ) signal . an a / d converter 114 in the receiver samples the if signal at a rate determined by a receive clock 116 and receive oscillator 117 , resulting in a plurality of received reference samples and data samples corresponding to samples of reference symbols and data symbols , respectively . the samples are provided to synchronization unit 50 , coupled to second reference symbol storage unit shown as rom 88 , adapted for retaining predetermined reference symbols being the same as : 1 ) the symbols of preamble 166 , 181 or cdvcc data 176 shown in fig1 and synchronization unit 50 analyzes the received reference samples it receives from a / d converter 114 to that of rom 88 and determines a sample timing b corresponding to a best match . data samples corresponding to the best sample timing b are passed to a frequency offset correction unit 70 . frequency offset correction unit 70 , then determines a frequency offset which represents the phase drift between transmit and receive oscillators 17 , 117 , respectively , and corrects the data by this offset . an equalizer 90 receives the data , equalizes it and passes the data to a subslot selection unit 130 which buffers the data . ( all elements in receiver 120 up until , but not including equalizer 90 , collectively may be referred to as synchronization and sampling ( s & amp ; s ) means 110 .) the buffered data is sectioned into two halfslots ( 148 , 149 of fig3 ) each sectioned into subslots numbered subslot 1 through subslot n . the first subslot from the beginning of the halfslot , subslot 1 , is provided to a equalizer / demodulator 150 to be demodulated in a forward sense . the first subslot from the end of the halfslot , subslot n , is also provided to equalizer / demodulator 150 to be demodulated in a reverse sense . the demodulated data is provided to a slot construction unit 170 to be stored . a forward metric is determined by equalizer / demodulator 150 for subslots demodulated in a forward sense such as f 11 pertaining to subslot 1 of first halfslot 148 . equalizer / demodulator 150 also determines a reverse metric for subslots demodulated in a reverse direction such as r 1n for subslot n of halfslot 148 . the metric is then passed to subslot selection unit 130 . subslot selection unit 130 then determines if f 11 indicates a greater snr than r 1n does , and if so , the next subslot from the beginning of halfslot 148 , subslot 2 , is demodulated by equalizer / demodulator 150 and a forward metric f 12 is calculated . slot construction unit 170 receives the demodulated digital information . f 12 is then compared to the last metric of opposite sense ( forward sense vs . reverse sense ) being r 1n . if r 1n indicates a greater snr than f 12 , subslot r 1n - 1 is demodulated in a reverse sense next . slot construction unit 170 then stores the demodulated information . the process of selecting subslots , demodulating them , storing the demodulated data , determining metrics and extending demodulation to the subslot adjacent the subslot having the lowest metric is repeated until all subslots have been demodulated . slot construction unit 170 provides the digital information to an output device 100 capable of utilizing digital information in the proper order and sense ( forward or reverse ) regardless of the order and sense of demodulation . output device may be a second vocoder 106 and a second d / a converter 104 and a second handset 102 , which convert the digital information into an audible signal at second handset 102 . in a second embodiment of the invention , all elements of fig4 function as in the first embodiment up until frequency offset correction means 70 . at this point , subslot selection unit 130 selects subslots 1 , 2 , 3 , . . . n passing each sequentially to equalizer / demodulator 150 which demodulates each subslots in a forward sense into digital information and stores the digital information . equalizer / demodulator 150 then calculates a forward metrics f 11 , f 12 , f 13 , . . . f 1n for subslots 1 , 2 , 3 , . . . n , respectively , and stores the forward metrics . subslot selection unit 130 then selects subslots n , n - 1 , n - 2 , . . . 1 passing each sequentially to equalizer / demodulator 150 which demodulates each subslots in a reverse sense into digital information and stores the digital information . equalizer / demodulator 150 then calculates a reverse metric r 1n , r 1n - 1 , r 1n - 2 . . . r 11 for subslots n , n - 1 , n - 2 , . . . 1 respectively , and stores the reverse metrics . equalizer / demodulator 150 then computes n + 1 slot metrics from the subslot metrics as follows : ## equ1 ## the first slot metric , m 0 pertains to all subslots demodulated in a forward sense . the second , m 1 pertains to all but the last slot demodulated in a forward sense with the last subslot being demodulated in a reverse sense . this pattern continues until the last slot metric m n pertains to all subslots being demodulated in a reverse sense . a best slot metric indicating the largest snr determines the sense of the demodulated digital information for each subslot . this information is sent from equalizer / demodulator 150 to slot construction means 170 to determine the correct sense of demodulation and arrangement of the subslots . for example , if m 3 is the best metric ( here a smallest value since the metric is the inverse of the snr ), equalizer / demodulator 150 would select the forward sense digital information for subslots 1 , 2 , 3 , . . . n - 3 , and reverse sense digital information for subslots n - 2 , n - 1 and n . the digital information for subslots n - 2 , n - 1 and n is passed to , and rearranged into the proper order by slot construction unit 170 . this digital information is then passed to an output device capable of utilizing the digital information . an advantage of the present invention over conventional single sided decoding is that it can isolate a subslot with a poor snr and can demodulate the samples up to this subslot from both directions , without significant loss of data . a second advantage of this method is that it mitigates the effect of non - minimum phase in a multipath channel . this condition simply means that a reflected path is stronger than the direct path . by decoding in the reverse direction the reflected path appears as the direct path and results in a minimum phase condition which is the desired situation for decoding . it may be noted that the present invention may also be employed with any other tdma system that have similar slot / frame structure to that described above . however , the present invention , by being more robust and fade resistant , does not require a great degree a complex channel impulse response estimation and tracking algorithm to be used in conjunction with the equalizer , and for this reason is of particular significance to realization of a low complexity mobile radio equalizer for the u . s . digital cellular systems . the decoding scheme is also not restricted to equalizers and π / 4 - shifted - dqpsk modulation but may be employed with other decoders such as sequential trellis decoders described in &# 34 ; sequential coding algorithms : a survey and cost analysis &# 34 ; by john b . anderson and seshadri mohan ; and mlse type decoders ( d &# 39 ; avella id .). it is also a variation of this invention to demodulate the entire slot by subslots and omit the intermediate halfslot division . while several presently preferred embodiments of the invention have been described in detail herein , many modifications and variations will now become apparent to those skilled in the art . it is , therefore , to be understood that the appended claims are intended to cover all such modifications and variations as fall within the true spirit of the invention .