text: fig3 illustrates a functional block diagram of a segmented sequence detector and identifier that compensates for frequency offsets . input signal 50 is received by segmented correlator / fht 52 . segmented correlator / fht 52 segments the collection of k input samples from input signal 50 into l segments . each of the l segments are individually used as inputs to a correlator / fht combination to detect and identify one of m possible expected sequences ( m = 0 to m - 1 ). as a result , segmented correlator / fht 52 produces l sets of m outputs . each set of m outputs correspond to a separate correlator / fht pair within segmented correlator / fht 52 . each output in the set of m outputs is associated with a particular expected sequence and indicates how well the segment of input samples being examined by the particular correlator / fht pair correspond to a particular expected sequence . fig4 illustrates a functional block diagram of correlator / fht segment 54 of segmented correlator / fht 52 . in this example , segmented correlator / fht 52 comprises 16 ( l = 16 ) of the segments illustrated in fig3 . fig5 illustrates the relationship between the l segments composing segmented correlator / fht 52 . each of the l segments receives samples of the input signal , where k is the number of chip periods or samples composing the sequence . as new samples are shifted into the first segment , the oldest samples are shifted out of the first segment and into the second segment . similarly , each of the remaining segments receives inputs from the prior segment and shifts out its oldest sample to the next segment . the detection and identification process begins after an initial set of k samples of the input signal has been received ( i . e ., each segment has an initial set of samples ). returning to fig4 , shift register 60 receives the initial or ( 256 ) samples of the received sequence , where l is the number of segments composing the correlator / fht segment and where k is the number of chips periods or samples composing the sequence received by a base station from a mobile station . ( in this example , k = 4096 .) other values of l may be used where larger values of l improve performance in a fast fading environment at the expense of increased hardware and / or processing . the received sequence in shift register 60 is deinterleaved and provided to correlators 62 , 64 through 66 . the deinterleaving is used to reverse any interleaving that was performed when the sequence was produced by the mobile station . the deinterleaving may be skipped if the transmitted sequence was produced without interleaving . it should be noted that only three correlators are shown , but in this embodiment 16 correlators of length 16 are used . sixteen correlators are used in this example because it is assumed that the signature sequence contains s = 16 symbols . generally , the number of correlators should match the number of symbols ( s ) in the sequence to be identified , and the correlators should have a length of where c is the number of chip periods per symbol period in the signature sequence . in this example , c = 256 . returning to the 16 symbol example , the first period chip value of each 16 chip long repeating period 70 is provided to correlator 62 ; the second chip period value of each 16 chip long repeating period 70 is provided to correlator 64 ; and in a similar fashion the remaining correlators are populated with input values until correlator 66 receives the last chip value of each 16 chip long repeating period 70 . the coefficients or representative symbols provided to correlators 62 , 64 and 66 are a ( 16 ) chip value sequence that is expected when taking into account the chip period by chip period multiplication between the interleaved sequence and the base station associated binary sequence . each correlator output indicates how well the chip values provided to the correlator correspond to the sequence of chip period values that are expected for a + 1 or − 1 symbol . the symbol correlation outputs of correlators 62 , 64 , and 66 are provided to 16 × 16 ( s × m ) fht 72 , where s is the number of symbols in a signature sequence and m is the number of different signature sequences that may be received . based on the outputs from the correlators , fht 72 provides an output value on each of its 16 ( m ) signal identity outputs indicating how well the signal represented by the symbol correlation inputs from the correlators correspond to each of 16 ( m ) possible signature sequences . for example , output 74 indicates how well the sequence in register 60 corresponds to a first signature sequence ( m = 0 ). similarly , output 76 indicates how well the sequence in register 60 corresponds to a second signature sequence ( m = 1 ). finally , output 78 indicates how well the sequence in register 60 corresponds to a sixteenth signature sequence ( m = m - 1 ). it should be noted that if m possible signature sequences are to be identified , an m output fht should be used . additionally , it is desirable for the number of symbols s to equal m . the input signal is shifted through segments 54 via input shift registers 60 and examined to attempt detection / identification of the known or expected sequence until a search window of n input signal sample periods has been examined . this is accomplished by examining the initial k samples of the input signal and then examining each of the following n - 1 new sets of k samples . a new set of k samples is produced each time shift registers 60 shift in a new input signal sample and shift out the oldest sample . a detected / identified sequence &# 39 ; s position in the search window is determined by the number of shifts made by shift registers 60 when a sequence is detected . the outputs from segmented correlator / fht 52 are provided to multiplier sets 90 , 92 and 94 . each set of multipliers receives a complete set of the outputs from segmented correlator / fht 52 . each set of multipliers is used to compensate for a different frequency offset affecting the input signal . the frequency offset is examined in terms of frequency bins . the frequency resolution or difference between the bins is frequency f δ which may , for example , be a value such as 200 hz . the number of bins used to compensate for the frequency offset is equal to b + 1 where , for example , b may equal a number such as 4 . each set of multipliers is associated with a different frequency bin or offset frequency and multiplies the signals received from segmented correlator / fht 52 with a sinusoid represented by e − j2πbf δ λt s where b × f δ defines the offset frequency , where b =− b / 2 , − b / 2 + 1 , . . . b / 2 and where t s the sampling period of the fht output signal . with c = 256 , t s corresponds to the symbol period of the signal , or a 256 chip period . for example , multipliers 96 , 98 and 100 of multiplier set 90 will have a frequency offset correction factor of − b / 2 × f δ . it should be noted that multiplier set 96 receives l groups of m inputs , that is , m outputs from each of the l segments within segmented correlator / fht 52 . each of the m outputs from each of the l segments is multiplied by a sinusoid that has a frequency that is indexed by the index value λ where the value of λ is based on the segment from which the outputs originate . it should be noted that multiplier 96 simply multiplies by the value 1 since λ = 0 for segment 0 . segment 1 ( λ = 1 ) is multiplied by the sinusoid that has its frequency indexed by the value 1 . similarly , segment l - 1 where λ = l - 1 is multiplied by a sinusoid whose frequency is indexed by the value l - 1 . this results in the separate segments produced by segmented correlator / fht 52 being multiplied by a different multiple of the frequency offset where (− b / 2 × f δ ) is the frequency offset or frequency bin associated with multiplier set 90 . this multiplication compensates for a frequency offset in the input signal equal to (− b / 2 × f δ ). since the frequency offset in the input signal is not known , multiplier sets 92 through 94 are each used to compensate for a different frequency offset in the input signal . for example , multiplier set 90 compensates for a frequency offset of − b / 2f δ , multiplier set 92 compensates for a frequency offset of (− b / 2 + 1 ) f δ , and multiplier set 94 compensates for a frequency offset of b / 2f δ . this results in the outputs of segmented correlator / fht 52 receiving different frequency offset compensation for each of the multiplier sets . the multiplier set associated with the frequency offset closest to the actual frequency offset in the input signal will produce an output having larger magnitudes . the outputs of each multiplier set 90 , 92 through 94 are provided to accumulators 110 . each of the accumulators receives l sets of m inputs from the multipliers . the accumulators perform the accumulation of l values for each of the m inputs . for example , for m = 0 , a sum of the l different m = 0 values received from the multipliers is formed and stored . this type of summation and accumulation is carried out for each set of l values for m = 0 to m = m - 1 . this is illustrated by accumulation positions 112 thorough 114 , where l values of m = 0 are accumulated in position 112 and where l values of m = m - 1 are accumulated in position 114 . fig6 illustrates the accumulation process carried out by accumulator 110 . outputs λ = 0 , λ = 1 and λ = l - 1 , are received from segmented correlator / fht 52 . the outputs of segmented correlator / fht 52 are multiplied by multipliers 96 , 98 and 100 and then passed to accumulator 110 . accumulator 110 forms a separate accumulation for each of the m inputs received from the multipliers . for example , output m = 0 for each of the segments λ = 0 to λ = l - 1 is summed by summer 120 and stored in accumulation 122 . similarly , output m = 1 for each of the segments λ = 0 to λ = l - 1 is summed by summer 124 and stored in accumulation 126 . this process continues for each of the m inputs where m = 0 to m - 1 so that output m = m - 1 for each of the segments λ = 0 to λ = l - 1 is summed by summer 128 and stored in accumulation 130 . after accumulations have been created for each of the m inputs , a new sample of the input signals is obtained by shifting a new input sample signal into segmented correlator / fht 52 . this results in a one input signal sample period shift in the n sample period wide search window . as a result of the new input signal sample set , new outputs are produced by multipliers 86 through 100 . these new outputs are also accumulated by accumulator 110 . once again , l values of each of the m inputs are accumulated in separate sums . in this case , since the search window has been shifted by one sample period , the separate accumulations are stored in accumulations 132 , 134 and 136 for accumulations associated with inputs m = 0 , m = 1 , m = m - 1 , respectively . it should be noted that for each potion in the search window ( n = 0 to n - 1 ), a separate accumulation is provided for each set of m inputs received by accumulator 110 from the multipliers . energy calculators 140 determine an energy content associated with each of the accumulations received from accumulators 110 . as a result , each of energy calculators 140 perform m × n energy calculations . the energy calculations are executed by taking either the absolute value or the square of the absolute value of each accumulation received from accumulator 110 . each energy calculation is stored so that it may be identified with a particular expected sequence m and a particular position n in the search window . the output of energy calculation 140 is provided to threshold units 150 . each of threshold unit 150 compare each energy calculation stored in energy calculator 140 with a predetermined threshold . fig7 illustrates threshold values for different probabilities of false alarms . the energy calculations that exceed the threshold are passed from threshold unit 150 to maximum detector 160 . maximum detector 160 selects the largest threshold crossing energy calculation provided by threshold units 150 . the largest threshold crossing energy calculation is used to identify and detect the sequence represented by the input signals and to establish the frequency offset associated with the input signal . the expected sequence contained in the input signal is identified by the value of m that is associated with the output selected by maximum detector 160 . the time delay associated with the input signal is determined by the value of n or the position in the search window associated with the output selected by maximum detector 160 . additionally , the frequency offset associated with the input signal is identified by the frequency bin ( b × f δ ) associated with the set of multipliers that were used to produce the output selected by maximum detector 160 . it should be noted that it is also possible to select the maximum output from energy calculations 140 and then compare that maximum output to the threshold . the maximum output that exceeds the threshold identifies and detects the sequence represented by the input signal , and determines the frequency offset associated with the input signal . s ( k )= a c p ( k ) c ( k ) v ( k ) , k = 0 , 1 , . . . , 4095 ( eq . 1 ) where a c is the chip amplitude at the transmitter , p ( k ) is the scrambling code , c ( k ) is the signature sequence , where h ( k ) is the channel gain and z ( k )= z_i ( k )+ j z_q ( k ) is complex white gaussian noise with variance σ 2 . at the receiver , the following hypothesis testing is carried out for every time delay h 1 : r ( k ) = s ( k ) h ( k ) + z ( k ). ( eq . 3 ) n c : coherent integration length in number of chips n seg : number of segments for noncoherent combining n div : number of diversity antennas i : number of frequency offset candidates q : threshold for detection p fa : false alarm probability for hypothesis h 0 , the decision statistic formed by energy computation ( or , squared l 2 norm ) for each frequency bin i has chi - squared distribution with n = 2 n seg n div degrees of freedom . the underlying noise variance after coherent accumulation is σ 2 n c / 2 . the cumulative distribution function ( cdf ) of the decision statistic for each frequency bin for hypothesis h 0 is given by f y ( y  ⁢ h 0 ) = 1 - ⅇ - y / ( σ 2 ⁢ n c ) ⁢ ∑ k = 0 n / 2 - 1 ⁢ ⁢ 1 k ! ⁢ ( y σ 2 ⁢ n c ) h . ( eq . ⁢ 4 ) the threshold for detection for i frequency bins is computed from the relation p fa = pr ⁡ [ y o & gt ; q ⁢ ⁢ or ⁢ ⁢ y 1 & gt ; q ⁢ ⁢ or ⁢ ⁢ … ⁢ ⁢ or ⁢ ⁢ y i - 1 & gt ; q ] = 1 - pr ⁡ [ y o ≤ q ⁢ ⁢ and ⁢ ⁢ y 1 ≤ q ⁢ ⁢ and ⁢ ⁢ … ⁢ ⁢ and ⁢ ⁢ y i - 1 ≤ q ] = 1 - ∐ i - 1 i = 0 ⁢ ⁢ f y i ⁡ ( q ) = 1 - f y i ⁡ ( q ) . ( eq . ⁢ 5 ) using the relation ( eq . 4 ) and ( eq . 5 ), we can find the threshold by a recursive search . for a desired value of p fa , we do a sequential search of threshold value q in steps of δq . the following pseudo - code summarizes the recursion . q = 0 ; f y ( q )= 0 ; δq = desired resolution for threshold search ; do while { (( 1 − p fa ) 1 / i & gt ; f y ( q )) q := q + δq ; update f y ( q ); fig7 illustrates the difference in threshold values for various detection algorithms for umts access preamble detection . the threshold is compared for three detection algorithms , i . e ., fully - coherent detection , 4 segment noncoherent detection , and the detection algorithm with frequency offset compensation . squared l 2 norm is used as the decision statistic . we assume that n div = 2 . the signals from two antennas are noncoherently combined . for fully - coherent detection , n seg = 1 , n c = 4096 and for 4 segment noncoherent detection , n seg = 4 , n c = 1024 . for coherent detection with frequency offset compensation , we have n seg = 1 , n c = 4096 and i = 5 . the noise is normalized to σ 2 = 1 .