Patent Application: US-82415207-A

Abstract:
a method is presented for determining an actual pulse position in a signal . this signal comprises a plurality of successive frames , wherein each frame has length l and contains one pulse with width w , a number of discrete possible pulse positions being considered within in each frame which is at least l / w . the method comprises the steps of a ) sampling the signal at a sampling rate below l / w with a varying sampling phase such that the whole frame length l is covered , b ) obtaining a set of samples with at least one at each of the possible pulse positions , c ) correlating this set of samples with a set of one or more predetermined values and d ) determining the actual pulse position from said correlation . the method provides a low - complex signal acquisition solution in a receiver and is particularly useful for low - complexity and low - power ir - uwb transceivers .

Description:
the present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims . the drawings described are only schematic and are non - limiting . in the drawings , the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes . the dimensions and the relative dimensions do not necessarily correspond to actual reductions to practice of the invention . furthermore , the terms first , second , third and the like in the description and in the claims , are used for distinguishing between similar elements and not necessarily for describing a sequential or chronological order . the terms are interchangeable under appropriate circumstances and the embodiments of the invention can operate in other sequences than described or illustrated herein . moreover , the terms top , bottom , over , under and the like in the description and the claims are used for descriptive purposes and not necessarily for describing relative positions . the terms so used are interchangeable under appropriate circumstances and the embodiments of the invention described herein can operate in other orientations than described or illustrated herein . the term “ comprising ”, used in the claims , should not be interpreted as being restricted to the means listed thereafter ; it does not exclude other elements or steps . it needs to be interpreted as specifying the presence of the stated features , integers , steps or components as referred to , but does not preclude the presence or addition of one or more other features , integers , steps or components , or groups thereof . thus , the scope of the expression “ a device comprising means a and b ” should not be limited to devices consisting only of components a and b . the present invention relates to a method for performing signal acquisition and a device for carrying out this acquisition algorithm . the signal acquisition method is in particular interesting for communication systems requiring low power consumption . a preferred embodiment of the invention uses an impulse - based ultra - wideband system ( ir - uwb ), and this preferred embodiment is described herein . in particular , an uwb system is used comprising an uwb transmitter and receiver system . the transmitter is demonstrated in j . ryckaert et al ., “ carrier - based uwb impulse radio : simplicity , flexibility and pulser implementation in 180 nm cmos ”, icu , zurich , switzerland , september 2005 , which is hereby incorporated by reference in its entirety . the measurements indicate that the pulser consumes only 2 mw burst power for a pulse repetition rate of 40 mhz . low - power receivers are more complex to design , but an analog - based solution is also more effective for low - power applications , implementing the matched filtering in analog domain and taking samples only at the pulse repetition rate [ 1 ]. such solutions have recently been implemented at low power , j . ryckaert et al ., “ a 16 ma uwb 3 - to - 5 ghz 20 mpulses / s quadrature analog correlation receiver in 0 . 18 μm cmos ”, isscc , san francisco , calif ., usa , february 2006 , which is hereby incorporated by reference in its entirety . fig1 describes an analog receiver , wherein the different elements are being clocked by a timing circuit ( 12 ). it considers carrier - based uwb , and works in i / q baseband after quadrature down - conversion ( 11 ). this limits the ( analog ) baseband processing to a bandwidth of 500 mhz , where the matched filtering operation takes place with a locally generated template . this architecture can work with both coherent bpsk and non - coherent ppm modulations , depending on the digital processing implemented afterwards . practically , this system assumes analog pre - processing of the incoming signal , providing matched filtering of the pulses via template i / q ( 11 ) and integrators of fig1 . this pre - processing and sampling of the signal takes place once per frame ( a frame being the duration inverse of the average pulse repetition frequency ), according to the timing circuit ( 12 ). this timing is set thanks to the flexible delay line . two samples per frame are taken for ppm , as two positions have to be considered . the signal acquisition block performing the signal acquisition algorithm described herein will be part of the digital receiver baseband block ( 13 ). in particular , the signal acquisition block provides two operating modes : 1 . synchronization modules responsible for time - domain - based code / timing acquisition and 2 . end of preamble detection module . the first module determines at which place ( s ) of the frames the pulses appear ( low - level pulse synchronization ) and which pulses are put together to form one bit or symbol ( spreading code phase synchronization ). the acquisition module searches simultaneous for pulse position and code phase . in order to describe the acquisition process , the overall air interface that is considered to transmit a data burst ( 21 ) is depicted in fig2 . a burst comprises a preamble ( 22 ) and a payload ( 23 ). one bit ( 24 ) is spread over n c chips . n c denotes the number of pulses that are required for one bit of information . each of them is transmitted as a pulse ( 25 ), and each pulse occurs somewhere within a frame ( 26 ) ( one per pulse ), the frame being the time unit matching the pulse repetition rate . for the design described herein , each frame ( 26 ) nominally lasts 25 ns ( 40 - mhz pulse repetition rate ), and contains one triangular pulse of 500 - mhz bandwidth , detected by a matched rectangular pulse . note that the algorithms of the present invention may also be used in other receiver designs . the spreading code is defined by a sequence { c j , 1 ≦ j ≦ n c }. depending on the modulation choice , we have two possible system descriptions , ( 1 ) for bpsk and ( 2 ) for ppm ( pulse position modulation ): x ⁡ ( t ) = ∑ k = - ∞ + ∞ ⁢ b ⌊ k / n c ⌋ ⁢ c ( k ⁢ ⁢ mod ⁢ ⁢ n c ) ⁢ p ⁡ ( t - k ⁢ ⁢ t p ) ( 1 ) x ⁡ ( t ) = ∑ k = - ∞ + ∞ ⁢ p ⁡ ( t - k ⁢ ⁢ t p - 1 - b ⌊ k / n c ⌋ ⁢ c ( k ⁢ ⁢ mod ⁢ ⁢ n c ) 2 ⁢ t ppm ) ( 2 ) where └ x ┘ denotes the integer part , k mod n the remainder of k modulo n , and p ( t ) is the basic pulse . in our system p ( t ) relies on carrier - based uwb ; all the synchronization and demodulation operations take place after down - conversion of p ( t ) in i and q baseband components . the acquisition has to determine at which place ( s ) of the frames ( 26 ) these pulses ( 25 ) appear ( low - level pulse synchronization ), which pulses are put together to form one bit ( 24 ) or symbol ( spreading code phase synchronization ), and where the data payload ( 23 ) effectively starts . the start of data payload is detected thanks to an end - of - preamble ( eop ) sequence , while the previous steps are based on repeated preamble symbols . two acquisition strategies are possible : either searching first for the pulse position in frames and afterwards for the spreading code phase at the selected position , or doing both simultaneously . in an acquisition method described herein , pulse and code phase synchronization are performed simultaneously . a comparison of both techniques is reproduced in the appendix below . the receiver searches for pulses by sampling the received signal with a clock whose phase can be varied in a number of delay steps covering the whole frame duration . fig3 illustrates the searching steps of the synchronization algorithm , scanning n samples at each possible position in the frame . where n equals n c × n b and wherein n c denotes the number of pulses that are required for one bit of information . n b is used in order to accumulate several bits of information before taking the decision over one position , which is needed given that the synchronization operation has more importance in case of failure than receiving one simple bit of data . this algorithm is exemplified in fig3 , where a first position is at t 0 ( 31 ), a second at t 0 + nt frame + t step ( 32 ), a third at t 0 + 2nt frame + 2t step ( 33 ) and a fourth at t 0 + 3nt frame + 3t step ( 34 ), covering the whole frame . for each position , all the possible phases of the spreading code are tested , using a pipelined implementation of the spreading code correlator . when the detected signal energy exceeds a threshold , a new scanning pass tests once again each possible position to make sure that the selected position has the highest energy . for a single - tap receiver as considered here , this translates into maximal effective signal - to - noise ratio . for each position , the code despreading takes place by coherent combination of the incoming pulses . for bpsk , both i and q inputs are separately despread in two parallel correlators . as the carrier phase is still missing to coherently recombine them , the maximum - energy position is then detected by computing the corresponding energy from i and q despread values . the phase of the selected maximum is used afterwards as carrier phase estimate for i / q recombination of data bits . when ppm is used , the energy at both possible positions is first computed within each frame . afterwards , the result difference between energy at position one and position two is computed . this difference is used as binary soft information for the despreading operation . for both modulations , in order to increase the signal - to - noise ratio in the acquisition process , the number of bits accumulated for one trial or n b symbols are averaged before taking the decision . in order to find the position of pulses within the frames , a discrete set of positions or delays is considered , with enough accuracy to make sure that the maximum energy point of received pulses is found while limiting the search duration to the necessary number of positions . in this respect , a delay step of 1 ns is a reasonable trade - off , as shown by fig4 . it leads to an error of maximum 0 . 5 ns from the peak , translating into a loss of 0 . 5 db ( correlation 0 . 89 ). a step of 2 or 3 ns would lose 2 or 5 db , respectively . for a 40 - mhz clock , using 1 - ns steps means that 25 pulse positions are checked . before searching for the signal , the threshold - based acquisition scheme computes the required threshold distinguishing signal from noise . the noise power is first estimated by averaging its energy over several samples , and the threshold is relatively defined with respect to it . in order to describe it , the relevant parameters are defined in table 1 . they also include preamble definition parameters , related to the number of symbols to consider for each acquisition search . the receiver gets signal samples from i and q branches , and in case of ppm also from both positions . without loss of generality , it can be assumed that the signal is aligned with the i direction , and consider the following inputs : the noise is assumed to be normalized to a unit variance in each branch , and accordingly the signal as the specified pulse signal - to - noise ratio snr = s i 2 . for ppm , two extra samples containing only noise are received at the other position . coherent accumulation of n c received samples by despreading leads to variables d i and d q , respectively . for bpsk , when the phase φ is known — 0 in equations ( 3 ) and ( 4 )— the coherent recombination of i / q as well as spreading code leads to the following decision variable : d bpsk = d i cos φ + d q sin φ = n c s i + n d , ( 5 ) where the signal part has an amplitude n c √{ square root over ( snr )} and the noise n d on the decision has a standard deviation √{ square root over ( n c )} after accumulation of n c independent samples as n i in the direction corresponding to φ . normalizing by √{ square root over ( n c )}, this leads to the bit signal - to - noise ratio , as snr b is defined as n c snr . during the acquisition phase , the spreading code is coherently recombined , but the i / q combination takes place by energy detection . this leads to a decision variable which is d i 2 + d q 2 . using the normalization by n c ( not its square root here as we work with signal energies ), it has an expected value snr b + 2 considering both i and q noise , and a variance which is 2 ( snr b + 1 ), for the non - central chi - squared distribution variance . in the case of ppm , the energy combination occurs first from i and q , followed by the difference between energy at both positions . this leads to a decision variable of average snr ( note that it is the pulse snr and not the bit snr in this case ), and variance 2 ( snr + 2 ). the required number of symbols is determined that should be used for each acquisition trial , in order to make sure the acquisition error ( false alarm or missed detection ) is small enough compared to the ber in data detection mode . as this approach assumes the noise level in the system is perfectly known , the effect of noise level estimation can be added and the corresponding required accuracy can be computed . first consider bpsk , with code despreading according to ( 5 ) and further scaling by a factor √{ square root over ( n c )} k . phase knowledge is assumed for coherent detection , unlike the analysis done above based on non - central chi - squared variables , and included later on the non - coherence penalty . the expected detected value is 0 for noise only , √{ square root over ( snr b )} for the expected signal with the right code phase , and −√{ square root over ( snr b )}/ n c for misaligned spreading code phases assuming a pn m - sequence . the standard deviation of the noise around these averages is 1 . this also leads to the threshold on signal acquisition , as middle point between signal value √{ square root over ( snr b )} and closest false alarm which is 0 in the noise - only case . hence , the threshold is computed as √{ square root over ( snr b )}/ 2 , provided the noise and signal power are known . this means that compared to bit detection , the acquisition process starts with a 6 - db loss as the separation between signal and noise is reduced by a factor 2 compared to the separation between positive and negative bits . moreover , as the carrier phase is not known yet , i and q are non - coherently recombined towards the maximum amplitude . for orthogonal detection , such as this distinction between signal presence and noise only , the loss is close to 1 db compared to coherent orthogonal detection . considering this loss on top of the 6 db mentioned above , using a reasonable n b = 10 bits per decision is proposed in the acquisition process , gaining 10 db as they are coherently recombined , which leads to a final gain of 3 db in signal - to - noise after subtracting the 7 - db loss . this is enough for making sure that the risk of error during synchronization is negligible compared to the system ber . reducing the margin to 1 . 5 db , we could use n b = 7 only . for ppm , the situation is actually slightly better . as soon as demodulation is started , a binary decision variable is created as the difference between energy at both positions without need for phase information hence acquisition can be completely coherent . hence , there is no 1 - db non - coherent recombination loss . based on this study , the overall preamble is rather small : considering n b = 10 in the search phase , this limits it to 500 bits ( 2 times 25 positions times 10 bit per position ). a design with less margin ( n b = 7 ) would limit it to 350 bits . these sizes do not include the part related to end - of - preamble detection . the thresholds previously defined were considering a perfect knowledge of signal and noise amplitude at the receiver . as a matter of fact , the signal - to - noise ratio can be considered known in the worst case : the minimal signal - to - noise ratio at which the system is considered working can be used as spec , and any higher value will improve the performance . however , the average noise level in the system still needs to be estimated , in order to define the detection threshold with respect to it . with perfect noise estimation and normalization to 1 , when the decision takes place with a design snr b = n c snr , the noise - related variance around it is 1 . on the other hand , with n n samples for noise estimation we have a noise estimator of standard deviation 1 /√{ square root over ( n n )} around its expected value 1 . as this noise estimation amplitude is used to derive the detection threshold by multiplication , this translates in an uncertainty on the threshold equal to a standard deviation of ½ √{ square root over ( snr b / n n )} on that value . from the previous subsection , the standard deviation due to gaussian noise and assuming a perfect threshold definition is equal to 1 . therefore it should be certain that the noise estimation error does not increase the total variance on the decisions by more than a factor 1 . 25 , which is less than 1 db loss , in order to keep satisfactory performance . this translates to the following requirement : ( 1 2 ⁢ snr n n ) 2 ≤ . 25 ( 6 ) with the squaring to move from standard deviation to variance . this easily leads to a constraint on the minimal number of samples to average in order to estimate the noise : hence , if the number of noise averaging samples is counted in bits , i . e ., sets of n c samples , a required number is found equal to the pulse - level signal - to - noise ratio , which is very small ( possibly less than one ), or stated in pulses , we find a number equal to the working snr b value . after acquisition , the receiver demodulates the remaining symbols of the preamble ( typically all ones ), up to the end of it where it reaches an eop marker . the eop marker is a special sequence with good autocorrelation properties as well as low cross - correlation with the previous part of the preamble in order to avoid false detections . a special threshold tells whether the eop is detected or not . by the time of eop detection , the system is fully synchronized and working in detection mode . hence , + 1 or − 1 bits are received with gaussian noise at a signal - to - noise ratio snr b on top of them . for eop detection , it is assumed that soft information is kept for these bits . when the eop pn sequence of length l , is correlated with the incoming bits , at the position of alignment there is an expected value of + l , and a noise increased by √{ square root over ( l )} compared to a single sample . at other positions , the expected values depend on the eop code and the previous part of the preamble that will correlate with it . considering that the preamble before the pn sequence is made of identical bits , either all ones or all zeros , table 2 summarizes the eop detection . the table shows , depending on the order of the pn sequence ( order n means 2 n − 1 elements ), the maximal correlation obtained just before the eop sequence with all + 1 or all − 1 preceding the sequence , in the second or third column , respectively . based on the worst case of these two , the eop aligned correlation ( 4th column ), and the noise expansion ( square root of the code length ), the gain is detected in eop detection snr compared to bit detection . this shows that a sequence of length 31 ( order 5 ) should be used to have enough gain for the eop detection ( 7 . 4 db in this case ). a second value of gain is proposed , assuming that the polarity of the preamble bits can be selected before eop sequence to + 1 , leading to the best separation . in that case , a shorter sequence ( length 15 ) is enough . this case is kept as the most realistic situation : the eop sequence can be designed knowing what is present before in the preamble . before looking for the eop sequence , the system estimates the signal power as reference , in order to derive the corresponding threshold and predict the eop correlator output when the signal is aligned or not . this is done because the actual signal level could be different from the design snr b . this is achieved using the same number of bits as the eop sequence . as both effects are additive on the final estimator , there remains in the end a 4 - db immunity out of the 7 db of the code , comparable to the immunity selected when recovering spreading code phase . in order to validate the acquisition approach , an analytical approach of previous sections is illustrated based on simulations . fig5 and 6 present the corresponding system performance for bpsk and ppm , respectively . fig5 shows the ber versus e b / n 0 with 7 ( 41 ) and 31 ( 42 ) pulses per bit and 2 ( 43 ), 6 ( 44 ) or 20 ( 45 ) bits per position for the searching step ( n b parameter ). for bpsk , using 6 or 20 bits per search gives a performance within 1 . 5 db of the theoretical curve ( 46 ) ( ideal synchronization ), in the zone of interest ( ber 10 − 3 to 10 − 5 ). the 20 - bit synchronization only has an advantage at lower values of e b / n 0 , but that zone is of limited practical use . this matches the recommendations of the theoretical study , recommending n b = 7 to 10 . 2 - bit synchronization yields an additional 5 - db loss , which is not acceptable . for ppm , the imperfect non - coherent recombination of multiple - pulse - per - bit systems needs to be considered . therefore , different theoretical curves are shown as function of n c in fig6 . fig6 shows the ber versus e b / n 0 with 7 ( 41 ) and 31 ( 42 ) pulses per bit and 2 ( 43 ), 6 ( 44 ) or 20 ( 45 ) bits per position for the searching step ( n b parameter ). the continuous theoretical curve ( 47 ) assumes a single - pulse - per - bit mode , the other curves also integrate the non - coherent recombination loss of ppm . the dashed theoretical curve ( 48 ) assumes a 7 pulse per bit mode and the dotted theoretical curve ( 49 ) assumes a 31 pulse per bit mode . however , similar conclusions hold , except that the various trends are a bit less pronounced . this confirms that single - step synchronization is an efficient proposal for low - power systems , especially in order to limit the transmitter power consumption via a short preamble length . these two figures only consider awgn channels , while non line - of - sight uwb scenarios show strong fading and multipath effects . with this respect , it should be noted that this does not impact the fundamental behavior of our algorithm . with a low - complexity one - tap analogue receiver , the best option is to find the maximal - energy position in the channel response , by exhaustive search . in this case the pulse snr is based on the energy received around the position of the largest channel tap . the energy spread elsewhere cannot be recovered without rake type of recombination . in order to evaluate the effect of multipath channels on the algorithm , a channel model matching a target scenario ( namely ultra - low - power body area networks [ 4 ]) of this study has to be considered . it contains both multipath effects and lognormal fading , but the channel delay spread is shorter than the pulse frame ( no inter - pulse interference ). fig7 shows that the system performance of the original algorithm ( 58 ) drops and shows an error floor around 10 − 2 ber due to fading effects . basically , as soon as the signal amplitude is reduced by more than a factor 2 due to fading , it falls below the detection threshold , whatever the signal - to - noise ratio . a solution is to compute the threshold based on a value of the e b / n 0 which is not the one actually occurring on the channel , but an optimized so - called “ design signal - to - noise ” parameter . as can be seen on fig7 , we can completely remove the error floor by taking a value from 6 ( 52 ) to 8 db ( 53 ) for this parameter . this means that whatever the actual value of e b / n 0 , the detection threshold is computed as if e b / n 0 was only 6 or 8 db , leaving more margin for fading . although this technique enables the removal of the error floor phenomenon , it cannot avoid a significant loss with respect to the ideal awgn curve ( 10 db at 10 − 4 to 10 − 5 ), a behavior typical for fading channels . other curves are plotted for 9 db ( 54 ), 10 db ( 55 ), 12 db ( 56 ) and 14 db ( 57 ). the adaptive curve ( 58 ) considers the expected actual signal - to - noise - ratio in the threshold computation . in order to support the synchronization solution described herein , the proposed digital baseband architecture is illustrated by fig8 . the incoming signal is being pre - processed ( 60 ) as mentioned before . the pre - processing block ( 60 ) adapts the incoming data in function of the modulation ( bpsk or ppm ) and the current operation ( synchronization , data detection . . . ), so that the next blocks can run on the correct input . before searching for the signal , the threshold - based acquisition scheme computes the required threshold distinguishing signal from noise . therefore noise is being accumulated by a noise accumulator ( 61 ), which also averages the noise level . from these results , ( 62 ) derives the acquisition threshold . the sliding correlator ( sc ) ( 63 ) is responsible for testing all the positions and code phases , while the code accumulator ( ca ) ( 64 ) is responsible for averaging n b bits before taking the decision . the module further comprises another sub - module : eop detection ( 66 ). the receiver operation is based on the presence of a fixed synchronization preamble ( 71 ) at the beginning of a burst . fig9 sketches the operating modes of the transmitter . this preamble ( 71 ) comprises a head sequence ( 72 ) and a eop sequence ( 73 ). first , a header made of repeated symbols with all the same sign is transmitted . each symbol s is spread or multiplied by a ternary code , i . e ., having values + 1 , − 1 and 0 for its pulses . after the header , the eop sequence is added , and also based on a ternary code but at symbol level , i . e ., + s , − s and no symbol transmitted . after the preamble ( 71 ), the payload ( 74 ) comprising the data sequence ( 75 ), is sent . before and after the burst , the transmitter remains in standby mode ( 76 ). fig1 represents schematically the operating modes of the uwb receiver . there are two groups of operating modes . the first group ( 701 ) operates after wake - up and during the silent time slots . after wake - up the receiver sets the frequency of the pll . at this stage it is assumed that the transmit and receive clocks are sufficiently equal to each other , such that the phase drift due to the frequency mismatch is small enough to guarantee a reliable correlation energy over the duration of a spreading code sequence . small errors in this frequency setting are corrected after the acquisition phase i . e . the tracking phase of the burst . after the wake - up and during some moments when the channel is silent , the receiver accumulates noise ( operation mode noiacc ( 703 )) and computes the noise threshold based on noise level measurements ( operation mode noithre ( 704 )). this phase is called the noise threshold computation ( 705 ). the threshold is used for pulse - and bit - level synchronization . this silent duration of the channel is typically determined by the mac . the second group of operating modes are executed at each burst ( 702 ). the reception starts by the acquisition mode ( 706 ). in this mode ( operation mode acq 1 ( 707 )) the correlator is utilized in a cyclic fashion to compute the correlations for every possible alignment of the spreading code and scanning successive delay positions . each correlation result from this computation is compared to the computed threshold in order to declare it as potential signal found . after this first alarm , the receiver searches for the maximum of the cyclic correlations for each possible delay offset of the received pulse in the frame ( operation mode acq 2 ( 708 )). if no result above the threshold is found through all cycles , then the system goes back to search for the first alarm . the sequence of the acquisition events is shown in fig1 . shift one position ( 81 ) and check if the signal is above the computed threshold ( 82 ). if this is not the case then start again ( 81 ). if it is above the threshold , loop all n p positions ( 83 ). for this design , n p equals 25 ( 25 ns frame duration divided by 1 ns resolution ). fig3 already illustrated the possible positions . then check if any one of the positions is above the threshold ( 84 ). if this is not the case then start again ( 81 ). otherwise , keep this maximum as the synchronized position ( 85 ) and proceed with the signal estimation and eop detection ( 86 ). since for ppm the correlation is performed on the difference of energies of two different ppm locations , only one correlator is needed . on the other hand , for bpsk , two correlators are needed ( one for the i - branch and the other for the q - branch ) since the carrier phase φ of the received bpsk pulse with respect to the i branch is unknown . for bpsk this requires an additional step ( 65 ), the estimation of the carrier rotation phase φ . the rotation phase is estimated by using the correlation results of the i and q branches ( 67 ). this is done by a coordination - rotation - digital - computer ( cordic ) ( 68 ) ( e . g . by computing first the φ = a tan ( q / i ) value and then the phasors cos ( φ ) and sin ( φ )). an iterative cordic that operates at the pulse repetition rate is used in order to reduce the hardware complexity in terms of number of gates [ 2 ]. afterwards , the i and q branches are combined at the input in order to form the decision variable . after this , q - path correlator is disabled . following the acquisition mode , the eop - threshold computation starts ( 709 ) and the carrier phase offset is compensated ( 710 ). in this mode the eop threshold is computed considering the average correlation energy , the length of eop sequence , and the snr of the channel . the final step is the detection of the eop sequence , marking the end of the header and enabling the system to go to the data detection state ( 712 ), which informs the start of the incoming data in the burst . the eop detection ( 711 ) is done on the following steps : ( 1 ) correlate the decision variable with the codeword , ( 2 ) correlate the correlation results of the first step to the eop sequence , ( 3 ) compare the correlation results of the second step to the eop threshold computed earlier . the reception ends when the number of received bits becomes the predefined burst length . synchronization module in the receiver consists of two sub - modules : ( 1 ) sliding correlator ( sc ) ( fig1 ) and ( 2 ) code accumulator ( ca ) ( fig1 ). the incoming 5 - bit decision variable ( 91 ) is serially shifted through the serial - to - parallel converter ( 92 ) until the position defined at the codeword length ( n c , for example 1 - 32 ) ( 93 ) and then loaded in parallel to a correlator buffer ( 94 ) at every n c pulse cycles . during acquisition , each tap of the correlator buffer is multiplied with each chip of the codeword ( 95 ). the results of the multiplication are then summed through a balanced binary adder tree ( 96 ) that has been pipelined for every eight taps . here , we have chosen eight in order to increase the maximum operating frequency while keeping a reasonable overhead in the number of flip - flops . the throughput for the pipelined correlator is one , i . e ., one new correlator value output for each clock cycle and new incoming data decision variable . since the lengths of code rotation / multiplication and shift / load operations scale with the codeword length , the dynamic power consumption of sc linearly scales with the codeword length . once the acquisition is completed , the incoming code is aligned with the codeword . therefore , the correlation is computed at every n c pulse cycles without a need for a cyclic rotation of the codeword . during the acquisition mode , the correlation results from the sliding correlator are accumulated n b times in the correlator accumulators ( 101 ) for each code phase inside the ca module . these results are shifted or cleaned after every n b × n c cycles . this code repetition is used in order to increase the snr of the received signal . at the n b - th accumulation , the results of accumulation are shifted one - by - one to the max detector ( 102 ) to store the code - phase that has the maximum energy ( i p , q p , c p are being stored and also the configuration of the delay line d p and the code phase of the correlator p p ). the max detector is being controlled by a control block ( 103 ), which also controls a delay counter ( 104 ) giving the delay line d e . during this shift , the corresponding tap of accumulator is loaded with the new incoming correlation result . by the above - mentioned word - serial architecture , the synchronization modules operate at the maximum throughput without a need for a local storage . also there is no need to increase the preamble size as the code phase and the timing offset are compensated at 2 × n b × n c pulse cycles per each delay step . here factor 2 comes from two - times scanning the delay - line to avoid false first - alarms described earlier in section a . during acquisition the delay line is configured at coarse steps of 1 ns up to 255 ns . a delay step of 1 ns leads to an error of maximum 0 . 5 ns from the peak correlation , translating into a loss of 0 . 5 db [ 3 ]. this leads to 25 coarse delay steps . for an awgn channel with e b / n o = 10 db , we typically have n b = 6 and n c = 31 in order to have a bit - error - rate ( ber ) of 2 × 10 − 5 . after acquisition , the receiver demodulates the remaining symbols of the preamble ( typically all ones ), up to the end of it where it reaches an eop marker . simulations show that selecting a pn - sequence of length 15 can reduce the risk of missing the eop to a negligible value . for the eop - detection module a correlator is used that has a similar architecture as the sliding correlator , however with a word length of 8 - bit at each tap . before looking for the eop sequence , the system estimates the signal power as reference , in order to derive the corresponding threshold and predict the eop correlator output when the signal is aligned or not . this is achieved using the cordic output that computes the code magnitude that uses the same number of codes as the eop sequence . in this appendix two acquisition algorithms suited to the low - power receiver architecture are compared . both algorithms minimize the preamble length for reduced transmitter power consumption while keeping good acquisition performance : either scanning pulse position and code phase either successively ( two - step ) or simultaneously ( single - step , the solution that is preferred ). the two - step acquisition technique starts by detecting the pulse position in the frame : the receiver searches for pulses by sampling the received signal with a clock whose phase can be varied in a number of delay steps covering the whole frame duration ( fig3 ). when the detected signal energy exceeds a threshold , a new scanning pass tests once again each possible position , to make sure that the final position has the highest energy , which translates into maximal communication distance . when pulses have been localized in the frames , the second step is to split bits from each other , as n c pulses per bit are used with a spreading code . this code phase synchronization is achieved by trying out the n c possible code phases , using a sliding window correlator , accumulating several successive bits to get enough snr . this step is achieved by coherent despreading . for ppm , the result of the differential energy detector over both positions is kept as bipolar soft information to be accumulated over pulses . for bpsk both i and q are coherently combined as the carrier phase is still missing ; after taking the maximum amplitude , the phase of this maximum is used as estimate for i / q recombination of data bits . typically n c = 30 , which is the number of code phases to test . hence , the search space size for the two - step approach is 25 positions for the pulse ( 25 - ns frames with 1 - ns steps ), followed by 30 phases for the code , in total 55 values to compute and compare to synchronization thresholds . however , each of these steps may require many samples to be accumulated . the two - step search has the advantage of a small search space , but its performance suffers from the non - optimality of the non - coherent recombination in step one . an alternative is to combine both steps in order to directly have a coherent code despreading at each position and with each spreading code phase , based on a parallel implementation of the correlation . this is the solution used herein , searching simultaneously for pulse position and spreading code phase . the search space size increases to the product of pulse positions by code length , in our case to 750 ( 30 × 25 ), but the signal - to - noise ratio is higher thanks to coherent recombination , meaning that we can detect the signal from less pulses . it also supports cdma differentiation of users , as codes are used from the beginning . each signal pulse sample comes on top of gaussian noise with signal - to - noise ratio snr on the i / q branch aligned with the signal , most likely to be small as many pulses per bit are required for successful communication . normalizing noise energy to 1 , this leads to an average energy of the signal plus noise equal to ( 1 + snr ), leading to a symmetrical decision threshold ( 1 + snr / 2 ) in order to detect a single pulse . statistics give for each such noise sample a variance 1 , and for signal plus noise a variance ( 1 + 2snr ) [ 9 ]. i and q energies are combined due to the non - coherent character , with in case of signal presence and after division by 2 an average energy ( 1 + snr / 2 ) and variance ( 1 + snr )/ 2 around it , as described before , but without division by 2 ( 4 on the variance ) there . this variance is reduced through averaging in order to enable a reliable decision , by taking n b bits or n = n b n c pulses . the corresponding standard deviations become σ n = 1 /√{ square root over ( n )} for noise only and σ s =√{ square root over (( 1 + snr )/ 2n )} for signal samples , and a gaussian assumption considering the central limit theorem . the risk of missing a burst depends on the ratio of this standard deviation to the decision distance snr / 4 between the signal energy ( 1 + snr / 2 ) and the threshold at ( 1 + snr / 4 ). this ratio is used to compute an equivalent awgn ( e b / n 0 ) and its corresponding ber , making the analogy with a bpsk detection from signals + 1 or − 1 and one - dimensional noise of variance 1 /( 2e b / n 0 ). in our case , the corresponding ( e b / n 0 ) synch is given by ( 8 ). this is obtained from the equivalence , using the one - dimensional noise standard deviation when the signal is normalized to unit energy , and scaled by the squared distance to the threshold which gives ( snr / 4 ) 2 : ( e b n 0 ) synch , bpsk = n · snr 2 16 ⁢ ( 1 + snr ) ( 8 ) for ppm , as two positions are averaged over each frame , the average in the presence of signal is only ( 1 + snr / 4 ), hence the threshold is ( 1 + snr / 8 ). however , the noise standard deviation is reduced by √{ square root over ( 2 )} due to averaging over two samples per frame , leaving finally the following equivalent ( e b / n 0 ) synch : ( e b n 0 ) synch , ppm = n · snr 2 32 ⁢ ( 1 + snr / 2 ) ( 9 ) we can rewrite ( 8 ) and ( 9 ) as function of snr b , which is a known design parameter . for bpsk , we have a linear gain , meaning that snr b = n c snr thanks to coherent combination . for ppm with non - coherent reception , the gain is smaller . it comes from the fact that each noisy pulse is converted into an energy value ( squaring operation ), before taking the difference between both pulse positions and finally accumulating these energy differences . to our knowledge , there is no closed - form expression for the resulting equivalent signal - to - noise . however , the corresponding gain was found to be close to ⅔ of the coherent gain on a log scale ( this is illustrated by theoretical curves of fig6 ), hence we use snr b = n c 2 / 3 snr . we assume that the required snr b varies between 5 and 10 db for bpsk , and between 8 and 13 for ppm to take into account its intrinsic 3 - db loss as orthogonal modulation . this gives the requirements on n , split in code length n c and number of bits n b . for bpsk , the number of bits required increases with the desired snr b as well as the number of pulses per bit ( table 3 ). as the accumulation of n c pulses per bit for detection is less efficient for ppm ( factor ⅔ ), the preamble overhead looks smaller in terms of equivalent bits ( table 4 ), but to be multiplied by the larger number of pulses per bit needed to enable detection . these conclusions are very negative for practical multiple - pulse - per - bit cases , as these numbers still have to be multiplied by the number of positions to be tested , in our case 25 , and again by 2 as 2 search passes are required . for bpsk at 100 ppb , the preamble would last 32 kbit ( 50 × 648 ). for ppm , we would anyhow need too many pulses per bit to achieve efficient communication in this snr range ( almost 3000 with snr =− 15 db ), which is not realistic . practically , this limits uwb with two - step acquisition to a pulse snr of − 5 to 5 db , but not less than that . compared to that , the number of pulses required for the second step concerning spreading code phase acquisition can be shown to be negligible , hence it is not detailed here . for the described two - step synchronization solution , the total preamble length was shown in the previous sections to reach into kilobits of length , which requires a large power consumption and channel occupation from the transmitter . this mainly comes from the difficult non - coherent energy accumulation , quantified in tables 3 and 4 . the more preferable solution , described herein , involves merging pulse position and spreading code phase acquisition . the corresponding computations have been fulfilled before , to come with a required n b = 7 to 10 . this is preferable to the results shown in tables 3 and 4 , which were asking many more bits simply for getting the same performance for acquisition as for . moreover , it does not depend on the number of pulses per bit in this case . based on this study , the overall preamble is much smaller than for 2 - step synchronization : considering n b = 7 in the search phase , this limits it to 350 bits ( 2 times 25 positions times 7 bit per position ), independently of the number of pulses per bit , compared to the kilobits of 2 - step synchronization . consequently , the single - step solution is preferable , especially for systems focusing on low - power transmitters . moreover , receiver complexity is not increased . each position is tested with any possible spreading code phase , which gives a number of operations quadratic in n c , instead of linear for the two - step case . however , there are fewer samples to process . as an example , taking n c = 100 ppb , one needs 100 times more computations on each position , but each position requires only 7 bits , while 648 are used in 2 - step mode ( table 3 ), making both approaches of similar complexity . all the following references are incorporated herein by reference in their entirety . m . verhelst , w . vereecken , m . steyaert , and w . dehaene . architectures for low power ultra - wideband radio receivers in the 3 . 1 - 5 ghz band for data rates & lt ; 10 mbps . in islped &# 39 ; 04 , international symposium on low power electronics and design , pages 280 - 285 , august 2004 . 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