Orthogona Muticode Channeization Appied to Subsamping Digita UWB Receiver Yves Vanderperren, Geert Leus, Wim Dehaene EE Dept. ESAT-MICAS), Kathoieke Universiteit Leuven, Begium Facuty of EE, Mathematics and CS, Deft University of Technoogy, The Netherands Emai: {yves.vanderperren,wim.dehaene}@esat.kueuven.be, eus@cas.et.tudeft.n Abstract This paper assesses in AWGN and dense mutipath environments severa equaization aternatives for a digita pused UWB receiver samping beow Nyquist rate. A suboptima but impementation efficient Minimum Mean-Square Error MMSE) equaizer which reaches performances simiar to the idea MMSE equaizer is proposed. By making an efficient use of orthogona codes, the UWB transceivers have fexibe channeization means to accomodate time-varying data rate in the order of magnitude of Mb/s with samping rates beow GHz. The proposed muticode approach takes into account the pecuiarities of pused UWB signas and avoids high peak-to-average ampitude ratios. I. INTRODUCTION The design of UWB receivers presents unique chaenges. The most popuar receiver is based on matched fitering correation) with the transmitted puse foowed by a RAKE structure capturing the mutipath diversity of the channe. However, the puse distortion introduced by the transceiver antennas and the channe can vary among the mutipaths. As a resut, the RAKE receiver can not achieve the optima performance. Transmitted reference TR) systems [] sampe the received signa avoid the need for oca tempate generation ans sampe at the puse repetition rate, but require extremey wideband deay ines in the anaog domain which are particuary difficut to reaize. On the other hand, digita based receivers provide more fexibiity and benefit from CMOS technoogy scaing, but require ADCs samping at Nyquist rate which are hardy reaizabe and highy power consuming. As the ADC power consumption of Fash ADCs, the standard soution for digita UWB architectures, scaes ineary with the samping rate and as a factor cose to 4 with the bit width [], the UWB system architect can choose either a high Nyquist) sampe rate or muti-bit resoution but not both. Severa high speed -bit receiver architectures have been proposed, e.g. in [3], [4]. However, -bit receivers suffer from poor robustness against interferers, which needs to be improved using notch fiters in the RF front-end or by shaping appropriatey the transmitted puse. The first soution comes at the cost of fexibiity, whereas the second requires the transmitter to know the interference at the receiver via some kind of feedback oop. Parae muti-bit ADC architectures based on signa channeization in time [4], [5]) or frequency domain [6], [7]) reach an aggregate samping rate equivaent to Nyquist s criterion and support interference canceation in the digita domain. However, this advantage comes at the cost of increased area and power consumption, as each ADC typicay consumes about mw using state-of-the-art Fash ADCs, see e.g. [8]. The samping rate speed is reaxed in [4] by using a bank of discrete-frequency matched fiters foowed by parae ADCs. Sti, a these soutions require carefu contro of the circuit mismatches between the parae branches. Subsamping techniques provide an attractive aternative. For exampe, a direct samping approach is used in [9]. However, it is ony appicabe for signas in the 3-5 GHz band and sti requires a GSampes/s ADC. In this paper, we compare different equaization techniques in the context of the subsamping receiver based on ine spectrum methods proposed in []. Foowing this comparison, we improve substantiay the receiver s performance without affecting its compexity. Additionay, we show how to reach data rates in the order of magnitude of Mb/s with samping rates beow GHz, by adopting a muticode approach which takes into account the pecuiarities of pused UWB signas and avoids high peak-to-average ampitude ratios. II. APPLICATION OF SUBSAMPLING TECHNIQUES TO PULSED UWB SIGNALS A. Basic Signa Mode and Subsamped Puse Detection Agorithms A received pused UWB signa s rx t) can be modeed as the convoution between a stream of Diracs sent at frame rate /T f, the received puse shape p rx t), and the channe ht): s rx t) =p rx t) ht) n= k= a n,k δt nt f t n,k )+nt) ) where a n,k {, ±A, ±3A,...} and t n,k {,,,...} are the data streams moduating K puse ampitudes and positions per period T f, respectivey, and nt) is the received additive whie gaussian noise AWGN). This mode is vaid provided that the channe ht) does not modify the puse shape, i.e. ht) = N p i= α iδt τ i ), where N p is the tota number of paths. Foowing the work on samping signas with finite rate of innovation [], it has been suggested in [], [], [3] to appy parametric PSD estimation methods in the frequency domain to estimate the position of the Diracs. Line spectrum PSD estimation methods can be used, for exampe, to retrieve the position of the puses after deconvoving the received signa by the puse shape [3]. This operation is done by
dividing in the frequency domain the samped received signa FFTs rx [n]) by the puse spectrum FFTp rx [n]). However, the number of paths which contribute significanty to the received energy is very high for typica UWB channes, requiring parametric estimation methods with unafordabe high order. Athough a reduced set of principa components is estimated in [3], the order remains prohibitive > for Channe Mode in [4]) and affects the receiver compexity and the samping rate. Moreover, it is assumed that the received puse shape is known at the receiver, whie it can differ significanty from the transmitted puse shape. Puse distortion is caused in particuar by the transceiver antennas if these do not have a constant gain and inear phase frequency response. Such distortion is hard to estimate independenty from the channe effect. A more reaistic mode which takes into account the frequency seective distortion is given by s rx t) =h c t) n= k= c n,k δt nt f t n,k )+nt) ) where h c t) = N p i= α ip i t τ i ) is the compound channe impuse response, which incudes the distortion caused by the antennas and the dispersive behavior of the buiding materias in the propagation channe. The deconvoution by the puse shape can therefore not be appied. A combination of rationa PSD estimation methods and a poynomia mode for the frequency domain representation of h c t) is proposed in [5]. However, this approach aso suffers from a high samping rate caused by the required poynomia order. Instead, the authors of [], [] propose to deconvove the received signa by the compound channe using a simpe Zero-Forcing equaizer, and appy a ine spectrum PSD estimation method of minima order. This approach is extended in section II-C to improved equaization techniques. B. Basic Principes of the Subsamping Receiver The received signa s rx t) is fitered and samped foowing [] and M + frequency domain sampes y =[y[ M],...,y[M]] are avaiabe, with M K. LetH fc be defined as a diagona matrix with the M+ frequency domain representation of the fitered compound channe. For the sake of simpicity, we consider here a singe user system and do not take the PN spreading into account. The received signa in the frequency domain y can be expressed as y = T f H fc Ba + n = H fc s + n 3) where n corresponds to the fitered noise in the frequency domain, B = [b... b K ], b k = [ z M ] k,...,zk M with z k = e πjt k/t f, a = [a,...,a K ], and s = T f Ba. We omit n in t n,k and a n,k since we focus in this section on a singe frame. The fitered compound channe impuse response h fc t) is assumed avaiabe via appropriate training of the receiver using a known preambe sent at the beginning of the data stream. An equaization fiter with frequency response H eq is constructed based on this training information, and is appied to the received signa in the frequency domain: ŝ = H eq y. A conventiona ine spectrum method of order K, for exampe ESPRIT or RootMUSIC, is then appied to the equaized signa ŝ to estimate the positions {ˆt } K i.the i= estimated ampitudes {â i } K i= are given by the east-squares LS) soution of system 3) after equaization: â = T f B ŝ 4) C. Channe Equaization Aternatives We consider here the particuar case of inear equaizers working at symbo rate, such as Zero-Forcing ZF) and Minimum Mean-Square Error MMSE) equaizers. Indeed, fractionay spaced equaizers exacerbate the samping rate issue and are not suitabe for subsamping digita UWB receivers. ) ZF: In this case, H eq = H fc and the deconvoution by h fc t) is impemented as a division in the frequency domain. This simpe soution requires ony M +) inversions during training and M +) mutipications for each data symbo. ) Optima MMSE: The MMSE equaizer minimizes J =E { s ŝ }. Soving for J / H eq =, the genera expression of the MMSE is given by H eq = H H fcr n H fc + R ) s H H fc R n 5) where R s =E { ss H} and R n =E { nn H} are the data and noise covariance matrices in the frequency domain. This equaizer invoves the inversion of a M +)-by-m +) matrix, as H eq = R s H H fc Hfc R s H H fc + R n ) 6) using the matrix inversion emma. The equaization of each data symbo y by H eq requires M+) operations. 3) Suboptima MMSE: Provided that the puse shape has a fat spectrum in the band seected by the receiver bandwidth, we can reax the assumption of coored noise and signa covariance matrices. By approximating R s and R n with their diagona ony, 6) requires then ony the inversion of M + numbers, since H fc is aready diagona. The estimation of the approximated noise covariance matrix R n,diag =σni M+ requires ony the estimation of the noise power at the equaizer input, which can be done during training. The approximated signa covariance matrix R s,diag = σsi M+ is known at the receiver since it corresponds to the power of the transmitted puse. This assumption is vaid provided that the Votage Gain Ampifier VGA) sets the signa power at a known reference eve according to the Automatic Gain Contro AGC), irrespective of the received power at the antenna. Otherwise the signa power at the equaizer input must be estimated as we. Defining SNR=σs/σ n, the suboptima MMSE equaizer can be expressed as H eq = H H fc Hfc H H fc + SNR I M+ ) 7) and ony invoves the manipuation of compex numbers with a compexity of OM +). The equaization of each data symbo requires M +) mutipications, ike the ZF equaizer.
subopt. subopt. Fig.. BER PPM, f s = 3.5 MHz, for AWGN channe top), CM averaged over reaizations midde), CM reaization bottom). Fig.. BER PPM, f s = 65 MHz, for AWGN channe top), CM averaged over reaizations midde), CM reaization bottom). D. Performance of the Equaization Aternatives A subsamping receiver based on ESPRIT has been simuated with an AWGN channe and mutipath conditions [4]. Given a desired E b /N ) des, the AWGN noise power σn added to) the receiver input signa is such that E b /N ) des = σ s /σn Tf W, where σs is the average signa power and W the mode bandwidth. This definition of SNR aows for a fair comparison of the receiver performance when using different fiter bandwidths and samping rates f s. The simuation resuts presented in this paper have been obtained with the second derivative of the gaussian monocyce, but no significant difference was observed with other puses. A singe puse per period K =) is assumed for simpicity. The puse repetition period is high enough T f =5. ns for CM) to avoid inter puse interference IPI). The centra frequency f c of the receiver bandpass fiter is chosen as the maximum of the puse PSD. Figures 3 iustrate the BER curves for PPM for various samping rates as a function of the moduation index. The MMSE and ZF equaizers present the same performance in AWGN channes since ony the puse PSD, which is amost fat in the considered band, is equaized. When considering reaistic mutipath conditions, such as CM, which present numerous ampitude dips in their frequency response, the ZF may sti be cose to the MMSE for particuar channe reaizations. However, the MMSE outperforms the ZF equaizer when the resuts are averaged over severa reaizations. The noise power term in 6) and 7) prevents noise enhancement at these ocations, as confirmed by the increasing performance improvement of the MMSE vs. the ZF equaizer for arger receiver bandwidths and samping rates. Interestingy, the suboptima MMSE based on diagona covariance matrices does not introduce any BER penaty for the samping rates which aow for reiabe communication, i.e. M min 8 or = ns E b /N [db] = ns E b /N [db] subopt. = ns E b /N [db] Fig. 3. BER PPM, f s = 5 MHz, for AWGN channe top), CM averaged over reaizations midde), CM reaization bottom). f s,min 6/T f. Indeed, the receiver bandwidth is then high enough, compared to the puse repetition rate, to guarantee amost diagona signa and noise covariance matrices. The comments for PAM moduation fig. 4) are simiar to PPM. The superior resuts of the MMSE vs. the ZF equaizer for increasing bandwidth are particuary visibe on figure 4 for the curves averaged over different CM reaizations. As a resut, the important concusions of this section are that ) the MMSE provides a cear performance advantage compared to a ZF soution, and ) the simpified MMSE provides a BER simiar to the optima MMSE but avoids inverting a M+)-by-M+) matrix.
78 MHz 65 MHz 5 MHz 78 MHz 65 MHz 5 MHz subopt. 78 MHz 65 MHz 5 MHz...3.4.5.6 Tx Tx...3.4.5.6 Tx 3 78 MHz 65 MHz 5 MHz 78 MHz 65 MHz 5 MHz 78 MHz 65 MHz 5 MHz...3.4.5.6 Tx 4 78 MHz 65 MHz 5 MHz 78 MHz 65 MHz 5 MHz 78 MHz 65 MHz 5 MHz...3.4.5.6 4 Tx tot. 4...3.4.5.6 Fig. 4. BER PAM, for AWGN top), CM midde), CM nr. bottom). III. ORTHOGONAL MULTICODE CHANNELIZATION The BER curves for PAM and PPM indicate that the subsamping receiver is more suitabe for ower data rates. Indeed, an important fraction F of the signa bandwidth is fitered out, and the pace at which the receiver coects the signa energy is reduced by a factor F. On the other hand, narrowband interference can easiy be rejected by avoiding the affected subband interference excision). Data rates in the order of few Mb/s ony can be typicay achieved at a puse repetition rate of MHz. Shorter puse periods aow reducing the puse peak ampitude and increasing the data rate, for a given moduation order and signa power. However, this soution is imited by the increased risk of IPI and cannot reach the target date rate of severa hundreds of Mb/s. Instead, we propose to mutipex N c substreams between two UWB transceivers by means of orthogona spreading codes of given ength L c N c, such as Wash codes, appied on top of the cassica PN spreading code. The transmitter sends the signa s tx t)= N c i= si) tx t), with s i) tx t) = w i) t nl c T f ) n= ) a i) p n Lc,k tx t nt f t i) 8) n Lc,k k= where w i) t) = L c ut T f ) is the Wash code appied to the ith substream w i) {, }, ut) = for t T f and otherwise). As in section II, we consider a singe user system for the sake of simpicity, and do not take into account the PN spreading in 8). The receiver recovers the different substreams by appying the different Wash codes to the received aggregated signa. This approach is simiar to the mutipexing of forwardtraffic channes in the IS-95 standard, but must be customized = w i) Fig. 5. Channeization technique N c = L c =4), no deay. The Wash codes and symbo boundaries are shown with bod and dashed ines respectivey. In this exampe, the bits sent on the mutipexed substreams are {,, }, {,, }, {,, }, {,, }. here towards the specificity of UWB. Indeed, the transmitted signa resuting from a direct appication of this channeization technique eads in worst case to a peak-to-average ratio increased by a factor N c fig. 5). This constructive addition may cause harmfu interferce and compicates the design of the transceivers anaog part. It can be avoided by sending the puses of each substream with a different time offset ɛ i fig. 6): s i) tx t) = n= k= w i) t nl c T f ) a i) n Lc,k p tx ) t nt f t i) ɛ n Lc,k i where ɛ i =i ) T f /N c. When we consider the impact of the UWB channe on the received signa, however, ony partia energy is coected if the receiver despreads the received signa with the Wash codes used by the transmitter fig. 7). The tai of the channe energy is ost as the time offset increases, and inter symbo interference ISI) is introduced. On the other hand, despreading the received signa with appropriatey deayed Wash codes is not appropriate either, since ony partia orthogonaity is obtained between deayed Wash codes. Perfect orthogonaity can be achieved using zero-correation zone ZCZ) sequences instead of orthogona codes. The issue of the imited size of code famiy for ong ZCZ is here strongy aeviated by the fact that the zero-correation zone has a ength of chip. A ZCZ muticode approach for UWB was suggested in [6], for exampe, but ignores the concern of constructive addition between the substreams. Instead, perfect orthogonaity can be obtained with shifted orthogona codes if the transmitter ) introduces a cycic prefix 9)
Tx Rx tot....3.4.5.6 Tx..4.6 Rx Despr....3.4.5.6 Tx 3...3.4.5.6 Tx 4...3.4.5.6 Tx tot....3.4.5.6..4.6 Rx..4.6 Rx 3..4.6 Rx 4..4.6..4.6 Despr...4.6 Despr. 3..4.6 Despr. 4..4.6 Fig. 6...4.6 Rx..4.6 Rx..4.6 Rx 3..4.6 Rx 4..4.6 Channeization technique, deayed substreams. Rx tot. Despr...4.6 Despr...4.6 Despr. 3..4.6 Despr. 4..4.6 Fig. 7. Contributions of the different substreams to the received signa eft) and suboptima despread signas right). The part of the despread signa equa to perfect despreading is shown in bod. For the sake of carity, we show here a hypothetica despread signa before subsamping. CP) in each substream, i.e. inserts at the beginning of each symbo a copy of the ast puse period of the symbo, and ) appies the same time offset ɛ i to the L c / pairs of Wash codes which ony differ by a deay when they are cycicay repeated such as w 3) t) and w 4) t) in the exampe on fig. 7). The transmitter uses N c / + different deays which are distributed uniformy over [,T f [ and aocated to the substreams as foows: [ɛ i ] Nc i= =[,,,, 3, 3, 4, 4,..., N c/ ] T f / N c / +), assuming w ) t) and w ) t) are the codes whose cycic repetition remains orthogona for any deay i.e. w ) = and w ) = ), L c ). The risk of the sma residua constructive addition between the pairs of substreams Fig. 8. Contributions of the different substreams to the received signa eft) and optima despread signas right). The ocation of the cycic prefix in each stream is shown in gray. [ɛ i ] Nc i= =[,T f /3, T f /3, T f /3]. which share the same vaue of time offset can easiy be reduced, e.g., by using shifted or different PN codes for the two substreams in each of these pairs. The insertion of the CP prevents ISI at the receiver if the channe impuse response is shorter than the puse period T f. It aso guarantees the cycic nature of the L c puse periods seected by the receiver after the CP is removed, i.e. orthogonaity between the Wash codes deayed by different time offset vaues. Compared to a soution based on ZCZ, the cost of the CP is much smaer than the ZCZ sequence ength required to achieve the same code famiy size and mutistream capabiity. Unike conventiona OFDM systems, where the receiver skips periodicay a fixed window of received corresponding to the CP, the seection of sampes varies here between the substreams. The deay ɛ i inserted by the transmitter is easiy handed at the receiver by introducing in the frequency domain a phase compensation term e πjɛi whie equaizing each substream. We refer to [] for an overview of the architecture of the subsamping receiver proposed in this paper, and to [7] for a study of the precision requirements of the ADC. IV. LINK BUDGET We foow here the guideines proposed in [8] for UWB ink budgets, based on cassica narrowband ink budgets using Friis transmission formua P r = P t G t λ ) / 4πd) with geometric average frequency f c = f min f max. The two cases in tabe I iustrate the ink budget for PAM and PPM for different code engths, assuming a samping rate equa to 3/T f =65 MHz, a target data rate of Mb/s and a channe coding gain of one order of magnitude. The minimum Rx sensitivity eve is defined as the minimum required average Rx power for a received symbo in AWGN.
TABLE I LINK BUDGET FOR LINE SPECTRUM SUBSAMPLING RECEIVER Term case case Unit Comment R b,tot Mb/s Bit rate L c 6 3 Wash code ength R b 6.875 3.348 Mb/s Bit rate for each substream P t -.5 -.5 dbm Tx power per substream G t dbi Tx antenna gain f c 5.7 5.7 GHz Geometric centra freq. PL m 47.6 47.6 db Path oss at m and at f c PL m db Extra oss at d =m G r db Rx antenna gain P r -7. -7. dbm Rx power N -74-74 dbm/hz Noise PSD N b -5.6-8.6 dbm Noise power per bit NF 7 7 db Rx noise figure referred to the antenna termina [4] P n -98.6 -.6 dbm/s Tota noise power per bit E b /N ) 3 3 Min E b /N to reach BER of e 5 AWGN chan.) I.5.5 db Impementation oss [4] M 3 6 Link margin T f 5 5 ns Puse Period B 6 6 Receiver bandwidth in mutipes of T f f s 3 3 MHz Samping rate R symb.5.65 Msymb/s Symbo rate b 5.5 5.5 b/symb Bits per symbo At a fixed puse repetition rate, increasing L c and N c improves the ink budget but does not augment the tota data rate. Longer codes increase the number of parae streams which can be sent and the number of puses per bit. The net data rate is therefore the same but the coding gain has improved. The number of bits per symbo is independent of the Wash code ength, since b = R b = R b,tot/n c R symb /L c T f ) = R b,tot/l c /L c T f ) = R b,tott f ) Consequenty, the two options to increase R b,tot and reach higher data rates are ) to reduce the puse period T f, unti the IPI affects the BER performance, ) to maximize b by resorting to high order PPM and/or PAM, unti the ink budget becomes negative, requiring onger codes to become again positive. The receiver compexity imits the maximum affordabe ength and number of codes. N c parae streams must indeed be accumuated before being processed by the FFT and the agorithm estimating the puse position and ampitude. Channeized streams aow matching dynamicay the data rate and quaity of service QoS) according to the user s needs. For a fixed ength L c and a given E b /N, ess streams N c <L c may be sent if the user s appication has temporariy ower requirements in terms of data rate. The power consumption of the transmitter is then reduced by a factor N c /L c with respect to the peak transmission power. At the receiver side, ess computation power is required to process N c <L c streams, which aso transates into ower power consumption if appropriate shutdown mechanisms are impemented. When the appication requires higher transmission rates, the transmitter sends the data using a possibe channes and reaches the peak transmission rate. The information concerning the actua number of codes used by the transmitter can be preiminary sent in a header within the preambe of each packet. V. CONCLUSIONS This paper has evauated different equaization aternatives for a digita based subsamping receiver in the 3.-.6 GHz frequency band. Orthogona channeization techniques are used to achieve high data rates, and accommodate for timevarying rate and QoS requirements of the user, despite ow samping rate. Future work wi concentrate on practica impementation aspects and assessment of the power consumption and computationa compexity of this receiver. ACKNOWLEDGEMENT This work has been deveoped in the context of the MEDEA+ UPPERMOST project. Y. Vanderperren gratefuy acknowedges the financia support from the IWT Begium. REFERENCES [] R. Hoctor and H. Tominson, Deay-Hopped Transmitted-Reference RF Communications, in IEEE Conf. on Utra Wideband Syst. and Technoogies,, pp. 65 7. [] B. Le, T. Rondeau, J. Reed, and C. Bostian, Anaog-to-Digita Converters, IEEE Signa Processing Mag., vo. 6), pp. 69 77, 5. [3] L. Smaini and D. Héa, RF Digita Transceiver for Impuse Radio Utra Wide Band Communications, in European Soid-State Circuits Conf. ESSCIRC) Workshop, 4. [4] S. Hoyos, B. Sader, and G. 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