PERFORMANCE OF TOA ESTIMATION TECHNIQUES IN INDOOR MULTIPATH CHANNELS

PERFORMANCE OF TOA ESTIMATION TECHNIQUES IN INDOOR MULTIPATH CHANNELS Xinong Li, Kaveh Pahlavan, and Jacques Beneat Cente fo Wiele Infomation Netwo Studies Electical and Compute Engineeing Depatment, Woceste Polytechnic Institute Institute Road, Woceste, MA, USA, {xinong, avah, beneat}@ece.wpi.edu Abstact In this pape the poblem of TOA estimation in multipath channels ae discued. Bief intoductions of TOA estimation techniques that can be used to impove the pefomance in multipath channels ae pesented. Some simulation esults based on channel measuement data in indoo envionment is pesented to demonstate and compae the pefomance of diffeent TOA estimation techniques. Keywods TOA, pefomance, indoo, multipath. I. INTRODUCTION With the emegence of location-based applications, locationfinding techniques ae becoming inceasingly impotant []. Time-of-aival (TOA) is one of the most widely used location metics in geolocation systems. The basic poblem of TOA-based techniques is to accuately estimate the popagation delay of the adio signal aiving fom the diect line-of-sight (DLOS) popagation path. Eestimation of TOA falls into the field of signal paamete estimation, and it was studied in the liteatue fo sona, ada, and GPS applications [,3]. In those taditional applications, the adio popagation channel is nomally aumed to be singlepath, only distubed by additive white Gauian noise (AWGN). But indoo geolocation systems suffe fom sevee multipath adio popagation situation. As a esult, thee is a need fo studies of TOA estimation techniques in indoo multipath channels. In this pape we discu iues elated to TOA estimation in multipath channels. Bief intoductions of TOA estimation techniques that can be used to impove the pefomance in multipath channels ae pesented. Some simulation esults based on channel measuement data in indoo envionment is pesented to demonstate and compae the pefomance of diffeent TOA estimation techniques. The est of the pape is oganized as follows. In section II, we discu some iues elated to the estimation of TOA as well as time-diffeence of aival (TDOA), which is an altenative of TOA and closely elated to TOA estimation, in multipath channels. Then a bief intoduction of the TOA estimation techniques is pesented in section III. In section IV, some simulation esults based on measuement data ae pesented to demonstate the pefomance of TOA estimation in indoo envionments. At last, summay and conclusions ae pesented in section V. II. TIME DELAY ESTIMATION IN MULTIPATH CHANNELS A. TOA Estimation The TOA estimation poblem is defined as follows. A nown adio signal s ( is emanated fom a tansmitte and the signal is monitoed at a spatially sepaated eceive, which estimates the popagation delay of the signal fom the tansmitte to eceive. Auming the adio popagation channel between tansmitte and eceive is single-path and distubed only by additive white Gauian noise. Then the eceived signal can be mathematically expeed as x ( α t D) + n(, () whee the paamete D is the signal popagation delay, α is the complex signal stength attenuation paamete, and n ( is additive white Gauian noise. The maximum lielihood (ML) estimate of the popagation delay can be obtained by finding the value of τ that maximizes the coelation function of eceived signal x ( and tansmitted signal s ( [], that is xs ( τ ) x( t τ ) dt T T () α ( τ D) + v( τ ), whee (τ ) is the auto-coelation function of the tansmitted signal and v (τ ) is additive noise tem. The coelation function xs (τ ) is often efeed to as delay pofile while the function xs ( τ ) is efeed to as powe delay pofile. In pactice, the delay pofile can be measued at eceive using a sliding coelato o a matched filte. The pefomance of the ML estimato is bounded by the Came- Rao lowe bound (CRLB), which is the minimum vaiance of TOA estimation eos about the tue time delay []. If the signal is tansmitted though a multipath channel, which is modelled as -783-7589-//$7. IEEE PIMRC

h( L p α δ ( ), (3) whee L p is the numbe of multipath components, α and τ ae complex amplitude and popagation delay of the th path, espectively, the eceived signal becomes x( h( + n( L p α ) + n(. In geolocation applications the popagation delay of the DLOS path τ needs to be estimated. So that in this pape, the tem TOA is used to only efe to the popagation delay of the DLOS path in multipath channels if not specified diffeently. Using the same coelation eceive as used in the ML estimato deived with the single-path channel model, the delay pofile measued in multipath channels is given by xs L p (4) ( τ ) α ( τ τ ) + v( τ ). (5) We note that in contast to that of single-path channels, in multipath channels the measued delay pofile is a weighted sum of multiple shifted auto-coelation functions of the tansmitted signal. In geneal, the same coelation technique is used fo TOA estimation in multipath channels. As discued in [4], whethe the popagation delay of the DLOS is detectable o not lagely depends on the instantaneous channel pofile between tansmitte and eceive and the chaacteistics of anging systems such as signal bandwidth, eceive sensitivity, and eceive dynamic ange. The eceive sensitivity specifies the minimum powe level of a signal that can be detected and the eceive dynamic ange defines the diffeence in the powe level of the stongest and the weaest detectable signals. Accoding to the detectibility of the DLOS path, adio popagation channel pofiles ae claified into thee categoies fo TOA estimation in indoo geolocation applications [4]. The fist categoy is dominant diect path (DDP) case, in which the DLOS path is detectable by measuement systems and it is the stongest path in the channel pofile. The second categoy is non-dominant diect path (NDDP) case, whee the DLOS path is detectable by measuement systems but it is not the dominant path in the channel pofile. The thid categoy is undetected diect path (UDP) case whee measuement systems cannot detect the DLOS path. The channel pofiles can also be gouped simply into DLOS and NLOS (no-los) cases accoding to whethe the DLOS path is detectable o not []. Figue pesents powe delay pofiles obtained using diectsequence spead-spectum (DSSS) signals with thee diffeent channel pofiles. In measuing delay pofiles using DSSS signals, a maximal-length shift egiste sequence (msequence) is commonly used as pseudo-noise (PN) code. The auto-coelation function of the m-sequence is a tiangula function simila to the one shown in Fig. a with a spead of ± Tc aound the coelation pea, whee T c is the chip inteval of the sequence. The spead of the coelation pea depends on the signal bandwidth since the bandwidth of baseband DSSS signals equals to /Tc without pulse shaping. When the channel is single-path, the popagation delay D can be detemined using the ML estimato by finding the delay value that coesponds to the pea of the powe delay pofile shown in Fig. a and the vaiance of the estimate is bounded by the CRLB..5 3 4 5 6 7 8 9.5 3 4 5 6 7 8 9.5.5 3 4 5 6 7 8 9 τ / Tc Fig.. Powe delay pofiles with diffeent channel pofiles. (a) Single-path channel with popagation delay D Tc ; (b) two-path channel with signal attenuation paametes α α, and popagation delays τ Tc and τ 5 T c ; (c) two-path channel with signal attenuation paametes α. 6 α, and popagation delays τ T c, and τ. 5 Tc. When a adio signal is paed though a multipath channel, the delay pofile consists of multiple copies of delayed vesion of auto-coelation function of the tansmitted signal as given by (5). Figue b shows the powe delay pofile obtained in a two-path channel. We can obseve that when the diffeence between adjacent path delays is geate than T c, clealy sepaated coelation peas appea in the powe delay pofile so that the delay of the DLOS can be detemined by finding the delay value that coesponds to the fist pea. When the fist pea is the stongest one of the delay pofile, the channel belongs to the DDP categoy. When the fist pea is not the stongest one but it is detectable with given eceive sensitivity and eceive dynamic ange, it falls into the NDDP case. If the stength

of the fist pea is below the eceive sensitivity o the diffeence between the stength of the fist pea and the stongest pea exceeds the eceive dynamic ange, the DLOS path is not detectable so that the channel pofile falls into the UDP categoy. In this case, damatically lage TOA estimation eos may occu. When the diffeence between adjacent delays is smalle than T c, the two delayed coelation functions ovelap. Due to the constuction and deconstuction effects between the two ovelapped coelation functions, as shown in Fig. c lage delay estimation eo occus if the TOA is estimated by detecting the fist pea of the powe delay pofile. Inceasing signal bandwidth educes the spead of the coelation pea and helps to esolve the DLOS path. Howeve, it is pactically impoible to incease the signal bandwidth feely due to the egulations on fequency spectum usage posed by FCC. An altenative way of inceasing the esolution lies in the application of advanced signal poceing techniques as discued in [5]. Fom the pevious discuion we can conclude that the same ML estimato designed fo AWGN channels can be used in multipath channels, but the pefomance of TOA estimation degades significantly, which lagely depends on the chaacteistics of the anging system and the instantaneous channel pofile that encounteed. In summay, the following geneal pinciples can be used to impove the TOA estimation in multipath channels: Incease the eceive dynamic ange and eceive sensitivity. Incease the esolution of estimation techniques by inceasing the signal bandwidth o by employing advanced signal poceing techniques. Place the anging tansmitte and eceive, o deploy the efeence points of indoo geolocation systems, in a way to minimize the occuence of NLOS popagation scenaios between the tansmitte and eceive. B. TDOA Estimation TDOA is usually used in geolocation systems as an altenative of TOA []. The poblem of TDOA estimation is geneally modelled as follows. A signal is tansmitted fom a emote souce and monitoed at two spatially sepaated eceives. When the adio popagation channel between the tansmitte and the eceives is aumed to be single-path AWGN channel, the eceived signals at two eceives can be mathematically epesented by x ( + n ( x ( α t + D) + n (, (6) whee α is the amplitude atio of the signals obseved at the two eceives and D is the diffeence in the aiving time of the signals obseved at the two eceives. The noises n ( and n ( ae aumed jointly independent stationay andom poce, and the tansmitted signal s ( is aumed to be uncoelated with the noises. The eceives ae synchonized in time so that the TDOA to be estimated is the time delay D. Nomally a co-coelation technique, simila to the one used in estimating TOA, is used to estimate TDOA. Fist the delay pofile, which is the cocoelation function of the two eceived signals, is obtained, ( τ ) x ( x ( t τ ) dt T T (7) α ( τ D) + v( τ ), whee T epesents the obsevation time inteval, the autocoelation function of the tansmitted signal (τ ) is the same as in (), and v (τ ) is additive noise tem. Then the TDOA is estimated by finding the value of delay that maximizes the delay pofile in (7). A genealized coelation method can also be used in estimating TDOA, whee each of the two eceived signals is pe-filteed. With pope choice of pe-filtes, the estimation of TDOA can be impoved using the genealized coelation method [6]. The CRLB can be deived fo the vaiance of the TDOA estimation eos about the tue value [,6]. When the signal is popagated though multipath channels, the eceived signals at the two eceives ae given by, x ( x ( Lp Lp l α α l l ) + n (, ) + n (, whee the two sets of paametes { Lp, α, τ }, Lp, and { Lp, α l, τ l}, l Lp, define the multipath channels between the tansmitte and the two eceives, espectively. Then the co-coelation function of the two eceived signals becomes ( τ ) L p L p l α α l ( τ ( τ τ l )) + (8) v( τ ). (9) We can obseve that simila to the case of TOA estimation in multipath channels, the delay pofiles fo TDOA estimation consists of multiple copies of auto-coelation function of the tansmitted signal with diffeent delays. In multipath channels, the TDOA to be measued is the time diffeence between the popagation delays of the two DLOS paths, that is TDOA τ τ. ()

Fom (9) we can obseve that the TDOA cannot be detected by finding the delay value that coesponds to the fist pea of the delay pofile since the fist occuing coelation function in the delay axis does not neceaily coesponds to the delay value ( τ τ ). On the othe hand, following a discuion simila to that about TOA estimation, we can deduce that in multipath channels, the delayed copy of the coelation function coesponding to the delay value ( τ ) τ is not neceaily the stongest one in the delay pofile given by (9). This means that in multipath channels thee is ambiguity in detecting TDOA fom the delay pofiles since the coelation pea to be detected is neithe the stongest one no the fist one fo sue. An intuitive conclusion following this fact is that in multipath channels the estimation of TDOA is much hade than the estimation of TOA. Moeove, the CRLB deived fo single-path channel model is no longe applicable fo the estimate of the TDOA in multipath channels and damatically lage eos occu in TDOA estimation due to the complexity of multipath adio popagation channels. Since in geolocation applications, the anging signal s ( tansmitted by a mobile teminal is usually nown to efeence points (RP), a moe obvious way of estimating TDOA is to calculate the diffeence of TOA estimates measued by the two eceives. This method avoids the ambiguity in estimating TDOA fom the delay pofile (9) that we just mentioned, but it equies synchonization between the tansmitte and both of the eceives while diect measuement of TDOA by co-coelation method only equies synchonization between the two eceives. III. TOA ESTIMATION TECHNIQUES In geneal, signals of any fomat can be employed fo TOA estimation using the ML estimation technique. But wideband DSSS signal is nomally used fo TOA-based anging systems because of seveal advantages as compaed with othe altenatives [3]. One advantage of using DSSS signal fo TOA estimation is its lage bandwidth, which helps to esolve multipath signals as we pesented in section II. Anothe advantage is that because of the poceing gain of the coelation poce in eceives, the DSSS signalbased anging system pefoms much bette than competing systems in suppeing intefeence fom othe adio systems opeating in the same fequency band. Received signal Hˆ ( f ) Estimation of channel fequency esponse Supe-esolution algoithm Pseudospectum S(τ ) Detection of TOA Estimate of TOA τ Fig.. Functional bloc diagam of the eceive of supeesolution TOA estimation systems. The pefomance of TOA estimation can be impoved using supe-esolution techniques [5]. Figue shows a functional bloc diagam of the eceive of supe-esolution TOA estimation systems. The output signal of the coelato eceive is fist used to estimate channel fequency esponse. Then a supe-esolution algoithm is applied to the channel fequency esponse to detect TOA with impoved esolution. It s also shown in [5] that divesity techniques such as fequency divesity can be used to futhe impove the pefomance of supe-esolution TOA estimation techniques. Divesity techniques tae advantage of the andom natue of the adio popagation channel and impove the estimation pefomance by combining uncoelated signals at a numbe of divesity banches. Inteested eades can efe to [5] and efeences theein fo moe detailed discuion on the supe-esolution algoithms and divesity techniques fo impoved estimation of TOA fo indoo geolocation applications. IV. SIMULATIONS FOR PERFORMANCE EVALUATION In multipath channels the CRLB is not diectly applicable because damatically lage TOA estimation eos may occu when the DLOS path is undetectable. Thee ae no suitable indoo adio popagation channel models fo pefomance evaluation of TOA estimation techniques. Consequently, in the liteatue, in designing TOA estimation techniques fo multipath channels the pefomance evaluation is usually conducted by studying the esolution of estimation techniques based on compute simulations with simple two-path channel model. As we discued peviously, in addition to the esolution of estimation techniques, the adio channel chaacteistics has temendous effects on the pefomance of TOA-based anging systems in eal application scenaios. So that in indoo aeas, pefomance of TOA estimation techniques can be evaluated moe appopiately by compute simulations based on channel measuements, by conducting field measuement using pototype systems, o by using the ay-tacing softwae to simulate the site-specific indoo adio channels. Due to the complexity of the indoo adio popagation channels, pefomance study based on these methods eveals much moe ealistic statistical esults than the esolution study of estimation techniques with simple theoetical channel models. Due to limitation on the space of this pape, in this section we only pesent some sample esults obtained by compute simulations based on channel measuement data. Inteested eades can efe to [5] fo moe detailed desciptions on the simulations and esults. Figue 3 pesents the pecentage of measuement locations whee absolute anging eos ae smalle than 3 metes obtained using thee diffeent TOA estimation techniques, i.e., DSSS signal-based cocoelation techniques (DSSS/xco), supe-esolution

Eigenvecto method with fowad and bacwad coelation matix (EV/FBCM), and the supe-esolution techniques with fequency divesity banches using coelation matix based divesity combing scheme (EV/FBCM/FD- CMDCS). Fom the esults we can obseve that supeesolution techniques and divesity techniques can impove the pefomance of TOA estimation in indoo multipath envionments when the signal bandwidth is small, such as o 4MHz as shown in the figue. But when the signal bandwidth becomes lage, no much diffeence is obseved. Figue 4 pesents cumulative distibution function of anging eos fo a bandwidth of MHz with the thee techniques. Fom the figue, we can clealy obseve the diffeence between the thee techniques. Fom the simulation esults, it is also noted that in indoo envionments, lage estimation eos occu, which is a esult of NLOS situations [], even with as lage a bandwidth as 6MHz, and that the CRLB deived with single-path AWGN channel model is not applicable fo multipath channels. Pecentage of absolute anging eos < 3 (m) 9 8 7 6 5 4 3 DSSS/xco EV/FBCM EV/FBCM/FD-CMDCS 4 6 8 4 6 8 bandwidth (MHz) Fig. 3. Pecentages of measuement locations whee absolute anging eos ae smalle than 3 metes, obtained using thee diffeent TOA estimation techniques. V. SUMMARY AND CONCLUSIONS In this pape, we pesent a bief discuion on the iues and techniques fo TOA estimation in multipath channels. Some simulation esults based on channel measuement data in indoo envionments ae pesented to demonstate and compae the pefomance of TOA estimation techniques, including DSSS signal-based co-coelation techniques, supe-esolution techniques, and supe-esolution techniques with divesity techniques. Fom the esults we obseve that when signal bandwidth is small the supe-esolution and divesity techniques can be used to impove the TOA estimation pefomance. But when the signal bandwidth becomes lage, e.g., lage than MHz, almost no impovements ae obseved. Fom the esults, we can also obseve that the CRLB deived with single-path AWGN channel model is no longe applicable fo multipath channels. CDF.9.8.7.6.5.4.3.. EV/FBCM/FD-CMDCS EV/FBCM DSSS/xco BW MHz 4 6 8 4 6 8 absolute anging eos (m) Fig. 4. Cumulative distibution function (CDF) of anging eos fo a bandwidth of MHz with thee diffeent TOA estimation techniques. AKNOWLEDGEMENTS The authos would lie to than NSF fo patially suppoting this poject. We also than membes of the CWINS at WPI, who have contibuted in vaious ways to this wo. REFERENCES [] K. Pahlavan, X. Li, and J. Maela, Indoo geolocation science and technology, IEEE Comm. Mag., pp. - 8, Feb. [] A. Quazi, An oveview on the time delay estimation in active and paive systems fo taget localization, IEEE Tans. ASSP, vol. ASSP-9, no. 3, Jun. 98. [3] E. Kaplan, Undestanding GPS: Pinciples and Applications, Atech House Publishe, 996. [4] K. Pahlavan, P. Kishnamuthy, and J. Beneat, Wideband adio channel modeling fo indoo geolocation applications, IEEE Comm. Mag., pp. 6-65, Ap. 998. [5] X. Li and K. Pahlavan, Supe-esolution TOA estimation with divesity fo indoo geolocation, submitted to IEEE Tans. Wiele fo publication. [6] C. Knapp and G. Cate, The genealized coelation method fo estimation of time delay, IEEE Tans. ASSP, vol. ASSP-4, no. 4, Aug. 976.