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Radio Location in Urban CDMA Microcells James J. Caery and Gordon L. Stuber School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, Georgia Abstract: A radio location

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Radio Location in Urban CDMA Microcells James J. Caery and Gordon L. Stuber School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, Georgia Abstract: A radio location method for code-division multiple-access (CDMA) microcellular networks is investigated. The method discussed focuses on the use of time dierence of arrival (TDOA) estimates for deriving the position of a mobile unit in a CDMA system, where the transmitted signal is received by several base stations (BSs). The TDOA estimates are obtained by using a delay-lock loop. A similar method is used in the global position system (GPS), but its performance in an urban microcellular propagation environment has not been previously studied. Simulation results are given for dierent radio propagation environments. I. INTRODUCTION Vehicle location systems have become the focus of intense research over the past few years and there seems to be no shortage of applications for automatic vehicle location technology. In Japan, taxi and delivery drivers use vehicle location technology to navigate through the streets of Tokyo. In the United States, eet truck operators are using location technology to guide drivers in unfamiliar areas to improve product delivery times and improve the eciency of the eet management process. Similarly, rental cars have been outtted with vehicle location devices in order to help visitors nd their way in unfamiliar cities. Of particular importance to the transportation industry are intelligent transportation systems (ITS), which include trac management, travel information, vehicle control, commercial vehicle operations, and public and rural transportation. Future planning includes services for travel and transportation management, travel demand management, public transportation operations, electronic payment, emergency management, and advanced vehicle control and safety systems. Finally, vehicle location technology is highly valuable for mobile 911 emergency services. Many of the existing location technologies use deadreckoning, the global position system (GPS), or a hybrid of the two, which require specialized equipment in the vehicle. The cost of such equipment can range from a several hundred dollars to a few thousand dollars, thus severely limiting its availability to average users. Other methods have been proposed that incorporate the cellular telephone network into the location process [1]. However, these services still require GPS receivers for determining location. A previous paper [2] investigated the use of cellular telephone networks for automatic vehicle location. Radiolocation This research was supported by GTE Laboratories, Inc. was considered in an IS-95 system where the mobile unit transmits a timer-based update that is received by three or more BSs. No additional equipment is required for the subscriber, since use is made of the existing cellular telephone equipment and network. Any additional equipment can be added to the BS or central processing site. In [2], TDOA estimates were determined through the use of a digital matched lter receiver, which was used to provide rough alignment of the received and local spreading codes. The quantization error limited the resolution and, hence the accuracy, that could be achieved. The delay-lock loop (DLL) is a technique for allowing ne synchronization of the incoming code and the local code. As a result, more accurate arrival time estimates can be obtained from the DLL. The DLL has been used for this purpose in GPS [3] and shown to provide good location accuracy for the earth-satellite propagation channel. This paper investigates the performance of a DLL-based vehicle location system for urban microcellular propagation environments that are characterized by multipath, shadowing, and pathloss. The urban microcell deployment studied in this paper is based on the Manhattan-type street layout where base stations are located at every other intersection. As a result of this layout, we will always assume that a mobile lies between at least two BSs (four at an intersection) on the same street and line-of-sight (LOS) propagation is assumed from the mobile to those BSs. The remainder of the paper is organized as follows. Section 2 gives a brief review of radio location using TDOA information. The algorithms used to estimate the position from the TDOA information are also discussed. Section 3 outlines the propagation model that is assumed for the performance analysis of the vehicle location system using the delay-lock loop. The location system employing the delay-lock loop is detailed in Section 4. Section 5 provides simulation results for ranging and two-dimensional location in a simple urban microcell scenario. Conclusions are provided in Section 6. II. LOCATION METHOD A technique often used in radio location systems is the TDOA method. This method uses the arrival times of a signal at several receivers to determine the transmitter location by forming dierences among the measured arrival times. Each receiver involved in the location process estimates the arrival time of the signal and TDOA estimates are then formed for each pair of receivers. It is necessary that the code generators at each receiver be synchronized so that the TDOA estimates have a common time base. This form of radio location is useful in asynchronous systems since time of transmission need not be known. In a geometric interpretation, this procedure reduces to nding the intersection of hyperbolas whose foci are at the receivers. Typically, to determine the location of a transmitter in two dimensions, at least three receivers are necessary. Two approaches are generally used for calculating the location of the vehicle from the TDOA estimates. One approach is to use the geometric interpretation above and determine the intersection of three hyperbolas, which can be dicult. The second approach is to calculate the position using a non-linear least squares solution [4, 5, 6], which is more statistically justiable than nding the intersection of hyperbolas. The algorithm assumes the mobile at location (x 0,y 0) transmits its sequence at time 0. The N receivers located at the coordinates (x 1,y 1), (x 2,y 2), : : :, (x N,y N ) receive the sequence at times 1, 2,..., N. We consider the vector of functions where ~f(x) = [f 1(x); ; f N (x)] T (1) f i(x) f i(x; y; ) = c( i? )? p (x i? x) 2 + (y i? y) 2 (2) and c is the speed of light, for i = 1; : : : ; N. The times i are generally in error due to multipath or other timing errors such as those caused by non-line-of-sight (NLOS) propagation. The functions f i(x) can be weighted to reect the reliability of the measurements from receiver i by f(x) = W ~ f(x) (3) where W = diag[ 1; : : : ; N]. To t the location estimate to the raw time of arrival data, the following function is formed: F (x) = f T (x)f(x) = NX i=1 2 i f 2 i (x): (4) The location estimate is determined by minimizing the function F (x) through an iterative process. Other forms of the function F (x) can be used such as replacing fi 2 with jf ij, but these methods usually do not perform as well as minimizing the sum of squares [4]. One approach to solving the non-linear least squares problem of (4) is the use of the method of steepest descent. In this method, the successive \guesses of the mobile position are updated using the equation x k+1 = x k? rf (x k ) (5) where is a constant (scalar or diagonal matrix), x k = [x k ; y k ; k ] T, and the gradient is given by h i T F F rf (x k ) rf (x)j xk = (6) x xk y yk Since is small (sec) compared to x and y, a scalar step size should be small enough to allow to converge to a solution. This will make the convergence of x and y extremely slow. To overcome this aect, we take to be = x # y F k (7) s(t) τ τ τ 0 w 0 w 1 Figure 1: Wideband channel model. where x; y. The algorithm continues by repeating the update of x k until krf (x k )k is greater than some prescribed tolerance,. One of the drawbacks of using the steepest descent method is its slow convergence. As a result, other algorithms have been utilized to overcome this and to reduce complexity. The algorithms given in [5, 6] form the solution to (4) by linearizing f i using a Taylor series expansion and keeping only the rst order terms yielding τ τ w M Σ n(t) r(t) f i(x) f (k) i + r xf i(x k ) (x k ) (8) where the gradient is with respect to x, (x k ) = [ x; y; ] T = x?x k, and f (k) i = f i(x k ). Substituting (8) into (4) and solving r F (x) = 0 (9) for, where the gradient is with respect to, the vector x k is updated by x k+1 = x k + : (10) This new \guess is substituted back into (8) and the process is reiterated until j xj + j yj + cj j , where is a prescribed tolerance. When the mobile is close to the receivers or near the \circle formed by the receivers, the algorithm in [5, 6] has trouble converging [4, 5]. For vehicle location in microcells, the mobile is always within a short distance of the serving BS, so this method is not appropriate in such a situation. The problem with convergence is due to the approximation of f i(x) with the linear terms of the Taylor series expansion. For our purpose, the algorithm described by equations (1){ (7) is used to perform radio location from the TDOA information. If (^x,^y) is an estimate of the mobile location, then the location error is given by R = p (^x? x 0) 2 + (^y? y 0) 2 (11) where (x 0,y 0) is the true mobile location. III. PROPAGATION ENVIRONMENT The radio propagation environment is characterized by multipath propagation, shadowing, and pathloss. The multipath channel is modeled by the -spaced tapped delay line illustrated in Fig. 1. In the simulations of Section 5, we use a spacing = T c=20 and a channel with M taps generated using Jakes' model [7]. The delay of the rst tap, 0, is the calculated distance between the mobile and BS for LOS propagation. For NLOS propagation, a delay uniformly distributed from T c=10 to T c is added to the calculated distance. For Jakes' model, the variance of each of the M? 1 multipath taps is 2 = 1 while the power of the direct path (rst tap) is K(M? 1) 2, where K is the Rice factor. For LOS propagation, fading is typically Rician and the Rice factor was chosen as K = 6 db. For NLOS propagation, fading is typically Rayleigh and the variance of the rst tap is also 2. A simple Markovian shadow model has been suggested by Gudmundson [8] that allows one to account for the spatial correlation of the shadows. The shadow that is experienced by the mobile station can be described by the equation k+1(db) = k(db) + (1? )v k (12) where v k is a zero-mean Gaussian random process with variance 2, k(db) is the shadowing in decibels at location k, and is a parameter that describes the spatial correlation of the shadowing. The autocorrelation of k is given by (db) (db) = 1? jnj (13) If we assume that the signal strength is sampled every T seconds, then the autocorrelation can be expressed as (db) (db) = 1? D 1 + D 2 (vt=d)jkj D (14) where D is the correlation between two points separated by a spatial distance D and v is the velocity of the vehicle. For our simulations, the shadow decorrelation at a distance D of 30 m was chosen to be D = 0:1. We can express the composite received signal in the form ^r(t) = r(t) v(t) (15) where r(t) is the received faded signal and v(t) is the shadow attenuation. Finally, we need to consider pathloss. In urban microcells, the pathloss is often modeled by a two-slope characteristic. The basic two-slope pathloss model is [9] 1 10 log 10 db (16) d a (1 + d=g) b where is the average pathloss, d is the distance between transmitter and receiver, g is the break point and a and b are the pathloss slopes before and after the breaking point, respectively. In our simulations, g = 150 m and a = b = 2. An important consideration for microcells is the corner effect. This occurs in urban microcellular settings where the mobile rounds a street corner. A model that accounts for this eect assumes LOS propagation until the mobile rounds the corner. Afterwards, it assumes LOS propagation from an imaginary BS located at the corner and having transmit power equal to that received from the serving BS. IV. LOCATION SYSTEM The delay-lock loop allows ne synchronization of the local spreading code with the incoming code. The non-coherent delay-lock loop is illustrated in Fig. 2 and operates by correlating the received signal with the early and late spreading codes, c(t? ^ + T c) and c(t? ^? T c), respectively. The delay estimate between the local and received codes, ^, is initially known to within one-half chip from course acquisition r(t) c(t τ Τ c) c(t τ+ Τ c) PN Code Generator BPF Time delay estimate, ( ) 2 BPF ( ) 2 VCC ^τ u(t) + - Σ e(t) Loop Filter F(s) Figure 2: The delay-lock loop used for vehicle location system. (matched lter or sliding correlator). The code phase error signal e(t) is obtained by squaring and dierencing the correlator outputs. The squaring operations serve to remove the eects of data modulation and carrier phase shift. The loop is closed by lowpass-ltering e(t), and the output of the loop lter u(t) is used to drive the voltage controlled clock (VCC) and correct the code phase error of the local code generator. The parameter, 0 1, is called the early-late discriminator oset. The output of the VCC which provides an estimate of the dierence between the incoming and local codes, ^, is used to form the TDOA pairs. For the simulations in the next section, = 1=2 and F (s) = 1. The output of the VCC is given by Z t ^(t) = K V CCT c u(x) dx (17)?1 where K V CC is the gain of the VCC and T c is the chip period. A simple accumulator is used to model the operation of the VCC in the computer simulations with the constant K V CCT c = 0:003. V. VEHICLE LOCATION SIMULATIONS The location system was simulated under dierent propagation conditions. We note that there is a limitation in the accuracy that can be achieved when simulating the delay-lock loop on a computer. As a result, we chose to limit the resolution of the delay-lock loop to 1/20 of a chip to limit the simulation time. Thus, all positions estimates will be in error due to this quantization, even when no multipath or shadowing is present. In the simulations that follow, the spreading code was a m-sequence of length 127 and chip rate T c?1 = 1:2288 Mcps. Two channel propagation scenarios are considered in the simulations. The rst contains no multipath components while the second contains a direct path and seven reected paths, corresponding to M = 1 and M = 8 in Fig. 1, respectively. The multipath delay prole for the second scenario was modeled with a uniform distribution where the mean delay was 1:5T c and the delay spread was 0:87T c. A chip energy to noise ratio of E c=n o=-20 db was used in the simulations. To study the performance of the delay-lock loop based location system in urban microcells, the standard deviation of Mean error, E[R] (m) M=1 M= Standard deviation of shadowing, σ (db) Figure 3: Mean absolute range error for varying standard deviation of shadowing for no multipath (M=1) and multipath (M=8). BS3 Figure 4: Scenario for two dimensional location in an urban microcell. shadowing was varied for the two propagation scenarios above. The ranging system was rst investigated, where only the distance of the mobile unit from a BS is determined. This was performed by assuring initial alignment between the spreading codes of the mobile unit and the BS. The results of the ranging simulations are given in Fig. 3. As can be seen from the gure, the shadowing has little eect for the case of no multipath (M = 1) as we would expect. However, when multipath is considered (M = 8), there are drastic eects with an increased shadow standard deviation. Also, for the light shadowing case, we see that the mean absolute error is increased due to the multipath propagation. Next, the performance of two-dimensional location in a typical urban microcell environment was studied. The mobile was placed in the microcell scenario shown in Fig. 4. In the gure, the street widths are assumed to be 20 m with a city block length of 280 m giving 600 m between BSs. In performing vehicle location, it is necessary to determine the number of BSs that will be required in providing a location x. This is important BS0 BS2 BS1 since more receivers means more processing and an increased load on the cellular network. At least two BSs are necessary since a single BS would only provide a circle on which the mobile must lie. From Fig. 4, we assume that in the rst 300 m of travel, the mobile will only be in LOS with BSs 0 and 2. After the mobile turns the corner, we assume that it will be in LOS with BSs 1 and 3. Since there will always be NLOS paths with two of the four BSs, there will be errors in the calculated position xes if either of the two NLOS BSs are used. This results from the extra propagation time that is necessary due to the additional distance that the signal must travel around the corner to reach the out of sight BSs. Since the location estimates are based on time of arrival estimates, this causes large errors in the position xes. To investigate the accuracy of the position xes when the NLOS BSs are used, simulations were performed to estimate the position of a vehicle using two, three, and four BSs in the scenario of Fig. 4. As the vehicle moved from BS0 to BS1, the location was estimated every fty meters of travel. For three BSs, BS0, BS1, and BS2 were used for location until the mobile rounded the corner where BS0,BS1, and BS3 were used. This was done to guarantee a LOS path exists between the mobile and at least two BSs. The weighted least squares approach using the method of steepest descent mentioned in Section 2 was used to calculate the position from the arrival time estimates. Weighting the contribution of the BSs equally ( i=1), the algorithm failed to converge in every case. This is due to the inaccurate arrival time estimates which are contributed by the NLOS BSs. The results are the same if using the method of Taylor's series approximation. However, if the NLOS BSs are weighted less than the LOS BSs, the steepest descent algorithm did converge. The weights chosen were i=1 for the LOS BSs and i=0.1 for the NLOS BSs. The algorithm using the truncated Taylor series approximation still did not converge and required much smaller weighting for the NLOS BSs. Location using two BSs may at rst seem odd since location in two-dimensions requires three receivers. However, the third receiver simply provides an additional constraint to nd the solution. We can use two BSs for location if we provide an additional constraint. We chose to constrain the location of the vehicle to a line connecting the two BSs. This can be accomplished in the location algorithm by providing an initial estimate which is on the line connecting the two BSs. Using two BSs, it is always assumed that the two BSs used are on the same street as the mobile (i.e, either BS0 and BS2 or BS1 and BS3) and thus are LOS with the mobile. A consequence of this constraint is that the estimated location will always be in the center of the street. The results of the simulations are summarized in Table 1 where the mean and standard deviation (std) for the three scenarios are given. The error increases signicantly when reducing the number of BSs from four to three. The same occurred in [4] where the error decreased with an increased number of receivers. However, the two BS location scenario provides much better results because only the LOS BSs and, thus accurate time estimates, were used for location. For the three and four BS scenarios, one and two BSs, respectively, were NLOS (due the the corner) and thus the algorithm used arrival time measurements that could be very inaccurate. Improved performance could be 4 BS 3 BS 2 BS M mean std mean std mean std Table 1: Location error statistics for 2, 3, and 4 BSs un

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