Geometrical-Based Statistical Macrocell Channel Model for Mobile Environments

Transcription

1 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 50, NO. 3, MARCH Geometrical-Based Statistical Macrocell Channel Model for Mobile Environments Paul Petrus, Jeffrey H. Reed, Senior Member, IEEE, and Theodore S. Rappaport, Fellow, IEEE Abstract In this paper, we develop a statistical geometric propagation model for a macrocell mobile environment that provides the statistics of angle-of-arrival (AOA) of the multipath components, which are required to test adaptive array algorithms for cellular applications. This channel model assumes that each multipath component of the propagating signal undergoes only one bounce traveling from the transmitter to the receiver and that scattering objects are located uniformly within a circle around the mobile. This geometrically based single bounce macrocell (GBSBM) channel model provides three important parameters that characterize a channel: the power of the multipath components, the time-of-arrival (TOA) of the components, and the AOA of the components. Using the GBSBM model, we analyze the effect of directional antennas at the base station on the fading envelopes. The level crossing rate of the fading envelope is reduced and the envelope correlation increases significantly if a directional antenna is employed at the base station. Index Terms Channel modeling, geometrical, smart antennas, spatial, statistical. I. INTRODUCTION THE RECENT tremendous growth in wireless communications has led to crowding of the radio spectrum. Traditionally, cell splitting has been employed to cope with the increase in the number of users in a cellular system, but cell splitting is expensive and requires reconfiguring the cellular network. Therefore, adaptive arrays are currently being investigated for cellular and personal communications to increase the capacity of a cell. Various adaptive array algorithms have been proposed for cellular applications [1] [3]. To test these algorithms using simulation, statistical channel models, which provide the angle-of-arrival (AOA) and time-of-arrival (TOA) of the multipath components, are required. The performance of adaptive array algorithms can significantly differ depending on the channel condition, and hence a realistic channel model is required. Classically, dense scattering is viewed as leading to a Rayleigh fading phenomenon for narrowband signals [4]. This Paper approved by R. A. Valenzuela, the Editor for Transmission Systems of the IEEE Communications Society. Manuscript received March 26, 1996; revised May 24, This work was supported by the MPRG Industrial Affiliates Program, the DARPA GloMo Program, and the Federal Highway Research Center for Excellence at Virginia Tech. This paper was presented in part in the IEEE Globecom Conferencein 1996, London, U.K. P. Petrus was with the Mobile and Portable Radio Research Group (MPRG) at Virginia Tech. He is now with the System Design Group, ArrayComm Inc., San Jose, CA USA. J. H. Reed and T. S. Rappaport are with the Mobile and Portable Radio Research Group (MPRG), Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA USA ( reedjh@vt.edu). Publisher Item Identifier S (02) model (Clarke s) assumes that the signals arrive horizontally at the receiver antenna and uniformly along the azimuthal coordinate. Aulin proposed a channel model [5] that takes into account the elevation coordinate and that assumes uniform AOAs along the azimuthal coordinate. Aulin s model is appropriate to model fading at a mobile unit because scatterers are located close to the mobile and are of different heights. Liberti and Rappaport [6] developed a statistical channel model for microcells called the geometrically based single bounce (GBSB) model. The GBSB model assumes that the scatterers lie in an ellipse which encompasses the transmitter and the receiver. In this paper, we develop a statistical channel model for macrocells called the geometrically based single bounce macrocell (GBSBM) 1 channel model that assumes that multipath reflection is caused by scatterers located close to the mobile. From this model, the probability density function (pdf) of the AOA along the azimuth can be computed. The assumption that the plane waves arrive horizontally is valid for the macrocellular environment since the distance between the mobile and the base station is larger than the difference between the height of the base station antenna and the scatterers around the mobile unit. Section II discusses the GBSBM channel model and the derivation of the pdf of AOA of the multipaths at the base station from a mobile surrounded by scatterers. Comparison of the theoretical and simulated results of the pdf of the AOA of the multipath components is also presented in this section. Section III relates the angle spread to the parameters in the GBSBM model, and in Section IV the parameters of the model are related to the delay spread. The effect of directional antennas at the base station is analyzed in Section V. The Doppler spectrum obtained when using directional antennas at the base station is presented in Section VI and compared to that obtained using Clarke s model. Fading statistics, i.e., level crossing rate (LCR) and correlation function of the fading envelope, are presented in Section VII. Section VIII presents the conclusions. II. GEOMETRICALLY BASED SINGLE BOUNCE MACROCELL (GBSBM) CHANNEL MODEL AND THE PDF OF THE AOA OF THE MULTIPATHS AT THE BASE STATION Here we introduce the GBSBM channel model and derive the pdf of the AOA of the multipath components in a macrocell at 1 The acronym GBSBM was derived from Liberti s channel model /02$ IEEE

2 496 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 50, NO. 3, MARCH 2002 Therefore,, and. Since the scatterers are assumed to be uniformly distributed within the scattering cell, the density of the area within the circle of radius is given by The area within the strip,, formed by and can be shown using calculus to be (4) (5) Fig. 1. Illustration of the GBSBM channel model. the base station. The following assumptions are made to develop the model: The signals received at the base station are assumed to be plane waves arriving from the horizon, and hence the AOA calculation includes only the azimuthal coordinate. The scatterers are assumed to be uniformly distributed within a circle around the mobile. We use the same assumption as in [7], where each scatterer is assumed to be an omnidirectional reradiating element whereby the plane wave, on arrival, is reflected directly to the mobile receiver antenna without the influence from other scatterers. The scatterers are assigned equal scattering coefficients with uniform random phases. Fig. 1 illustrates the GBSBM channel model. The base station is marked as and is the mobile unit. The base station and the mobile unit are separated by a distance. The location of the scatterer is marked as. The scatterers are assumed to be uniformly located around the mobile inside a circle of radius. Since the scatterers are confined to a circle around the mobile, the AOA of the multipath components at the base station is restricted to an angular region of. The maximum angle of the arrival of the multipath component is given by Using this result, the cumulative distribution function (cdf) of the AOA,, can be expressed as The pdf of the AOA,, is the derivative of the cdf with respect to and is given by which can be reduced to Therefore, the pdf of the AOA of the multipath components is given by (6) (7) (8) (1) In Fig. 1, let us consider the strip between and. Since the scatterers are assumed to be uniformly distributed within the scattering circle, the area within the strip is proportional to the probability of the AOA of the multipath components. The AOA,, line meets the scattering boundary around the mobile,,at and at. Let the length of the line segment be and be. The scattering boundary around the mobile can be expressed as where is the length of the line from to the circle, and this line makes an angle degrees with. From (2), can be expressed as (2) (3) otherwise. Let us now validate the above theoretical model using simulation. The true pdf in (9) is evaluated for a test case where the distance of separation between the base station and the mobile unit is 10 km. The scatterers are uniformly located within a circles of radii 0.5, 1, and 1.5 km. Simulated normalized histograms are generated by creating uniformly located scatterers around the mobile, and for each location of the scatterer, the AOA of the signal at the base station is calculated. The histogram for the AOA is then calculated by carrying out Monte Carlo trials. The normalized histograms and the theoretical pdf are plotted in Fig. 2. The simulated histograms closely match the theoretical pdfs. The pdf derived in this section can be used to simulate a power-delay-angle (PDA) profile and to quantify angle spread and delay spread for a given ratio. (9)

3 PETRUS et al.: GEOMETRICAL-BASED STATISTICAL MACROCELL CHANNEL MODEL FOR MOBILE ENVIRONMENTS 497 Fig. 2. PDF for the AOA of the multipaths at the base station from a mobile located 10 km away from the base station and the radius of the scatterers are 0.5, 1, and 1.5 km. III. ANGLE SPREAD Using the model derivation in Section II, here we relate angle spread to the parameters in the model. Due to scattering, multipath components arrive at angles different from the direct component, and angle spread is a measure used to determine the angular dispersion of the channel. A measure for angle spread,, based on the central moment is defined [6] as (10) where is the power and is the AOA of the th multipath component arriving at the base station. Here we have not included the direct component. The angle spread based on the central moment is a measure of the spread of the multipath components (other than the direct component), and it gives a measure to which multipaths can be reduced using directional antennas. The GBSBM model predicts that the range of AOA of the multipaths from the mobile is restricted. To eliminate the interfering multipaths at the base station directional antennas, whose beamwidths are smaller than the range of the AOA of the multipaths, are needed. A sectorized antenna of 120 may mitigate the effects of interference but not the effects of multipaths from the desired user that are caused by the local scatterers around the desired mobile unit. Finer beams are necessary at the base station to achieve multipath rejection. But a directional antenna at the mobile can significantly reduce multipath interference because the AOA of the multipaths from the base station is as- Fig. 3. Plot of angle spread as a function of ratio of radius of the scattering circle to distance between the base station and the mobile unit for a path-loss exponent of 4. The number of multipaths are 5, 20, 50 and 200. In the R=D calculation, D is maintained at 10 km and R is varied. sumed to be arriving uniformly from all directions around the mobile. Let us define as the ratio of the radius of the scattering circle to the distance between the base station and the mobile unit. In the limiting case, can take a maximum value of 1. Angle spread as a function of is shown in Fig. 3. Fig. 3 compares the angle spread for a path loss exponent of 4 and the number of multipaths are 5, 20, 50, and 200. In this test case is maintained at 10 kms and is varied. As the ratio of increases, the angle spread increases linearly. Also as the number of multipath components increases, the angle spread

4 498 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 50, NO. 3, MARCH 2002 Fig. 5. Illustration of the AOA at the mobile when a directional antenna with beamwidth of 2. The scattering region illuminated by the base station antenna beam is the area marked by EFGHIJ. Fig. 4. Plot of delay spread as a function of ratio of radius of the scattering circle to distance between the base station and the mobile unit for a path-loss exponent of 4. The number of multipaths are 5, 20, 50 and 200. In the R=D calculation, D is maintained at 10 km and R is varied. also increases. It has also been found 2 that the angle spread is independent of path loss exponent, because the scatterers are located closer to the mobile. IV. DELAY SPREAD Here we characterize the delay spread of the channel in terms of the parameters of the GBSBM model. Delay spread is a measure of time dispersion of the channel. A measure based on the central moment is the square root of the second central moment of the power delay profile, defined as (11) the Doppler spectrum, we have to characterize the AOA of the multipath components at the mobile when a directional antenna is used at the base station. Fig. 5 illustrates the condition when a flat-top directional antenna with unity gain and beamwidth is used at the base station. If, then the base station antenna will illuminate all the scatterers, and hence the pdf of the AOA at the mobile is uniform. But, if, then the base station antenna will partially illuminate the scatterers, and hence the pdf of the AOA of the multipath components at the mobile will not be uniform. Here we derive the pdf of the AOA when a directional antenna is used at the base station, and the Doppler spectrum is then derived. In Fig. 5, the scatterer s region EFGHIJ is illuminated by the base station antenna. Let us now derive the pdf of when. Let us consider only the region EFGMJ where because the same holds true for the region GHIJM, where. Let us divide the region EFGMJ into three distinct regions, JEM, EFM, and FGM. The value of and marks the three regions. The pdf of the AOA can be derived by computing the area within a thin strip (shaded region) shown in Fig. 5. The area ( ) within a strip (shaded region in Fig. 5) between and can be shown using calculus to be where is the power and is the delay of the th multipath component arriving at the base station. We now calculate the central moment delay spread as a function of. Similar to the angle spread, as the ratio of increases, the delay spread increases linearly. Fig. 4 compares the delay spread for a path loss exponent of 4 and the number of multipaths are 5, 20, 50, and 200. In this test case also is maintained at 10 km and is varied. The delay spread obtained for 20, 50, and 200 multipaths are very close to each other. The delay spread is smaller when the number of multipaths is equal to 5. V. CHARACTERIZING THE AOA OF THE SIGNAL AT THE MOBILE WHEN A DIRECTIONAL ANTENNA IS EMPLOYED AT THE BASE STATION The GBSBM model can be used to analyze the effect of directional antennas on the Doppler spectrum. However, to derive 2 Results for different path-loss exponents are not included in the paper due to space constraints. where the value of for the three regions can be shown to be (12) (13) Let us now calculate and. From Fig. 5, and can be related by Squaring (14) and solving for, we can express as (14) (15)

5 PETRUS et al.: GEOMETRICAL-BASED STATISTICAL MACROCELL CHANNEL MODEL FOR MOBILE ENVIRONMENTS 499 Now and can be determined by substituting in (15) to yield (16) (17) Since the scatterers are uniformly distributed within the region EFGHIJ, the density of the area within the region is the reciprocal of the area within the region. The area ( ) within the region EFGHIJ can be expressed as The area density is given by Using (12), (13), and (18), the cdf of the AOA, region can be expressed as (18), for the (19) where is a dummy variable. For the regions and, the cdf is given by (20) The pdf, the derivative of the cdf, can then be expressed as shown in (21) at the bottom of the page where and are given by (16) and (17). Fig. 6 validates the theoretical pdf developed in this section. Let us consider a test case where km and km, therefore degrees. If a flat-top beam with unity gain and beamwidth of 10 degrees is used at the base station, then the theoretical pdf is evaluated using (21) and shown in Fig. 6. To obtain the normalized simulated histogram for the AOA, scatterers are uniformly created around the mobile, and from the scatterers that are illuminated by the beam, the histogram of the AOA at the mobile is computed. The nor- Fig. 6. Theoretical pdf and simulated normalized histograms of the AOA at the mobile. The base station uses a directional antenna with beamwidth (2)10 degrees and D=R = 3 and 2 = 38:9 degrees. malized histogram is also shown in Fig. 6. It can be seen that simulated normalized histogram fits closely with the theoretical pdf curve. VI. DOPPLER SPECTRUM Here we use the pdf of the AOA derived in Section V to derive the Doppler spectrum. The received signal at the mobile experiences Doppler spread due to the motion of the receiver. Fig. 7 illustrates the condition when the mobile is moving at an angle of with respect to the direct line-of-sight (LOS) component. The th multipath component arrives at the mobile at an angle of with respect to the LOS component. The multipath components at the receiver experience Doppler shift depending on the direction of the motion of the mobile. The th multipath component experiences a Doppler shift given by (22) where is the maximum possible Doppler shift, which is given by, is the velocity of the mobile, and is the wavelength of the carrier signal. Let the received signal be. The Doppler spectrum was shown in [6] to be (23) (21)

6 500 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 50, NO. 3, MARCH 2002 Fig. 7. Illustration of a multipath component arriving at the mobile from the base station. where and is the pdf of the distribution of the Doppler frequency. Assuming an omnidirectional antenna at the receiver, it was shown in [6] that is given by (a) (24) where is the pdf of the AOA of the multipath components at the mobile unit. Therefore, the power spectral density is given by [8] (25) If the AOA of the signal at the mobile is uniform, then the Doppler spectrum is given by Clarke s model [8] as (26) If a directional antenna is used at the base station, then the pdf of the AOA of the multipath components is given by (21). Substituting (21) into (25), the Doppler spectrum can be obtained when using a directional beam at the base station. Let us consider a test case where the mobile is traveling at a velocity of 54 km/h and a carrier frequency of 2 GHz is assumed. The maximum Doppler shift is 100 Hz. The radius of the scattering circle is 1 km, and the T-R separation is 3 km. The directional antenna has beamwidths: 2,10, and 30. For the above parameters, the range of AOA of the multipath components ( )is Two different directions of motion of the mobile are considered: and. Fig. 8(a) and (b) show the Doppler spectrum for and, respectively. For, the spectrum is skewed to the right, i.e., more negative Doppler frequency components than positive frequency components. This is because, when the mobile is moving in the direction of the LOS component toward the base station [see Fig. 9(a)], the positive Doppler frequency components result from the scatterers located in the region marked and the negative Doppler frequency components from region. Since the area of the region is larger than the area of the region, there are more negative Doppler frequency components than positive frequency components in the Doppler spectrum. For, the spectrum is symmetrical about the zero Doppler frequency component. When the mobile is moving in a direction perpendicular to the LOS component (b) Fig. 8. Doppler spectra when using a directional antenna at the base station is compared with the Clarke s model. The radius of the scattering circle is 1 km and the T-R separation is 3 kms. The motion of the mobile is: (a) 0 degrees and (b) 90 degrees with respect to the direct component and is traveling at 54 km/h. The carrier frequency is 2 GHz and the directional antenna uses a flat-top beam with beamwidths 2, 10, and 30 degrees. [see Fig. 9(b)], the area of the region is equal to the area of the region, therefore the Doppler spectrum is symmetrical about zero Doppler frequency. Both for and 90, from Fig. 8(a) and (b), the Doppler spread decreases significantly as the beamwidth of the antenna reduces. As the beamwidth reduces, the antenna is able to mitigate multipath components with large AOAs, hence the reduction in the Doppler spread, which translates to slow variation in the fading envelopes. For larger beamwidths, the Doppler spectrum tends toward the U-shaped Clarke s spectrum because the pdf of the AOA at the mobile tends toward the uniform distribution. VII. FADING STATISTICS In this section, we quantify the effects of using a directional antenna at the base station on the fading envelopes in terms of

7 PETRUS et al.: GEOMETRICAL-BASED STATISTICAL MACROCELL CHANNEL MODEL FOR MOBILE ENVIRONMENTS 501 (a) Fig. 11. Comparison of the correlation function when using a directional antenna at the base station with the Clarke s model. The directional antenna has beamwidths 2 and 10. The D=R ratio is 3 and hence 2 =38:9. (b) Fig. 9. Illustration of the scatterers region that causes positive and negative frequency components when the mobile is moving: (a) toward the base station and (b) perpendicular to the base station. The scatterers in the region A and A cause the positive and negative Doppler frequency components, respectively. of maximum Doppler frequency. Here the fading envelopes are normalized by their rms value and the number of level crossings are measured. The level used here is 1 and crossings are measured in the positive-going direction. The LCR increases linearly with increase in Doppler frequency. The directional antenna significantly reduces the LCR compared to the Clarke s model. For a maximum Doppler frequency of 100 Hz, a directional antenna with a beamwidth of 10 can reduce the LCR by approximately 40%, while a 2 antenna can reduce the LCR by 65% compared to the Clarke s method. Also, the slope of the LCR curve decreases as the beamwidth reduces. Fig. 11 is a plot of the correlation function of the fading envelopes generated using the model for beamwidths 2 and 10 and compared to the Clarke s model. The correlation of the fading envelopes increases as the beamwidth reduces due to the reduction in the Doppler spread. VIII. CONCLUSION Fig. 10. Plot of LCR as a function of maximum Doppler frequency when using a directional antenna (beamwidths 2 and 10 ) at the base station and compared to Clarke s model. The level used to calculate LCR is 1. Here D=R = 3 and therefore the maximum AOA range is level crossing rate and correlation function. We consider the case when and the ratio is 3. The directional antenna at the base station has beamwidths 2 and 10. The level crossing rate and the correlation characteristics of the fading envelopes are measured at the base station with the directional antenna and compared to the Clarke s model or an omnidirectional case. Using the Doppler spectrum developed in Section VI, we generate fading envelopes and then compute LCR and the correlation function. Fig. 10 shows the LCR plotted as a function In this paper, we have introduced a statistical geometric propagation model for a macrocell mobile environment. This channel model assumes that each multipath component of the mobile transmission undergoes only one bounce traveling from the transmitter to the receiver and that the scatterers are located uniformly within a circle around the mobile. This GBSBM channel model provides three important parameters that characterize a channel: the power of the multipath component, the TOA of the component, and the AOA of the components. This paper has presented a technique to generate such models for an arbitrary wireless system. The model shows that the angle spread and the delay spread increase linearly as the radius of the scattering circle increases. We have also analyzed the effect of a directional antenna at the base station on the Doppler spectrum. Significant reduction in the level crossing rate and an increase in correlation of the fading envelopes can be achieved by employing directional antennas at the base station.

8 502 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 50, NO. 3, MARCH 2002 ACKNOWLEDGMENT The authors wish to thank Dr. J. C. Liberti and R. Ertel in the development of the GBSBM channel model. REFERENCES [1] B. G. Agee, K. Cohen, J. H. Reed, and T. C. Hsia, Simulation performance of a blind adaptive array for realistic channels, in Proc. IEEE Veh. Tech. Conf., vol. 1, 1993, pp [2] J. H. Winters, J. Salz, and R. D. Gitlin, The impact of antenna diversity on the capacity of wireless communication systems, IEEE Trans. Commun., vol. 42, pp , Feb./Mar./Apr [3] P. Petrus and J. H. Reed, AMPS cochannel interference rejection using spectral correlation properties and an adaptive array, in Proc. IEEE Veh. Tech. Conf., vol. 1, July 1995, pp [4] R. H. Clarke, A statistical theory of mobile-radio reception, Bell Syst. Tech. J., vol. 47, no. 6, pp , July Aug [5] T. Aulin, A modified model for the fading signal at a mobile radio channel, IEEE Trans. Veh. Technol., vol. VT-28, no. 3, pp , [6] J. C. Liberti and T. S. Rappaport, A geometrically based model for line-of-sight multipath radio channels, in Proc. IEEE Veh. Tech. Conf., Apr. 1996, pp [7] F. Amoroso and W. W. Jones, Geometric model for DSPN satellite reception in the dense scatterer mobile environment, IEEE Trans. Commun., vol. 41, pp , Mar [8] W. C. Jakes, Microwave Mobile Communication. New York: Wiley, Paul Petrus received the Ph.D. degree from Virginia Polytechnic and State University, Blacksburg, in He later joined ArrayComm, Inc., San Jose, CA, as a member of the research group. He now heads the research and development group at ArrayComm that develops the protocol for their high-speed wireless data product, i-burst. He has published more than 20 journal and conference papers. He holds four U.S. patents and has five more pending with the USPTO. His research interests are in the field of smart antenna processing, multichannel modeling, resource allocation, and adaptive system parameter optimization. His interests also include implementing complex signal processing algorithms in a combination of general purpose signal processors and dedicated hardware. Theodore S. Rappaport (S 83 M 84 SM 91 F 98) received the B.S.E.E., M.S.E.E., and Ph.D. degrees from Purdue University, West Lafayette, IN, in 1982, 1984, and 1987, respectively. Since 1988, he has been on the faculty of the Electrical and Computer Engineering Department, Virginia Polytechnic and State University, Blacksburg, where he is the James S. Tucker Professor and founding director of the Mobile & Portable Radio Research Group (MPRG), a university research and teaching center dedicated to the wireless communications field. In 1989, he founded TSR Technologies, Inc., a cellular radio/pcs manufacturing firm that he sold in He has 22 patents issued or pending and has authored, co-authored, and co-edited 17 books in the wireless field, including the popular text book Wireless Communications: Principles & Practice (Englewood Cliffs, NJ: Prentice-Hall, 1996), Smart Antennas for Wireless Communications: IS-95 and Third Generation CDMA Applications (Englewood Cliffs, NJ: Prentice-Hall, 1999), and several compendia of papers, including Cellular Radio & Personal Communications: Selected Readings (New York: IEEE Press, 1995), Cellular Radio & Personal Communications: Advanced Selected Readings (IEEE Press, 1996), and Smart Antennas: Selected Readings (New York: IEEE Press, 1998), and he has co-authored more than 150 technical journal and conference papers. Dr. Rappaport received the Marconi Young Scientist Award in 1990, an NSF Presidential Faculty Fellowship in 1992, and the Sarnoff Citation from the Radio Club of America in He was recipient of the 1999 IEEE Communications Society Stephen O. Rice Prize Paper Award. Since 1998, he has been series editor for the Prentice-Hall Communications Engineering and Emerging Technologies book series. He serves on the editorial board of International Journal of Wireless Information Networks and the advisory board of Wireless Communications and Mobile Computing. He is active in the IEEE Communications and Vehicular Technology societies and is also chairman of Wireless Valley Communications, Inc., a microcell and in-building design and management product company. He is a registered professional engineer in the state of Virginia and is a Fellow and past member of the board of directors of the Radio Club of America. He has consulted for over 25 multinational corporations and has served the International Telecommunications Union as a consultant for emerging nations. Jeffrey H. Reed (S 78 M 80 SM 98) received the B.S.E.E., M.S.E.E., and Ph.D. degrees from the University of California, Davis, in 1979, 1980, and 1987, respectively. From 1980 to 1986, he worked for Signal Science, Inc., a consulting firm specializing in DSP and communication systems. After graduating with his Ph.D., he worked as a private consultant and as a part-time faculty member at the University of California, Davis. In August 1992, he joined the faculty of the Bradley Department of Electrical and Computer Engineering at Virginia Polytechnic and State University (Virginia Tech), Blacksburg, where he is now a Professor with the Bradley Department of Electrical and Computer Engineering and is director of the Mobile and Portable Radio Research Group. He specializes in software radios, smart antennas, location systems, wireless networking, spread spectrum, digital signal processing, interference rejection, wireless video, and modem design. He is the co-author or co-editor of seven books and has contributed chapters to four. He has authored 25 papers in refereed journals, 58 conference presentations, and 37 technical reports. He has led or assisted with research projects totaling over $5 million. His book on radio resource management was published this year by Kluwer and his book on software radios is set for publication later this year. Dr. Reed received the Outstanding Researcher Award from Virginia Tech s College of Engineering in 2002.