ADAPTIVE ANTENNAS FORWIRELESS COMMUNICATIONS

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ADAPTIVE ANTENNAS FORWIRELESS COMMUNICATIONS

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Adaptive antennas for wireless communications / edited by George V. Tsoulos.p. em.

Includes bibliographical references and index.ISBN 0-7803-6016-81. Adaptive antennas. 2. Wireless communication systems--Equipment and supplies. I.Tsoulos, George V., 1968-

TK7871.67.A33 A33 2000621.382'4--dc21

00-040990

Contents

Preface xi

Chapter 1 Introduction and Channel Models 1

Adaptive Antenna Systems 3B. Widrow, P. E. Mantey, L. J. Griffiths, and B. B. Goode (IEEE Proceedings, December 1967).Overview of Spatial Channel Models for Antenna Array Communication Systems 20R. B. Ertel, P. Cardieri, K. W. Sowerby, T. S. Rappaport, and J. H. Reed (IEEE Personal CommunicationsMagazine, February 1998).

Antenna Systems for Base Station Diversity in Urban Small and Micro Cells 33F. C. F. Eggers, J. Tcttgard, and A. M. Oprea (Journal on Selected Areas of Communication, September1993).

A Statistical Model for Angle of Arrival in Indoor Multipath Propagation 44Q. Spencer, M. Rice, B. Jeffs, and M. Jensen (IEEE Vehicular Technology Conference, May 1997).

Chapter 2 Adaptive Algorithms 49

Highlights of Statistical Signal and Array Processing 51A. Hero (IEEE Signal Processing Magazine, September 1998).Application of Antenna Arrays to Mobile Communications, Part II: Beamforming and Direction-of-ArrivalConsiderations 95

L. C. Godara (Proceedings of the IEEE, August 1997).High-Resolution Frequency-Wavenumber Spectrum Analysis 146J. Capon (Proceedings of the IEEE, August 1969).An Algorithm for Linearly Constrained Adaptive Array Processing 157O. L. Frost III(Proceedings of the IEEE, August 1972).The Application of Spectral Estimation Methods to Bearing Estimation Problems 167D. H. Johnson (Proceedings of the IEEE, September 1982).On Spatial Smoothing for Direction-of-Arrival Estimation of Coherent Signals 178T-J. Shan, M. Wax, and T. Kailath (IEEE Transactions on Acoustics, Speech, and Signal Processing, August1985).

Detection of Signals by Information Theoretic Criteria 184M. Wax and T. Kailath (IEEE Transaction on Acoustics, Speech, and Signal Processing, April 1985).Multiple Emitter Location and Signal Parameter Estimation 190R. O. Schmidt (IEEE Transactions on Antennas and Propagation, March 1986).Using Spectral Estimation Techniques in Adaptive Processing Antenna Systems 195W. F. Gabriel (IEEE Transactions on Antennas and Propagation, March 1986).Implementation of Adaptive Array Algorithms 205R. Schreiber (IEEE Transactions on Acoustics, Speech, and Signal Processing, October 1986).

v

Contents

Steady State Analysis of the Generalized Sidelobe Canceller by Adaptive Noise CancellingTechniques 213

N. K. Jablon (IEEE Transactions on Antennas and Propagation, March 1986).Adaptive-Adaptive Array Processing 221E. Brookner and J. M. Howell (Proceedings of the IEEE, April 1986).ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques 224R. Roy and T. Kailath (IEEE Transactions on Acoustics, Speech, and Signal Processing, July 1989).Spectral Self-Coherence Restoral: A New Approach to Blind Adaptive Signal Extraction Using AntennaArrays 236

B. G. Agee, S. V. Schell, and W. A. Gardner (Proceedings of the IEEE, April 1990).Sensor Array Processing Based on Subspace Fitting 250M. Viberg and B. Ottersten (IEEE Transactions on Signal Processing, May 1991).Direction-of-Arrival Estimation via Exploitation of Cyclostationarity-A Combination of Temporal andSpatial Processing 261

G. Xu and T. Kailath (IEEE Transactions on Signal Processing, July 1992).Space-Alternating Generalized Expectation Maximization Algorithm 272J. A. Fessler and A. O. Hero (IEEE Transactions on Signal Processing, October 1994).Unitary ESPRIT: How to Obtain Increased Estimation Accuracy with a Reduced ComputationalBurden 286

M. Haardt and J. A. Nossek (IEEE Transactions on Signal Processing, May 1995).Joint Angle and Delay Estimation (JADE) for Multipath Signals Arriving at an Antenna Array 297M. C. Vanderveen, C. B. Papadias, and A. Paulraj (IEEE Communications Letters, January 1997).

Chapter 3 Performance Issues 301

Smart Antennas for Mobile Communication Systems: Benefits and Challenges 303G. V. Tsoulos (Electronics & Communication Engineering Journal, April 1999).An Adaptive Array in a Spread-Spectrum Communication System 314R. T. Compton, Jr. (Proceedings of the IEEE, March 1978).On the Performance of a Polarization Sensitive Adaptive Array 324R. T. Compton, Jr. (IEEE Transactions on Antennas and Propagation, September 1981).Effect of Mutual Coupling on the Performance of Adaptive Arrays 332I. J. Gupta and A. A. Ksienski (IEEE Transactions on Antennas and Propagation, September 1983).Optimum Combining in Digital Mobile Radio with Co-channel Interference 339J. H. Winters (IEEE Transactions on Vehicular Technology, August 1984).On Optimum Combining at the Mobile 351R. G. Vaughan (IEEE Transactions on Vehicular Technology, November 1988).The Performance of an LMS Adaptive Array with Frequency Hopped Signals 359L. Acar and R. T. Compton, Jr. (IEEE Transactions on Aerospace and Electronic Systems, May 1985).An LMS Adaptive Array for Multipath Fading Reduction 371Y. Ogawa, M. Ohmiya, and K. Itoh (IEEE Transactions on Aerospace and Electronic Systems, January1987).

Optimum Combining for Indoor Radio Systems with Multiple Users 378J. H. Winters (IEEE Transactions on Communications, November 1987).The Performance Enhancement of Multibeam Adaptive Base-Station Antennas for Cellular Land MobileRadio Systems 387

S. C. Swales, M. A. Beach, D. J. Edwards, and J. P. McGeehan (IEEE Transactions on VehicularTechnology, February 1990).

Combination of an Adaptive Array Antenna and a Canceller of Interference for Direct-Sequence Spread-Spectrum Multiple-Access System 399

R. Kohno, H. Imai, M. Hatori, and S. Pasupathy (IEEE Journal on Selected Areas in Communications, May1990).

Direction Finding in the Presence of Mutual Coupling 406B. Friendlander and A. J. Weiss (IEEE Transactions on Antennas and Propagation, March 1991).

vi

Contents

Improving the Performance of a Slotted ALOHA Packet Radio Network with an Adaptive Array 418J. Ward and R. T. Compton, Jr. (IEEE Transactions on Communications, February 1992).Signal Acquisition and Tracking with Adaptive Arrays in the Digital Mobile Radio System IS-54 with FlatFading 427

J. H. Winters (IEEE Transactions on Vehicular Technology, November 1993).Effect of Fading Correlation on Adaptive Arrays in Digital Mobile Radio 435J. Salz and J. H. Winters (IEEE Transactions on Vehicular Technology, November 1994).Capacity Improvement with Base-Station Antenna Arrays in Cellular CDMA 444A. F. Naguib, A. Paulraj, and T. Kailath (IEEE Transactions on Vehicular Technology, August 1994).Analytical Results for Capacity Improvements in COMA 452J. C. Liberti and T. S. Rappaport (IEEE Transactions on Vehicular Technology, August 1994).Adaptive Transmitting Antenna Arrays with Feedback 463D. Gerlach and A. Paulraj (IEEE Signal Processing Letters, October 1994).Adaptive Antennas for Third Generation DS-CDMA Cellular Systems 466G. V. Tsoulos, M. A. Beach, and S. C. Swales (Proceedings of 45th Vehicular Technology Conference, July1995).

The Spectrum Efficiency of Base Station Antenna Array System for Spatially SelectiveTransmission 471

P. Zetterberg and B. Ottersten (IEEE Transactions on Vehicular Technology, August 1995).Capacity Enhancement and BER in a Combined SDMA/TDMA System 481J. Fuhl and A. F. Molisch (Proceedings of the 46th Vehicular Technology Conference, April 1996).Performance of Wireless CDMA with M-ary Orthogonal Modulation and Cell Site AntennaArrays 486

A. F. Naguib and A. Paulraj (IEEE Journal of Selected Areas in Communications, December 1996).Smart Antenna Arrays for CDMA Systems 500J. S. Thompson, P. N. Grant, and B. Mulgrew (IEEE Personal Communications Magazine, October 1996).Efficient Direction and Polarization Estimation with a COLD Array 510J. Li, P. Stoica and D. Zheng (IEEE Transactions on Antennas and Propagation, April 1996).Upper Bounds on the Bit-Error Rate of Optimum Combining in Wireless Systems 519J. H. Winters and J. Salz (IEEE Transactions on Communications, December 1998).The Range Increase of Adaptive Versus Phased Arrays in Mobile Radio Systems 525J. H. Winters and M. J. Gans (IEEE Transactions on Vehicular Technology, March 1999).A Comparison of Two Systems for Downlink Communication with Base Station Antenna Arrays 535P. Zetterberg (IEEE Transactions on Vehicular Technology, September 1999).

Chapter 4 Implementation Issues 551

Fundamentals of Digital Array Processing 553D. E. Dudgeon (Proceedings of the IEEE, June 1977).A Novel Algorithm and Architecture for Adaptive Digital Beamforming 560C. P. Ward, P. J. Hargrave, and J. G. McWhirter (IEEE Transactions on Antennas and Propagation, March1986).

Nonlinearities in Digital Manifold Phased Arrays 569B. D. Mathews (IEEE Transactions on Antennas and Propagation, November 1986).Adaptive Beamforming with the Generalized Sidelobe Canceller in the Presence of ArrayImperfections 579

N. K. Jablon (IEEE Transactions on Antennas and Propagation, August 1986).An Efficient Algorithm and Systolic Architecture for Multiple Channel Adaptive Filtering 596S. M. Yuen, K. Abend, and R. S. Berkowitz (IEEE Transactions on Antennas and Propagation, May 1988).Mutual Coupling Compensation in Small Array Antennas 603H. Steyskal and J. S.Herd (IEEE Transactions on Antennas and Propagation, December 1995).A Unified Approach to the Design of Robust Narrow-Band Antenna Array Processors 607M-H. Er and A. Cantoni (IEEE Transactions on Antennas and Propagation, January 1990).

vii

Contents

Design Trades for Rotman Lenses 614R. C. Hansen (IEEE Transactions on Antennas and Propagation, April 1991).Optimum Networks for Simultaneous Multiple Beam Antennas 623E. C. DuFort (IEEE Transactions on Antennas and Propagation, January 1992).Direction Finding in Phased Arrays with a Neural Network Beamformer 630H. L. Southall, J. A. Simmers, and T. H. O'Donnell (IEEE Transactions on Antennas and Propagation,December 1995).

Application of Orthogonal Codes to the Calibration of Active Phased Array Antennas for CommunicationSatellites 636

S. D. Silverstein (IEEE Transactions on Signal Processing, January 1997).The Analogy Between the Butler Matrix and the Neural-Network Direction-Finding Array 649R. J. Mailloux and H. L. Southall (IEEE Antennas and Propagation Magazine, December 1997).Forward-Backward Averaging in the Presence of Array Manifold Errors 655M. Zatman and D. Marshall (IEEE Transactions on Antennas and Propagation, November 1998).

Chapter 5 Experiments 661

Multiple Source DF Signal Processing: An Experimental System 663R. O. Schmidt and R. E. Franks (IEEE Transactions on Antennas and Propagation, March 1986).An Implementation of a CMA Adaptive Array for High Speed GMSK Transmission in MobileCommunications 673

T. Ohgane, T. Shimura, N. Matsuzawa, and H. Sasaoka (IEEE Transactions on Vehicular Technology,August 1993).

A Four-Element Adaptive Antenna Array for IS-136 PCS Base Stations 680R. L. Cupo, G. D. Golden, C. C. Martin, K. L. Sherman, N. R. Sollenberger, J. H. Winters, and P. W.Wolniasky (IEEE 46th Vehicular Technology Conference, May 1996).

Ericsson/Mannesmann GSM Field-Trials with Adaptive Antennas 685S. Anderson, U. Forssen, J. Karlsson, T. Witzschel, P. Fischer, and A. Krug (IEEE 46th VehicularTechnology Conference, May 1996).

Preliminary Measurement Results from an Adaptive Antenna Array Testbed for GSM/UMTS 690P. E. Mogensen, K. I. Pedersen, P. Leth-Espensen, B. Fleury, F. Frederiksen, K. Olesen, and S. L. Larsen(IEEE Vehicular Technology Conference, May 1997).

Performance Evaluation of a Cellular Base Station Multibeam Antenna 695Y. Li, M. Feuerstein, and D. O. Reudink (IEEE Transactions on Vehicular Technology, February 1997).Space Division Multiple Access (SDMA) Field Trials. Part 1: Tracking and BER Performance 704G. V. Tsoulos, J. McGeehan, and M. Beach (lEE Proceedings of Radar, Sonar, and Navigation, February1998).

Space Division Multiple Access (SDMA) Field Trials. Part 2: Calibration and Linearity Issues 710G. V. Tsoulos, J. McGeehan, and M. Beach (lEE Proceedings of Radar, Sonar, and Navigation, February1998).

Chapter 6 Applications and Planning Issues 717

High Data Rate Indoor Wireless Communications Using Antenna Arrays 719M. J. Gans, R. A. Valenzuela, J. H. Winters, and M. J. Carloni (6th International Symposium on Personal,Indoor and Mobile Radio Communications, September 1995).

On Optimizing Base Station Antenna Array Topology for Coverage Extension in Cellular RadioNetworks 726

J-W. Liang and A. J. Paulraj (IEEE 45th Vehicular Technology Conference, July 1995).Usage of Adaptive Arrays to Solve Resource Planning Problems 731M. Frullone, P. Grazioso, C. Passerini, and G. Riva (Proceedings of the 46th Vehicular TechnologyConference, April 1996).

viii

Contents

Subscriber Location in CDMA Cellular Networks 735J. Caffery, Jr. and G. L. Stuber (IEEE Transactions on Vehicular Technology, May 1998).On the Capacity Formula for Multiple Input-Multiple Output Wireless Channels: A GeometricInterpretation 745

P. F. Driessen and G. J. Foschini (IEEE Transactions on Communications, February 1999).Optimum Space-Time Processors with Dispersive Interference: Unified Analysis and Required FilterSpan 749

S. L. Ariyavisitakul, J. H. Winters, and I. Lee (IEEE Transactions on Communications, July 1999).

Author Index 761

Subject Index 763

ix

Preface

O VER the last few years, the demand for service provi-sion via the wireless communication bearer has risenbeyond all expectations. This fact introduces one of themost demanding technological challenges: the need to in-crease the spectrum efficiency of wireless networks.Whereas great effort until today has been focused towardthe development of modulation methods, coding tech-niques, communication protocols, and so forth, the an-tenna-related technology has received significantly less at-tention up to now. Nevertheless, in order to achieve theambitious requirements introduced for future wireless sys-tems, new "intelligent" or "self-configured" and highlyefficient systems will most certainly be required. In thepursuit for schemes that will solve these problems, atten-tion has recently turned to spatial filtering methods usingadvanced antenna techniques: adaptive or "smart" anten-nas. Filtering in the space domain can separate spectrallyand temporally overlapping signals from multiple mobileunits, and hence the spatial dimension can be exploited as ahybrid multiple access technique complementing the basicunderlying multiple access technique.Adaptive antennas have been studied for many years by

the sonar and radar research communities as interference-resistant aids (the first known case of an adaptive antennadates back to 1959: L. C. Van Atta, Electromagnetic Reflec-tion, U.S. Patent 29080002, October 6, 1959), and theirmain application until recently has been military. Advancesin processor cost and speed have only recently made itpossible to overcome the major obstacle of hardware costand complexity and start considering the possibility ofapplying this technique to commercial communications.This book targets a very wide audience. It can be used

as a reference source (e.g., in conjunction with other textson signal processing, antennas, mobile communications)for students at the undergraduate and/or postgraduatelevel, academics, researchers, professionals, and managerswho either are specifically interested or want to understandgeneral aspects of this technology. In order to achievethese goals, a large number of published works on a varietyof issues related to adaptive antennas have been gathered.The papers included in this volume, along with the citedreferences, constitute a very detailed source of informationdealing with almost all the important issues related to this

technology. The key areas are separated in six chapters

as follows:

Chapter 1: One introductory paper that provides impor-tant background information on adaptive antennas, fol-lowed by three papers with the channel models necessaryfor simulations and material dealing with the spatialcharacteristics of the radio channel for different opera-tional environments.

Chapter 2: Nineteen papers with the most representa-tive, widely used and researched adaptive methods andalgorithms such as MUSIC, ESPRIT, and SAGE.

Chapter 3: Twenty-seven papers dealing with the issuethat has attracted most of the attention in terms of re-search up to now, the performance of adaptive antennaswith different adaptive methods and algorithms undera variety of conditions in mobile communication envi-ronments.

Chapter 4: Thirteen papers dealing with implementationissues for adaptive antennas: beamforming techniques,calibration, mutual coupling, nonlinearity problems, andso forth.

Chapter 5: Eight papers presenting experimental resultsfor issues related to this technology, mainly from adap-tive antenna test beds.

Chapter 6: Six papers that deal with more general issuesrelated to adaptive antennas such as specific applicationsfor user location, indoor wireless high data rate net-works, planning issues for adaptive antennas, and noveltechniques that seem promising to open new directionsfor this technology in the future.

The work included in the different chapters is sortedchronologically except for papers that present overviewsor comparisons for the issues of focus in a chapter. Thelatter are always at the beginning of the chapter.I sincerely hope that you find this source of reference

useful. If it manages to stimulate you and as a result opensnew horizons for you in this very exciting and promisingarea, then it will have succeeded in its purpose.

George V. Tsoulos

xi

Chapter One

Introduction and Channel Models

A DAPTIVE antenna arrays have long been an attrac-tive solution to a plethora of problems related tosignal detection and estimation. An array of antenna ele-ments can overcome the directivity and beamwidth limita-tions of a single antenna element, and when it is combinedwith methods from statistical detection and estimation andcontrol theory, a self-adjusting or adaptive system emerges.This key capability was recognized in 1967 by Widrow andhis colleagues in their publication in the IEEE Proceedings,with which this book opens. This paper offers a valuableintroduction to the adaptive antenna concepts.A smart antenna system relies heavily on the spatial

characteristics of the operational environment to improvethe output signal. In order to study the performance of

adaptive algorithms in radio operational environments(Chapters 2 and 3), it is essential to employ suitable channelmodels that provide both spatial and temporal information.For that reason, three papers are included in this chapter.There is still a lot of work to be done in terms of character-izing the radio channel and producing propagation modelscapable of providing all the information needed to effi-ciently study wideband systems that also exploit the spatialdimension. This need was recently underlined by the inter-national standardization organisations, and several re-search activities are already under way (e.g., subgroup onspatial propagation models of the COST-EuropeanUnion Forum for Cooperative Scientific Research-Action 259).

Adaptive Antenna SystemsB. WIDROW, MEMBER, IEEE, P. E. MANTEY, MEMBER, IEEE, L. J. GRIFFITHS,

STUDENT MEMBER, IEEE, AND B. B. GOODE, STUDENT MEMBER, IEEE

Ahstract-A system consisting of an antenna array and an adaptiveprocessor can perform filtering in both the space and the frequency domains,

thus reducing the sensitivity of the signal-receiving system to interfering

directional noise sources.Variable weights of a signal processor can be automatically adjusted by a

simple adaptive technique based on the least-mean-squares (LJ\lS) algorithm.During the adaptive process an injected pilot signal simulates a received signalfrom a desired "Iook' direction. This allows the array to be "trained" sothat its directivity pattern has a main lobe in the previously specified look

direction. At the same time, the array processing system can reject anyincident noises, whose directions of propagation are different from the

desired look direction, by forming appropriate nulls in the antenna directivity

pattern. The array adapts itself to fonn a main lobe, with its direction and

bandwidth determined by the pilot signal, and to reject signals or noisesoccurring outside the main lobe as well as possible in the minimum mean-square error sense.

Several examples illustrate the convergence of the L~IS adaptationprocedure toward the corresponding Wiener optimum solutions. Rates of

adaptation and misadjustments of the solutions are predicted theoretically

and checked experimentally. Substantial reductions in noise reception are

demonstrated in computer-simulated experiments. The techniques describedare applicable to signal-reech'ing arrays for use over a wide range of fre-

quencies.

INTRODUCTIO~

T HE SENSITIVITY of a signal-receiving array to. interfering noise sources can be reduced by suitableprocessing of the outputs of the individual array ele-ments. The combination of array and processing acts as afilter in both space and frequency. This paper describes amethod of applying the techniques of adaptive filtering! I}to the design of a receiving antenna system which can extractdirectional signals from the medium with minimum dis-tortion due to noise. This system will be called an adaptivearray. The adaptation process is based on minimization ofmean-square error by the LMS algorithm.[2 1- [-+] Thesystem operates with knowledge of the direction of arrivaland spectrum of the signal, but with no knowledge of thenoise field. The adaptive array promises to be useful when-ever there is interference that possesses some degree ofspatial correlation ~ such conditions manifest themselvesover the entire spectrum, from seismic to radar frequencies.

Manuscript received May 29. 1967; revised September 5, 1967.B. Widrow and L. J. Griffiths are with the Department of Electrical

Engineering, Stanford University, Stanford, Calif.

P. E. Mantey was formerly with the Department of Electrical Engineer-ing, Stanford University. He is presently with the Control and DynamicalSystems Group, IBM Research Laboratories, San Jose. Calif.

B. B. Goode is with the Department of Electrical Engineering, Stan-ford University, Stanford, Calif., and the Navy Electronics Laboratory,San Diego, Calif.

The term "adaptive antenna" has previously been usedby Van Atta[5] and others!"! to describe a self-phasing an-tenna system which reradiates a signal in the direction fromwhich it was received. This type of system is called adaptivebecause it performs without any prior knowledge of thedirection in which it is to transmit. For clarity, such a sys-tern might be called an adaptive transmittinq array: whereasthe system described in this paper might be called an adap-tive receiving array.The term "adaptive filter" has been used by Jakowatz,

Shuey, and White[7] to describe a systern which extracts anunknown signal from noise, where the signal waveformrecurs frequently at random intervals. Davisson!"! hasdescribed a method for estimating an unknown signal wave-form in the presence of white noise of unknown variance.Glaser!"! has described an adaptive system suitable for thedetection of a pulse signal of fixed but unknown waveform,

Previous work on array signal processing directly relatedto the present paper was done by Bryn. Merrnoz, and Shor.The problem of detecting Gaussian signals in additiveGaussian noise fields was studied by Bryn, (lOl who showedthat. assuming K antenna elements in the array, the Bayesoptimum detector could be implemented by either K2 linearfilters followed by "conventional" beam-forming for eachpossible signal direction, or by K linear filters for eachpossible signal direction. In either case, the measurementand inversion of a 2K by 2K correlation matrix was requiredat a large number of frequencies in the band of the signal.Merrnoz! 11] proposed a similar scheme for narrowbandknown signals, using the signal-to-noise ratio as a perfor-mance criterion. Shor[l:!] also used a signal-to-noise-ratiocriterion to detect narrowband pulse signals. He proposedthat the sensors be switched off when the signal was knownto be absent, and a pilot signal injected as if it were a noise-free signal impinging on the array from a specified direction.The need for specific matrix inversion was circumventedby calculating the gradient of the ratio between the outputpower due to pilot signal and the output power due tonoise, and using the method of steepest descent. At the sametime, the number of correlation measurements required wasreduced, by Shor's procedure, to 4K at each step in theadjustment of the processor. Both Mermoz and Shor havesuggested the possibility of real-time adaptation.

This paper presents a potentially simpler scheme for ob-taining the desired array processing improvement in realtime. The performance criterion used is minimum mean-square error. The statistics of the signal are assumed

Reprinted from IEEE Proceedings, \'01 55, No. 12, pp. 2143-2159, December 1967.

3

to be known, but no prior knowledge or direct measure-ments of the noise field are required in this scheme. Theadaptive array processor considered in the study may beautomatically adjusted (adapted) according to a simpleiterative algorithm, and the procedure does not directlyinvolve the computation of any correlation coefficients orthe inversion of matrices. The input signals are used onlyonce, as they occur, in the adaptation process. There is noneed to store past input data; but there is a need to store theprocessor adjustment values, i.e., the processor weightingcoefficients C4weigh ts" ). Methods of adaptation are pre-sented here, which may be implemented with either analogor digital adaptive circuits, or by digital-computer realiza-tion.

in which

wfo = frequency of received signal;"0 = wavelength at frequency j~b = time-delay difference between neighboring-element

outputsd = spacing between antenna elementsc = signal propagation velocity = ;"oj~.

The sensitivity is maximum at angle t/J because signals re-ceived from a plane wave source incident at this angle" anddelayed as in Fig. l(b), are in phase with one another andproduce the maximum output signal. For the exampleillustrated in the figure, d=A.o/2, 5=(0.12941/j~), and there-fore t/!=sin- 1 (25/0)= 15.There are many possible configurations for phased arrays.

Fig. 2(a) shows one such configuration where each of theantenna-element outputs is weighted by two weights inparallel, one being preceded by a time delay of a quarter of

DIRECTIONAL AND SPATIAL FILTERING

An example ofa linear-array receiving antenna is shown inFig. l(a) and (b). The antenna of Fig. l(a) consists of sevenisotropic elements spaced ;"0/2 apart along a straight line,where i..o is the wavelength of the center frequency j~ ofthe array. The received signals are summed to produce anarray output signal. The directivity pattern.. i.e., the relativesensitivity of response to signals from various directions,is plotted in this figure in a plane over an angular range of-n/2 < f) < rc/2 for frequency J~. This pattern is symmetricabout the vertical line 8= o. The main lobe is cen tered at() = O. The largest-amplitude side lobe.. at V= 24 . has amaximum sensitivity which is 12.5 dB below the maximummain-lobe sensitivity. This pattern would be different if itwere plotted at frequencies other than f~.The same array configuration is shown in Fig. ltb): how-

ever.. in this case the output of each element is delayed intime before being summed. The resulting directivity pattern.now has its main lobe at an angle of'" radians.. where

(3)

For this output to be equal to the desired output of p(t)=Psin wot (which is the pilot signal itself), it is necessary that

a cycle at frequency j~ (i.e., a 90 phase shift), denoted by1/(4/0}. The output signal is the sum of all the weightedsignals, and since all weights are set to unit values, the direc-tivity pattern at frequency fo is by symmetry the same as thatof Fig. l(a). For purposes of illustration, an interferingdirectional sinusoidal "noise" of frequency wfo incident onthe array is shown in Fig. 2(a), indicated by the dottedarrow. The angle of incidence (45.5) of this noise is suchthat it would be received on one of the side lobes of thedirectivity pattern with a sensitivity only 17 dB less thanthat of the main lobe at 0=0.

If the weights are now set as indicated in Fig. 2(b)., thedirectivity pattern at frequency j~ becomes as shown in thatfigure. In this case, the main lobe is almost unchanged fromthat shown in Figs. l(a) and 2(a), while the particular sidelobe that previously intercepted the sinusoidal noise inFig. 2(a) has been shifted so that a null is now placed in thedirection of that noise. The sensitivity in the noise directionis 77 dB below the main lobe sensitivity, improving the noiserejection by 60 dB.A simple example follows which illustrates the existence

and calculation of a set of weights which will cause a signalfrom a desired direction to be accepted while a "noise froma different direction is rejected. Such an example is illus-trated in Fig. 3. Let the signal arriving from the de-sired direction 0= 0 be called the "pilot" signal p( t)=Psin wot., where Wo~ 2rrj~, and let the other signal. the noise,be chosen as n(l)=N sin ((Jot, incident to the receiving arrayat an angle 0= rt/6 radians. Both the pilot signal and thenoise signal are assumed for this example to be at exactlythe same frequency .f~. At a point in space midway betweenthe antenna array elements, the signal and the noise areassumed to be in phase. In the example shown, there aretwo identical omnidirectional array elements. spaced i~o/2apart. The signals received by each element are fed to twovariable weights., one weight being preceded by a quarter-wave time delay of 1/(4j~). The four weighted signals arethen summed to form the array output.The problem of obtaining a set of weights to accept p(t)

and reject net) can now be studied. Note that with any setof nonzero weights, the output is of the form A sin (wa t+4,and a number of solutions exist which will make the outputbe p(t). However, the output of the array must be indepen-dent of the amplitude and phase of the noise signal if thearray is to be regarded as rejecting the noise. Satisfaction ofthis constraint leads to a unique set ofweights determined asfollows.The array output due to the pilot signal is

( 1). - 1 (;~oc5j~) . -1 (C6)'~ = SID -- = sIn -d d

4

"S NOSES~RECTION/(NOISE AT FRED. t.)

.....- - 1 233.... ... - 0 18 2""10=-- 1.6 10'* 11 - 0 266w1z - 1 5 19'IIIII[] _ -0999....\. - - I 255

LOOKDIRECTION

o

DIRECTIVITYPATTERN

W, ""' 0 .099w:t- - 1.255w]= - 0 266.....4 =- I 51 8""",""' 0 . 18 2w. ~- I 6 10w.," O.OCX>

I bl

ANTENNAELEMENTS

/\d \

o,

I a)

Fig . I . Dir ecti vit y pattern fo r a linea r a rray . (a ) Simple a rray .(0 ) Delays added .

Fig. 2. Direct ivity pa ttern o f linea r a rray . (a ) With equal weighting.(b ) With weighting fo r noise elimina tio n.

/

/ 'NOISE"/ n(t )=NSl n( )..1/I

/--K /I 6 ;.'i i

"PILOT" SIGNAL lp(t)=PSltlw..t

'-------ot~f~TFig. 3. Array confi guration for noise elimination example.

5

With respect to the midpoint between the antenna ele-ments, the relative time delays of the noise at the two an-tenna elements are [1/(4fo)]sin n/6= 1/(810)= Ao/(8c),which corresponds to phase shifts of n/4 at frequency.fo .The array output due to the incident noise at () = n/6 is then

N [WI sin (root -~) +W2sin (root - 34n)+ W3 sin (root + ~) + W4 sin (wot - ~)] (4)

For this response to equal zero, it is necessary that

(5)Fig . 4. Adaptive array configuration for receiving narrowband signals .

Thus the set of weights that satisfies the signal and noiseresponse requirements can be found by solving (3) and (5)simultaneously. The solution is

(6)

With these weights, the array will have the desired proper-ties in that it will accept a signal from the desired direction.while rejecting a noise, even a noise which is at the samefrequency 10 as the signal, because the noise comes from adifferent direction than does the signal.The foregoing method of calculating the weights is more

illustrative than practical. This method is usable when thereare only a small number of directional noise sources, whenthe noises are monochromatic, and when the directions ofthe noises are known a priori. A practical processor shouldnot require detailed information about the number and thenature of the noises. The adaptive processor described inthe following meets this requirement. It recursively solvesa sequence of simultaneous equations. which are generallyoverspecified, and it finds solutions which minimize themean-square error between the pilot signal and the totalarray output.

CONFIGURAnONS OF ADAPTIVE ARRAYS

Before discussing methods of adaptive filtering and signalprocessing to be used in the adaptive array, various spatialand electrical configurations of antenna arrays will beconsidered. An adaptive array configuration for processingnarrowband signals is shown in Fig. 4. Each individualantenna element is shown connected to a variable weightand to a quarter-period time delay whose output is inturn connected to another variable weight. The weightedsignals are summed, as shown in the figure. The signal,assumed to be either monochromatic or narrowband, isreceived by the antenna element and is thus weighted by acomplex gain factor AeP. Any phase angle

where n is the number of weights: or, using vector notation

The procedure should produce a given array gain in thespecified look direction while simultaneously nulling outinterfering noise sources.

Fig. 6 shows an adaptive signal-processing element. Ifthis element were combined with an output-signal quantizer,it would then comprise an adaptive threshold logic unit.Such an element has been called an "Adaline"[13] or athreshold logic unit (TLU).[141Applications of the adaptivethreshold element have been made in pattern-recognitionsystems and in experimental adaptive control sys-tems.[2],[3],[14j-[17]

In Fig. 6 the input signals xt(t), ... , xi(t), ... , xn(t) are thesame signals that are applied to the multiplying weightsWI' ... , Wi' ... , Wn shown in Fig. 4 or Fig. 5. The heavy linesshow the paths of signal flow; the lighter lines show func-tions related to weight-changing or adaptation processes.The output signal s(t) in Fig. 6 is the weighted sum

s lt)OUTPUT

d(t)DESIREDRESPONSE

Fig. 6. Basic adaptive element.

This signal is used as a control signal for the "weight ad-justment circuits" of Fig. 6.

Solving Simultaneous Equations

The purpose of the adaptation or weight-changing pro-cesses is to find a set of weights that will permit the outputresponse of the adaptive element at each instant of time tobe equal to or as close as possible to the desired response.For each input-signal vector XU), the error e(j) of (10)should be made as small as possible.Consider the finite set of linear simultaneous equations

(8)

(7)n

s(t) == L Xi(t)Wii==: 1

where W T is the transpose of the weight vector WTX(l) = d(l)WTX(2) = d(2)

(11)

WTX(N) = d(N)

where N is the total number of input-signal vectors; eachvector is a measurement of an underlying n-dimensionalrandom process. There are N equations, corresponding toN instants of time at which the output response values areof concern ~ there are n "unknowns," the n weight valueswhich form the components of W. The set of equations (11)will usually be overspecified and inconsistent, since in thepresent application, with an ample supply of input data, it isusual that N 11. [These equations did have a solution inthe simple example represented in Fig. 3. The solution isgiven in (6). Although the simultaneous equations (3) in thatexample appear to be different from (11), they are really thesame, since those in (3) are in a specialized form for the casewhen all inputs are deterministic sinusoids which can beeasily specified over all time in terms of amplitudes, phases,and frequencies.]When N is very large compared to n, one is generally

interested in obtaining a solution of a set of N equations[each equation in the form of (10)] which minimizes thesum of the squares of the errors. That is, a set of weights Wis found to minimize

and the signal-input vector is

For digital systems, the input signals are in discrete-timesampled-data form and the output is written

(9)

where the index j indicates the jth sampling instant.In order that adaptation take place, a "desired response"

signal., d(t) when continuous or dU) when sampled, must besupplied to the adaptive element. A method for obtainingthis signal for adaptive antenna array processing will bediscussed in a following section.The difference between the desired response and the out-

put response forms the error signal U):

(10)

N

L c;2U)j= I

(12)

7

When the input signals can be regarded as stationarystochastic variables, one is usually interested in finding a setof weights to minimize mean-square error. The quantity ofinterest is then the expected value of the square of the error,i.e., the mean-square error, given by

E[2(j)] 2. (13)

The set of weights that minimizes mean-square error canbe calculated by squaring both sides of (10) which yields

c; 2U)= d2(j) + WTX(j)XU)TW - 2dU)WTX(j) (14)and then taking the expected value of both sides of (14)

E[82U)] = E[d 2 + WTXU)XTU)JV - 2W TdU)XU)]= E[d2 ] + WT(x, (/). (18)

When the choice of the weights is optimized, the gradientis zero. Then

From (10)

The gradient estimate of(21) is unbiased, as will be shownby the following argument. For a given weight vector W(j),

V[r.(j)] = V[d(j) - WT(j)X(j)]

= - X(j).

the expected value of the gradient es timate is

E[V(j)J = - 2E[ ld(j) - WT(j)X(j)}X(j)J= - 2[$ (x , d) - WT(j )$(x, x )].

Comparing (18) and (22), we see th at

E[V(j)J = VE[I;2]

(22)

wE IGHTSETTING

d- W(f) = -2k,;;( )Xlt ).dt

and therefore, for a given weight vector. the expec ted valueo f the estimate eq ua ls the true va lue.

Using the grad ient es timation formula given in (2 1), th eweight iteration rule (20) becomes

WEIGHTSETT ING

( b )" It )

ERRORSlGNAL

Fig . 7, Bloc k d iag ra m rep resentat ion or LMS a lgo rith m.(a) Digital rea lization, (b) Ana log real iza tio n,

' . o--- _-{/}-- - -"'

,,--- - --{ /}-- '-----.,.

(23)W(j + I ) = W(j) - 2k,l;(j)X(j)

and th e next weight vecto r is obtai ned by adding to th epresent weight vect or the input vector sca led by th e valueof the error.The LMS a lgo rithm is given by (23). It is d irectl y usable

as a weight-adaptation formula for digital sys tems. Fig.7(a) shows a block-diagram represe n ta tio n of thi s eq ua tionin terms of one component lV i o f the weight vector W. Aneq uiva len t diffe rent ial equation which can be used inanalog implementation of continuo us sys tems (see Fig. 7(b))is given by

This equat ion can a lso be writt en as

J

O t

WIt) = - 21\, 1 ;1~)Xf~J d~ .o

d=OESlRED.RESPONSE .SIGNAL

Fig . x. Anulog d igita l rmplcmentution of L7vlSweig ht-adjustment a lgo rithm.

F ig. S sho ws how ci rc ui try of the type indi ca ted in Fig.7(a) o r tb ) might be inco rpora ted into the implementa tionof the ba sic adaptive element o f Fig. 6.

E[Wlj + I I] = [ I + ~k ,$\ s..,,}] j - ln/ (Ol1

- 2k, L: [ I + 2k ,$(s. S)T$(s. d) .i = 0

(~ 5 )

$\ s . s l = Q- I EQ

Equati on (25) ma y be put in di agon al form by using theappropriate similarity transformation Q for th e matri x$ (s. .x}, that is.

is th e diagon al matrix of eigen values. The eigenvalues area ll positi ve, since $ (x, x) is positive definite [ see (16)].Equat ion (25) may now be expressed as

= Q -t[! + 2k,E]i + I QW(O)j

- 2ksQ - I I [1 + 2ksE]iQ$(X, d). (26)i =O

oo

E[ WU + 1)] = [ I + 2k,Q - 1EQ]i+ tW(0)j

- 2k, I [I + 2ksQ - tEQJ I>(x, d)i = O

whe re

L' l 0

0 e ,E~

0 0

E[W(j + 1)]= E[ W( j)] - 2k,E[ :tI(j) - W /(j)X(j ))X(j )]= [I + 21-:,$ (.\: . .\: )]E[W(j)] - 2k,$( .\:. til (24)

Conterqence of the ,\1 l!all or the Pr'l!iyhr VeClvrFor the purpose of the following di scu ssion. we assume

that the time between successive iterations of the LMSa lgo rithm is sufficien tly lon g so that the sample inpu tvecto rs X(j ) and Xtj + I) are unco rrela ted , Thi s assumptio nis co mmon in the field of stocha stic approxi ma tion.1201-122]

Becau se the weigh t vecto r W(j) is a func tio n only of theinput vecto rs X(j-I ), X(j-2), " ' . XIO) [ see (23)J and be-ca use th e successive in put vectors are uncorrelat ed. W(j )is independent o f X(j). For sta tiona ry input pr ocessesmeeting thi s condition, the expected valu e E[W(j)] of theweight vecto r afte r a la rge number of ite ra tio ns can thenbe shown to conve rge to the Wiener so lution given by(19 ). Taking the ex pec ted va lue of bo th sides of (23). weobtain a difference eq ua tion in the expected va lue of theweight vector

where 1 is the identity matrix. With an initial weight vect orWID). j + I iterations o f (24) yield

9

where ep is the pth eigenvalue of the input-signal correlationmatrix (J)(x, x],In the special case when all eigenvalues are equal, all

time constants are equal. Accordingly,

It is the opinion of the authors that the assumption ofindependent successive input samples used in the fore-going convergence proof is overly restrictive. That is, con-vergence of the mean of the weight vector to the LMSsolution can be achieved under conditions of highly cor-related input samples. In fact, the computer-simulationexperiments described in this paper do not satisfy the con-dition of independence.

Time Constants and Learning Curve with LMS Adaptation

State-variable methods, which are widely used in moderncontrol theory, have been applied by Widrow!'! and Kofordand Gronerlf to the analysis of stability and time constants(related to rate of convergence) of the LMS algorithm. Con-siderable simplifications in the analysis have been realizedby expressing transient phenomena of the system adjust-ments (which take place during the adaptation process) interms of the normal coordinates of the system. As shown byWidrow, [1} the weight values undergo transients duringadaptation. The transients consist of sums of exponentialswith time constants given

(30)

(29)-1

" k, < o.I E[x?Ji= 1

1r= ,p=1~2~.np 2( - ks)ep

lim [1 + 2ksEJi+ 1 --+ 0i- 00

lim E[W(j + I)J= Q-1E-1Q(x, d))- 00

= (J) - 1(x, X )

Estimation of the rate of adaptation is more complex whenthe eigenvalues are unequal.When actual experimental learning curves are plotted,

they are generally of the form of noisy exponentials becauseof the inherent noise in the adaptation process. The slowerthe adaptation, the smaller will be the amplitude of thenoise apparent in the learning curve.

M isadjustment with Ll\1S Adaptation

All adaptive or learning systems capable of adapting atreal-time rates experience losses in performance becausetheir system adjustments are based on statistical averagestaken with limited sample sizes. The faster a system adapts.in general" the poorer will be its expected performance.When the LMS algorithm is used with the basic adaptive

element of Fig. 8, the expected level of mean-square errorwill be greater than that of the Wiener optimum systemwhose weights are set in accordance with (19). The longer thetime constants of adaptation" however" the closer the ex-pected performance comes to the Wiener optimum per-formance. To get the Wiener performance. i.e .. to achievethe minimum mean-square error. one would have to knowthe input statistics a priori, or. if (as is usual) these statisticsare unknown. they would have to be measured with anarbitrarily large statistical sample.When the LMS adaptation algorithm is used. an excess

mean-square error therefore develops. .A measure of theextent to which the adaptive system is rnisadjusted as com-pared to the Wiener optimum system is determined in aperformance sense by the ratio of the excess mean-squareerror to the minimum mean-square error. This dimension-less measure of the loss in performance is defined as the"misadjustrnent" AJ. For LMS adaptation of the basicadaptive element. it is shown by Widrow' 11 that

M " di 1 ~ 1isa justrnent ,\;f == ,. L _.- p= 1 Tp

(31)

ADAPTIVE SPATIAL FILTERING

If the radiated signals received by the elements of anadaptive antenna array were to consist of signal componentsplus undesired noise, the signal would be reproduced (andnoise eliminated) as best possible in the least-squares senseif the desired response of the adaptive processor were madeto be the signal itself. This signal is not generally availablefor adaptation purposes, however. If it were available,there would be no need for a receiver and a receiving array.

In the adaptive antenna systems to be described here.the desired response signal is provided through the use ofan artificially injected signal" the "pilot signal", which iscompletely known at the receiver and usually generatedthere. The pilot signal is constructed to have spectral anddirectional characteristics similar to those of the incomingsignal of interest. These characteristics may, in some cases,be known a priori but, in general, represent estimates of theparameters of the signal of interest.Adaptation with the pilot signal causes the array to

form a beam in the pilot-signal direction having essentiallyflat spectral response and linear phase shift within the pass-band of the pilot signal. Moreover. directional noisesimpinging on the antenna array will cause reduced arrayresponse (nulling) in their directions within their passbands.These notions are demonstrated by experiments which willbe described in the following.Injection of the pilot signal could block the receiver and

render useless its output. To circumvent this difficulty,two adaptation algorithms have been devised, the .... one-mode" and the "two-mode." The two-mode process alter-nately adapts on the pilot signal to form the beam and thenadapts on the natural inputs with the pilot signal off toeliminate noise. The array output is usable during the second1110de., while the pilot signal is off. The one-mode algorithmpermits listening at all times. but requires more equipmentfor its implementation.

The value of the rnisadjustment depends on the timeconstants (settling times) of the filter adjustment weights.Again. in the special case when all the time constants areequal, M is proportional to the number q( weights and in-versely proportional to the time constant. That is.

11A1 ==-

2r

n(32)

Although the foregoing results specifically apply tostatistically stationary processes, the LMS algorithm canalso be used with nonstationary processes. It is shown byWidrow[ 2 31that, under certain assumed conditions, the rateof adaptation is optimized when the loss of performanceresulting from adapting too rapidly equals twice the loss inperformance resulting from adapting too slowly.

The Two-Mode Adaptation Alqorithm

Fig. 9 illustrates a method for providing the pilot signalwherein the latter is actually transmitted by an antennalocated some distance from the array in the desired lookdirection. Fig. 10 shows a more practical method for pro-viding the pilot signal. The inputs to the processor are con-nected either to the actual antenna element outputs (during"mode II"), or to a set of delayed signals derived from thepilot-signal generator (during "mode 1'''). The filtersb l' ... , bK (ideal time-delays if the array elements are identi-cal) are chosen to result in a set of input signals identicalwith those that would appear if the array were actuallyreceiving a radiated plane-wave pilot signal from the de-sired "look" direction, the direction intended for the mainlobe of the antenna directivity pattern.

During adaptation in mode I, the input signals to theadaptive processor derive from the pilot signal, and thedesired response of the adaptive processor is the pilot signal

11

OUTPuT

Fig. 9. Adaptation with external pilot-signal generator. Mode I: adap-ration with pilot signal present ; Mode II : adaptation wah pilot signalabsent.

ANTENNASI ~-..,.-----l

\\\

)/

//

//

//

Fig. II. Single-mode adaptation with pilot signal.

of all signals received by the antenna elements which areuncorrelated with the pilot signals, subject to the constraintthat the gain and phase in the beam approximate predeter-mined values at the frequencies and angles dictated by thepilot-signal components.

The One-Mode Adaptation Algorithm

In the two-mode adaptation algorithm the beam isformed during mode L and the noises are eliminated in theleast-squares sense (subject to the pilot-signal constraints)in mode II. Signal reception during mode I is impossiblebecause the processor is connected to the pilot-signalgenerator. Reception can therefore take place only duringmode II. This difficulty is eliminated in the system of Fig.II. in which the actions of both mode [ and mode II can beaccomplished simultaneously. The pilot signals and thereceived signals enter into an auxiliarv. adaptive processor.just as des~ribed previously . For this processor. the desiredresponse is the pilot signal p(t ). A second weighted processor(linear element) generates the actual array output signal.but it performs no adaptation . Its input signals do not con-tain the pilot signal. It is slaved to the adaptive processorin such a way that its weights track the correspondingweights of the adapting system. so that it never needs toreceive the pilot signal.In the single-mode system of Fig. II. the pilot signal is on

continuously. Adaptation to minimize mean-square errorwill force the adaptive processor to reproduce the pilotsignal as closely as possible, and. at the same time. to rejectas well as possible (in the mean-square sense) all signals re-ceived by the antenna elements which are uncorrelated withthe pilot signal. Thus the adaptive process forces a directiv-ity pattern having the proper main lobe in the look directionin the passband of the pilot signal (satisfying the pilot sig-nal constraints), and it forces nulls in the directions of thenoises and in their frequency bands. Usually, the strongerthe noises , the deeper are the corresponding nulls.

COMPUTER SIMULATION OF ADAPTIVE ANTENNA SYSTEMS

To demonstrate the performance characteristics ofadaptive antenna systems, many simulation experiments,involving a wide variety of array geometries and signal-

, OUTPUT

!ERROR

MOOE n .~--_.

MOOE ;r DESIRED RESPONSEI : PILOT~-----_._- SIGNAL

GENERATCR

ADAPTIVE, """-----1 SIGNAL 1--...--.".."""1..----fS,t-

array output power due to signalSNR =

array output power due to noise

, Signal-to-noi se ratio is defined as

used . The pilot signal was a unit-amplitude sine wave(power = 0.5, frequency fo) which was used to train the arrayto look in the ()= 0 direction. The noise field consisted of asinusoidal noise signal (of the same frequency and power asthe pilot signal) incident at angle () = 40, and a smallamount of random, uncorrelated, zero-mean, "white"Gaussian noise of variance (power)=O.1 at each antennaelement. In this simulation, the weights were adapted usingthe LMS two-mode algorithm.

Fig. 13 shows the sequence of directivity patterns whichevolved during the "learning" process. These computer-plotted patterns represent the decibel sensitivity of the arrayat frequency fo. Each directivity pattern is computed fromthe set of weights resulting at various stages of adaptation.The solid arrow indicates the direction of arrival of theinterfering sine-wave noise source. Notice that the initialdirectivity pattern is essentially circular. This is due to thesymmetry of the antenna array elements and of the initialweight values. A timing indicator T, the number of elapsedcycles of frequency j~, is presented with each directivitypattern. The total number of adaptations equals 20T inthese experiments. Note that if j~ = I kl-lz, T = I corre-sponds to I ms real time : if j~= 1 MHz. T= 1 correspondsto I us. etc.Several observations can be made from the series of

directivity patterns of Fig . 13. Notice that the sensitivityof the array in the look direction is essentially constantduring the adaptation process. Also notice that the arraysensitivity drops very rapidly in the direction of the sinus-oidal noise source : a deep notch in the directivity patternforms in the noise direction as the adaptation processprogresses. After the adaptive transients died out. the arraysensitivity in the noise direction was '27 dB below that ofthe array in the desired look direction.The total noise power in the array output is the sum of the

sinusoidal noise power due to the directional noise sourceplus the power due to the "white" Gaussian. mutually un-correlated noise-input signals. The total noise power gener-ally drops as the adaptation process commences, until itreaches an irreducible level.A plot of the total received noise power as a function of

T is shown in Fig. 14. This curve may be called a "learningcurve." Starting with the initial weights, the total outputnoise power was 0.65, as shown in the figure. After adapta-tion. the total output noise power was 0.01. In this noisefield, the signal -to-noise ratio of the array! after adaptationwas better than that of a single isotropic receiving elementby a factor of about 60.A second experiment using the same array configuration

and the two-mode adaptive process was performed toinvestigate adaptive array performance in tile presence ofseveral interfering directional noise sources. In this exam-ple, the noise field was composed of five directional sinus-

r ..

r

.. ..,.

T_ 400 ~.. '

;- .. 30 0

T ~ I OO

o

o

9~o'I

i9 0!I+ - - -0 - - 9~90'

-DIRECTION OFSINUSQlQAL

NOISE

r

o

r

o

"

"

I. '

ANTENNA

~&----j

Fig. 12. Array configuration and processing fornarrowband experiments .

I b)

( 0 I

r-50

T- 4

T- 0 5

DESIRED"LOOK" DlRECOON '

' I .. - 40" .- ".

Fig . 13. Evolution of the directivity pattern while learning to eliminatea dirccuonal no ise and uncorrelatcd noises . (Array configuration ofFig . 12.) T= number of elapsed cycles of frequencyj., (total number ofadaptations = 20n.

and noise-field configurations, have been carried out usingan IBM 1620-11 computer equipped with a digital outputplotter.For simplicity of presentation, the examples outlined in

the following are restricted to planar arrays composed ofideal isotropic radiators . In every case, the LMS adaptationalgorithm was used . All experiments were begun with theinitial condition that all weight values were equal.

Narrowband Processor Experiments

Fig. 12 shows a twelve-clement circular array and signalprocessor which was used to demonstrate the performanceof the narrowband system shown in Fig. 4. In the first com-puter simulation, the two-mode adaptation algorithm was

13

1.0

a:O.B

~w!!l06oz

INITIAL NOISE POWER

DESIRED

'. r -. .....___" LOOK" DIRECTION. - :.-- "

\ 'J- RECTIONCF; - SlNUSC1DAL! ... NOISES

T- 150

...::>a.

~O.4o...J

~0.2

'.= - 0 0 0 25

T-IO'- --- T_300

40010 0 200 300TIME . T (cycles of f.)

oL_---I.-=========~o

Fig. 14. Learning curve for narrowband system of Fig . 12. withnoise from one direction onl y.

I(

T.50 0,.

TABLE I

SENSITIVITIES OF ARRAY IN DIRECTlO:-;S Of HIE FIVE :-JOISE SOl'R(,[~~OF FIG. 15. AFTER ADAPTATlo:-;

I '

NoiseDirectiontdegrecs )

NoiseFrequency(times 10 )

Array Sensitivity inNoise Direcuon , Relativeto Sensitivity in DesiredLook Directi on (dB)

T-70

( a)

T-682r-

This is a very low value of misadjustment, indicating a veryslow, precise adaptive process. This is evidenced by the

oidal noises , each of amplitude 0.5 and power 0.125. actingsimultaneously, and, in addition. superposed uncorrelated"white" Gaussian noises of power 0,5 at each of the an-tenna elements. The frequencies of the five directionalnoises are shown in Table 1.

Fig. 15(a) shows the evolution of the directivity pattern.plotted at frequency j ;j, from the initial conditions to thefinally converged (adapted) state. The latter was achievedafter 682 cycles of the frequency j~. The learning curve forthis experiment is shown in Fig . 15(b). The final arraysensitivities in the five noise directions relative to the arraysensitivity in the desired look direction are shown in Table 1.The signal-to-noise ratio was improved by a factor of aboutIS over that of a single isotropic radiator, In Fig. 15(b),one can roughly discern a time constant approximatelyequal to 70 cycles of the frequency fo. Since there were 20adaptations per cycle of j~, the learning curve time constantwas approximately 'mse = 1400 adaptations. Within about400 cycles of 10, the adaptive process virtually converges tosteady state. If fo were 1 MHz, 400 J1s would be the real-time settling time . The misadjustment for this process canbe roughly estimated by using (32), although actually alleigenvalues were not equal as required by this equation :

n 24 6M = -- = -- = -00 = 0.43 percent.

4rmse 4rmse 14

67134191236338

1.\00.951.00O.l)OI.OS

-26-30- 2S-30- .~X

Fiu, 15. Evolution of the direcriv uv pattern whr lc lcurrung III elim inate- live directional noise s and uncorrelutcd no ises. I.\rra~ configurationo f Fig . 12.) (a) Sequence of dircctiv ity patterns Juring adaptation.(b) Learning curve uotal number of adaptations = 20T) .

learning curve Fig. 15(b) for this experiment. which is verysmooth and noise-free.

Broadband Processor Experiments

Fig . 16 shows the antenna array configuration and signalprocessor used in a series of computer-simulated broad-band experiments. In these experiments, the one-mode orsimultaneous adaptation process was used to adjust theweights, Each antenna or element in a five-element circulararray was connected to a tapped delay line having fivevariable weights. as shown in the figure. A broadband pilotsignal was used, and the desired look direction was chosen(arbitrarily, for purposes of example) to be ()= - 13 . Thefrequency spectrum of the pilot signal is shown in Fig.17(a). This spectrum is approximately one octave wideand is centered at frequency lo. A time-delay increment of

I /(4j~) was used in the tapped delay line, thus providing adelay between adjacent weights of a quarter cycle at fre-

14

2.0

1.6

a::...~ 1.2

25 50 75 10 0TIME . T (cycles of f.)

0.0

...'"g

~ O.80.....(5

( 0 I

19=0'-\~. r

II-0-"I -,

I ;q-, rA I. , I,,,,0 '

lJf:SlREDLOOK

DIRECTION

10 I

2.0

Fig. 16. Array configura tion and processing for broadband experiments.(a) Array geometry. (b) Ind ividu al d ement signa l processor.

1.6

a:~:r 12...'"6z....0 8~:0o k

l== - 0 .00025

0 .0

02

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9- - 13' ' 8 - 0 '

250 500 750 1000TIME. T (cyCles 01 t.l

JESrRED_OOK

DIRECTION

10 )

( b )

F ig. 18. Learning. curves for broa d band experiments. ta ) Rapidlearni ng 1.\1= 13 percent ). (b l Slow lea rmng IM = 1.3 percent ).

.PILOT SIGNALAT - i ,3-

0L..L-_ _ ..J,---:>....~2----:-3- ---:.RELATIVE FREOUENCY. f I I.

1.

0

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.J 06

~ Iinw

~ 0 .4"...wa:

10 )

' 0

0 8

a::

~0 6

w'"6zw

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0.2

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SPECTRUM OF NOiSEINCIDENT AT - 70

SPECTRUM OF NOISEINCIDENT AT 50'

I 2 3RELATI VE FREOUENCY, f / f.

4

DESIRED 8--13'LOOK

DIRECTION-

Fig. 19. Comparison o r optimum broadband dire ctivity pattern withexperimental pattern after former has been adapted during 625 cycleso r .I~ . (Plo tted at frequency fo ') (a ) Optimum pattern. (b) Adaptedwith k , = -0.00025.

Fig. 17. Frequency spect ra to r br oadband experiments. (a I Pilot signa la t 0= - 13 ' . (b) Incid ent noises at 0= 50 ' and 0= - 70 '

15

quency 10, and a total delay-line length of one wavelengthat this frequency.The computer-simulated noise field consisted of two

wideband directional noise sources/ incident on the arrayat angles ()= 50u and 0 = - 70u Each source of noise hadpower 0.5. The noise at 8= 50 had the same frequencyspectrum as the pilot signal (though with reduced power):while the noise at 8 = - 70 was narrower and centered ata slightly higher frequency. The noise sources were un-correlated with the pilot signal. Fig. 17(b) shows these fre-quency spectra. Additive "white" Gaussian noises (mutuallyuncorrelated) of power 0.0625 were also present in each ofthe antenna-element signals.To demonstrate the effects of adaptation rate, the experi-

ments were performed twice, using two different values(-0.0025 and -0.00025) for ks' the scalar constant in (23).Fig. 18(a) and (b) shows the learning curves obtained underthese conditions. The abscissa of each curve is expressedin cycles ofj~, the array center frequency ~ and, as before,the array was adapted at a rate of twenty times per cycleof j~. Note that the faster learning curve is a much morenoisy one.Since the statistics of the pilot signal and directional

noises in this example are known (having been generated inthe computer simulation), it is possible to check measuredvalues of misadjustment against theoretical values. Thusthe D(x, x) matrix is known, and its eigenvalues have beencomputed.'

Using (30) and (31) and the known eigenvalues, the mis-adjustment for the two values of k, is calculated to give thefollowing values:

k..Theoretical ExperimentalValue of.W Value of Jt

-0.0025 0.1288 0.134-0.00025 0.0129 0.Ol70

The theoretical values of misadjustment check quite wellwith corresponding measured values.From the known statistics the optimum (in the least-

squares sense) weight vector Wl MS can be computed, us-ing(19).The antenna directivity pattern for this optimum weightvector WLMS is shown in Fig. 19(a). This is a broadbanddirectivity pattern, in which the relative sensitivity of thearray versus angle of incidence eis plotted for a broadbandreceived signal having the same frequency spectrum as thepilot signal. This form of directivity pattern has few sidelobes, and nulls which are generally not very deep. In Fig.

2 Broadband directional noises were computer-simulated by firstgenerating a series of uncorrelated ("white") pseudorandom numbers.applying them to an appropriate sampled-data (discrete. digital) filter toachieve the proper spectral characteristics. and then applying the re-sulting correlated noise waveform to each of the simulated antenna ele-ments with the appropriate delays to simulate the effect of a propagatingwavefront.

3 They are: 10.65,9.83, 5.65~ 5.43, 3.59, 3.44,2.68, 2.13. ).45~ 1.35. 1.20.0.99,0.66, 0.60,0.46, 0.29, 0.24, 0.20, 0.16, 0.12. 0.01,0.087,0.083.0.075,0.069.

19(b), the broadband directivity pattern which resultedfrom adaptation (after 625 cycles of 10' with ks= -0.0025)is plotted for comparison with the optimum broadbandpattern. Note that the patterns are almost indistinguishablefrom each other.The learning curves of Fig. 18(a) and (b) are composed

of decaying exponentials of various time constants. Whenk, is set to - 0.00025, in Fig. 18(b), the misadjustment isabout 1.3 percent, which is a quite small, but practical value.With this rate of adaptation, it can be seen from Fig. 18(b)that adapting transients are essentially finished after about500 cycles of"j~. If j~ is 1 MHz, for example, adaptationcould be completed (if the adaptation circuitry is fastenough) in about 500 ps. If j~ is 1 kHz, adaptation couldbe completed in about one-half second. Faster adaptationis possible, but there will be more misadjustment. Thesefigures are typical for an adaptive antenna with broadbandnoise inputs with 25 adaptive weights. For the same levelof misadjustment, convergence times increase approxi-mately linearly with the number of weights.!!'The ability of this adaptive antenna array to obtain

"frequency tuning" is shown in Fig. 20. This figure givesthe sensitivities of the adapted array (after 1250 cycles ofj~ at k...= - 0.(0025) as a function of freq uency for thedesired look direction. Fig. 20(a), and for the two noisedirections. Fig. 20(b) and (c). The spectra of the pilot signaland noises are also shown in the figures.

In Fig. 20(a). the adaptive process tends to make thesensitivity of this simple array configuration as close aspossible to unity over the band of frequencies where thepilot signal has finite power density. Improved performancemight be attained by adding antenna elements and by add-ing more taps to each delay line: or.. more simply. by band-limiting the output to the passband of the pilot signal. Fig.20(b) and (c) shows the sensitivities of the array in the direc-tions of the noises. Illustrated in this figure is the very strik-ing reduction of the array sensitivity in the directions ofthe noises, within their specific passbands. The same idea isillustrated by the nulls in the broadband directivity patternswhich occur in the noise directions" as shown in Fig. 19.After the adaptive transients subsided in this experiment,the signal-to-noise ratio was improved by the array overthat of a single isotropic sensor by a factor of 56.

IMPLEMENTATION

The discrete adaptive processor shown in Figs. 7(a) and8 could be realized by either a special-purpose digital ap-paratus or a suitably programmed general-purpose ma-chine. The antenna signals would need analog-to-digitalconversion, and then they would be applied to shift regis-ters or computer memory to realize the effects of the tappeddelay lines as illustrated in Fig. 5. If the narrowband schemeshown in Fig. 4 is to be realized, the time delays can beimplemented either digitally or by analog means (phaseshifters) before the analog-to-digital conversion process.The analog adaptive processor shown in Figs. 7(b) and 8

could be realized by using conventional analog-computer

16

10

0.8

0 6

0 .4

0.2

-,.-ARRAY SENSITIVITY8~-13'

structure would be a capacitive voltage divider rather than aresistive one . Other possible realizations of analog weightsinclude the use of a Hall -effect multiplier combiner withmagnetic storage[241and also the electrochemical memistorof Wid row and HoffYSI

Further effort s will be required to improve existingweighting ' elements and to develop new ones which aresimple, cheap, and adaptable according to the requ irementsof the various adaptation algorithms. The realization of theprocessor ultimately found to be useful in cert ain applica-tion s may be composed of a combination of analog anddigital techniques.

4I 2 3RELATIVE FREOUENCY, t / I.

o o~'----'--_>-J._---'------'(a)

R ELAXATION ALGORITHMS AND THEIR IMPLEMENTATION

Algorithms other than the LMS procedure described inthe foregoing exist that may permit considerable decreasein complexity with specific adaptive circuit implementa-tions. One method of adaptation which may be easy toimp lement electronicall y is based on a relaxation algorithmdescribed by Southwell. [26 ] This algo rithm uses the sameerro r signal as used in the LMS technique. An estimatedmean-square error formed by squaring and averaging thiserror signal over a finite time interval is used in determiningthe proper weight adjustment. Th e relaxat ion algorithmadjusts one weight at a time in a cyclic sequence, Eachweight in its turn is adjusted to minimize the measuredmean-square err or. This method is in contras t to the simul-taneou s adjustment procedure of the LMS steepest-descenta lgorithm. The relaxation procedure can be shown to pro-duce a misadjustment that increases with the square of thenumber of weight s, as opposed to the LMS algorithm whosemisadju stment increases only linearly with the number ofweights. For a given level of misadjustment, the adapta tionsett ling time of the relaxation process increases with thesqua re of the number of weights.

For implementation of the Southwell relaxation algo -rithm. the configura tions of the array and adaptive proces-sor remain the same, as does the use of the pilot signal. Therelaxat ion a lgorithm will work with either the two-modeor the one-mode adaptation process. Savings in circu itrymay result , in that changes in the adjustments of the weightvalues depend only upon error measurements and not uponconfi gurations of error measurements and simultaneousinput-signal measurements. Circuitry for implementing theLMS systems as shown in Fig. 7(a)' and (b) may be morecomplicated.The relaxati on method may be applicable in cases where

the adjustments are not obvious "weight" settings. Forexample, in a microwave system, the adjustments might be asystem ofmotor-driven apertures or tuning stubs in a wave-guid e or a network of waveguides feeding an antenna. Orthe adjustments may be in the antenna geometry itself. Insuch cases, the mean-square error can still be measured,but it is likely that it would not be a simple quadratic func-tion of the adjustment parameters, In any event, some veryinteresting possibilities in automatic optimization are pre-sented by relaxation adaptation methods.

4

4

J.RRAY.' SENSITIVITY

AT - 70 '

ARRAY/ SENSITIVITY.' AT~

k.~ - 0 .00025

.sPECTRUM. OF NOISEAT - 70

I 2 3RELATIVE FREOUENCY. 1 / t.

I 2 3RELATIVE FREOUENCY. f / f.

0 8

02

0.2

0 8

10

0 6

~ 04a:

"

>-j-,

~ 0 6;;;z

~

0 4

O ;--~-7"':-----"~---~--~Ib ) 0

O~-~--:---=-'->-::---:------'( c)

F ig. 20. Array sensitivity versus frequency, for broadband experiment ofF ig. 19. (a) Desired look direct ion. Ii= -13 . (b) Sensiti vity In oneno ise di rection. Ii= 50' . (e) Sen sitivity in the o ther noise d irection.IJ= - 70 .

apparatus, such as multipliers, integrators, summers, etc.More economical realizations that would , in add ition. bemore suitable for high-frequency operation might use field-effect transistors as the variable-gain multipliers , whosecontrol (gate ) signals could come from capacitors used asintegrators to form and store the weight values . On theother hand, instead of using a va riable resistance struc tureto form the vector dot products, the same functi on couldbe achieved using variable-voltage capacitors, with ordinarycapacitors again storing the weight values . The resulting

17

OTHER ApPLICATIONS AND FURTHER WORK ON

ADAPTIVE ANTENNAS

Work is continuing on the proper choice of pilot signalsto achieve the best trade-off between response in the desiredlook direction and rejection of noises. The subject of "null-steering, 'I" where the adaptive algorithm causes the nulls ofthe directivity pattern to track moving noise sources" is alsobeing studied.The LMS criterion used as the performance measure in

this paper minimizes the mean-square error between thearray output and the pilot signal waveform. It is a usefulperformance measure for signal extraction purposes. Forsicnal detection, however, maximization of array outputsignal-to-noise ratio is desirable. Algorithms which achievethe maximum SNR solution are also being studied.Goode[27] has described a method for synthesizing theoptimal Bayes detector for continuous waveforms usingWiener (LMS) filters. A third criterion under investigationhas been discussed by Kelley and Levin[28] and .. more re-cently" applied by Capon et ale [29] to the processing of largeaperture seismic array (LASA) data. This filter. the maxi-mum-likelihood array processor .. is constrained to providea distortionless signal estimate and simultaneously mini-mize output noise power. Griffiths'

ters," Geophysics, vol. 29, pp. 693-713, October 1964.lJ9) J. F. Claerbout, "Detection of P waves from weak sources at great

distances," Geophysics, vol. 29, pp. 197-211, April 1964.[20)H. Robbins and S. Monro, "A stochastic approximation method,"

Ann. Math. Stat., vol. 22, pp. 400-407, March 1951.[21]J. Kiefer and J.Wolfowitz, "Stochastic estimation of the maximum

of a regression function," Ann. Math. Stat., vol. 23, pp. 462-466, March1952.

[221 A. Dvoretzky, "On stochastic approximation," Proc. 3rd BerkeleySymp. on Math. Stat. and Prob., J. Neyman, Ed. Berkeley, Calif.: Univer-sity of California Press, 1956, pp. 39-55.

[231 B. Widrow, "Adaptive sampled-data systems," Proc. 1st lnternat'lCongress ofthe Internat'l Federation ofAutomatic Control (Moscow, 1960).London: Butterworths, 1960.

[241 D. Gabor, W. P. L. Wilby, and R. Woodcock, "A universal non-linear filter predictor and simulator which optimizes itself by a learningprocess," Proc. lEE (London), vol. 108B, July 1960.

125] B. Widrow and M. E. Hoff, Jr., "Generalization and informationstorage in networks of adaline 'neurons'," in SelfOrganizing Systems 1962,

M. C. Yovits, G. T. Jacobi, and G. D. Goldstein, Eds. Washington, D. C.:Spartan, 1962, pp. 435-461.

[26) R. V. Southwell, Relaxation Methods in Engineering Science,London: Oxford University Press, 1940.

127) B. B. Goode, "Synthesis of a nonlinear Bayes detector for Gaussiansignal and noise fields using Wiener filters," IEEE Trans. InformationTheory (Correspondence), vol. IT-13, pp.116-118, January 1967.

[28) E. J. Kelley and M. J. Levin, "Signal parameter estimation forseismometer arrays," M.LT. Lincoln Lab., Lexington, Mass., Tech. Rept.339, January 8,1964.

[291 J. Capon, R. J. Greenfield, and R. J. Kolker, "Multidimensionalmaximum-likelihood processing of a large aperture seismic array," Proc.IEEE, vol. 55, pp. 192-211, February 1967.

[301 L. J. Griffiths, "A comparison of multidimensional Wiener andmaximum-likelihood filters for antenna arrays," Proc. IEEE (Letters),vol. 55, pp. 2045-2047, November 1967.

[31) B. Widrow, "Bootstrap learning in threshold logic systems," pre-sented at the American Automatic Control Council (Theory Committee),IFAC Meeting, London, England, June 1966.

19

AbstractThroughout the history of wireless communications. spatial antenna diversity has been important in improving the radio link between wirelessusers. Historically, microscopic antenna diversity has been used to reduce the fading seen by a radio receiver. whereas macroscopic diversity

provides multiple listening posts to ensure that mobile communication links remain intact over a wide geographic area. In recent years, the con-cepts of spatial diversity have been expanded to build foundations for emerging technologies, such as smart (adaptive) antennas and positionlocation systems. Smart antennas hold great promise for increasing the capacity of wireless communications because they radiate and receive

energy only in the intended directions, thereby greatly reducing interference. To properly design, analyze, and implement smart antennas and toexploit spatial processing in emerging wireless systems. accurate radio channel models that incorporate spatial characteristics are necessary. Inthis tutorial. we review the key concepts in spatial channel modeling and present emerging approaches. We also review the research issues in

developing and using spatial channel models for adaptive antennas.

Overview ofSpatial Channel Models forAntennaAlTay Communication Systems

RICHARD B. ERTEL AND PAULO CAROIERI, VIRGINIA POLYTECHNIC INSTITUTE

KEVIN W. SOWERBY, UNIVERSITY OF AUCKLAND, NEW ZEALAND

THEODORE S. RAPPAPORT AND JEFFREY H. REED,

VIRGINIA POLYTECHNIC INSTITUTE

ith the advent of antenna arraysystems for both interference cancellation and position loca-don applications comes the need to better understand thespatial properties of the wireless communications channel.These spatial properties of the channel will have an enormousimpact on the performance of antenna array systems: hence,an understanding of these properties is paramount to effectivesystem design and evaluation.

The challenge facing communications engineers is to devel-op realistic channel models that can efficiently and accuratelypredict the performance of a wireless system. It is importantto stress here that the level of detail about the environment achannel model must provide is highly dependent on the type ofsystem under consideration. To predict the performance ofsingle-sensor narrowband receivers .. it may be acceptable toconsider only the received signal power and/or time-varyingamplitude (fading) distribution of the channel. However. foremerging wide band multisensor arrays, in addition to signalpower level, information regarding the signal multipath delayand angle of arrival (ADA) is needed.

Classical mode Is provide information about signal powerlevel distributions and Doppler shifts of the received signals.These models have their origins in the early days of cellularradio when wideband digital modulation techniques were notreadily available. As shown subsequently, many of the emerg-ing spatial .nodels in the literature utilize the fundamentalprinciples 01 the classical channel models. However, modernspatial channel models build on the classical understanding offading and Doppler spread, and incorporate additional con-

This work was partially supported by the DARR4 Globdo program, Vir-ginia Tech's FederalHighwaysResearch Center ofExcellence. VirginiaTech's BradleyFoundation. the Brazilian National Science Coullcil-C.VPq, and .VSFPresidentialFaculty Fellowship.

cepts such as time delay spread, ADA. and adaptive arrayantenna geometries.

In this article, we review the fundamental channel modelsthat have led to the present-day theories of spatial diversityfrom both mobile user and base station perspectives. The evo-lution of these models has paralleled that of cellular systems.Early models only accounted for amplitude and time-varyingproperties of the channel. These models were then enhancedby adding time delay spread information. which is importantwhen dealing with digital transmission performance. Now,with the introduction of techniques and features that dependon the spatial distribution of the mobiles, spatial informationis required in the channel models. IA.S shown in the next sec-tions. more accurate models for the distribution of the scatter-ers surrounding the mobile and base station are needed. Thedifferentiation between the mobile and base station is impor-tant. Classical work has derno nst r ate d that models mustaccount for the physical geometry of scattering objects in thevicinity of the antenna of interest. The number and locationsof these scattering objects are dependent on the heights of theantennas, particularly regarding the local environment.

This article, then, explores some of the emerging modelsfor spatial diversity and adaptive antennas, and includes thephysical mechanisms and motivations behind the models. Aliterature survey of existing RF channel measurements withADA information is also included. The article concludes witha summary and suggestions for future research.

Wireless l\1ultipath Channel ModelsThis section describes the physical properties of the wirelesscommunication channel that must be modeled. In a wirelesssystem, a signal transmitted into the channel interacts with theenvironment in a very complex way. There are reflectionsfrom large objects, diffraction of the electromagnetic waves

Reprinted from IEEE Personal Communications Magazine, Vol 5, No.1, pp. 10-22, February 1998.

20

(a)

A (t)e j~I , 2(t)S(r - 't1,2 ~

Mobile 2

(b) Base

-e;, ~lBeam of the base sta tionste ered toward mobile

(I )

Figure 1,Multipath propagation channel: a) side view; b ) top view.

around objects. and signal scattering. The result of these com-plex interactions is the presence of many signal components.or multipatli signals. at the receiver. Another property of wire-less channels is the presence of Doppler shift , which is causedby the motion of the receiver, the transmitter, and /or anyother objects in the channel. A simplified pictorial of the rnul-tipath environment with two mobile stations is shown in Fig.1. Each signa l component expe riences a different path envi-ronment. which will determine the amplitude A /.k . carrierphase shift /.k, time delay ' I.b AOA 8u , and Doppler shift ifof the lth sign a l compo ne n t of the kth mobile . In ge ne ra l.each of these signal parameters will be time-varying.

The early classical models. which were developed for nar-rowb and transmission system s. only provide information aboutsignal amplitude level distributions and Doppler sh ifts of thereceived signals. These models have their ori gins in the earl vdays of cellular radio [1--1] when wideband digital modul ationtechniques were not readily ava ilable.

As cellular systems became more complex and more accu -rate models were required . additional co nce pts. such as timedelay spread . were incorporated int o the mode l. Representingthe RF channel as a time -vari ant channe l and using a base -band complex envelope representation . the channel impulseresponse for mobile 1 has class ically beer: represented as [51

L (r) - I

h\(1.,)= I AI.I (r )e!

Received signal

90. , I Mobile 1 I9" 92,1

fi}.'

1*'' ~it 2. , Delay

(a)

Received signal

902IMobile 21

Received signal

(c)Delay

Received signal

(d)Delay

Delay

II Figure 2. Channel impulse responses for mobiles I and 2: a) received signal from mobile I to the base station: b) received signal frommobile 2 to the base station: c) combined received signal from mobiles I and 2 at the base station: d) received signal at the base stationwhen a beam steered toward mobile I is employed.

Figure 3.Arbitrary antenna arrayconfiguration.

!I

X Ii

e

Planewave

Space: The Final FrontierDetails ofthe Spatial Channel Models

In the past when the distribution of angle of arrival of multi-path signals was unknown, researchers assumed uniform dis-tribution over [0, 21tJ [7J. In this section, a number of morerealistic spatial channel models are introduced. The definingequations (or geometry) and the key results for the models

~ /vlicrocell Environment - In the micro-cell environment. the base stationantenna is usuallv mounted at the sameheight as the surrounding objects. Thisimplies that the scattering spread ofthe AOA of the received signal at thebase station is larger than in themacrocell case since the scattering pro -cess also happens in the vicinity of thebase station. Thus. as the base stationantenna is lowered. the tendencv is forthe multipath AOA spread to increase.This change in the behavior of thereceived signal is very important as faras antenna array applications are con-cerned. Studies have shown that statis-tical characteristics of the receivedsignal are functions of the angle

spread . Lee [3J and Adachi [6J found that the correlationbetween the signals received at two base station antennasincreases as the angle spread decreases.

This section has presented some of the physical propertiesof a wireless communication channel, A mathematical expres-sion that describes the time-varying spatial channel impulseresponse was given in Eq. 2. In the next section , several mod-els that provide varying levels of information about the spatialchannel are presented.

o Basestatio n

Basestation

til Figure 4.Macrocell environment - the mobile station perspective.

Rayleigh fading envelope with deepfades approximatelv 1../2 apartemanates from this model [5J.

However. the AOA of the receivedsignal at the base station is quite dif-fe-rent. In a macrocell environment.typically. the base station is deployedhigher than the surrounding scatter-er;. Hence . the received signals atthe base station result from the scat-tering process in the vicinity of themobile station. as shown in Fig . 5 .The multipath components at~thebase station are restricted to a small-er angular region . BBW. and the dis-tribution of the AOA is no longeruniform over [O.2lt] . Other AOA dis-tributions are considered later in thisarticle .

The base station model of Fig. 5 was used to develop thetheory and practice of base station diversity in today's cellularsvstem and has led to rules of thumb for the spacing of diver-sity antennas on cellular towers [3J.

22

Top view

angle spreads and e lement spacings resultin lower corre la tions, which provide anincreased diversi ty gai n. Measurements ofthe correlation observed a t both the basestation and the mobile are consisten t witha narrow angle spread at the base sta tionand a large a ngle spread at the mobile .Correlation measu