IF ONE OR MORE of the antennas in a wireless communication

1976 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST 2004 Adaptive Crossed Dipole Antennas Using a Genetic Algorithm Randy L. Haupt, Fellow, IEEE Abstract Antenna misalignment in a mobile wireless communications system results in a signal loss due to a decrease in antenna directivity and a polarization mismatch. A genetic algorithm (GA) is used to adaptively alter the polarization and directivity of a crossed dipole receive antenna in order to increase the link budget. The three orthogonal dipole configuration works better than only two crossed dipoles, but both improved the link loss as the angular pointing errors increased. A GA with a high mutation rate works best for a noiseless open loop adaptation, while a GA with a low mutation rate works best for noisy fully adaptive system. Index Terms Adaptive antenna, crossed dipole, genetic algorithm (GA), polarization, smart antenna. I. INTRODUCTION IF ONE OR MORE of the antennas in a wireless communication system is mobile, then as the antennas move, the direction of the peak gains and the polarization of the antennas change. As a result, the power received goes down. For instance, a wireless system that transmits vertical polarization has some of its power converted to horizontal polarization as the signal reflects from the environment. Unless the receive antenna can detect both polarizations, the received power decreases. Another example is when a spacecraft orbits the earth; the antennas in the communications system no longer align for optimum power transfer. Antenna engineers design the antennas for maximum directivity and polarization match when the antennas point at each other. Both the directivity and polarization of an antenna change with angle. If the antennas do not point at each other, then the product of the receive and transmit antenna directivities goes down. The directivity loss coupled with the polarization mismatch reduces the received power. An obvious solution to this problem is to keep the antennas pointing at each other. Constantly maneuvering a spacecraft requires an unacceptable expenditure of precious fuel, though. Steering the ground antenna is another option but only solves half of the problem, since the spacecraft might still be out of alignment. If the antenna is a phased array, then steering the main beam maximizes the directivity but does not improve the polarization mismatch. One way to improve the link budget is to adaptively change the antenna polarization and directivity to maximize the power transfer. In order to improve the link budget, the polarization Manuscript received February 10, 2003; revised May 27, 2003. The author was with the Utah State University, Electrical and Computer Engineering, Logan, UT 84322-4120 USA. He is now with the Applied Research Laboratory, Pennsylvania State University, State College, PA 16804 USA (e-mail: haupt@ieee.org). Digital Object Identifier 10.1109/TAP.2004.832493 and directivity of the receive and/or transmit antennas must be adaptively changed if the positions of the two antennas change. Adaptive antennas usually place a null in the antenna pattern to reject interference or steer a beam toward a desired signal. Phased arrays have more than one antenna, so they are perfect for adapting their patterns. Adapting the polarization, however, requires an antenna that can modify the major and minor axes of its polarization ellipse. Crossed dipoles are perfect for this application. The crossed dipole antenna has found use before in systems requiring antennas that change their polarization. A wireless communications system in a high multipath environment can improve the link better through polarization diversity in the form of crossed dipoles than through spatial diversity (antenna separation) [1]. A crossed dipole consists of two or three orthogonal dipoles. When linearly polarized signals become depolarized due to reflections, each dipole can receive the electric field component parallel to it. Using three orthogonal crossed dipoles has been experimentally shown to significantly increase channel capacity of a wireless communication system inside a building [2]. The polarization and directivity of a crossed dipole antenna are easy to control. One dipole controls the electric field parallel to it and the orthogonal dipoles control the electric fields parallel to them. Each dipole has an independent complex weight. Controlling the amplitude and phase of the signal at each dipole modifies the electric field amplitude and phase in orthogonal directions resulting in any polarization from linear through elliptical to circular. Modifying the amplitude and phase of the signal at the dipoles also modifies the directivity of the antenna as well. Adaptive crossed dipoles alter their polarization based upon environmental conditions. When a transmitted circularly polarized millimeter wave passes through rain, it becomes elliptically polarized. The depolarization can be calculated if the rainfall rate is known. Reference [3] proposed an open loop adaptive transmit antenna that adjusted its polarization based upon the measured rainfall in the propagation path. In [4], a least mean square (LMS) algorithm adapted the polarization and pattern of a two element array of crossed dipoles to improve the signal to interference plus noise ratio (SINR). As long as the desired and interference signals are not at the same angles and have the same polarizations, the SINR was improved. In another paper, the LMS algorithm was used to find amplitude and phase weights for three orthogonal dipole antennas in order to improve the SINR. This arrangement provided some rejection for interference signals for most angles of arrival and polarizations [5]. A previous paper presented results from adaptively adjusting the 0018-926X/04$20.00 2004 IEEE

HAUPT: ADAPTIVE CROSSED DIPOLE ANTENNAS USING A GA 1977 the crossed dipole current is the sum of the constant currents on each short dipole Substituting this current into the equation for the magnetic vector potential for a short dipole yields (1) (2) Fig. 1. Coordinate system for the crossed dipole transmit and receive antennas. amplitude and phase of the current fed to one dipole while the other dipole had an amplitude of one and phase of zero. The Numerical Electromagnetic Code generated the electromagnetic response of the dipole antennas and a local optimizer performed the optimization [6]. It was found that optimizing only for circular polarization produces losses in radiated power that offset the polarization correction. An improvement in the power transferred increased up to a maximum of 2.0 db at. Using adaptive crossed dipoles at the transmitter and receiver was also considered and further improved the model. This paper expands upon a recent presentation that introduced the application of a genetic algorithm (GA) to adaptively change the current fed to crossed dipole antennas in order to improve the link budget [7]. The dipole model consists of three orthogonal short dipoles with variable control of the phase and amplitude fed to each element. A GA is used to maximize the received signal by improving the directivity and polarization match through weighting the currents at each dipole. Improvements in the link budget of up to 6 db are possible. where distance from the origin to the field point at ; dipole length in the and directions; radial frequency; wave number; permeability; constant current in or direction. In the far field, the electric field in rectangular coordinates is found from the magnetic vector potential by The transmitted electric field is given by Converting this rectangular form of the electric field into spherical coordinates produces the far field components The directivity is given by and the polarization loss factor is (3) (4) (5) (6) II. CROSSED DIPOLE MODEL Satellite communications systems use circularly polarized antennas for the satellite and the ground antennas. In this paper, the circularly polarized antennas are modeled as crossed dipoles. Consequently, controlling the amplitude and phase of the signals at the dipoles of the transmit and receive antennas, modifies the directivity and polarization of both antennas. In this case, the crossed dipole has three orthogonal dipoles. The receive antenna is located at an angle of from the transmit antenna (Fig. 1). Similarly, the transmit antenna is located at an angle of from the receive antenna. Maximum power transfer occurs when and. In order to determine the directivity and polarization of the antennas, the electric fields can be found from the currents on the dipoles. If the dipoles are assumed to be short, where with a perfect match. The and subscripts represent transmit and receive, respectively. Equations (10) and (11) are key ingredients to the link budget. The examples presented here assume the earth station consists of a pair of orthogonal crossed dipoles in the plane transmitting a circularly polarized field in the -direction. Increasing toward the horizon transitions from circular polarization through elliptical until linear polarization results at the horizon. In this paper, the transmit antenna has the following (7)

1978 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST 2004 Fig. 2. Circularly polarized crossed dipoles along the x and y axes. This is a hemispherical plot of the inverse axial ratio. Light color indicates high with a value of 1 in the z-direction and a value of 0 in the x 0 y plane. Fig. 4. Circularly polarized crossed dipoles along the x and y axes. This is a hemispherical plot of the directivity. Light color indicates high with a value in the y-direction and a low value in the x 0 y plane. Fig. 3. Plot of the inverse axial ratio versus the elevation angle. Fig. 5. Plot of the directivity versus the elevation angle. currents:,, and. Fig. 2 shows a hemispherical plot and Fig. 3 a linear plot of the inverse axial ratio as a function of. White (at the poles) represents an inverse axial ratio of one (circular polarization), while black (at the equator) is an inverse axial ratio of zero (linear polarization). Increasing also changes the antenna directivity as shown in Figs. 4 and 5 from a maximum at 0 (white) to a minimum at 90 (black). Compensating for the loss in directivity and polarization match can improve the link budget by several decibels. III. GENETIC ALGORITHM OPTIMIZATION In a wireless communications system, the goal is to maximize the power transfer between the transmit and receive antennas. The following fitness function calculates the portion of the link budget relating to polarization and directivity from the amplitude and phase of the currents for each dipole: where is the directivity of the transmit crossed dipoles in the direction of the receive crossed dipoles, and is the directivity of the receive crossed dipoles in the direction of the transmit (8) crossed dipoles. Since the crossed dipoles have a maximum directivity close to one, the directivities are not normalized in the objective function. The maximum possible value of this fitness function is approximately 2.25 or 3.5 db. There are several approaches to performing the adaptation. With current technology, the most likely approach is to do an open loop adaptation. The satellite uses various sensors to make it aware of its orientation. Once its orientation is known, then the dipole currents can be found from a lookup table of optimized values, or the optimization could be done at that time. Noise and orientation errors limit the improvement possible. The other approach is a fully adaptive system capable of correcting for noise and system inaccuracies. This approach would be necessary for using the adaptive dipoles on another mobile system, such as an airplane, where the orientation and environment of the dipoles quickly changes and cannot be predicted ahead of time. A continuous parameter GA was used to find the values of the amplitude and phase of the receive dipole currents that maximize (12). The GA has a population size of 8, mutation rate of.2, single point crossover, and 50% replacement. This small population size and high mutation rate results in a very fast convergence as will be shown in the following section. The goal of

HAUPT: ADAPTIVE CROSSED DIPOLE ANTENNAS USING A GA 1979 Fig. 6. Average number of function calls needed to get the fitness above 3 for various population sizes and mutation rates. Fig. 8. In this case, varies with time and =0. The receive antenna consists of two crossed dipoles. The solid line results from adaptation and the dashed line has no adaptation. Fig. 7. Link is optimal when the two antennas face each other or = =0. the optimization process is to quickly improve the communications link, not necessarily find the global minimum. Fig. 6 shows the results of optimizing (8) using a GA for population sizes between 8 and 32 and mutation rate between 0.1 and 0.2. No noise was used in these runs. The plot is of the mean number of function calls to get (8) above 3 db averaged over 50 independent runs when the GA begins with a random population. A small population size and large mutation rate produce the fastest convergence on average for the open loop adaptation. IV. RESULTS In all the examples presented here, the orientation of the ground and satellite antennas are assumed to change with time unless otherwise specified Fig. 7. Even though the distances between the antennas would also change, this variation is ignored. As the orientations of the antennas vary with time, so do their directivity and polarizations in the directions of each other. Assume that the transmit antenna (ground station) tracks the satellite and the receive antenna (satellite) points at the ground ( varies). The transmit antenna continues to deliver a circularly polarized signal at maximum directivity to the moving receive antenna. If the receive antenna consists of two crossed dipoles, then the maximum receive power transfer occurs when the receive antenna is directly overhead of the transmit antenna. If the receive antenna remains circularly polarized as it moves, then the power received drops off at the rate shown by the dashed line in Fig. 8. The loss in power transfer Fig. 9. In this case, varies with time and =0. The receive antenna consists of three crossed dipoles. The solid line results from adaptation and the dashed line has no adaptation. is due to the reduction in the directivity and the PLF. If the currents at each dipole are optimally weighted using the GA, then the power loss follows the solid line in Fig. 8. This curve results from running the GA to find the optimum weights for a range of angles. The difference between the two curves is the link improvement. The link improvement is as much as 3 db at. In this case, all the improvement is due to increasing the directivity of the receive antenna. Adding a third orthogonal dipole to the receive antenna provides another degree of freedom. Now, adapting the receive antenna to the tracking transmit antenna results in no change in the link budget as a function of (solid line in Fig. 9). The three orthogonal dipoles can compensate for the change in directivity and polarization of the receive antenna as it moves. This scenario produces up to 6 db improvement in the link budget at. Another scenario has both two dipole antennas pointing straight ahead (no tracking) while the satellite moves ( and change with time). Fig. 10 shows the improvement (solid line) possible through adaptation compared to the link loss with no adaptation (dashed line). The link improvement is as much as 3 db at. Adding a third dipole produces even better

1980 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST 2004 Fig. 10. In this case, = vary with time. The receive antenna consists of two crossed dipoles. The solid line results from adaptation and the dashed line has no adaptation. Fig. 11. In this case, = vary with time. The receive antenna consists of three crossed dipoles. The solid line results from adaptation and the dashed line has no adaptation. link improvement than the two dipole case, particularly at smaller angles (Fig. 11). The maximum improvement is 3 db at. How fast can a GA adapt? If the receive antenna continuously adapts as it moves, then only small perturbations are necessary at each angle and the adaptation is very fast. As an example, consider maximizing the link budget of the receive antenna with three orthogonal dipoles at. If the adaptation starts with the optimal weightings at, then the solid curve in Fig. 12 results. In order to reach the steady state solution at generation 21, the number of fitness function evaluations made by this GA run is A fitness function evaluation equates to a power measurement in a real system. If the adaptation starts with the optimal weightings at, then the dashed curve in results. Continuously (9)

HAUPT: ADAPTIVE CROSSED DIPOLE ANTENNAS USING A GA 1981 Fig. 12. Typical link improvement versus generation for a three orthogonal dipole receive antenna at an angle of 50. If the adaptation process is started with the receive antenna at circular polarization (0 ), then the GA finds an optimum in 21 generations or about 100 power measurements (solid line). If the process starts with the optimum dipole weights at 45, then minimal adaptation is necessary (dashed line). TABLE I AVERAGE MAXIMUM AND MEAN OF THE POPULATION OVER 100 GENERATIONS FOR VARIOUS MUTATION RATES AND NOISE VARIANCES Fig. 13. Performance of the GA when normally distributed noise is added to the amplitude and phase of the currents fed to the dipoles ( = 0 and =0:1). The GA has a population size of 8 and mutation rate of 0.2. adapting the signal results in constant incremental improvement of the link. Even if the antenna must be adapted from circular polarization, the GA quickly finds an acceptable solution. The results are not dependent upon. Noise was added to the currents of the dipoles of the transmit antennas to see how well the GA performs in a noisy environment. Using a population size of 8 and mutation rate of 0.2, a plot of the link improvement versus generation shows ups and downs due to the random variations (Fig. 13). The transmit dipole current amplitude and phase errors are normally distributed with a mean and standard deviation given by and. Note that the mean of the population has high variations due to the large mutation rate. Using a small mutation rate of 0.02, results in a much lower variations in the mean of the population (Fig. 14). Even though the higher mutation rate finds an optimal solution faster than the lower mutation rate, the average power measurements associated with the high Fig. 14. Performance of the GA when normally distributed noise is added to the amplitude and phase of the currents fed to the dipoles ( =0and =0:1). The GA has a population size of 8 and mutation rate of 0.02. mutation rate are lower. Consequently, when noise is included, a lower mutation rate is more desirable. Table I shows that the average for the population mean over 100 generations is better when the mutation rate is smaller.

1982 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST 2004 V. CONCLUSION The received signal in a mobile communications system loses strength due to a decrease in antenna directivity and polarization mismatch. The current fed to a set of crossed dipoles can be modified to increase the directivity and polarization match between the transmit and receive antennas. Two orthogonal dipoles can compensate for the loss in gain but not polarization. Three adaptive orthogonal dipoles can fully restore the loss due to loss in directivity and polarization mismatch if tracked by the transmit antenna. A GA quickly adapts the receive antenna to the transmitted signal. Three orthogonal dipoles provide more improvement than just two orthogonal dipoles. Fig. 15. Performance of the GA when normally distributed noise is added to the amplitude and phase of the currents fed to the dipoles ( = 0 and =0:1) and the satellite is moving 1 per generation. The GA has a population size of 8 and mutation rate of 0.2. REFERENCES [1] A. Singer, Space versus polarization diversity, Wireless Review, pp. 164 168, Feb. 15, 1998. [2] M. R. Andrews, P. P. Mitra, and R. decarvalho, Tripling the capacity of wireless communications using electromagnetic polarization, Nature, vol. 409, pp. 316 318, Jan 18, 2001. [3] R. E. Marshall and C. W. Bostian, An adaptive polarization correction scheme using circular polarization, in Proc. IEEE Int. Antennas and Propagation Society Symp., Atlanta, GA, June 1974, pp. 395 397. [4] R. T. Compton, On the performance of a polarization sensitive adaptive array, IEEE Trans. Antennas Propagat., vol. AP-29, pp. 718 725, Sept. 1981. [5], The tripole antenna: an adaptive array with full polarization flexibility, IEEE Trans. Antennas Propagat., vol. AP-29, pp. 944 952, Nov. 1981. [6] B. D. Griffin, R. Haupt, and Y. C. Chung, Adaptive polarization for spacecraft communications system, presented at the Proc. IEEE Aerospace Conf., Big Sky, MT, Mar. 2002. [7] R. Haupt, Adaptive crossed dipole antennas, in URSI General Assembly, Maastricht, Netherlands, Aug. 2002. Fig. 16. Performance of the GA when normally distributed noise is added to the amplitude and phase of the currents fed to the dipoles ( =0and =0:1) and the satellite is moving 1 per generation. The GA has a population size of 8 and mutation rate of 0.02. In a fully adaptive system, the GA would also have to adapt while the satellite moves. The next set of simulations used the same error statistics as before and had the satellite move 1 per generation. Fig. 15 shows the convergence curve when the mutation rate is 0.2. Again, the mean of the population has very high variations. Fig. 16 shows the convergence curve when the mutation rate is 0.02. The smaller mutation rate is more desirable, because the variations in the population mean are small. A high mutation rate works best for a no noise environment, and a low mutation rate works best in the presence of noise. Randy L. Haupt (M 82 SM 90 F 00) received the B.S. degree in electrical engineering from the U.S. Air Force Academy, U.S. Academy, CO, the M.S. degree in engineering management from Western New England College, Springfield, MA, in 1981, the M.S. degree in electrical engineering from Northeastern University, Boston, MA, in 1983, and the Ph.D. degree in electrical engineering from the University of Michigan, Ann Arbor, in 1987. He was a Professor of electrical engineering at the U.S. Air Force Academy and Professor and Chair of Electrical Engineering at the University of Nevada - Reno. In 1997, he retired as a Lt. Col. in the U.S. Air Force. He was a Project Engineer for the OTH-B radar and a Research Antenna Engineer for Rome Air Development Center. From 1999 to 2003, he was Professor and Department Head of Electrical and Computer Engineering at Utah State University, Logan. He is currently a Senior Scientist at the Applied Research Laboratory, Pennsylvania State University, State College. He has many journal articles, conference publications, and book chapters on antennas, radar cross section and numerical methods and is coauthor of the book Practical Genetic Algorithms, 2nd edition (New York: Wiley, May 2004). He has eight patents in antenna technology. Dr. Haupt is a Member of Tau Beta Pi, Eta Kappa Nu, International Scientific Radio Union (URSI) Commission B, and the Electromagnetics Academy. He was the Federal Engineer of the Year in 1993.