Showing papers on "Antenna array published in 2002"

Deconstructing multiantenna fading channels

Abstract: Accurate and tractable channel modeling is critical to realizing the full potential of antenna arrays in wireless communications. Current approaches represent two extremes: idealized statistical models representing a rich scattering environment and parameterized physical models that describe realistic scattering environments via the angles and gains associated with different propagation paths. However, simple rules that capture the effects of scattering characteristics on channel capacity and diversity are difficult to infer from existing models. We propose an intermediate virtual channel representation that captures the essence of physical modeling and provides a simple geometric interpretation of the scattering environment. The virtual representation corresponds to a fixed coordinate transformation via spatial basis functions defined by fixed virtual angles. We show that in an uncorrelated scattering environment, the elements of the channel matrix form a segment of a stationary process and that the virtual channel coefficients are approximately uncorrelated samples of the underlying spectral representation. For any scattering environment, the virtual channel matrix clearly reveals the two key factors affecting capacity: the number of parallel channels and the level of diversity. The concepts of spatial zooming and aliasing are introduced to provide a transparent interpretation of the effect of antenna spacing on channel statistics and capacity. Numerical results are presented to illustrate various aspects of the virtual framework.

MIMO antenna subset selection with space-time coding

Abstract: This paper treats multiple-input multiple-output (MIMO) antenna subset selection employing space-time coding. We consider two cases differentiated based on the type of channel knowledge used in the selection process. We address both the selection algorithms and the performance analysis. We first consider the case when the antenna subsets are selected based on exact channel knowledge (ECK). Our results assume the transmission of orthogonal space-time block codes (with emphasis on the Alamouti (see IEEE J. Select. Areas Commun., vol.16, p.1451-68, Oct. 1998) code). Next, we treat the case of antenna subset selection when statistical channel knowledge (SCK) is employed by the selection algorithm. This analysis is applicable to general space-time coding schemes. When ECK is available, we show that the selection algorithm chooses the antenna set that maximizes the channel Frobenius norm leading to both coding and diversity gain. When SCK is available, the selection algorithm chooses the antenna set that maximizes the determinant of the covariance of the vectorized channel leading mostly to a coding gain. In case of ECK-based selection, we provide analytical expressions for average SNR and outage probability improvement. For the case when SCK-based selection is used, we derive expressions for coding gain. We also present extensive simulation studies, validating our results.

Antenna arrays formed of spiral sub-array lattices

Abstract: A antenna array ( 20 ) includes a plurality of periodic or aperiodic arranged sub-arrays ( 22 ). Each sub-array ( 22 ) includes a plurality of antenna elements ( 32 ) arranged in the form of a spiral ( 30 ). The sub-arrays ( 22 ) can comprise various spiral shapes to provide the required physical configuration and operational parameters to the antenna array ( 20 ). The elements ( 32 ) of each sub-array ( 22 ) are arranged to minimize the number of such elements ( 32 ) that intersect imaginary planes perpendicular to the spiral and passing through the spiral center. Such an orientation of the elements ( 32 ) minimizes grating lobes in the antenna pattern.

Space-Time Wireless Channels

Abstract: A practical, "first-principles" approach to space-time wireless channel design. A practical approach to space-time wireless channel design Integrates essential principles from communications, electromagnetics, and random process theory Includes detailed coverage of diversity, multipath applications, and antenna array design Contains extensive examples, illustrations, and problem setsNext-generation broadband radio systems must deliver unprecedented performance and higher data rates, while coping with increased spectral congestion. To achieve these goals, engineers need an in-depth understanding of radio channels that fade in time, frequency, and space. In Space-Time Wireless Channels, leading researcher Gregory D. Durgin presents a pragmatic, first-principles approach that integrates crucial concepts and techniques from communications, electromagnetics, and random process theory.Durgin focuses on comprehension and practicality, offering extensive examples, illustrations, and problem sets, while avoiding gratuitious mathematics and moving most derivations to end-of-chapter appendices. Coverage includes: Fundamentals of space, time, and frequency transmission and random process theory Electromagnetic description of space-time channels and the physics of small-scale fading First- and second-order statistics of fading channels Angle spectrum concepts and applications, including vector/scalar space and multipath shape factors Antenna diversity, temporal diversity, and bit error rates Multipath channels: separation, signaling, block coding, and antenna array design Appendices list special functions, Fourier transform examples, and random process theory concepts, as well as all relevant mathematical symbols, conventions, and acronyms.

Performance of multiantenna signaling techniques in the presence of polarization diversity

Abstract: Multiple-input multiple-output (MIMO) antenna systems employ spatial multiplexing to increase spectral efficiency or transmit diversity to improve link reliability. The performance of these signaling strategies is highly dependent on MIMO channel characteristics, which, in turn, depend on antenna height and spacing and richness of scattering. In practice, large antenna spacings are often required to achieve significant multiplexing or diversity gain. The use of dual-polarized antennas (polarization diversity) is a promising cost- and space-effective alternative, where two spatially separated uni-polarized antennas are replaced by a single antenna structure employing orthogonal polarizations. This paper investigates the performance of spatial multiplexing and transmit diversity (Alamouti (see IEEE J. Select. Areas Commun., vol.16, p.1451-58, Oct. 1998) scheme) in MIMO wireless systems employing dual-polarized antennas. In particular, we derive estimates for the uncoded average symbol error rate of spatial multiplexing and transmit diversity and identify channel conditions where the use of polarization diversity yields performance improvements. We show that while improvements in terms of symbol error rate of up to an order of magnitude are possible in the case of spatial multiplexing, the presence of polarization diversity generally incurs a performance loss for transmit diversity techniques. Finally, we provide simulation results to demonstrate that our estimates closely match the actual symbol error rates.

Method and system in a transceiver for controlling a multiple-input, multiple-output communications channel

Abstract: The present invention makes it possible to increase a data rate between a transmitter and receiver using a multiple-input, multiple-output radio frequency channel. A multiple-stream, multiple-antenna receiver measures a composite channel between a multiple-antenna transmitter and a multiple-antenna receiver to produce a composite channel measurement. The receiver selects a plurality of antenna array weight sets for use in the multiple-antenna transmitter in response to the composite channel measurement, where each antenna array weight set is associated with one of multiple data streams. Information describing the plurality of antenna array weight sets for use in the multiple-antenna transmitter are then transmitted.

Retrodirective arrays for wireless communications

Abstract: This article reports the recent progress in active and passive retrodirective arrays using phase-conjugation techniques. The arrays presented here are designed for wireless communications in microwave bands and have other features in addition to self-phasing aspects such that they can be applied to practical communication systems. The reliance on purely analog circuitry offers system simplicity and high-speed response. The self-beam-steering feature potentially offers the improvement of communication link gain between an interrogator and a retrodirective array, reducing the burden on transmitting and receiving amplifiers. By implementing a receiving function, it has been demonstrated that retrodirective arrays can also be used in bidirectional communications in either a full or semiduplex manner, initiating a new class of transceiver architecture.

Angular power distribution and mean effective gain of mobile antenna in different propagation environments

Abstract: We measured the elevation angle distribution and cross-polarization power ratio of the incident power at a mobile station in different radio propagation environments at 2.15 GHz frequency. A novel measurement technique was utilized, based on a wideband channel sounder and a spherical dual-polarized antenna array at the receiver. Data were collected over 9 km of continuous measurement routes, both indoor and outdoor. Our results show that in non-line-of-sight situations, the power distribution in elevation has a shape of a double-sided exponential function, with different slopes on the negative and positive sides of the peak. The slopes and the peak elevation angle depend on the environment and base-station antenna height. The cross-polarization power ratio varied within 6.6 and 11.4 dB, being lowest for indoor and highest for urban microcell environments. We applied the experimental data for analysis of the mean effective gain (MEG) of several mobile handset antenna configurations, with and without the user's head. The obtained MEG values varied from approximately -5 dBi in free space to less than -11 dBi beside the head model. These values are considerably lower than what is typically used in system specifications. The result shows that considering only the maximum gain or total efficiency of the antenna is not enough to describe its performance in practical operating conditions. For most antennas, the environment type has little effect on the MEG, but clear differences exist between antennas. The effect of the user's head on the MEG depends on the antenna type and on which side of the head the user holds the handset.

Smart-antenna systems for mobile communication networks. Part 1. Overview and antenna design

Abstract: This paper focuses on the interaction and integration of several critical components of a mobile communication network using smart-antenna systems. This wireless network is composed of communicating nodes that are mobile, and its topology is continuously changing. One of the central motivations for this work comes from the observed dependence of the overall network throughput on the design of the adaptive antenna system and its underlying signal processing algorithms. Part 1 of this two-part paper gives a brief overview of smart-antenna systems, including the different types of smart-antenna systems, and the reason for their having gained popularity. Moreover, details of typical antenna array designs suitable for the wireless communication devices are included in this part.

Wide-scan spherical-lens antennas for automotive radars

Abstract: A new approach to wide scan-angle antennas at millimeter-wave frequencies is introduced with special focus on ease of manufacturing and reliability. The system is composed of planar feed antennas (tapered-slot antennas), which are positioned around a homogeneous spherical Teflon lens. Beam scanning can be achieved by switching between the antenna elements. The spherical-lens system is analyzed through a combined ray-optics/diffraction method. It is found that a maximum efficiency of 50%-55% can be achieved using Teflon, Rexolite, or quartz lenses. The efficiency includes taper, spillover, and reflection loss. Calculations also indicate that the maximum lens diameter is 30-40 /spl lambda//sub 0/, which results in a maximum directivity of 39.5-42 dB. Measurements done on a single-element feed and a 5-cm Teflon lens agree very well with theory and result in a 3-dB beamwidth of 5.5/spl deg/ and better than -20-dB sidelobe levels at 77 GHz. Absolute gain measurements show a system efficiency of 46%-48% (including dielectric loss). A 23- and 33-element antenna array with a scan angle of /spl plusmn/90/spl deg/ and a -3.5- and -6-dB crossover, respectively, in the far-field patterns was also demonstrated. The 23-element array resulted in virtually no gain loss over the entire 90/spl deg/ scan angle. This represents, to our knowledge, the first wide scan-angle antenna at millimeter-wave frequencies.

A random matrix model of communication via antenna arrays

Abstract: A random matrix model is introduced that probabilistically describes the spatial and temporal multipath propagation between a transmitting and receiving antenna array with a limited number of scatterers for mobile radio and indoor environments. The model characterizes the channel by its richness delay profile which gives the number of scattering objects as a function of the path delay. Each delay is assigned the eigenvalue distribution of a random matrix that depends on the number of scatterers, receiving antennas, and transmitting antennas. The model allows one to calculate signal-to-interference-and-noise ratios (SINRs) and channel capacities for large antenna arrays analytically and quantifies to what extent rich scattering improves performance.

Joint transmitter receiver diversity for efficient space division multiaccess

Abstract: The beamforming problem is studied in wireless networks where both the transmitters and receivers have linear adaptive antenna arrays. Algorithms are proposed that find the antenna array weight vectors at both the transmitters and receivers as well as the transmitter powers with one of the following two objectives: (1) to maximize the minimum signal-to-interference-and-noise ratio (SINR) over all receivers and (2) to minimize the sum of the total transmitted power satisfying the SINR requirements at all links. A numerical study is performed to compare the network capacity and the power consumption among systems having a different number of antenna array elements in a code division multiple access network.

Blind channel identification and equalization in OFDM-based multiantenna systems

Abstract: Wireless systems employing multiple antennas at the transmitter and the receiver have been shown to have the potential of achieving extraordinary bit rates. Orthogonal frequency division multiplexing (OFDM) significantly reduces the receiver complexity in multiantenna broadband systems. We introduce an algorithm for blind channel identification and equalization in OFDM-based multiantenna systems. Our approach uses second-order cyclostationary statistics, employs antenna precoding, and yields unique channel estimates (up to a phase rotation for each transmit antenna). Furthermore, it requires only an upper bound on the channel order, it does not impose restrictions on channel zeros, and it exhibits low sensitivity to stationary noise. We present simulation results demonstrating the channel estimator and the corresponding multichannel equalizer performance.

On optimum MIMO with antenna selection

Abstract: Wireless communication systems with transmit and receive antenna arrays are studied when antenna selection is used. A case with very limited feedback of information from the receiver to the transmitter is considered, where the only information fed back is the selected subset of transmit antennas to be employed. It is shown that the optimum signaling, for largest ergodic capacity with antenna selection, is generally different from that which is optimum without antenna selection for some range of signal-to-noise ratios.

Data throughputs using multiple-input multiple-output (MIMO) techniques in a noise-limited cellular environment

Abstract: We present a general framework to quantify the data throughput capabilities of a wireless communication system when it combines: (1) multiple transmit signals; (2) adaptive modulation for each signal; and (3) adaptive array processing at the receiver. We assume a noise-limited environment, corresponding to either an isolated cell or a multicell system whose out-of-cell interference is small compared with the thermal noise. We focus on the user data throughput, in bits per second/Hertz (bps/Hz), and its average over multipath fading, which we call the user spectral efficiency. First, an analysis method is developed to find the probability distribution and mean value of the spectral efficiency over the user positions and shadow fadings, both as a function of user distance from its serving base station and averaged over the cell coverage area. We assume fading conditions and receiver processing that lend themselves to closed-form analysis. The resulting formulas are simple and straightforward to compute, and they provide a number of valuable insights. Next, we run Monte Carlo simulations, both to confirm the analysis and to treat cases less amenable to simple analysis. A key contribution of this paper is a simple formula for the mean spectral efficiency in terms of the propagation exponent, mean signal-to-noise ratio at the cell boundary, number of antennas, and type of coding. Under typical propagation conditions, the mean spectral efficiency using three transmit and three receive antennas ranges from 19.2 bps/Hz (uncoded) to 26.8 bps/Hz (ideally coded), highlighting the potential benefits of multiple transmissions combined with adaptive techniques. This is much higher than the spectral efficiencies for a link using a single transmitter and a threefold receive diversity under the same conditions, where the range is from 8.77 bps/Hz to 11.4 bps/Hz. Moreover, the latter results are not nearly as practical to achieve, as they can for large signal constellations that would be highly vulnerable to impairments.

Millimeter-wave folded reflector antennas with high gain, low loss, and low profile

Abstract: Periodic and quasi-periodic structures, printed on a dielectric substrate, can be employed to control the reflection and transmission properties of incident waves as a function of structure geometry. Local variations of the element geometry on a substrate with backside metallization - resulting in respective variations of the reflection phase angle - can be used to design printed reflectarray antennas. The dual-polarization properties of such antennas, together with polarizing grids or slot arrays, can be exploited for the realization of compact, low-profile folded reflector antennas. Examples of some antennas of this type are presented, covering the 60 GHz range for communication and ISM applications, and 76 to 77 GHz for automotive radars.

High-resolution signal processing for a switch antenna array FMCW radar with a single channel receiver

Abstract: Standard high resolution array processing techniques are based on simultaneous sampling of the whole multiple sensor array and, hence, require that the number of receivers should be equal to the number of receiving antennas. A switch antenna array FMCW radar system is introduced as a promising substitute for the multiple-channel array due to its lower cost and a simpler front-end circuitry. New high-resolution signal processing algorithms for the system composed of a single transmitter, m receiving antennas, and a single receiving channel are based on the new nonstationary version of the Capon (1969) beamforming. Simulation demonstrates that the new algorithms yield very good performance in terms of both estimation accuracy and multiple-target resolution. These algorithms give better estimation than the MUSIC algorithm even for the case of slow moving targets.

Apparatus and method for transmitting and receiving data using an antenna array in a mobile communication system

Abstract: A data transmitting/receiving apparatus and method using an antenna array in a mobile communication system. A Node B measures a transmission status of each transmission antenna, classifies transmission data according to priority, and transmits to a UE high-priority data through a transmission antenna at a relatively good transmission status and low-priority data through a transmission antenna at a relatively poor transmission status.

On the capacity of cellular systems with MIMO

Abstract: It is shown that the mutual information of a single, isolated, multiple transmit and receive antenna array link is maximized by transmitting the maximum number of independent data streams for a flat Rayleigh fading channel with independent fading coefficients for each path. However, if such links mutually interfere, in some cases the overall system mutual information can be increased by transmitting fewer streams.

Omnidirectional sonde and line locator

Abstract: At least one antenna array including three mutually orthogonal antennas each sharing a common center point senses an electromagnetic signal emitted by a buried object such as a utility line, pipe or sonde. A circuit at least partially mounted in a housing is connected to the array and determines a location of the buried object by measuring signal strength and field angles in three dimensions without having to align the antenna array relative to the buried object while eliminating nulls and false peaks. A graphical user interface (GUI) has user-friendly icons, symbols, menus, numbers and graphical and auditory representation of signal strength. A SEARCH view indicates signal strength by showing a rotating strength indicator, a trace mode MAP view in which line location is shown by a line that moves side-to-side, and a sonde mode MAP view in which sonde location is shown by a moving line, pole and equator.

MIMO Channel Capacity for the Distributed Antenna Systems

Abstract: We examine the multi-input multi-output (MIMO) channel capacity where one side of the link constitutes a largely spaced antenna array, e.g. distributed antenna system (DAS), which prompts the need to model the channel that has both mi- croscopic and macroscopic fading. Specifically, we consider a MIMO system comprising M antennas co-located at one side of the link and N largely separated ports each with L antennas co- located within a port at the other, named as generalized distributed antenna system (GDAS) (1). We assume independent macro- scopic and microscopic fading between ports and common macro- scopic but independent microscopic fading at each antenna in a port. Using a simple composite fading channel model, a Rayleigh- lognormal composite fading, the influence of the macroscopic di- versity as well as the microscopic diversity on the channel capacity, especially the outage capacity, of the MIMO GDAS is investigated for both the uplink and the downlink.

Experimental study of mutual coupling compensation in smart antenna applications

Abstract: This paper investigates the benefit of mutual coupling compensation via a method of moments (MoM) approach in a uniform circular antenna array operating at 1.8 GHz. This mutual coupling compensation technique is applied to a direction of arrival (DOA) study of up to two cochannel mobile users. Field measurements and computer simulations are examined to explore the assumptions of the technique and verify its effect when using the Bartlett and MUSIC DOA algorithms. Computer simulations considering the application of the technique to down-link beamforming are also included. Experimental results show that the mutual coupling compensation technique improves up-link DOA algorithm performance primarily by reducing unwanted sidelobe levels. This reduction in sidelobe levels aids in down-link beamforming weight design. Specifically, simulation results show that use of the compensation technique allows DOA-based down-link beamforming algorithms to perform similarly to spatial signature-based algorithms. All field measurements were made using the smart antenna testbed at the University of Texas at Austin.

Correlation and channel capacity of MIMO systems employing multimode antennas

Abstract: A novel way of exploiting higher modes of antennas as diversity branches in multiple-input-multiple-output (MIMO) systems is introduced. Essentially, antennas employing multiple modes offer characteristics similar to an antenna array, through multiple modes and using only a single element. The physical mechanism that yields different received signals is the fact that each mode has a different radiation pattern. Analytical expressions for the correlation between signals received by different modes are presented for a biconical and a circular microstrip antenna that employs higher order modes. It is found that the correlation is low enough to yield a significant diversity gain. Furthermore, the channel capacity of a MIMO system using a multimode antenna, i.e., an antenna employing multiple modes, is found to be comparable to the capacity of an array. Since only one element is needed, the multimode antenna offers several advantages over traditional arrays, and is an interesting antenna solution for future high capacity MIMO systems.

MIMO channel capacity for the distributed antenna

Abstract: We examine the multi-input multi-output (MIMO) channel capacity where one side of the link constitutes a largely spaced antenna array, e.g. distributed antenna system (DAS), which prompts the need to model the channel that has both microscopic and macroscopic fading. Specifically, we consider a MIMO system comprising M antennas co-located at one side of the link and N largely separated ports each with L antennas colocated within a port at the other, named as generalized distributed antenna system (GDAS). We assume independent macroscopic and microscopic fading between ports and common macroscopic but independent microscopic fading at each antenna in a port. Using a simple composite fading channel model, a Rayleigh-lognormal composite fading, the influence of the macroscopic diversity as well as the microscopic diversity on the channel capacity, especially the outage capacity, of the MIMO GDAS is investigated for both the uplink and the downlink.

Touch control display screen with a built-in electromagnet induction layer of septum array grids

Abstract: A touch control display screen with built-in membrane antenna array lattice electromagnetic induction layer, including at least a display screen and a shell; wherein an induction layer is provided in the rear of the display screen, the output of the induction layer is connected to an induction control circuit, a display screen control circuit is also provided in the shell; the induction layer is the antenna array printed on the insulation membrane and arranged along the X, Y axes, therein the area enclosed by each lattice unit constitutes one induction cell. Because the electromagnetic induction layer is provided in the rear of the display screen and flexible membrane-type, printed electromagnetic induction array antenna is used as the identifying induction component according to the present invention, the manufacture is easy, the cost is low, and the advantage in cost-cut is prominent in comparison with the prior art when the area of the display screen is larger. The accuracy of identification is high, and the mouse information or handwriting information can be input exactly by means of brush strokes of finger strokes; as a touch screen, the display screen is covered by a protecting film to avoid the physical damage, so it has long operating life.

Blind adaptive space-time multiuser detection with multiple transmitter and receiver antennas

Abstract: The demand for performance and capacity in cellular systems has generated a great deal of interest in the development of advanced signal processing techniques to optimize the use of system resources. In particular, much work has been done on space-time processing in which multiple transmit/receive antennas are used in conjunction with coding to exploit spatial diversity. We consider space-time multiuser detection using multiple transmit and receive antennas for code-division multiple-access (CDMA) communications. We compare, via analytical bit-error-probability calculations, user capacity, and complexity, two linear receiver structures for different antenna configurations. Motivated by its appearance in a number of third-generation (3G) wideband CDMA standards, we use the Alamouti (see IEEE J. Select. Areas Commun., vol.16, p.1451-58, Oct. 1998) space-time block code for two-transmit-antenna configurations. We also develop blind adaptive implementations for the two transmit/two receive antenna case for synchronous CDMA in flat-fading channels and for asynchronous CDMA, in fading multipath channels. Finally, we present simulation results for the blind adaptive implementations.

Method of detection of signals using an adaptive antenna in a peer-to-peer network

Abstract: An adaptive antenna signal identification process to provide increased interference rejection in a wireless data network such as a wireless Local Area Network (LAN) (11-1, 11-2), The adaptive antenna (20-1, 20-2)is located at an access point (14-1, 14-2) and can be steered to various angle of arrival orientations with respect to received signals. Associated radio receiving equipment utilizes two distinct signal detection modes. In a first mode, the directional antenna array is set to have an omni-directional gain pattern. When the invention is deployed in a relay function, where messages received from a first node (12-1-1, 12-2-2, 12-1-n) are to be forwarded to a second node (12-2-p), the recorded direction of its best reception is retrieved for the second node (12-2-p) and used when the antenna array (20-1, 20-2)is used to transmit the signal to the second node (12-2-p). Storage of the best antenna angle for propagation to neighbor nodes can be handled by control functions in a manner that is analogous to other router lookup tables, such as being contained in a lookup table (25) that stores IP addresses.

Smart-antenna system for mobile communication networks .Part 2. Beamforming and network throughput

Abstract: Part 1 of this paper provided an overview of smart-antenna systems, and presented a planar array as a design example. In addition, Part 1 discussed the potential of smart antennas with regard to providing increased capacity in wireless communication networks. Part 2 introduces the signal-processing aspects of the antenna array. In particular, it describes the utility of direction-of-arrival algorithms in array-antenna systems, and gives an overview of the signal-processing algorithms that are used to adapt the antenna radiation pattern. The adaptive-algorithm descriptions are accompanied by simulation results obtained for a specific network topology. In particular, the antenna system is simulated assuming a mobile network topology that is continuously changing. Basic results presented are the dependence of the overall network throughput on the design of the adaptive-antenna system, and on the properties of the adaptive-beamforming algorithms and associated antenna patterns.

Wideband smart antenna theory using rectangular array structures

Abstract: Smart antenna techniques at the base station can dramatically improve the performance of the mobile radio system by employing spatial filtering. The design of a fully spatial signal processor using rectangular array configuration is proposed. Two-dimensional (2-D) spatial filters that can be implemented by microstrip technology are capable of filtering the received signal in the angular domain as well as the frequency domain. Furthermore, it has wideband properties and, hence, eliminates the requirement of different antenna spacing for applications including various carrier frequencies. The desired frequency selectivity of the smart antenna can be combined with compensation of the undesired frequency performance of a single antenna element, and the result is quite satisfactory for practical implementation. In addition, if the elements of the array are not perfectly omnidirectional or frequency independent, we can compensate for these deficiencies in the design algorithm. Two different algorithms for calculating the real-valued weights of the antenna elements are proposed. The first algorithm is more complex but leads to sharper beams and controlled performance. The second method is simpler but has wider beam and lower fractional bandwidth. Some computer simulation results demonstrating the directional beam patterns of the designed beamformers are also presented.