Abstract: Various embodiments of the present invention provide systems, apparatuses and methods for performing analog to digital conversion. For example, an analog to digital converter circuit is discussed that includes an analog input, a number of analog to digital converters and a generalized beamformer. The analog to digital converters are operable to receive the analog input and to yield a number of digital streams. Each of the analog to digital converters samples the analog input with different phase offsets. The generalized beamformer is operable to weight and combine the digital streams to yield a digital output.

Abstract: A method of and system for calibrating a repeater in a wireless communications system are provided. The one or more calibration parameters for the repeater are derived from (a) time measurements derived from one or more signals relayed by the repeater and received at a plurality of different measurement positions, and (b) the positions of the measurement locations. In one application, the one or more parameters are used in determining the positions of subscriber stations in the wireless communications system.

Abstract: Disclosed is an electronic scanning array antenna which can be used as a UWB radar having an occupied band of not less than 500 MHz. An impulse generator is connected to each of a plurality of antenna elements constituting the electronic scanning array antenna, and a transmission trigger time to each of the impulse generators connected to the antenna elements is changed, whereby the phase of radio waves emitted from an antenna is equivalently changed. Moreover, a transmission trigger repletion interval is changed to thereby control a direction of a beam emitted from the array antenna. As means of changing a transmission trigger timing to each of the impulse generators connected to the antenna elements, a method of changing a frequency of a transmission trigger pulse and a method of changing a pulse position are adopted.

Abstract: A multi-antenna system using adaptive beamforming includes a phase shift unit, a signal combination unit, a frequency down-converter, and an analog-to-digital (A/D) converter, and a beamforming control unit. The phase shift unit includes a plurality of phase shifters which shift the phases of signals received from a plurality of antennas. The signal combination unit combines phase-shifted signals output from the plurality of phase shifters. The frequency down-converter down-converts a signal output from the signal combination unit into a baseband signal. The A/D converter converts the baseband signal into a digital signal. The beamforming control unit searches for a weight vector higher than a preset threshold signal-to-noise ratio (SNR) when a reception SNR of the digital signal output from the A/D converter is lower than the threshold SNR, and changes a currently set weight vector into the searched weight vector to provide to the phase shift unit.

Abstract: Systems and methods to determine electromagnetic properties are provided. A particular method includes directing electromagnetic energy toward an article under test. The method also includes taking measurements of electromagnetic energy scattered by the article under test. The method further includes determining expected baseline values of at least one electromagnetic property of the article under test. The expected baseline values are based on electromagnetic energy scattered by a control article. The method also includes determining output data based on a difference between the expected baseline values and characteristic values of the article under test determined based on the measurements of electromagnetic energy scattered by the article under test. The output data includes values indicative of inhomogeneous distribution of an electromagnetic property of the article under test.

Abstract: In one aspect, a system includes a first circuit board that includes integrated circuits, a first thermal spreader coupled to the integrated circuits of the first circuit board, a first compliant board coupled to the first circuit board, a second circuit board that includes integrated circuits and a second thermal spreader coupled to the integrated circuits of the second circuit board. The first circuit board and the first thermal spreader have a first thickness. The second daughter board and the second thermal spreader have a second thickness. The system further includes a second compliant board coupled to the second circuit board, a board assembly coupled to first and second compliant boards and a cold-plate assembly in contact with the first and second thermal spreaders. Either of the first or the second compliant boards is configured to expand or contract to account for the differences between the first and second thicknesses.

Abstract: A true time delay beamforming system and calibration method for transmission and reception of a beam is disclosed. The true time delay beamforming system comprises at least one input signal received by at least one signal conditioning device, wherein the signal conditioning device is adapted to provide selective, independent, and variable control of one of a phase delay, a time delay and an amplitude of the input signal to produce an output signal. A control logic device is adapted to provide a control logic signal to the at least one signal conditioning device for selectively activating and controlling the signal conditioning device. The true time delay beamforming system may further include an automatic calibration system that generates an error correction signal based on errors detected in the output signal, and selectively adjusts the control logic signal based thereon.

Abstract: A reflection-type phase shifter is provided. The reflection-type phase shifter has a coupler, a first reflection load, and a second reflection load. The coupler has an input port for receiving an input signal and an isolated port for outputting an output signal due to a first reflected signal at a through port and a second reflected signal at a coupled port. The first reflection load reflects the first fraction of the input signal to thereby generate the first reflected signal. The second reflection load reflects the second fraction of the input signal to thereby generate the second reflected signal. In addition, at least one of the first and second reflection loads is a transmission line.

Abstract: An optical path is configured to propagate an input optical signal. A plurality of electrodes are configured to produce a plurality of discrete phase shifts on the optical signal. An output optical signal is phase-shifted with respect to the input optical signal by a sum of the plurality of discrete phase shifts.

Abstract: An apparatus and method for receiving electromagnetic waves using photonics includes a transmission unit transmitting electromagnetic waves in intervals; a time delay unit coupled to the transmission unit and controlling the transmission unit to transmit the electromagnetic waves in the intervals; an antenna receiving the electromagnetic waves reflected from the target; an interferoceiver coupled to the antenna and receiving the electromagnetic waves from the antenna, the interferoceiver comprising an optical recirculation loop to produce replica electromagnetic waves; and a computer identifying the target from the reflected electromagnetic waves.

Abstract: The present invention relates to a device for realizing beam-forming in CDMA mobile telecommunication system by employing smart antenna technique and method thereof, which forms multiple fixed beams in a sector, and uses multiple fixed beams to form the traffic channel with narrow beams and the common channel with sector beams simultaneously in the same smart antenna system, and overcomes the problem of inconsistency of phrases of respective channels due to the variations of time and temperature without complicated correction technique, thereby improving the capacity and performance of CDMA system with multiple antennas.

Abstract: A method of beamforming a radiofrequency array having multiple antenna elements is provided. The method includes transmitting two or more sub-beams of a modulated light beam through a switched fabric, using wavelength switching to designate a respective path through the switched fabric for each sub-beam, and converting each sub-beam to a driving signal for one or more of the antenna elements or to a received signal from one or more of the antenna elements. Each path through the switched fabric has a selected cumulative true time delay.

Abstract: A path sharing transceiver array architecture is disclosed. A plurality of channels are linked to antennas of an array for transmitting and receiving wireless signals that are offset in one of phase or time relative to one another. Each channel is associated with a delay element. In the receiving case, an offset signal is received at a first channel, processed, and shifted by a first delay element. The resulting signal is combined with the processed signal of a second, adjacent channel where a phase or time delayed signal is received. The combined signal is then shifted by a second delay element to produce a net signal. The first delay element is used to generate a shifted signal for both the first and second channel. The architecture can be extended to another number of channels.

Abstract: A phased-array antenna with electronic beam steering that provide simultaneous operation at transmit and receive frequencies and polarization control is disclosed. The antenna architecture reduces the number of beam steering and polarization control devices used compared to conventional array designs. The extremely compact, low-loss, and largely passive design reduces the number of active amplifiers needed using micro-electromechanical systems MEMs and advanced micro-coaxial circuits.

Abstract: An HPEM module (1,10) is provided, wherein the output pulse or the trigger pulse is transmitted on a single input trigger pulse (Trigger 2, 11) with an intermediate TTD network (5, 14) in a phase-defined and time-defined manner independent of frequency depending on the selected input of the electromagnetic lens via the geometric form of the lens. The trigger signal defines the time point for the generation of an UWB pulse in the pulse generator (3, 16). The main lobe of an antenna array (1*n) of several antennae (7, 15) is thus altered in the same number of positions in a plane accordingly as the number of adjustable phase differences or time differences. For an m*n array the alignment of the antenna lobe is no longer restricted to the plane.

Abstract: A System and Method for Person or Object Position Location Utilizing Impulse Radio, comprising a plurality of reference impulse radios; an object or person to be tracked having a mobile impulse radio associated therewith; an architecture with an associated positioning algorithm associated with said plurality of impulse radio reference radios and said mobile impulse radio; and display means for displaying the position of the person or object whose position is to be determined.

Abstract: Method for obtaining a predetermined position for a satellite antenna, whereby a controller (9) is made to transfer information to a velocity controller (3), in turn being made to transfer information to a current regulator (4), being made to transfer current to a motor which is intended for setting the desired position of the satellite antenna. The electrical motor (5) is made to receive current from the current regulator so that the electrical motor is made to turn a predetermined angle during a predetermined time interval. An angle sensor (6) is positioned on the satellite antenna and is made to read an absolute angle or an angular displacement of the satellite antenna, and the angle sensor is connected to the controller so as to create a feedback loop. An automatic control system is also disclosed.

Abstract: An antenna arrangement comprising at least two antenna arrays, each array comprising a plurality of radiating elements being arranged so as to have at least a plurality of corresponding radiating element positions, wherein for each radiating element there is associated an excitation means comprising a magnitude weight and a delay weight, wherein there is a first set of excitation means associated with a first array providing a first radiation pattern and a second set of excitation means associated with a second array providing a second radiation pattern. At least two respective excitation means associated with a corresponding radiating element position of at least two respective arrays have at least two different magnitude weights, and at least two respective excitation means associated with a corresponding radiating element position of at least two respective arrays have at least two different delay weights.

Abstract: A radar system, apparatus, and method includes at least one radar transmitter for transmitting an electromagnetic waveform; a receiving antenna comprising a plurality of receiving antenna elements and delay lines, each of the plurality of receiving antenna elements receiving the return signal operatively associated with a predetermined delay line; each delay line having a delay length which produces a different phase delay in the return signal; the different phase delays producing substantially different antenna patterns for the received signal at a given frequency; at least one processor operatively connected to receive data from the plurality of delay lines; the at least one processor operating to analyze the substantially different beam patterns for a given frequency; whereby the processing of the data produces results indicating the presence and location of a target.

Abstract: A microwave antenna system having a plurality of antenna elements arranged in an array having two spaced ends. A phase shifter is electrically connected to a first group of at least two adjacent antenna elements at one end of the array and is also electrically connected to a second group of at least two adjacent antenna elements adjacent the other end of the array. Individual phase shifters are connected to individual middle antenna elements for at least several of the antenna elements between the first and second groups of antenna elements. A switch selectively electrically connects a phase delay line in series between the phase shifter and the second group of antenna array elements to effectively double the number of good beam positions of the antenna array.

Abstract: Method and apparatus for minimizing antenna backside signal response and ambiguity in low frequency applications, particularly low frequency synthetic aperture radar (SAR). Various time delay elements are selectably switched into the signal path so as to cause a null to be placed in the antenna response pattern in the direction of undesired radar returns. The means for selectably switching may be dithered so as to introduce modulation onto the undesired radar return to aid in the discrimination and removal of the undesired radar return from the SAR image during post processing.

Abstract: There are provided a method of determining real time location of a reflecting object and a system thereof.

Abstract: The present invention relates to a device for adjusting the beam direction of an antenna. The device has a source connection terminal to be connected to a signal source and at least two feed connection terminals to be connected to antenna element feed points. A feed line structure is elongated in a main direction at a distance from and in parallel to a fixed ground plane on at least one side of said feed line structure, wherein a movable dielectric element is located between said feed line structure and said ground plane so as to change the signal phase of signal components being transferred between said source connection terminal and the respective feed connection terminals. The device includes means for allowing said ground plane to be positioned relatively close to said feed line structure without risking accidental contact between said feed line structure and said ground plane.

Abstract: A beam-forming antenna for transmission and/or reception of an electromagnetic signal having a given wavelength in a surrounding medium includes a transmission line electromagnetically coupled to an array of individually controllable antenna elements, each of which is oscillated by the signal with a controllable amplitude. The oscillation amplitude of each of the individual antenna elements is controlled by a switch. The antenna elements are arranged in various shapes such as a parabolic arc, a circular arc, a cylindrical surface or a conic surface. The antenna elements have various spacing such as uniform, parabolic, circular, or raised cosine.

Abstract: Disclosed is an electronic scanning array antenna which can be used as a UWB radar having an occupied band of not less than 500 MHz. An impulse generator is connected to each of a plurality of antenna elements constituting the electronic scanning array antenna, and a transmission trigger time to each of the impulse generators connected to the antenna elements is changed, whereby the phase of radio waves emitted from an antenna is equivalently changed. Moreover, a transmission trigger repletion interval is changed to thereby control a direction of a beam emitted from the array antenna. As means of changing a transmission trigger timing to each of the impulse generators connected to the antenna elements, a method of changing a frequency of a transmission trigger pulse and a method of changing a pulse position are adopted.

Abstract: Provided is a sensing device having a multi beam antenna array. The sensing device includes an antenna array including a plurality of antennas, a plurality of low noise amplifiers respectively connected to the antennas to amplify radio frequency signals received from the respective antennas, a delay line box including a plurality of delay lines, each delay line delaying the signals amplified by the low noise amplifiers for a predetermined time, and a detector detecting the output signals of the delay ling box.

Abstract: Disclosed is an Radio Frequency (RF) volumetric direction finding (DF) methodology, utilizing an Half Maxwell Fish-eye (HMFE) Lens having a semi-spherical shape, a focal plane with a feed structure composed of near-equally spaced frequency-independent antenna elements disposed uniformly to form a 2-dimentional feed array; and RF power splitters for each element and combiners for combining the RF energy received by the elements; forming rows and columns; thereby reducing the number of required RF receiver channels for subsequent processing, where the maximum row/column and differential amplitude comparison is used for deriving DF estimation of intercepted signals; as part of a robust signal detection and direction-finding (DF) system; for detecting and processing a plurality of signals emanating from navigation, radar and communication equipment on surface and airborne platforms.

Abstract: An array antenna apparatus which has an away antenna formed by a plurality of antenna elements, and subjects received signals, which are received by the antenna elements, to weighting using array weights of complex numbers. The array antenna apparatus includes a delay device for delaying a signal; a weighting device for separating ea of the received sirs into first and second received signals, delaying any one of the first and second received signals by using the delay device, so as to weight the first and second received signals at different timings; and a first adding device for adding the weighted first and second received signals to each other. The weighting device weights any one of the first and second received signals by using the real part of the relevant array weight, and weights the other received signal by using the imaginary part of the array weight.

Abstract: A beamforming apparatus obtains the beamforming parameters that realize arbitrary desirable PSF by using optimization theories. The apparatus uses at least one of the beamforming parameters such as the intensities, frequencies, bandwidths and shapes of the signals transmitted by the transmitting unit, the filtering of noises, amplifications (gains) and shapes of the signals received by the receiving unit, delays of the directions of propagation and array used by the delay units, apodization functions of the directions of propagation and array used by the apodization units, the number of the additions of the signals by the addition unit, array element parameters such as element size or shape and how to implement the elements in transducers (e.g., connections by leads between the elements and with the surroundings), which are determined by the specified optimization process to realize the desirable PSF.

Abstract: An arrangement for electronically steering a radiation lobe of an antenna. Radiators of the antenna are located in a row and two radiators, which are equidistant from a midpoint of the row, form a radiator pair. To steer the radiation lobe, each pair is associated with a reflection-type phase shifter, implemented by a shared transmission line and reflection point, which can be moved. Phase changes take place by moving the reflection point along the transmission line using one movable or several fixed reflection circuits. The phase adjusting for all radiator pairs in a row is implemented simultaneously by a common control circuit. In the former case the reflection circuits of the different transmission lines are slides attached to one and the same movable arm. In the latter case one of the reflection circuits of each transmission line is activated at a time.

Abstract: A beam-forming antenna for transmission and/or reception of an electromagnetic signal having a given wavelength in a surrounding medium includes a transmission line electromagnetically coupled to an array of individually controllable antenna elements, each of which is oscillated by the signal with a controllable amplitude. The antenna elements are arranged in a linear array and are spaced from each other by a distance that does not exceed one-third the signal's wavelength in the surrounding medium. The oscillation amplitude of each of the individual antenna elements is controlled by an amplitude controlling device, such as a switch, a gain-controlled amplifier, or a gain-controlled attenuator. The amplitude controlling devices, in turn, are controlled by a computer that receives as its input the desired beamshape, and that is programmed to operate the amplitude controlling devices in accordance with a set of stored amplitude values derived empirically for a set of desired beamshapes.

Abstract: An HPEM module (1,10) is provided, wherein the output pulse or the trigger pulse is transmitted on a single input trigger pulse (Trigger 2, 11) with an intermediate TTD network (5, 14) in a phase-defined and time-defined manner independent of frequency depending on the selected input of the electromagnetic lens via the geometric form of the lens. The trigger signal defines the time point for the generation of an UWB pulse in the pulse generator (3, 16). The main lobe of an antenna array (1 *n) of several antennae (7, 15) is thus altered in the same number of positions in a plane accordingly as the number of adjustable phase differences or time differences. For an m*n array the alignment of the antenna lobe is no longer restricted to the plane.

Abstract: A time delay beamformer comprises input channels, which have associated samplers arranged to sample inputs signal carried upon the input channels. The samplers sample the input channels at a number of points in time to produce a number of sampled signals. An adaptive processor receives each of the input signals and each of the sampled signals, and generates processed signals therefrom. Time delay devices introduce a steering time delay to the processed signals and a summer generates a beamformed output signal the delayed processed signals.

Abstract: An optical time delay module has a plurality of time delay elements connected in a series and a plurality an optical output couplers wherein each of said optical output couplers is operationally connected between one or more time delay elements in said series, the optical output couplers providing a plurality of optical outputs from said module with different optical delays controlled by an analog voltage.

Abstract: Disclosed herein is a front-end device for a phased array system. The front-end device includes an array of horn antennas, a first set of transmission lines coupled to the horn antenna array for a first polarization, a second set of transmission lines coupled to the horn antenna array for a second polarization orthogonal to the first polarization, and a plurality of L-shaped excitation elements. Each L-shaped excitation element of the plurality of L-shaped excitation elements couples a transmission line from each of the first and second sets of transmission lines to a respective horn antenna of the horn antenna array.

Abstract: An optical time delay module has a plurality of time delay elements connected in a series and a plurality an optical output couplers wherein each of said optical output couplers is operationally connected between one or more time delay elements in said series, the optical output couplers providing a plurality of optical outputs from said module with different optical delays controlled by a digital control word.

Abstract: A receiver, such as a miniaturized microwave-photonic coherent receiver (MMPR) is disclosed. The receiver includes an antenna to output an electrical RF signal received on a section of the antenna, a laser to produce an optical signal, a photonic modulator to receive the optical signal and the electrical RF signal and produce an EO-RF signal and to receive the optical signal and an electrical LO signal and produce an EO-LO signal, a signal combiner to provide a combined EO-RF and EO-LO signal and a photodiode to receive the combined signal and produce an IF signal. A method of detecting an object using the MMPR includes receiving an electrical RF signal corresponding to the object, outputting the electrical RF signal to a photonic modulator, modulating the electrical RF signal onto an optical carrier, demodulating the electrical RF signal to produce an IF signal and processing the IF signal.

Abstract: Apparatus and methods are used for controlling electromagnetic radiation pulse duration in a lithographic apparatus. A dividing element is arranged to divide an electromagnetic radiation pulse into a first portion and a second portion. A prism receives, refracts, and subsequently emits the first portion of the electromagnetic radiation pulse. A directing element is arranged to direct the first and second portions of the electromagnetic radiation pulse parallel to a common optical axis. The first portion combines with the second portion to form a combined radiation beam pulse. The combined radiation beam pulse has a longer pulse duration than the divided electromagnetic pulse and experiences no corresponding loss in intensity.

Abstract: Embodiments of the invention are concerned with frequency scanning antennas for transceiving radio frequency energy for use in detecting and monitoring ground-based targets. In one arrangement the frequency scanning antenna is embodied as a structure that is capable of steering a radio frequency beam to a plurality of different angles about the antenna structure: the antenna structure comprises at least two array antennas and a controller for controlling input of energy to the two array antennas, and the array antennas are disposed within the antenna structure such that the antenna structure is capable of steering a beam to a first angle using one of said two array antennas and of steering a beam to a second angle, different to said first angle, using the other of said two array antennas.

Abstract: A method for electronically scanning a predetermined geostationary orbital arc segment around the earth with an antenna system. The antenna system includes a planar array. A number of fixed electronic squints is selected. Lengths of the total plurality of fixed delay line lengths are generated for the planar array based on the number of fixed electronic squints. All of the antenna elements in the planar array for the mobile earth station are fitted with the generated lengths. The orbital arc segment is electronically scanned with a single linear scan with the planar array. This method is extendable to the case of multiple beams by adding additional phase shifters at each column and keeping the number of fixed line lengths the same, regardless of the number of additional beams.

Abstract: Methods and apparatus for constructing phased array antenna beamforming networks are provided, that allow to scan multiple beams and select appropriate sets of delay lines simultaneously. The beamforming networks disclosed herein generate less losses than conventional ones and in some cases, do not require active switching, making them completely passive. Three main methods are comprised in the invention: (1) laser wavelength hierarchies, (2) arrangements of Wavelengths Division Multiplexing (WDM) components, (3) re-use of laser wavelengths. Multiple laser wavelengths are arranged in groups and subgroups (wavelength hierarchies) in the wavelength domain. By switching between these wavelength groupings, the arrangements of WDM components disclosed herein enable the beamforming network to direct the beam signals to the proper time delay lines, and to differentiate multiple beams.

Abstract: A method of two-source passive ranging comprising the steps of determining the coordinates of a first position and a second position wherein a first soldier or ground vehicle is located at the first position and a second soldier or ground vehicle is located at the second position; determining individual angles between said first and second positions and a radio frequency source; and using individual single-angle accuracy values to estimate the range from the first and second positions to the radio frequency source.

Abstract: An apparatus and method for steering a beam of light using an array of tunable optical phase delay elements is presented. The sidelobes of an angular spectrum of light reflected from the array are causing an optical crosstalk. The selected sidelobes are suppressed by perturbing the phase delay pattern of the array elements. The pattern of perturbations is found by linearizing a system of equations describing dependence of the angular spectrum of the reflected light on the phase delays introduced into the wavefront of light by the elements of the array.

Abstract: An multi-beam multifunction electro optical scanning antenna having a first variable wavelength tunable laser having an output wavelength variable within a first range and a second variable wavelength tunable laser having an output wavelength variable within a second range, different from the first range. The outputs from both lasers are modulated by independent microwave sources and the modulated outputs from both lasers are combined by an optical combiner into a combined output signal. An antenna array includes a plurality of radiators and a photodetector is associated with each radiator which converts the combined optical output from the lasers to microwave signals. Beam splitters divide the combined output signals to each of the antenna radiators while first and second wavelength-dependent time delay elements are optically connected in series between each sequential beam splitter.

Abstract: An apparatus includes antenna elements configured to receive a signal including pseudo-random code, and electronics configured to use the pseudo-random code to determine time delays of signals incident upon the antenna elements and to compensate the signals to coherently combine the antenna elements.

Abstract: An antenna system may include an antenna array which includes a plurality of radiating elements. The system may also include a phase shifter controller and algorithm to apply a non-periodic modulation to an excitation of each radiating element.

Abstract: An antenna apparatus attachable to the front-end of a transceiver circuitry, includes at least two balanced radiation elements forming a planar structure for transmitting and/or receiving a corresponding number of partial signals. The antenna apparatus also includes a signal splitter and/or combiner for splitting a signal received from an attached transceiver circuitry into said partial signals and/or combining said partial signals into a signal to be transmitted to an attached transceiver circuitry, a phase shifter device that applies relative phase shifts between at least two of said partial signals. The relative phase shifts are selectable from a group of at least two relative phase shift values provided by the phase shifter device.

Abstract: A multicarrier data transmission method and a base station (200) are provided. The base station comprises an antenna arrangement (204 to 208) configured to form multiple antenna beams, and a first controller (800) configured to divide subcarriers of the multicarrier transmission into more than one subcarrier group and allocate each subcarrier group to an antenna beam, and a second controller (238) configured to control the antenna beams formed by the antenna arrangement during transmission to sweep constantly over a given area at a constant mean beam specific angular velocity.

Abstract: A method of two-source passive ranging comprising the steps of determining the coordinates of a first position and a second position wherein a first soldier or ground vehicle is located at the first position and a second soldier or ground vehicle is located at the second position; determining individual angles between said first and second positions and a radio frequency source; and using individual single-angle accuracy values to estimate the range from the first and second positions to the radio frequency source.

Abstract: There is provided a communication method including: generating a channel estimated value for each antenna by performing channel estimation using a received signal by each antenna; calculating reception weights by which subcarriers assigned the received signal of each antenna are to be multiplied using a set of the channel estimated values; calculating a reception weight time profile for each antenna by converting the reception weights calculated for each antenna to data on a time domain; generating a transmission weight time profile for each antenna by extracting a certain section of each reception weight time profile; calculating transmission weights by which subcarriers assigned a transmission signal for each antenna are to be multiplied by converting each transmission weight time profile to data on a frequency domain; and multiplying subcarriers assigned the transmission signal for each antenna by the transmission weights of each antenna and transmit multiplied subcarriers through each antenna.