The present disclosure relates to a method of installing an antenna array.
The principle of phased array antennas has been known for many decades. Phased array antennas have been used for many applications, including steerable radar, signal broadcasting, satellite communications, wireless HDMI, the wireless networking standard IEEE 802.11ad, and many other uses. One recent development is the use of phased array antennas for cellular communication equipment at millimeter wave frequencies introduced with the New Radio (NR) standard of 3GPP, also known as 5G. A typical application is a MiFi router that provides internet access to private homes through a wireless connection with a cellular base station. The connection to the base station comprises phased array antennas at the terminal as well as at the base station.
Phased arrays provide both a high directivity, or gain, and a programmable steer direction. A focused beam of radio waves can be aimed into a range of desired directions by applying a phase offset to the signals transmitted or received at each element in the array.
However, the range of steer directions of the phased array can be relatively restricted, because the array gain reduces at higher scan angles. As one example, the 3GPP requirements for high power fixed wireless access (FWA) equipment specify performance for just 15% of the total spherical coverage (i.e. 15% of solid angle) around the device. The relationship between the spherical coverage of an antenna array and the beam angle is shown in
In addition to the throughput loss at higher scan angles, the frequencies used for 5G communication systems (i.e. between 24 GHz and 48 GHz) easily suffer high losses when passing through most materials, including window panes, tree foliage and even rainfall. Losses are particularly high if the signal path is blocked by walls or other solid structures.
Connection quality between a user device and a base station is often assessed by measuring the total observed incoming power. In mobile communications, this is often referred to as RSSI (received signal strength indicator). Most mobile devices display an indicator of signal strength to the user. With phased arrays, however, the received signal power depends on the location and orientation of the array (owing to the losses at higher scan angles as described above).
When equipment is installed for industrial or professional use, directive antennas for signal strength measurements and knowledge of nearby base stations may be available, so that optimal device location and orientation can be identified. However, for other users, such guidance is often unavailable. Therefore, installation of phased array equipment often involves a trial-and-error based setup (similar to attempting to point a domestic TV aerial in the right direction), and the optimum placement and orientation is often difficult to determine. This means that these users can experience poor throughput performance.
Accordingly, there exists a need to minimize throughput loss in phased array systems.
This summary introduces concepts that are described in more detail in the detailed description. It should not be used to identify essential features of the claimed subject matter, nor to limit the scope of the claimed subject matter.
According to one aspect of the present disclosure, there is provided a method as defined in claim 1. According to another aspect of the present disclosure, there is provided a non-transitory computer-readable medium as defined in claim 14. According to a further aspect of the present disclosure, there is provided a phased array antenna as defined in claim 15.
Set out below are a series of numbered clauses that disclose features of further aspects, which may be claimed. The clauses that refer to one or more preceding clauses contain optional features.
1. A method for installation of a phased array antenna receiving a signal, the method comprising:
2. A method according to clause 1, wherein determining that a higher directivity of the phased array antenna comprises:
3. A method according to clause 1 or clause 2, wherein the orientation of the phased array antenna at which the higher directivity is achievable is an orientation at which the signal is received via a main lobe of the phased array antenna.
4. A method according to clause 2, wherein determining that the signal is received via a grating lobe of the phased array antenna comprises:
5. A method according to clause 4, wherein a third spacing between the first antenna element and a fourth antenna element adjacent to the first antenna element in a second direction is different to a fourth spacing between the fourth antenna element and a fifth antenna element adjacent to the fourth antenna element in the second direction, wherein the second direction is nonparallel to the first direction.
6. A method according to clause 5, wherein the first direction is orthogonal to the second direction.
7. A method according to any of clauses 4 to 6, wherein the plurality of antenna elements comprises:
8. A method according to any of clauses 4 to 7, wherein the first spacing is about 50 percent greater than the second spacing.
9. A method according to any of clauses 4 to 8, wherein the first antenna element is displaced in the first direction from a hypothetical uniform array of equally spaced elements, wherein the displacement of the first antenna element in the first direction is about 10 percent of the spacing between the elements of the hypothetical uniform array.
10. A method according to any of clauses 4 to 9, wherein determining that the signal is received via a grating lobe of the phased array antenna comprises:
11. A method according to any of clauses 1 to 10, wherein the phased array antenna is included in a device comprising a plurality of LEDs, and wherein providing instructions for adjusting the orientation of the phased array antenna comprises illuminating at least one of the plurality of LEDs.
12. A method according to any of clauses 1 to 11, wherein the phased array antenna is included in a device, the device in communication with an external device comprising a user interface, and wherein providing instructions for adjusting the orientation of the phased array antenna comprises providing instructions via the user interface of the external device.
13. A method according to clause 12, wherein the external device is a smartphone.
14. A method according to clause 2, wherein determining that the signal is received via a grating lobe of the phased array antenna comprises:
15. A method according to any of clauses 1 to 14, wherein determining that a higher directivity of the phased array antenna is achievable comprises:
16. A method according to clause 15, wherein determining that the signal is a reflected signal comprises determining that a higher directivity is achievable at the phased array antenna by optimizing the received power of a candidate signal path and the received signal quality (RSQ) of the candidate signal path.
17. A method according to any of clauses 1 to 16, wherein the signal is a first signal received from a first base station at a first angle of arrival, and wherein determining that a higher directivity of the phased array antenna is achievable comprises:
18. A method according to clause 17, wherein determining the normalized signal power of the first signal comprises dividing the received power of the first signal by the antenna gain corresponding to the first angle of arrival.
19. A non-transitory computer-readable medium comprising instructions that, when executed by a processor of a device, cause the device to carry out a method according to any of clauses 1 to 18.
20. A phased array antenna comprising a plurality of antenna elements, wherein a first spacing between a first antenna element and a second antenna element adjacent to the first antenna element in a first direction is different to a second spacing between the second antenna element and a third antenna element adjacent to the second antenna element in the first direction.
21. A phased array antenna according to clause 20, wherein a third spacing between the first antenna element and a fourth antenna element adjacent to the first antenna element in a second direction is different to a fourth spacing between the fourth antenna element and a fifth antenna element adjacent to the fourth antenna element in the second direction, wherein the second direction is nonparallel to the first direction.
22. A phased array antenna according to clause 21, wherein the first direction is orthogonal to the second direction.
23. A phased array antenna according to any of clauses 20 to 22, wherein the plurality of antenna elements comprises:
24. A phased array antenna according to any of clauses 20 to 23, wherein the first spacing is about 50 percent greater than the second spacing.
25. A phased array antenna according to any of clauses 20 to 24, wherein the first antenna element is displaced in the first direction from a hypothetical uniform array of equally spaced elements, wherein the displacement of the first antenna element in the first direction is about 10 percent of the spacing between the elements of the hypothetical uniform array.
Specific embodiments are described below by way of example only and with reference to the accompanying drawings, in which:
An incoming wave with wavelength λ from a distant source meets the antenna 200 at angle θ from the array normal, and is received by N elements 202 equidistantly spaced at distance D. The signals from adjacent elements 202 are delayed by a constant phase offset Δφ by N phase shifters 204 (corresponding to the N elements 202). If this phase offset Δφ matches the delay the wavefront experiences between two elements 202 then the delayed signals from each element 202 coherently add up. If the phase offset Δφ does not match the external delay difference, then the summation yields a smaller signal.
The phase offset Δφ that maximizes received signal power is directly related to the angle of arrival of the incoming beam. In particular, coherent signal summation is achieved if:
Δφ=2π·(D/λ)·sin θ (Equation 1)
This is referred to herein as the “coherence condition”. Most phased arrays use a uniform array pitch (i.e. spacing D) and the phase offset Δφ between any two neighboring elements follows the rule above. The relationship holds even for arrays with non-uniform element pitch as long as the phase offset Δφ between two neighboring elements is related to the physical distance between them.
A related method involves inverting the phases of half the antenna elements. In that case, the incoming beam angle corresponds to a minimum power level observed. Both methods are often combined to improve accuracy.
Note that the paths lengths difference D·sin θ in Equation 1 creates a time difference between two adjacent paths. On the other hand, commercial phased array implementations create a phase different between two paths (using the I/Q vector modulation technique). For a single-frequency sinewave, time and phase correspond exactly. However, for wideband signals, the two cannot be matched precisely across the whole bandwidth of the signal.
The ratio D/λ is a critical design parameter for phased arrays. For an array pitch D up to half the signal wavelength λ (0<D/λ<½), the coherency condition creates a unique mapping between any incoming wave angle −π/2<θ<π/2 (−90°<g<)+90° and the programmed phase offset, Δφ. However, most practical phased array implementations utilize a pitch D between half and the full wavelength A of the targeted signal (½<D/λ<1). This is because a wider pitch increases the aperture and thereby the gain of the array, at least near boresight directions. The disadvantage of the wider spacing is only apparent at steeper steer angles that anyway suffer from reduced performance, because for larger scan angles not all of the power is concentrated in a single beam.
When ½<D/λ<1, the coherence condition does not allow an unambiguous mapping between incoming wave angle θ and programmed delay offset Δφ across the antenna.
For most angles, there are two possible directions from which the signal may be originating. For example, when D/λ=0.8, incoming signal from 6=60° is generally indistinguishable from signal incoming from around θ˜−22.5° (corresponding to Δφ of approximately −110° in
When the array is used to transmit a signal, a beam is directed into direction θ using the value of Δφ given by the same array equation as above. However, for a large range of angles, not just one but two beams will be created, the intended one and a second, called the grating lobe. The main beam, at angles up to ±arcsin(λ/2D) as shown in
In the two-dimensional case, up to three grating lobes generally appear that are indistinguishable from the mean beam. In the example shown in
Without unambiguous angle-of-arrival measurements for most practical array designs, there is no way to assist a user with setting up the device with the best possible orientation (which is with the incoming signal direction close to the array normal vector). If the system cannot discriminate whether an incoming signal is received via a stronger main beam or a weaker grating lobe, it is also impossible to estimate the true antenna power level. Furthermore, if signals from different stations are received at different angles and these angles are ambiguous, it is not easily possible to select the strongest station (or report the correct signal strength to the network for the network to make the most appropriate selection). The present disclosure addresses these issues by providing instructions to the user to allow them to reorient the antenna array of their device so that it receives the strongest signal at an angle close to the array normal vector, thereby improving throughput.
There are three main scenarios in which a local optimum may be identified during installation of a phased array antenna. These scenarios are shown in
After the user has positioned the device, the device sweeps the phase offset Δφ of the antenna from −180° to 180°, in order to determine an optimal phase offset Δφ. The optimal phase offset Δφ is the phase offset that maximizes the power of the received signal (i.e. by achieving coherent signal summation).
However, as shown in
Alternatively, the method may commence at 806 following an earlier determination of a phase offset Δφ after the user has positioned the antenna.
At 806, a number of candidate signal paths received at the antenna is determined. For example, the determination may comprise sweeping the phase offset Δφ from −180° to +180°. Each candidate signal path may be associated with a candidate phase offset Δφ identified when sweeping the phase offset. For example, signal paths may be associated with N (e.g. three, five, etc.) local maxima identified when sweeping the phase offset. For each detected signal, determining the number of candidate signal paths may include decoding the physical cell identification number (PCI) transmitted in the primary and secondary synchronization signals (PSS and SSS). If more than one PCI is identified, then signals are received from multiple base stations. If the same PCI is received twice, then a reflected signal may be identified by poor de-correlation between the two MIMO layers because one of the polarization directions is attenuated more by the reflection than the other. This can be estimated from the reference symbols received.
At 808, it is determined whether each candidate signal path is received via the main lobe of the antenna or via a grating lobe of the antenna. Determining whether a candidate signal path is received via the main lobe of the antenna or via a grating lobe may comprise determining the true angle of arrival of the candidate signal path at the antenna.
At 810, it is determined for each candidate signal path whether receiving the signal path via the main lobe of the antenna would result in the highest potential antenna directivity. For example, the power of a candidate signal path at the true angle of arrival is measured and subsequently normalized to the expected power that would be achieved if the antenna array were oriented such that the candidate signal path is received at an angle of arrival close to the array normal (i.e. a low value of ay Normalization of the candidate signal path may be achieved by dividing the power of the candidate signal path at the true angle of arrival by an angle-dependent function such as the cosine of the true angle of arrival, or a similar function of the true angle of arrival that describes the array response (e.g. takes into account higher losses at steep angles). Optionally, at 812, the candidate signal path that provides the highest potential directivity is selected (if more than one signal path is received at the antenna). Continuing the above example, selecting the candidate signal path that provides the highest potential directivity may comprise comparing normalized signal powers of all signal paths, and selecting the candidate signal path with the highest normalized signal power.
Optionally, in order to account for reflected signals, the determination at 810 also factors in the received signal quality (RSQ). A reflected signal may have high power, but poor signal quality. Therefore, the determination of the highest potential directivity at 810 may seek to optimize both the received power of the signal and the received signal quality. In most cases, a reflected signal will have lower power anyway, as a result of a 3 dB loss resulting from the loss of information in one of the polarization directions. Given that a reflected signal will usually have lower power, a determination based additionally on signal quality may alternatively be omitted.
At 814, an orientation of the phased array antenna at which the highest potential directivity is achievable is identified. The orientation at which the highest potential directivity is achievable may be an orientation at which the angle of arrival of the candidate signal path that provides the highest potential directivity is approximately normal to the antenna array.
At 816, a user of the phased array antenna is provided with instructions to orientate the antenna so that it receives the signal that provides the highest potential antenna directivity. For example, the user may be provided with instructions to adjust the orientation of the antenna from its initial orientation (e.g. as positioned at 802) to the orientation determined at 814. As one example, the instructions provided to the user may be in the form of LEDs that indicate the angle of arrival of the signal that provides the highest potential directivity. Once the array is oriented so that the angle of arrival of the signal that provides the highest potential directivity is approximately normal to the antenna array, the phase offset Δφ can be fine-tuned to maximize the received power of the selected signal. As another example, the instructions provided to the user may be in the form of graphically displayed reorientation instructions provided to an application running on a separate user device that is connected to the device comprising the phased array antenna via Bluetooth or a similar data interface.
The guidance to the user to reorient the antenna array can be provided in a number of forms. For example, the guidance may take the form of a “virtual compass”, where a needle points towards the signal source identified as having the highest potential received power. Alternatively, the guidance may be provided via an application on a user's mobile device. Another example is a series of LEDs in a circular pattern, with an additional LED at the center of the circle. The LED aligned with the direction of the most promising signal is initially lit up. Then, as the user turns the unit, different LEDs in the circle light up in turn, in accordance with the current orientation of the unit. Once the unit is oriented in line with the LED indicating the most promising signal, the LED at the center of the circle lights up to indicate that the unit is optimally oriented.
An example of the guidance provided to the user at 812 in
As shown in
There are two distinct ways of discriminating between signals received via the main lobe (i.e. at lower steer angles, as shown in
First Method—Modified Array Geometry
A first method involves measuring the gain of received signals using an antenna array with non-uniform element spacing. An example of an antenna array with non-uniform spacing is shown in
As shown in
In the example shown in
The arrangement shown in
In the example shown in
By moving the antenna elements away from their positions on a uniform grid 1112 with spacing D, the contributions of the elements to the radiation pattern can still be made to add up in phase in the desired main lobe direction (by choosing phase offsets Δφ that ensure this), but now the element contributions no longer add up perfectly in phase in the direction of the grating lobes, so the amplitudes of the grating lobes are reduced.
Assume an array with two different pitch sizes D·(1−2 ΔD) and D·(1+2 ΔD). An example configuration is shown in
Δφ−ΔD=2π·D·(1−2 ΔD)/λ·sin θ and
Δφ+ΔD=2π·D·(1+2 ΔD)/A·sin θ.
For small ΔD the array gain response is still similar to the uniform array. In particular, the gain of the main lobe is unchanged. However, signals arriving from the direction previously corresponding to the grating lobe direction no longer perfectly add up coherently. The array gain for signals to or from this direction is therefore reduced. The introduction of the pitch offset parameter ΔD breaks the symmetry between main and grating lobes.
The following process can then be applied, in order to discriminate between a signal received via the main lobe, and a signal received via a grating lobe.
Firstly, the full hemisphere is scanned (by applying appropriate phase offsets Δφ). Then, the signal power level is measured for each direction in which a signal is detected. For each direction, grating lobe directions are looked up from a stored table of performance (or calculated). Phase weights are then applied to look in the grating lobe directions, and the signal power level is measured.
If the signal power level is larger when the phase weights are deliberately set to a grating lobe direction, then the true angle of arrival corresponds to the grating lobe.
This is because the array gain for signals received via the main lobe is now reduced (as a result of the broken symmetry). Therefore, if the true angle of arrival was via the main lobe (e.g.)−22.5°, then the signal would have initially been stronger, and would have been attenuated when the phase weights were set to the grating lobe direction.
However, if the signal power level is smaller when the phase weights are deliberately set to a grating lobe direction, then the true angle of arrival corresponds to the main lobe. This is because the array gain for signals received via the grating lobe is now increased (as a result of the broken symmetry). Therefore, if the true angle of arrival was via the grating lobe (e.g. +60°), then the signal would initially have been attenuated, and the true signal strength would have been received when the phase weights were set to the grating lobe direction.
As noted above,
The effect of the array perturbation can be assessed by the following process, which illustrates the choice of ΔD=0.1 as the optimal value:
A. Implement an array with a defined grid spacing D and perturbation ΔD.
B. Calculate phase weights (phase offsets Δφ−ΔD and Δφ+ΔD) to form a beam into a target direction (i.e. to maximize the power of a received signal).
C. Calculate the array radiation pattern for the phase weights calculated at B over all directions, and determine the directivity (gain).
D. Record the difference in directivity of the main beam and the largest observed grating lobe.
E. Repeat B to D to target beams in all directions in a hemisphere (i.e. all potential signal paths such as reflected signals and signals from different base stations).
F. Repeat A to E for values of ΔD ranging from −0.3 to +0.3, recording the lowest difference in directivity between the main beam and grating lobe for each ΔD.
The result of the above analysis is shown in
The peak in difference between main beam and grating lobe directivity is observed at ΔD=±0.1 for all values of D<λ.
The irregular spacing architecture illustrated schematically in
If ΔD=0, for a uniform grid, the first grating lobe power is cos2(0)=1, so this grating lobe is the same intensity as the main beam. The secondary grating lobe amplitude is zero. As ΔD is increased, the first grating lobe amplitude decreases, so the main beam and grating lobe can be distinguished. However as this happens, the secondary grating lobe amplitude increases. The value of ΔD at which there is maximum difference between the main beam and the largest grating lobe occurs when the size of the two grating lobes are identical and this happens when ΔD= 1/10, exactly.
At this value of ΔD, sin( 3/10π)=cos( 2/10π)=(1+√/5)/4, which happens to be exactly half of the Golden Ratio.
For a large array, the best case power ratio between main beam and the largest grating lobe is 20·log 10((1+√5)/4)=−1.84 dB. For a smaller array, the difference will be very slightly smaller (1.5 dB for a square 16 element array), and the grating lobes may not exactly sit at the ideal locations, but ΔD=0.1 is still the configuration with the greatest difference between main beam and the largest grating lobe.
The calculations and figures described in the above paragraphs assume an original square grid and a single displacement parameter ΔD. There are many ways to achieve this displacement from a regular grid. As one alternative example to the arrangement shown in
As another example, one or more of the antenna elements of a one-dimensional 4×1 antenna array (such as those commonly used in smartphones) may be displaced from a uniform 4×1 array (with equally spaced elements), so that the array has two pitch values. For example, the four antenna elements may be arranged using pitches of large-small-large or small-large-small.
Second Method—Exploiting Wideband Nature of Signals
A second method involves exploiting the wideband nature of the signals. This method is applicable to regular arrays but may also be applied to the previously described irregular arrays. Under this method, the array phase gradient is swept to exercise all possible beam directions, including those well outside the targeted scan range of the device. At the same time, the strength of the received signals is measured at the bottom edge and top edge of all available channels sent by the base station. In NR, the signal strength may be expressed in terms of RSRP (power of reference symbols embedded in the downlink signal) or RSRQ (a measure of received signal quality, similar to signal to interface and noise ratio, SINR). From the power versus angle responses, two likely beam angles can be identified by mathematically fitting the peaks of the responses against a suitable (near-parabolic) profile. The beam angle for which the estimates at the lower and upper band edge agree is the true angle of arrival. The beam angle where there is a (analytically predictable) discrepancy in estimated beam direction between the two frequency components cannot be the true angle of arrival, and is discarded.
This is illustrated schematically in
Analytically, this can be understood as follows. The calculations assume a large 1D array, but the same equations hold in two dimensions as well, independently for each array dimension.
Assume the actual signal direction is θ. Therefore, the maximum power level is observed when Δφ=2π·(D/λ)·sin θ, where we assume the array is configured to sweep −π<Δφ<+π(−180°<Δφ<+180°). For frequency components at the bottom of the band, the wavelength takes the value of A1=c/f1, where c is the speed of electromagnetic radiation. For the upper frequencies, A2=c/f2. Therefore, from a multitude of measurements, two slightly different beam configurations Δφ1 and Δφ2 are found to maximize received signal strength.
When the values Δφ1 and Δφ2 are used to calculate the beam direction, there may be two possible solutions to the coherency conditions, assuming the array design uses ½<D/λ<1.
A first solution, corresponding to the direction of the main lobe and labelled with index M, is given by:
θ1,M=arcsin(λ1/D·Δφ1/2π), and
θ2,M=arcsin(λ2/D·Δφ2/2π),
using the usual definition of arcsin( ) which returns an angle between −π/2 and +π/2 (between −90° and +90°). This solution will return the candidate angle corresponding to the main lobe of the signal.
However, as long as Δφ1 and Δφ2 are large enough, specifically |Δφ|>2π·(1·D/λ), there is a second set of possible solutions for the coherency conditions corresponding to the grating lobe and labelled with index G, as follows:
If Δφ1, Δφ2<0:
θ1,G=arcsin(λ1/D·(Δφ1+2π)/2π), and
θ2,G=arcsin(λ2/D·(Δφ2+2π)/2π).
Or, if Δφ1, Δφ2>0:
θ1,G=arcsin(λ1/D·(Δφ1·2π)/2π), and
θ2,G=arcsin(λ2/D·(Δφ2·2π)/2π).
If θ1,M=θ2,M then the true angle of arrival is θ=θ1,M=θ2,M, which will provide the result θ1,G≠θ2,G (i.e. the signal is received via the main lobe). Conversely, if θ1,G=θ2,G, then the true angle of arrival is θ=θ1,G=θ2,G with θ1,M≠θ2,M (i.e. the signal is received via the grating lobe).
The above analyses assume that only the principle beams formed by the arrays are considered, which are strongly dominant when the number of elements is large. Many practical arrays have a limited size which also creates a number of side beams at lower power levels.
Aside from the main and grating lobes shown in
An alternative way of using the measurements of Δφ1 and Δφ2 that correspond to the peak power seen for frequencies f1 and f2 when sweeping the array phase gradient is now described. For |Δφ|<2π·(1·D/λ), there is no angle ambiguity, as there is no grating lobe (again as shown in
If sign(Δφ2−Δφ1)=sign(Δφ1)=sign(Δφ2) then the signal is received via the main beam, i.e. |θ|<arcsin (λ/2D).
If sign(Δφ2−Δφ1)≠sign(Δφ1) (or sign(Δφ2)), then the signal is received through the grating lobe and |θ|>arcsin (λ/2D).
This can be understood from the coherency condition when expressed in terms of frequency rather than bandwidth. That is: Δφ1,2=2π·f1,2·(D/c)·sin θ. Without restricting generality, assume θ is positive. Then, as long as θ<arcsin (λ/2D), i.e. the signal is received via the main beam, angles Δφ1 and Δφ2 are also positive. The derivative of the beam phase gradient with respect to frequency is also positive. For larger positive angles (θ>arcsin (λ/2D), corresponding to the grating lobe), the sign of the array phase gradient switches to negative. However, the derivative with respect to frequency remains a positive number.
Looking more closely at the relationship between main lobe hypothesis θM and grating lobe hypothesis θG we find |2π·f·D/c (sin θM−sin θG)|=2π, as they both satisfy the coherency condition.
To discriminate between the two cases, the value of (Δφ2·Δφ1) must be determined. Unsurprisingly, this is proportional to the bandwidth of the signal δf=f2·−f1. It can be found that the phase accuracy that must be achieved for making the distinction is given by δφ=2π δf/f. For example, for a 28 GHz signal with a bandwidth of 400 MHz, the beam peaks' locations must be measured with better than 5.1° accuracy. This corresponds almost precisely to the beam step size of a six-bit phase shifter (360°/26=5.625°).
However, using appropriate curve fitting and signal averaging, the peak beam angle can be determined to a finer precision that the array phase resolution. For example, the steeper flanks of the signal gain response will usually provide a more accurate view of the location of the peak than the broader peak.
Because of the small dispersion in frequency, this method is most useful for very wide signal bandwidths.
The phased array antennas described herein may be included in a device. The phased array antenna of the device may include a plurality of antenna elements (which may, for example, be arranged in a uniform pattern or in a non-uniform pattern such as the arrangements shown in
The described methods may be implemented using computer executable instructions. A computer program product or computer readable medium may comprise or store the computer executable instructions. The computer program product or computer readable medium may comprise a hard disk drive, a flash memory, a read-only memory (ROM), a CD, a DVD, a cache, a random-access memory (RAM) and/or any other storage media in which information is stored for any duration (e.g., for extended time periods, permanently, brief instances, for temporarily buffering, and/or for caching of the information). A computer program may comprise the computer executable instructions. The computer readable medium may be a tangible or non-transitory computer readable medium. The term “computer readable” encompasses “machine readable”.
The singular terms “a” and “an” should not be taken to mean “one and only one”. Rather, they should be taken to mean “at least one” or “one or more” unless stated otherwise. The word “comprising” and its derivatives including “comprises” and “comprise” include each of the stated features, but does not exclude the inclusion of one or more further features.
The above implementations have been described by way of example only, and the described implementations are to be considered in all respects only as illustrative and not restrictive. It will be appreciated that variations of the described implementations may be made without departing from the scope of the invention. It will also be apparent that there are many variations that have not been described, but that fall within the scope of the appended claims.