Adultez Temprana o Emergente

Limits, with regard to finances and data bandwidth, had a major impact on the maximum number of elements for the array. Ideally, a ULA could be constructed from patch antennas spaced no further than 0.5λ, occuping an aperture of 1.6 m, giving a beamwidth of 1◦ with no grating lobes. However, such an array would require over 100 channels, in the case of the AIR. From Table 4.1 and discussed in detail in a later section, the digital receiver is capable of 14-bit resolution. For I and Q sampling at 40 MSs−1_{, over 14 GBs}−1 _{of data would need to be stored.}

Further, 100 channels require an equal number of expensive components such as low-noise amplifiers (LNAs), RF filters, reference oscillators, and enclosures.

Rather than attempt a project with such high uncertainty, a more practical design was created. Instead of single patch elements comprising the baseline dimension of the array, subarrays incorporating pairs of patch antennas were selected. Due to the limitations of the physical structure of the subarray, the patch antennas are separated by 0.7λ, and the subarray dimension along the baseline is 0.057 m. The inter-subarray spacing is primarily a factor of the subarray radome, which encloses the entire patch antenna structure. Due to these limitations, grating lobes became an issue and mitigation strategies to this dilemma were explored.

While the physical dimension of the subarrays was less than ideal, an opportu- nity to attempt grating lobe mitigation techniques resulted. By design, individual

subarray locations on the array can be altered, allowing for exploration of alterna- tive array spacings, like the techniques discussed in Chapter 3. Before committing to a design, simulations were performed to ascertain the ideal beam patterns and the effectiveness of the irregular array spacing. While many of the results of such an analysis were given in the previous chapter, additional figures are presented here which illuminate the design process specifically for the AIR.

First, a simulation of the full two-way antenna pattern was developed for understanding the interaction between the transmit and receive beams. It is anticipated that grating lobes should be attenuated by the shape of the transmit beam. The two-way antenna pattern for the ideal 100 element array with λ inter- subarray spacing is given in Figure 4.3. Shown are the estimated element pattern,

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Two−Way Antenna Pattern − AIR 100 element ULA, d=0.5λ, ∆SA=λ, azimuthal axis

Two−Way Pattern Subarray Element Transmit (a) −60 −40 −20 0 20 40 60 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 Angles (deg) Power (dB)

Two−Way Antenna Pattern − AIR 100 element ULA, d=0.5λ, ∆SA=λ, elevation axis

Two−Way Pattern Subarray Element Transmit

(b)

Figure 4.3: A two-way antenna pattern in both (a) azimuthal and (b) elevation planes for a 100 element, λ spaced array. Patch element (blue), subarray (green), transmit (black) and full array patterns are included in the simulation of the two-way pattern (red). The transmit pattern has a dramatic effect on the overall shape of the beam. No tapering is available in the azimuthal dimension and no weights were applied to the ULA.

Gaussian approximation for the transmit pattern, subarray factor, and the two- way pattern. The azimuthal cut of the respective antenna patterns is shown in Figure 4.3(a) while the elevation, beamformed cut is shown in Figure 4.3(b). Note the influence of the transmit beam on the receive pattern in both horizontal and vertical dimensions and how the FOV is determined by the characteristics of the transmit pattern. It should be mentioned that the Gaussian approximation for the transmit beam is somewhat unrealistic in that the measured patterns plateau at -40 dB at approximately ±45◦ _{for both azimuthal and elevation axes.}

Additionally, the azimuthal pattern has some sidelobes present, none exceeding -23 dB, between 2◦_{and 45}◦_{(see Figure 4.28). Thus, the azimuthal pattern will}

still act to reduce the impact of the subarray sidelobes, though not to the degree indicated in the simulation. For completeness and clarity, the two dimensional pattern is presented in Figure 4.4. The majority of the energy is focused in a small region though sidelobes from the Fourier beamforming algorithm are present and indicate angular leakage.

Incorporating the actual physical dimensions and characteristics of the 36 receive channels into the simulations provided a detailed view of the array per- formance before any fabrication was initiated. The actual size of the subarray elements in the beamforming dimension is 0.05715 m, or roughly 1.8λ. To further enhance the simulations and provide more realistic representation, a spacing of 0.7λ was used between the patch antennas that comprise each subarray. Again, many simulation results based on this element spacing were presented in Chap- ter 3, however, the full two-way pattern was not examined. Now the results of the two-way pattern simulations will be presented and the results are shown in Figure 4.5. It is with the inclusion of the realistic array spacing that the grating lobes appear. Additionally, the subarray pattern, having increased in the ele-

Figure 4.4: A two-dimensional representation of an ideal 100 element ULA with 0.5λ spacing. The two-way pattern is shown as a narrow band oriented in the vertical dimension. Note that the actual 3 dB beamwidth of the beam is quite narrow.

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Two−Way Antenna Pattern − AIR 36 element ULA, d=0.7λ, ∆SA=1.8λ, azimuthal axis

Two−Way Pattern Subarray Element Transmit (a) −60 −40 −20 0 20 40 60 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 Angles (deg) Power (dB)

Two−Way Antenna Pattern − AIR 36 element ULA, d=0.7λ, ∆SA=1.8λ, elevation axis

Two−Way Pattern Subarray Element Transmit

(b)

Figure 4.5: As in Figure 4.3, except for a 36 element array with 1.8λ subarray spacing. Each patch array is separated by 0.7λ due to the actual constraints in array fabrication. Note the emergence of the sidelobes in the elevation pattern (b). The magnitude of the grating lobes is approximately accurate despite the Gaussian approximation for the transmit beam.

±45◦_{. The transmit beam again has a significant effect on the grating lobe mag-}

nitudes. Again, the transmit beam is an approximation, however, the effect is representative of the true two-way pattern. The two-dimensional pattern is given in Figure 4.6. Observe the grating lobes at approximately ±38◦ _{in the elevation}

Figure 4.6: As in Figure 4.4, except for the realistic 36 element, 1.8λ spaced array. Note the appearance of the grating lobes in the vertical dimension. Techniques to mitigate the effects of grating lobes were presented in Chapter 3.

dimension.

Grating lobe ambiguities are a concern when observing at the array broadside, but can have an even greater impact when steering off-broadside. For instance, at the limits of the FOV, one of the grating lobes will move closer to the broadside position, reducing the attenuation caused by the transmit beam. A simulation with the main beam steered to -10◦ _{was performed and the results are given}

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Two−Way Antenna Pattern − AIR: −10 degrees 36 element ULA, d=0.7λ, ∆SA=1.8λ, azimuthal axis

Two−Way Pattern Subarray Element Transmit (a) −60 −40 −20 0 20 40 60 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 Angles (deg) Power (dB)

Two−Way Antenna Pattern − AIR: −10 degrees 36 element ULA, d=0.7λ, ∆SA=1.8λ, elevation axis

Two−Way Pattern Subarray Element Transmit

(b)

Figure 4.7: As in Figure 4.5, except the beam is steered to -10◦ _{in elevation. Note}

the increase in the grating lobe magnitude due to the reduction in transmit beam attenuation at the shifted location. Also, note the reduction in the main lobe magnitude resulting from a similar effect. The azimuthal axis is normalized to the peak of the main lobe, but the pattern remains unchanged.

vertical axis image while the positive-side grating lobe has increased in magnitude by more than 20 dB. The two-dimensional pattern is presented in Figure 4.8.

Figure 4.8: As in Figure 4.6, except the beam is steered to -10◦_{. Note the increase}

in the grating lobe level on the upper portion of the vertical axis.

As discussed in Chapter 3, traditional amplitude tapering (windowing) and adaptive techniques will not reduce the impact of the grating lobe. Instead, staggered spacing or some form of irregular spatial arrangement is required, thus inducing a sidelobe-like behavior in the grating lobes, allowing Capon or RCB algorithms to reduce the interference/ambiguities.

A simulation of the irregular spacing arrangement discussed in Chapter 3 was performed, with the six-element subarray arrangements, each separated by 0.995λ. The results are displayed in Figure 4.9. As expected, the grating lobes have been deformed and will now behave like sidelobes after the application of an adaptive beamforming algorithm. The two-dimensional pattern is given in Figure 4.10. For completeness, the single and dual-axis images for the irregularly

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Two−Way Antenna Pattern − AIR 36 element Irreg−ULA, d=0.7λ, ∆SA=1.8λ, azimuthal axis

Two−Way Pattern Subarray Element Transmit (a) −60 −40 −20 0 20 40 60 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 Angles (deg) Power (dB)

Two−Way Antenna Pattern − AIR 36 element Irreg−ULA, d=0.7λ, ∆SA=1.8λ, elevation axis

Two−Way Pattern Subarray Element Transmit

(b)

Figure 4.9: As in Figure 4.5, except an irregular array spacing is implemented. The irregular pattern is described in Chapter 3 and is composed of six-element subarray arrangements. The spacing between each six-element group is 0.995λ. The deformed grating lobes are now treated as sidelobes in adaptive beamforming algorithms such as Capon or RCB.

Figure 4.10: As in Figure 4.6, except for an array of irregular spacing. Note the deformation of the grating lobes in the elevation axis.

spaced array are given in Figures 4.11 and 4.12 with the main beam steered to -10◦_{. Note that the peak of the now deformed grating lobe is lower than that of}

the ULA case when the main beam is steered to -10◦_.

To facilitate exploration of spatial arrangements, the array supporting frame for the AIR is larger than the space occupied by the 36 subarrays when positioned side-by-side. By providing the additional space, irregular arrangements can be explored, though none were completed for this dissertation.

What follows is a subsystem-level description of the AIR. Each subsystem is defined in its role in the overall system, construction and operation. Also included are any subsystem testing and validation results.

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Two−Way Antenna Pattern − AIR: −10 degrees 36 element Irreg−ULA, d=0.7λ, ∆SA=1.8λ, azimuthal axis

Two−Way Pattern Subarray Element Transmit (a) −60 −40 −20 0 20 40 60 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 Angles (deg) Power (dB)

Two−Way Antenna Pattern − AIR: −10 degrees 36 element Irreg−ULA, d=0.7λ, ∆SA=1.8λ, elevation axis

Two−Way Pattern Subarray Element Transmit

(b)

Figure 4.11: As in Figure 4.7, except for an irregularly spaced array. Though the deformed grating lobes increase in magnitude as the beam steers away from broadside, adaptive beamforming algorithms will significantly reduce the impact of any leakage cased by their presence.